Tracking controller for robot manipulators via composite nonlinear feedback law
Institute of Scientific and Technical Information of China (English)
Peng Wendong; Su Jianbo
2009-01-01
A composite nonlinear feedback tracking controller for motion control of robot manipulators is de-scribed. The structure of the controller is composed of a composite nonlinear feedback law plus full robot nonlinear dynamics compensation. The stability is carried out in the presence of friction. The controller takes advantage of varying damping ratios induced by the composite nonlinear feedback control, so the transient performance of the closed-loop is remarkably improved. Simulation results demonstrate the feasibility of the proposed method.
Implementation of Nonlinear Control Laws for an Optical Delay Line
Hench, John J.; Lurie, Boris; Grogan, Robert; Johnson, Richard
2000-01-01
This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.
Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity
Yin, Jiu-Li; Zhao, Liu-Wei; Tian, Li-Xin
2014-02-01
The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.
A disturbance decoupling nonlinear control law for variable speed wind turbines
DEFF Research Database (Denmark)
Thomsen, Sven Creutz; Poulsen, Niels Kjølstad
2007-01-01
This paper describes a nonlinear control law for controlling variable speed wind turbines using feedback linearization. The novel aspect of the control law is its ability to decouple the effect of wind fluctuations. Furthermore, the transformation to feedback linearizable coordinates is chosen...... intelligently so that the majority of the system structure is invariant under the transformation. Consequently the physical interpretation is preserved. The method assumes that the effective wind speed and acceleration are estimated from measurements on the wind turbine. The performance of the control...
Rudra, Shubhobrata; Maitra, Madhubanti
2017-01-01
This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...
Energy evaluation on bounded nonlinear control laws for civil engineering applications
Gattulli, Vincenzo
1994-09-01
In the last decades researchers in the field of structural engineering have challenged the idea of facing natural hazard mitigation problems by adding to structures particular systems which are designed to protect buildings, bridges and other facilities from the damaging effects of destructive environmental actions. Among most protective systems and devices, active structural control, although having already reached the stage of full-implemented systems, still need theoretical investigation to achieve a complete exploitation of its capacity in reducing structural vibrations. In most of the operating systems (e.g. Soong and Reinhorn, 1993), linear control laws based on some quadratic performance function criteria are used since the design process for these linear strategies are fully developed and investigated. Moreover, the performances of structural systems controlled by linear techniques bring about some question concerning the complete and wise utilization of the capacity of control devices. Indeed, some of these inefficiencies are evident such as the inability to produce a significant peak response reduction in the first cycles of recorded or simulated time histories. (e.g. Reinhorn et al., 1993). Realizing that the expected maximum value for the required control force is a fundamental parameter in all processes to design the complete control system, in this paper it is shown that appropriate nonlinear control laws can significantly enhance the reduction of the system response under the same constraints imposed on the control force. Energy evaluation on the performance of different kinds of nonlinearities are reported such that a common base is built to perform comparative studies. These techniques have been successfully experimented on a structural model with ground excitations supplied by shaking table (e.g. Gattulli et al., 1994).
Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy
Directory of Open Access Journals (Sweden)
M. Ilyas
2016-01-01
Full Text Available Modeling of complex air vehicles is a challenging task due to high nonlinear behavior and significant coupling effect between rotors. Twin rotor multi-input multioutput system (TRMS is a laboratory setup designed for control experiments, which resembles a helicopter with unstable, nonlinear, and coupled dynamics. This paper focuses on the design and analysis of sliding mode control (SMC and backstepping controller for pitch and yaw angle control of main and tail rotor of the TRMS under parametric uncertainty. The proposed control strategy with SMC and backstepping achieves all mentioned limitations of TRMS. Result analysis of SMC and backstepping control schemes elucidates that backstepping provides efficient behavior with the parametric uncertainty for twin rotor system. Chattering and oscillating behaviors of SMC are removed with the backstepping control scheme considering the pitch and yaw angle for TRMS.
Directory of Open Access Journals (Sweden)
MOHAMED BAHITA
2012-02-01
Full Text Available In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the k-means algorithm. Asymptotic Lyapunov stability is established without the use of a supervisory (compensatory term in the control law and with the tracking errors converging to a neighbourhood of the origin. Finally, a simulation is provided to explore the feasibility of the proposed neuronal controller design method.
Control Law Design for Propofol Infusion to Regulate Depth of Hypnosis: A Nonlinear Control Strategy
Khaqan, Ali; Bilal, Muhammad; Ilyas, Muhammad; Ijaz, Bilal; Ali Riaz, Raja
2016-01-01
Maintaining the depth of hypnosis (DOH) during surgery is one of the major objectives of anesthesia infusion system. Continuous administration of Propofol infusion during surgical procedures is essential but increases the undue load of an anesthetist in operating room working in a multitasking setup. Manual and target controlled infusion (TCI) systems are not good at handling instabilities like blood pressure changes and heart rate variability arising due to interpatient variability. Patient safety, large interindividual variability, and less postoperative effects are the main factors to motivate automation in anesthesia. The idea of automated system for Propofol infusion excites the control engineers to come up with a more sophisticated and safe system that handles optimum delivery of drug during surgery and avoids postoperative effects. In contrast to most of the investigations with linear control strategies, the originality of this research work lies in employing a nonlinear control technique, backstepping, to track the desired hypnosis level of patients during surgery. This effort is envisioned to unleash the true capabilities of this nonlinear control technique for anesthesia systems used today in biomedical field. The working of the designed controller is studied on the real dataset of five patients undergoing surgery. The controller tracks the desired hypnosis level within the acceptable range for surgery. PMID:27293475
Control Law Design for Propofol Infusion to Regulate Depth of Hypnosis: A Nonlinear Control Strategy
Directory of Open Access Journals (Sweden)
Ali Khaqan
2016-01-01
Full Text Available Maintaining the depth of hypnosis (DOH during surgery is one of the major objectives of anesthesia infusion system. Continuous administration of Propofol infusion during surgical procedures is essential but increases the undue load of an anesthetist in operating room working in a multitasking setup. Manual and target controlled infusion (TCI systems are not good at handling instabilities like blood pressure changes and heart rate variability arising due to interpatient variability. Patient safety, large interindividual variability, and less postoperative effects are the main factors to motivate automation in anesthesia. The idea of automated system for Propofol infusion excites the control engineers to come up with a more sophisticated and safe system that handles optimum delivery of drug during surgery and avoids postoperative effects. In contrast to most of the investigations with linear control strategies, the originality of this research work lies in employing a nonlinear control technique, backstepping, to track the desired hypnosis level of patients during surgery. This effort is envisioned to unleash the true capabilities of this nonlinear control technique for anesthesia systems used today in biomedical field. The working of the designed controller is studied on the real dataset of five patients undergoing surgery. The controller tracks the desired hypnosis level within the acceptable range for surgery.
Target Tracking in 3-D Using Estimation Based Nonlinear Control Laws for UAVs
Directory of Open Access Journals (Sweden)
Mousumi Ahmed
2016-02-01
Full Text Available This paper presents an estimation based backstepping like control law design for an Unmanned Aerial Vehicle (UAV to track a moving target in 3-D space. A ground-based sensor or an onboard seeker antenna provides range, azimuth angle, and elevation angle measurements to a chaser UAV that implements an extended Kalman filter (EKF to estimate the full state of the target. A nonlinear controller then utilizes this estimated target state and the chaser’s state to provide speed, flight path, and course/heading angle commands to the chaser UAV. Tracking performance with respect to measurement uncertainty is evaluated for three cases: (1 stationary white noise; (2 stationary colored noise and (3 non-stationary (range correlated white noise. Furthermore, in an effort to improve tracking performance, the measurement model is made more realistic by taking into consideration range-dependent uncertainties in the measurements, i.e., as the chaser closes in on the target, measurement uncertainties are reduced in the EKF, thus providing the UAV with more accurate control commands. Simulation results for these cases are shown to illustrate target state estimation and trajectory tracking performance.
Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System
Directory of Open Access Journals (Sweden)
Zhanshan Zhao
2015-01-01
Full Text Available A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.
NONLINEAR PREDICTIVE CONTROL FOR TERRAIN FOLLOWING
Institute of Scientific and Technical Information of China (English)
1998-01-01
A nonlinear continuous predictive control method was used for design of cruise missile terrain-following controller. A performance index which combined the tracking error and rate of tracking error is presented. Then an optimal nonlinear feedback control law is generated to minimize the performance index. The tracking performance and robustness of controller are discussed. The advantage of the control law is demonstrated by successfully designing cruise missile terrain following controllers. The results show that the controller exhibits robustness and excellent tracking performance.
Nonlinear self-adjointness and conservation laws
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.se [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2011-10-28
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation u{sub t} - {Delta}u = 0 becomes strictly self-adjoint after multiplying by u{sup -1}. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems. (fast track communication)
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
航天器非线性鲁棒自适应姿态机动控制律%Nonlinear robust adaptive attitude maneuver control law for spacecraft
Institute of Scientific and Technical Information of China (English)
王卫杰; 任元; 李怡勇; 罗元
2015-01-01
In the presence of uncertainties in the moment of inertia and the external disturbance torque,the nonlinear robust adaptive control law for the control torque and estimation of moment of inertia is designed com-bining the nonlinear backstepping and Lyapunovo stability.In the control law for the control torque,the nonlin-ear damping is added to compensate the external disturbance torque,and the globally uniformly ultimately bounded stability of the system is demonstrated.The nonlinear dynamic coefficient is introduced to increase the dynamic performance of the system,shortening the regulating time after fast attitude maneuver.By Matlab/Simulink programming,the simulation of spacecraft attitude manoeuver control is discussed,and the simulation results demonstrate the effectiveness and feasibility of the proposed controller.%针对存在未知转动惯量和外部干扰力矩的敏捷航天器快速大角度姿态机动问题，结合非线性反步法和 Lyapunovo 稳定性分析方法设计控制力矩和转动惯量估计值的非线性鲁棒自适应控制律。在控制力矩控制律中，加入非线性阻尼项对外部干扰力矩进行补偿，证明了系统的全局一致最终有界稳定性。引入非线性动系数增加系统的动态性能，提高了姿态快速机动后的快速稳定能力。在 Maltlab／Simulink 环境下进行航天器姿态机动控制仿真研究，仿真结果验证了所设计控制器的有效性和可行性。
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
The composition of heterogeneous control laws
Kuipers, Benjamin; Astrom, Karl
1991-01-01
The fuzzy control literature and industrial practice provide certain nonlinear methods for combining heterogeneous control laws, but these methods have been very difficult to analyze theoretically. An alternate formulation and extension of this approach is presented that has several practical and theoretical benefits. An example of heterogeneous control is given and two alternate analysis methods are presented.
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Nonlinear feedback control of highly manoeuvrable aircraft
Garrard, William L.; Enns, Dale F.; Snell, S. A.
1992-01-01
This paper describes the application of nonlinear quadratic regulator (NLQR) theory to the design of control laws for a typical high-performance aircraft. The NLQR controller design is performed using truncated solutions of the Hamilton-Jacobi-Bellman equation of optimal control theory. The performance of the NLQR controller is compared with the performance of a conventional P + I gain scheduled controller designed by applying standard frequency response techniques to the equations of motion of the aircraft linearized at various angles of attack. Both techniques result in control laws which are very similar in structure to one another and which yield similar performance. The results of applying both control laws to a high-g vertical turn are illustrated by nonlinear simulation.
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
Cluster-based control of nonlinear dynamics
Kaiser, Eurika; Spohn, Andreas; Cattafesta, Louis N; Morzynski, Marek
2016-01-01
The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is de...
Nonlinear Robust Control for Spacecraft Attitude
Directory of Open Access Journals (Sweden)
Wang Lina
2013-07-01
Full Text Available Nonlinear robust control of the spacecraft attitude with the existence of external disturbances is considered. A robust attitude controller is designed based on the passivity approach the quaternion representation, which introduces the suppression vector of external disturbance into the control law and does not need angular velocity measurement. Stability conditions of the robust attitude controller are given. And the numerical simulation results show the effectiveness of the attitude controller.
Law of nonlinear flow in saturated clays and radial consolidation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.
Nonlinear Control of Delay and PDE Systems
Bekiaris-Liberis, Nikolaos
In this dissertation we develop systematic procedures for the control and analysis of general nonlinear systems with delays and of nonlinear PDE systems. We design predictor feedback laws (i.e., feedback laws that use the future, rather than the current state of the system) for the compensation of delays (i.e., after the control signal reaches the system for the first time, the system behaves as there were no delay at all) that can be time-varying or state-dependent, on the input and on the state of nonlinear systems. We also provide designs of predic- tor feedback laws for linear systems with constant distributed delays and known or unknown plant parameters, and for linear systems with simultaneous known or unknown constant delays on the input and the state. Moreover, we intro- duce infinite-dimensional backstepping transformations for each particular prob-lem, which enables us to construct Lyapunov-Krasovskii functionals. With the available Lyapunov-Krasovskii functionals we study stability, as well as, robust- ness of our control laws to plant uncertainties. We deal with coupled PDE-ODE systems. We consider nonlinear systems with wave actuator dynamics, for which we design a predictor inspired feedback law. We study stability of the closed-loop system either by constructing Lyapunov functionals, or using arguments of explicit solutions. We also consider linear sys- tems with distributed actuator and sensor dynamics governed by diffusion or wave PDEs, for which we design stabilizing feedback laws. We study stability of the closed-loop systems using Lyapunov functionals that we construct with the intro- duction of infinite-dimensional transformations of forwarding type. Finally, we develop a control design methodology for coupled nonlinear first-order hyperbolic PDEs through an application to automotive catalysts.
Conservation Laws in Higher-Order Nonlinear Optical Effects
Kim, J; Shin, H J; Kim, Jongbae
1999-01-01
Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schrödinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schrödinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schrödinger equation.
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Chen, Gui-Qiang; Zhang, Yongqian
2012-01-01
We establish an $L^1$-estimate to validate the weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws with arbitrary initial data of small bounded variation. This implies that the simpler geometric optics expansion function can be employed to study the properties of general entropy solutions to hyperbolic systems of conservation laws. Our analysis involves new techniques which rely on the structure of the approximate equations, besides the properties of the wave-front tracking algorithm and the standard semigroup estimates.
Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Gorban, A N
2015-01-01
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
Linear and Nonlinear Controllers Applied to Fixed-Wing UAV
Tadeo Espinoza; Alejandro Dzul; Miguel Llama
2013-01-01
This article presents a comparison of controllers which have been applied to a fixed‐wing Unmanned Aerial Vehicle (UAV). The comparison is realized between classical linear controllers and nonlinear control laws. The concerned linear controllers are: Proportional‐ Derivative (PD) and Proportional‐Integral‐Derivative (PID), while the nonlinear controllers are: backstepping, sliding modes, nested saturation and fuzzy control. These controllers are compared and analysed for altitude, yaw and rol...
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Nonlinear Phase Control and Anomalous Phase Matching in Plasmonic Metasurfaces
Almeida, Euclides; Prior, Yehiam
2015-01-01
Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute a particularly attractive set of materials. By means of modern nanolithographic fabrication techniques, flat, ultrathin optical elements may be constructed. However, in spite of their strong optical nonlinearities, plasmonic metasurfaces have so far been investigated mostly in the linear regime. Here we introduce full nonlinear phase control over plasmonic elements in metasurfaces. We show that for nonlinear interactions in a phase-gradient nonlinear metasurface a new anomalous nonlinear phase matching condition prevails, which is the nonlinear analog of the generalized Snell law demonstrated for linear metasurfaces. This phase matching condition is very different from the other known phase matching schemes. The subwavelength phase control of optical nonlinearities provides a foundation for the design of flat nonlinear optical elements based on metasurfaces. Our demonstrated flat nonlinear elements (i.e. lenses) act...
Nonlinear inversion flight control for a supermaneuverable aircraft
Snell, S. Antony; Garrard, William L., Jr.; Enns, Dale F.
1990-01-01
This paper describes the use of nonlinear dynamic inversion for the design of a flight control system for a supermaneuverable aircraft. First, the dynamics to be controlled were separated into fast and slow variables. The fast variables were the angular rates and the slow variables were the attitude angles. Then a nonlinear inversion controller was designed for the fast variables. This stabilized the longitudinal short-period and improved the lateral-directional responses over a wide range of angle of attack by making use of a combination for aerodynamic surfaces and thrust vectoring control. Outer loops were then closed to allow the pilot to control the slow dynamics, the angle of attack, side-slip angle and the velocity bank angle. Nonlinear inversion was also used to design of the outer loop control laws. The dynamic inversion control laws were compared with more conventional, gain-scheduled control laws and were shown to yield much better performance.
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Conservation laws of inviscid Burgers equation with nonlinear damping
Abdulwahhab, Muhammad Alim
2014-06-01
In this paper, the new conservation theorem presented in Ibragimov (2007) [14] is used to find conservation laws of the inviscid Burgers equation with nonlinear damping ut+g(u)ux+λh(u)=0. We show that this equation is both quasi self-adjoint and self-adjoint, and use these concepts to simplify conserved quantities for various choices of g(u) and h(u).
Control of nonlinear flexible space structures
Shi, Jianjun
With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Nonlinear control of chaotic systems:A switching manifold approach
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
2000-01-01
Full Text Available In this paper, a switching manifold approach is developed for nonlinear feed-back control of chaotic systems. The design strategy is straightforward, and the nonlinear control law is the simple bang–bang control. Yet, this control method is very effective; for instance, several desired equilibria can be stabilized by using one control law with different initial conditions. Its effectiveness is verified by both theoretical analysis and numerical simulations. The Lorenz system simulation is shown for the purpose of illustration.
Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control
Selisteanu, Dan; Petre, Emil; Popescu, Dorin; Bobasu, Eugen
2008-01-01
In this work, two nonlinear high-frequency control strategies for bioprocesses are proposed: a feedback sliding mode control law and a vibrational control strategy. In order to implement these strategies, a prototype bioprocess that is carried out in a Continuous Stirred Tank Bioreactor was considered. First, a discontinuous feedback law was designed using the exact linearization and by imposing a SMC that stabilizes the output of the bioprocess. When some state variables used in the control ...
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
Nonlinear control for global stabilization of multiple-integrator system by bounded controls
Institute of Scientific and Technical Information of China (English)
Bin ZHOU; Guangren DUAN; Liu ZHANG
2008-01-01
The global stabilization problem of the multiple-integrator system by bounded controls is considered.A nonlinear feedback law consisting of nested saturation functions is proposed.This type of nonlinear feedback law that is a modification and generalization of the result given in[1] needs only[(n+1)/2](n is the dimensions of the system)saturation elements,which is fewer than that which the other nonlinear laws need.Funhermore.the poles of the closedloop system Can be placed on any location on the left real axis when none of the saturafion elements in the control laws is saturated.This type of nonlinear control law exhibits a simpler structure and call significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods.Simulation on a fourth-order system is used to validate the proposed method.
Success Stories in Control: Nonlinear Dynamic Inversion Control
Bosworth, John T.
2010-01-01
NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.
Nonlinear Decoupling PID Control Using Neural Networks and Multiple Models
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential (PID) controller is proposed, which consists of a traditional PID controller, a decoupling compensator and a feedforward compensator for the unmodeled dynamics. The parameters of such controller is selected based on the generalized minimum variance control law. The unmodeled dynamics is estimated and compensated by neural networks, a switching mechanism is introduced to improve tracking performance, then a nonlinear decoupling PID control algorithm is proposed. All signals in such switching system are globally bounded and the tracking error is convergent. Simulations show effectiveness of the algorithm.
Nonlinear Control of Magnetic Bearings
Institute of Scientific and Technical Information of China (English)
Khac Duc Do; Dang Hoe Nguyen; Thanh Binh Nguyen
2010-01-01
In this paper, recent results controling nonlinear systems with output tracking error constraints are applied to the design of new tracking controllers for magnetic bearings. The proposed controllers can force the rotor to track a bounded and sufficiently smooth refer-ence trajectory asymptotically and guarantee non-contactedness be-tween the rotor and the stator of the magnetic bearings. Simulation results are included to illustrate the effectiveness of the proposed con-trollers.
A generalization of the power law distribution with nonlinear exponent
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Quantized pressure control in large-scale nonlinear hydraulic networks
Persis, Claudio De; Kallesøe, Carsten Skovmose; Jensen, Tom Nørgaard
2010-01-01
It was shown previously that semi-global practical pressure regulation at designated points of a large-scale nonlinear hydraulic network is guaranteed by distributed proportional controllers. For a correct implementation of the control laws, each controller, which is located at these designated poin
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
UAV Formation Flight Based on Nonlinear Model Predictive Control
Directory of Open Access Journals (Sweden)
Zhou Chao
2012-01-01
Full Text Available We designed a distributed collision-free formation flight control law in the framework of nonlinear model predictive control. Formation configuration is determined in the virtual reference point coordinate system. Obstacle avoidance is guaranteed by cost penalty, and intervehicle collision avoidance is guaranteed by cost penalty combined with a new priority strategy.
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
Discontinuous stabilization of nonlinear systems : Quantized and switching controls
Ceragioli, Francesca; De Persis, Claudio
2007-01-01
In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for thi
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Bentaallah, Abderrahim; Massoum, Ahmed; Benhamida, Farid; Meroufel, Abdelkader
2012-03-01
This paper studies the nonlinear adaptive control of an induction motor with natural dynamic complete nonlinear observer. The aim of this work is to develop a nonlinear control law and adaptive performance for an asynchronous motor with two main objectives: to improve the continuation of trajectories and the stability, robustness to parametric variations and disturbances rejection. This control law will independently control the speed and flux into the machine by restricting supply. A complete nonlinear observer for dynamic nature ensuring closed loop stability of the entire control and observer has been developed. Several simulations have also been carried out to demonstrate system performance.
Nonlinear Direct Robust Adaptive Control Using Lyapunov Method
Directory of Open Access Journals (Sweden)
Chunbo Xiu
2013-07-01
Full Text Available The problem of robust adaptive stabilization of a class of multi-input nonlinear systems with arbitrary unknown parameters and unknown structure of bounded variation have been considered. By employing the direct adaptive and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the system states. By employing our result, a kind of nonlinear system is analyzed, the concrete form of the control law is given and the meaningful quadratic control Lyapunov function for the system is constructed. Simulation of parallel manipulator is provided to illustrate the effectiveness of the proposed method.
Aircraft nonlinear optimal control using fuzzy gain scheduling
Nusyirwan, I. F.; Kung, Z. Y.
2016-10-01
Fuzzy gain scheduling is a common solution for nonlinear flight control. The highly nonlinear region of flight dynamics is determined throughout the examination of eigenvalues and the irregular pattern of root locus plots that show the nonlinear characteristic. By using the optimal control for command tracking, the pitch rate stability augmented system is constructed and the longitudinal flight control system is established. The outputs of optimal control for 21 linear systems are fed into the fuzzy gain scheduler. This research explores the capability in using both optimal control and fuzzy gain scheduling to improve the efficiency in finding the optimal control gains and to achieve Level 1 flying qualities. The numerical simulation work is carried out to determine the effectiveness and performance of the entire flight control system. The simulation results show that the fuzzy gain scheduling technique is able to perform in real time to find near optimal control law in various flying conditions.
Power-law rheology controls aftershock triggering and decay
Zhang, Xiaoming; Shcherbakov, Robert
2016-11-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.
Guidance law based on piecewise constant control for hypersonic gliders
Hull, David G.; Seguin, Jean-Marie
A midcourse guidance law is developed for the descent of a hypersonic glider to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N+1 nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14 percent of the true values are obtained for the downrange and crossranges considered.
A nonlinear plate control without linearization
Directory of Open Access Journals (Sweden)
Yildirim Kenan
2017-03-01
Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.
Biped control via nonlinear dynamics
Hmam, Hatem M.
1992-09-01
This thesis applies nonlinear techniques to actuate a biped system and provides a rigorous analysis of the resulting motion. From observation of human locomotion, it is believed that the 'complex' dynamics developed by the aggregation of multiple muscle systems can be generated by a reduced order system which captures the rough details of the locomotion process. The investigation is begun with a simple model of a biped system. Since the locomotion process is cyclic in nature, we focus on applying the topologically similar concept of limit cycles to the simple model in order to generate the desired gaits. A rigorous analysis of the biped dynamics shows that the controlled motion is robust against dynamical disturbances. In addition, different biped gaits are generated by merely adjusting some of the limit cycle parameters. More dynamical and actuation complexities are then added for realism. First, two small foot components are added and the overall biped motion under the same control actuation is analyzed. Due to the physical constraints on the feet, it is shown using singular perturbation theory how the gross behavior of the biped dynamics are dictated by those of the reduced model. Next, an analysis of the biped dynamics under added nonlinear elasticities in the legs is carried out. Moreover, using a slightly modified model, forward motion is generated in the sagittal plane. At each step, a small amount of energy is consistently derived from the vertical plane and converted into a forward motion. Stability of the forward dynamics is guaranteed by appropriate foot placement. Finally, the robustness of the controlled biped dynamics is rigorously analyzed and illustrated through extensive computer simulations.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Safe Haven Laws as "Crime Control Theater"
Hammond, Michelle; Miller, Monica K.; Griffin, Timothy
2010-01-01
Objectives: This article examines safe haven laws, which allow parents to legally abandon their infants. The main objective is to determine whether safe haven laws fit the criteria of "crime control theater", a term used to describe public policies that produce the appearance, but not the effect, of crime control, and as such are essentially…
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Recursive design of nonlinear H∞ excitation controller
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
Nonlinear feedback control of Timoshenko beam
Institute of Scientific and Technical Information of China (English)
冯德兴; 张维弢
1995-01-01
This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the Lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.
Variable structure control of nonlinear systems through simplified uncertain models
Sira-Ramirez, Hebertt
1986-01-01
A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Advances and applications in nonlinear control systems
Volos, Christos
2016-01-01
The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.
Indian Academy of Sciences (India)
Chaudry Masood Khalique
2013-03-01
In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
Institute of Scientific and Technical Information of China (English)
A H Bokhari; F D Zaman; K Fakhar; A H Kara
2011-01-01
@@ First,we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.%First, we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved Bows.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Observability and Controllability for Smooth Nonlinear Systems
Schaft, A.J. van der
1982-01-01
The definition of a smooth nonlinear system as proposed recently, is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input-output system. Minimality for such systems can be defined in a very direct geometric way, and already implies a usual notion of observability, namely, local weak observability. As an application of this theory, it is shown that observable nonlinear Hamiltonian systems are necessarily controllable, and vice versa.
Extending satisficing control strategy to slowly varying nonlinear systems
Binazadeh, T.; Shafiei, M. H.
2013-04-01
Based on the satisficing control strategy, a novel approach to design a stabilizing control law for nonlinear time varying systems with slowly varying parameters (slowly varying systems) is presented. The satisficing control strategy has been originally introduced for time-invariant systems; however, this technique does not have any stability proof for time varying systems. In this paper, first, a parametric version of the satisficing control strategy is developed. Then, by considering the time as a frozen parameter, the parametric satisficing control strategy is utilized. Finally, a theorem is presented which suggested a stabilizing satisficing control law for the slowly varying control systems. Moreover, in this theorem, the maximum admissible rate of change of the system dynamics is evaluated. The efficiency of the proposed approach is demonstrated by a computer simulation.
Robust direct adaptive fuzzy control for nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
ZHANG Huaguang; ZHANG Mingjun
2006-01-01
For a class of nonlinear multi-input multi-output systems with uncertainty, a robust direct adaptive fuzzy control scheme was proposed. The feedback control law and adaptive law for parameters were derived based on Lyapunov design approach. The overall control scheme can guarantee that the tracking error converges in the small neighborhood of origin, and all signals of the closed-loop system are uniformly bounded. The main advantage of the proposed control scheme is that in each subsystem only one parameter vector needs to be adjusted on-line in the adaptive mechanism, and so the on-line computing burden is reduced. In addition, the proposed control scheme is a smooth control with no chattering phenomena. A simulation example was proposed to demonstrate the effectiveness of the proposed control algorithm.
H-infinity control for cascade minimum-phase switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
Shengzhi ZHAO; Jun ZHAO
2005-01-01
This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems.Each switched system in this class is composed of a zero-input asymptotically stable nonlinear part,which is also a switched system,and a linearizable part which is controllable.Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively.The nonlinear state feedback and switching law are designed.We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law.The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.
An open plus nonlinear closed loop control of chaotic oscillators
Institute of Scientific and Technical Information of China (English)
陈立群
2002-01-01
An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of non-autonomous second-order ordinary differential equations. It is proven that the basins of entrainment are global whenthe right-hand sides of the equations are given by arbitrary polynomial functions. The forced Duffing oscillator and theforced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Junhai Luo; Heng Liu
2014-01-01
This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of th...
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
Machine learning control taming nonlinear dynamics and turbulence
Duriez, Thomas; Noack, Bernd R
2017-01-01
This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs
Institute of Scientific and Technical Information of China (English)
MEI Jian-Qin
2009-01-01
The algorithm for constructing conservation laws of Etder-Lagrange--type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.
FORCED OSCILLATIONS IN NONLINEAR FEEDBACK CONTROL SYSTEM
Since a nonlinear feedback control system may possess more than one type of forced oscillations, it is highly desirable to investigate the type of...method for finding the existence of forced oscillations and response curve characteristics of a nonlinear feedback control system by means of finding the...second order feedback control system are investigated; the fundamental frequency forced oscillation for a higher order system and the jump resonance
Aeroelastic scaling laws for gust load alleviation control system
Institute of Scientific and Technical Information of China (English)
Tang Bo; Wu Zhigang; Yang Chao
2016-01-01
Gust load alleviation (GLA) tests are widely conducted to study the effectiveness of the control laws and methods. The physical parameters of models in these tests are aeroelastic scaled, while the scaling of GLA control system is always unreached. This paper concentrates on studying the scaling laws of GLA control system. Through theoretical demonstration, the scaling criterion of a classical PID control system has been come up and a scaling methodology is provided and veri-fied. By adopting the scaling laws in this paper, gust response of the scaled model could be directly related to the full-scale aircraft theoretically under both open-loop and closed-loop conditions. Also, the influences of different scaling choices of an important non-dimensional parameter, the Froude number, have been studied in this paper. Furthermore for practical application, a compen-sating method is given when the theoretical scaled actuators or sensors cannot be obtained. Also, the scaling laws of some non-linear elements in control system such as the rate and amplitude sat-urations in actuator have been studied and examined by a numerical simulation.
Aeroelastic scaling laws for gust load alleviation control system
Directory of Open Access Journals (Sweden)
Tang Bo
2016-02-01
Full Text Available Gust load alleviation (GLA tests are widely conducted to study the effectiveness of the control laws and methods. The physical parameters of models in these tests are aeroelastic scaled, while the scaling of GLA control system is always unreached. This paper concentrates on studying the scaling laws of GLA control system. Through theoretical demonstration, the scaling criterion of a classical PID control system has been come up and a scaling methodology is provided and verified. By adopting the scaling laws in this paper, gust response of the scaled model could be directly related to the full-scale aircraft theoretically under both open-loop and closed-loop conditions. Also, the influences of different scaling choices of an important non-dimensional parameter, the Froude number, have been studied in this paper. Furthermore for practical application, a compensating method is given when the theoretical scaled actuators or sensors cannot be obtained. Also, the scaling laws of some non-linear elements in control system such as the rate and amplitude saturations in actuator have been studied and examined by a numerical simulation.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Control synthesis for polynomial nonlinear systems and application in attitude control
Institute of Scientific and Technical Information of China (English)
Chang-fei TONG; Hui ZHANG; You-xian SUN
2008-01-01
A method for positive polynomial validation based on polynomial decomposition is proposed to deal with control synthesis problems. Detailed algorithms for decomposition are given which mainly consider how to convert coefficients of a polynomial to a matrix with free variables. Then, the positivity of a polynomial is checked by the decomposed matrix with semidefinite programming solvers. A nonlinear control law is presented for single input polynomial systems based on the Lyapunov stability theorem. The control synthesis method is advanced to multi-input systems further. An application in attitude control is finally presented. The proposed control law achieves effective performance as illustrated by the numerical example.
Nonlinear estimation and control of automotive drivetrains
Chen, Hong
2014-01-01
Nonlinear Estimation and Control of Automotive Drivetrains discusses the control problems involved in automotive drivetrains, particularly in hydraulic Automatic Transmission (AT), Dual Clutch Transmission (DCT) and Automated Manual Transmission (AMT). Challenging estimation and control problems, such as driveline torque estimation and gear shift control, are addressed by applying the latest nonlinear control theories, including constructive nonlinear control (Backstepping, Input-to-State Stable) and Model Predictive Control (MPC). The estimation and control performance is improved while the calibration effort is reduced significantly. The book presents many detailed examples of design processes and thus enables the readers to understand how to successfully combine purely theoretical methodologies with actual applications in vehicles. The book is intended for researchers, PhD students, control engineers and automotive engineers. Hong Chen is a professor at the State Key Laboratory of Automotive Simulation and...
Modeling and Non-Linear Self-Tuning Robust Trajectory Control of an Autonomous Underwater Vehicle
Directory of Open Access Journals (Sweden)
Thor Inge Fossen
1988-10-01
Full Text Available A non-linear self-tuning algorithm is demonstrated for an autonomous underwater vehicle. Tighter control is achieved by a non-linear parameter identification algorithm which reduces the parameter uncertainty bounds. Expensive hydrodynamic tests for parameter determination can thus be avoided. Excellent tracking performance and robustness to parameter uncertainty are guaranteed through a robust control strategy based on the estimated parameters. The nonlinear control law is highly robust for imprecise models and the neglected dynamics. The non-linear self-tuning control strategy is simulated for the horizontal positioning of an underwater vehicle.
Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
Active vibration control of nonlinear benchmark buildings
Institute of Scientific and Technical Information of China (English)
ZHOU Xing-de; CHEN Dao-zheng
2007-01-01
The present nonlinear model reduction methods unfit the nonlinear benchmark buildings as their vibration equations belong to a non-affine system. Meanwhile,the controllers designed directly by the nonlinear control strategy have a high order, and they are difficult to be applied actually. Therefore, a new active vibration control way which fits the nonlinear buildings is proposed. The idea of the proposed way is based on the model identification and structural model linearization, and exerting the control force to the built model according to the force action principle. This proposed way has a better practicability as the built model can be reduced by the balance reduction method based on the empirical Grammian matrix. A three-story benchmark structure is presented and the simulation results illustrate that the proposed method is viable for the civil engineering structures.
Advanced nonlinear engine speed control systems
DEFF Research Database (Denmark)
Vesterholm, Thomas; Hendricks, Elbert
1994-01-01
: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as input/output-linearization and sliding mode control. These techniques take advantage of a nonlinear model......Several subsidiary control problems have turned out to be important for improving driveability and fuel consumption in modern spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one...
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Nonlinear-dynamical arrhythmia control in humans.
Christini, D J; Stein, K M; Markowitz, S M; Mittal, S; Slotwiner, D J; Scheiner, M A; Iwai, S; Lerman, B B
2001-05-08
Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear predictive control in the LHC accelerator
Blanco, E; Cristea, S; Casas, J
2009-01-01
This paper describes the application of a nonlinear model-based control strategy in a real challenging process. A predictive controller based on a nonlinear model derived from physical relationships, mainly heat and mass balances, has been developed and commissioned in the inner triplet heat exchanger unit (IT-HXTU) of the large hadron collider (LHC) particle accelerator at European Center for Nuclear Research (CERN). The advanced regulation\\ maintains the magnets temperature at about 1.9 K. The development includes a constrained nonlinear state estimator with a receding horizon estimation procedure to improve the regulator predictions.
Fractional Order Nonlinear Feedback Controller Design for PMSM Drives
Directory of Open Access Journals (Sweden)
Jian-Ping Wen
2013-01-01
Full Text Available Fractional order integral is introduced into active disturbance rejection controller (ADRC to establish the structure of fractional order proportional integral controller (FPI. Fractional order ADRC (FADRC is designed by replacing the nonlinear state error feedback control law using nonlinear function combination in ADRC with FPI, which can combine the high performance of ADRC estimating disturbances with the characteristics of fractional order calculus more really describing the physical object and spreading the stable region of the system parameters. The proposed FADRC is applied to permanent magnet synchronous motor (PMSM speed servo system in order to improve robustness of system against the disturbances. Compared with ADRC, simulation results verify that the proposed control method has given very good robust results and fast speed tracking performance.
Robust Nonlinear Control with Compensation Operator for a Peltier System
Directory of Open Access Journals (Sweden)
Sheng-Jun Wen
2014-01-01
Full Text Available Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine method. Finally, simulation results are given to show the effectiveness of the proposed scheme.
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
TF/TA2 trajectory tracking using nonlinear predictive control approach
Institute of Scientific and Technical Information of China (English)
Tang Qiang; Zhang Xinguo; Liu Xicheng
2006-01-01
The use of a methodology of nonlinear continuous predictive control to design the guidance control law for the aircraft TF/TA2 trajectory tracking problem is emplojed. For the derivation of the predictive control law, by using Taylor series expansion, and based on optimizing a performance index which is a quadratic function of both the predictive value of the state variables and the control inputs, a state variable feedback controller for nonlinear systems is obtained, and it provides a tradeoff between satisfactory tracking performance and the control magnitude requirements. Numerical simulation results for a supersonic fighter aircraft model show the viability of this approach.
Noninteracting control of nonlinear systems based on relaxed control
Jayawardhana, B.
2010-01-01
In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to
Wang, Chongwen; Yu, Xiao; Lan, Weiyao
2014-10-01
To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.
Exact Controllability for a Class of Nonlinear Evolution Control Systems
Institute of Scientific and Technical Information of China (English)
L¨u Yue; Li Yong
2015-01-01
In this paper, we study the exact controllability of the nonlinear control systems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are imposed in the main results.
Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings
Institute of Scientific and Technical Information of China (English)
ZHAO Min; LI Ning; LI ShaoYuan
2009-01-01
A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying (LPV) models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented.
Adaptive Control of Nonlinear Flexible Systems
1993-01-18
disturbances. The following example illustrates the need for a robust state-feedback law and the sensi- tivity of the exact - linearization based control law... exact linearization , one can bring an input-output approach to a particular case of certainty- equivalence based adaptive control design. We now...are available for this model, exact linearization can be performed. Let C(s) be the compensator that is being used so far in the previous three
Adaptive control of Hammerstein-Wiener nonlinear systems
Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong
2016-07-01
The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.
Polarization shaping for control of nonlinear propagation
Bouchard, Frédéric; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W
2016-01-01
We study the nonlinear optical propagation of two different classes of space-varying polarized light beams -- radially symmetric vector beams and Poincar\\'e beams with lemon and star topologies -- in a rubidium vapour cell. Unlike Laguerre-Gauss and other types of beams that experience modulational instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Polarization Shaping for Control of Nonlinear Propagation.
Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W
2016-12-02
We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Wind farm non-linear control for damping electromechanical oscillations of power systems
Energy Technology Data Exchange (ETDEWEB)
Fernandez, R.D. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina); Laboratorio de Electronica. Facultad de Ingenieria, Universidad Nacional de la Patagonia San Juan Bosco, Ciudad Universitaria, Km. 4, 9000 Comodoro Rivadavia (Argentina); Battaiotto, P.E. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina); Mantz, R.J. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, CICpba, Universidad Nacional de La Plata, CC 91, 1900 La Plata (Argentina)
2008-10-15
This paper deals with the non-linear control of wind farms equipped with doubly fed induction generators (DFIGs). Both active and reactive wind farm powers are employed in two non-linear control laws in order to increase the damping of the oscillation modes of a power system. The proposed strategy is derived from the Lyapunov Theory and is independent of the network topology. In this way, the strategy can be added to the central controller as another added control function. Finally, some simulations, showing the oscillation modes of a power system, are presented in order to support the theoretical considerations demonstrating the potential contributions of both control laws. (author)
First-order D-type Iterative Learning Control for Nonlinear Systems with Unknown Relative Degree
Institute of Scientific and Technical Information of China (English)
SONGZhao-Qing; MAOJian-Qin; DAIShao-Wu
2005-01-01
The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.
Hsiao, Ling
2000-01-01
This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of L^1-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in...
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
Controllability of nonlinear degenerate parabolic cascade systems
Directory of Open Access Journals (Sweden)
Mamadou Birba
2016-08-01
Full Text Available This article studies of null controllability property of nonlinear coupled one dimensional degenerate parabolic equations. These equations form a cascade system, that is, the solution of the first equation acts as a control in the second equation and the control function acts only directly on the first equation. We prove positive null controllability results when the control and a coupling set have nonempty intersection.
Second law of thermodynamics under control restrictions.
Wilming, H; Gallego, R; Eisert, J
2016-04-01
The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios. However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics. Here we study the maximum extractable work with limited control over the working system and its interaction with the heat bath. We derive a general second law when the set of accessible Hamiltonians of the working system is arbitrarily restricted. We then apply our bound to particular scenarios that are important in realistic implementations: limitations on the maximum energy gap and local control over many-body systems. We hence demonstrate in what precise way the lack of control affects the second law. In particular, contrary to the unrestricted case, we show that the optimal work extraction is not achieved by simple thermal contacts. Our results not only generalize the second law to scenarios of practical relevance, but also take first steps in the direction of local thermodynamics.
Coordinated nonlinear robust control of TCSC and excitation for multi-machine systems
Institute of Scientific and Technical Information of China (English)
Shengwei MEI; Juming CHEN; Qiang LU; Akihiko YOKOYAMA; Masuo GOTO
2004-01-01
An advanced nonlinear robust control scheme is proposed for multi-machine power systems equipped with thyristor-controlled series compensation (TCSC). First, a decentralized nonlinear robust control approach based on the feedback linearization and H∞ theory is introduced to eliminate the nonlinearities and interconnections of the studied system, and to attenuate the exogenous disturbances that enter the system. Then, a system model uilt up, which has considered all the generators' and TCSC's dynamics, and the effects of uncertainties such as disturbances. Next, a decentralized nonlinear robust coordinated control law is developed based on this model. Simulation results on a six-machine power system show that the transient stability of the power system is obviously improved and the power transfer capacity of long distance transmission lines is enhanced regardless of fault locahons and system operation points. In addition, the control law has engineering practicality since all the variables in the expression of he control strategy can be measured locally.
Fractional conservation laws in optimal control theory
Frederico, Gastao S F
2007-01-01
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum, and the fractional derivative of the state variable.
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Nonlinear Scaling Laws for Parametric Receiving Arrays. Part II. Numerical Analysis
1976-06-30
8217" " .’Ml’.1 ’.■■’: ■ ’ ^ t- Nonlinear Scaling Laws for Parametric Receiving Arrays Part II Numerical Analysis » - m • o prepared ...8217 ’ ■ — Nonlinear Scaling Laws for Parametric Receiving Arrays » z Part II. Numerical Analysis prepared under: A ——^ N0ÖJ339- 7 5 - C -J02 59, //V-ARPA Order...IF ’IP ,6T, 10 .HNO. IR .I_E. £0> riELTI = LiELTrJ IF ’IP .GT. 3 0 .HMD. IP .LE. 3 0;. [ IELT I = IiELT3 IF
Estimation of Nonlinear Three-dimensional Constitutive Law for DNA Molecules
Palanthandalam-Madapusi, Harish J
2010-01-01
Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of DNA molecules. The elastic rod model predictions are however very sensitive to the constitutive law (material properties) of the molecule, which in turn, vary along the molecules length according to its base-pair sequence. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we develop techniques to use elastic rod model equations in combination with limited experimental measurements or high-fidelity molecular dynamics simulation data to estimate the nonlinear constitutive law governing DNA molecules. We first cast the elastic rod model equations in state-space form and express the effect of the unknown constitutive law as an unknown input to the...
Gradient realization of nonlinear control systems
Cortes monforte, J.; Cortés, J.; Crouch, P.E.; Astolfi, A.; van der Schaft, Arjan; Gordillo, F.
2003-01-01
We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
A polynomial approach to nonlinear system controllability
Zheng, YF; Willems, JC; Zhang, CH
2001-01-01
This note uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input-single-output (SISO) nonlinear systems. The condition is presented in terms of common factors of a noncommutative polynomial expression. This result exposes controllability
Impulsive control for synchronization of nonlinear R(o)ssler chaotic systems
Institute of Scientific and Technical Information of China (English)
Li Yang; Liao Xiao-Feng; Li Chuan-Dong; Chen Guo
2006-01-01
This paper reports that an impulsive control theory for synchronization of nonlinear R(o)ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R(o)ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.
Approximation-Based Adaptive Tracking Control for MIMO Nonlinear Systems With Input Saturation.
Zhou, Qi; Shi, Peng; Tian, Yang; Wang, Mingyu
2015-10-01
In this paper, an approximation-based adaptive tracking control approach is proposed for a class of multiinput multioutput nonlinear systems. Based on the method of neural network, a novel adaptive controller is designed via backstepping design process. Furthermore, by introducing Nussbaum function, the issue of unknown control directions is handled. In the backstepping design process, the dynamic surface control technique is employed to avoid differentiating certain nonlinear functions repeatedly. Moreover, in order to reduce the number of adaptation laws, we do not use the neural networks to directly approximate the unknown nonlinear functions but the desired control signals. Finally, we provide two examples to illustrate the effectiveness of the proposed approach.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
A conservation law formulation of nonlinear elasticity in general relativity
Gundlach, Carsten; Erickson, Stephanie J
2011-01-01
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress-energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
Aftershocks and Omori's law in a modified Carlson-Langer model with nonlinear visco-elasticity
Sakaguchi, Hidetsugu
2015-01-01
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.
Terminal Sliding Modes In Nonlinear Control Systems
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
López, Rosa; Sánchez, David
2013-07-01
We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the transport coefficients are functions of the nonequilibrium screening potential that builds up in the system due to interactions. Within a mean-field approximation, we self-consistently calculate the heat rectification properties of a quantum dot attached to two terminals. We discuss nonlinear contributions to the Peltier effect and find departures from the Wiedemann-Franz law in the nonlinear regime of transport.
Transmitting information by controlling nonlinear oscillators
Tôrres, Leonardo A. B.; Aguirre, Luis A.
2004-09-01
The transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner. This can be accomplished by making use of the Information Transmission Via Control principle, which is stated and proved in the present work. In short, this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators, including chaotic ones as a special case, can be actually employed as demodulator/decoder in the process of information recovery. Other theoretical results related to the practical realization of the ITVC principle are presented and experimental data is provided showing a good agreement with the proposed theory.
SUBOPTIMAL NONLINEAR CONTROL OF PACKAGING MACHINERY DRIVE
Kudin, V. F.; Toropov, A.V.
2013-01-01
This paper deals with the procedure of synthesis of a nonlinear position controller for the «feeder» of packaging mechanism. The mathematical model of «feeder» drive with regard to the restriction on the control output of external PLC. Linearization of nonlinear characteristic by the «secants» method is implemented and selected functional quality that defines the minimal time of transients is selected. Quality functional in the form of a quadratic functional with a variable weighting factor i...
Directory of Open Access Journals (Sweden)
Faten Baklouti
2016-01-01
Full Text Available The trajectory tracking of underactuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical sliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding surfaces and chattering by adopting different reaching laws. The unknown system functions are approximated by fuzzy logic systems and free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in this paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the chattering phenomenon. The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller and two other control laws which keep the coupling in the underactuated system. The tracking performances of each control law are evaluated. Simulation examples including different amplitudes of external disturbances are made.
A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo; Yang Chao-Ping
2005-01-01
A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced,and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)thorder as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a During-Holmes system with uncertainty.
Linear and non-linear control of wind farms. Contribution to the grid stability
Energy Technology Data Exchange (ETDEWEB)
Fernandez, R.D. [Laboratorio de Electronica, Facultad de Ingenieria, Universidad Nacional de la Patagonia San Juan Bosco, Ciudad Universitaria, Km. 4, 9000, Comodoro Rivadavia (Argentina); Mantz, R.J. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina); Comision de Investigaciones Cientificas de la Provincia de Buenos Aires, CICpBA, La Plata (Argentina); Battaiotto, P.E. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina)
2010-06-15
This paper deals with linear and non-linear control of wind farms equipped with doubly-fed induction generators (DFIG). Both, active and reactive wind farm powers are employed in two independent control laws in order to increase the damping of the oscillation modes of a power system. In this way, it presented a general strategy where two correction terms are added, one by each independent control, to the normal operating condition of a wind farm. The proposed control laws are derived from the Lyapunov approach. Meanwhile for the reactive power a non-linear correction is presented, for the wind farm active power it is demonstrated that the classical proportional and inertial laws can be considered via the Lyapunov approach if wind farms are considered as real power plants, i.e. equivalent to conventional synchronous generation. Finally, some simulations are presented in order to support the theoretical considerations demonstrating the potential contributions of both control laws. (author)
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Indian Academy of Sciences (India)
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...... and Control Lyapunov Functions (CLF's). The results show that based on the lowest possible cost function and shortest settling time, the exact linearisation performs marginally better than the other methods....
Adaptive Control of Nonlinear Flexible Systems
1994-05-26
Proceedings of the American Control Conference , pp. 547-551, San Francisco, June 1993. 3 2 1.3 Personnel Dr. Robert Kosut and Dr. M. Giintekin Kabuli worked on...Control of Nonlinear Systems Under Matching Conditions," Proceedings of the American Control Conference , pp. 549-555, San Diego, CA, May 1990. [10] I...Poolla, P. Khargonekar, A. Tikku, J. Krause and K. Nagpal, "A time-domain ap- proach to model validation," Proceedings
Unmodeled Dynamics in Robust Nonlinear Control
2000-08-01
IEEE Transactions on Automatic Control , vol. 44, pp. 1975–1981, 1999. [6] D. Bestle...systems,” IEEE Transactions on Automatic Control , vol. 41, pp. 876–880, 1996. 95 [9] C.I. Byrnes and A. Isidori, “New results and examples in...Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control , vol. 44, pp. 328–333, 1999. [14] J. Eker and K.J.
Optimization-Based Robust Nonlinear Control
2006-08-01
IEEE Transactions on Automatic Control , vol. 51, no. 4, pp. 661...systems with two time scales", A.R. Teel, L. Moreau and D. Nesic, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1526-1544, September 2003...Turner, L. Zaccarian, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1509- 1525, September 2003. 5. "Nonlinear Scheduled anti-windup
Control of nonlinear systems with applications
Pan, Haizhou
In practical applications of feedback control, most actuators exhibit physical constraints that limit the control amplitude and/or rate. The principal challenge of control design problem for linear systems with input constraints is to ensure closed-loop stability and yield a good transient performance in the presence of amplitude and/or rate-limited control. Since actuator saturation manifests itself as a nonlinear behavior in an otherwise linear system, the development of a nonconservative saturation control design methodology poses a significant challenge. In particular, it is well known that unstable linear systems can be stabilized using smooth controllers only in a local sense in the presence of actuator saturation. Thus, it is of paramount importance to develop a saturation control design methodology that yields a nonconservative estimate of the stability domain for closed-loop system. The first part of this research focuses on a numerically tractable formulation of the control synthesis problem for linear systems with actuator amplitude and rate saturation nonlinearity using a linear-matrix-inequality (LMI) framework. Following the recent trend in the actuator saturation control research, we (i) utilize absolute stability theory to ensure closed-loop stability and (ii) minimize a quadratic cost to account for the closed-loop system performance degradation. In order to reduce the inherent conservatism of the absolute stability based saturation control framework, we exploit stability multipliers (of, e.g., weighted circle criterion, Popov criterion, etc.). For the control of linear systems with simultaneous actuator amplitude and rate saturation nonlinearities, by virtue of a rate limiter that is predicated on designing the control amplitude and then computing the control rates, we directly account for rate constraints. Both continuous- and discrete-time systems with actuator saturation are considered. A number of design examples are presented to demonstrate
Conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation
Institute of Scientific and Technical Information of China (English)
Ouyang Shi-Gen; Quo Qi; Wu Li-Jun; Lan Sheng
2007-01-01
The derivations of several conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation are presented. These invariants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
Nonlinear signal-based control with an error feedback action for nonlinear substructuring control
Enokida, Ryuta; Kajiwara, Koichi
2017-01-01
A nonlinear signal-based control (NSBC) method utilises the 'nonlinear signal' that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design.
Modified μ-law Companding For LED Nonlinearity Alleviation in DCO-OFDM VLC System
Yan, Chaowen; Wang, Jianping; Lu, Huimin; Shi, Yinjia
2016-10-01
In this paper, the direct current (DC)-biased optical orthogonal frequency division multiplexing (DCO-OFDM) visible light communication (VLC) system using modified μ-law companding is modeled and investigated. The simulation results reveal that the high peak to average power ratio (PAPR) induced by multi-carrier modulation (MCM) and DC bias, can aggravate signal distortion that is caused by the nonlinear characteristic of light emitting diode (LED). Thus, a pre-distortion method based on modification of μ-law companding is proposed for DCO-OFDM VLC system to resolve this problem. With the proposed method, the system can achieve a good performance of PAPR reduction and bit error rate (BER), compared to the original DCO-OFDM VLC system. It is demonstrated that the modified μ-law companding is appropriate to alleviate LED nonlinearity without degradation of the signal quality in DCO-OFDM VLC system.
Nonlinear Cascade Strategy for Longitudinal Control of Electric Vehicle.
El Majdoub, K; Giri, F; Ouadi, H; Chaoui, F Z
2014-01-01
The problem of controlling the longitudinal motion of front-wheels electric vehicle (EV) is considered making the focus on the case where a single dc motor is used for both front wheels. Chassis dynamics are modelled applying relevant fundamental laws taking into account the aerodynamic effects and the road slope variation. The longitudinal slip, resulting from tire deformation, is captured through Kiencke's model. Despite its highly nonlinear nature the complete model proves to be utilizable in longitudinal control design. The control objective is to achieve a satisfactory vehicle speed regulation in acceleration/deceleration stages, despite wind speed and other parameters uncertainty. An adaptive controller is developed using the backstepping design technique. The obtained adaptive controller is shown to meet its objectives in presence of the changing aerodynamics efforts and road slope.
Improvements and applications of entrainment control for nonlinear dynamical systems.
Liu, Fang; Song, Qiang; Cao, Jinde
2008-12-01
This paper improves the existing entrainment control approaches and develops unified schemes to chaos control and generalized (lag, anticipated, and complete) synchronization of nonlinear dynamical systems. By introducing impulsive effects to the open-loop control method, we completely remove its restrictions on goal dynamics and initial conditions, and derive a sufficient condition to estimate the upper bound of impulsive intervals to ensure the global asymptotic stability. We then propose two effective ways to implement the entrainment strategy which combine open-loop and closed-loop control, and we prove that the feedback gains can be chosen according to a lower bound or be tuned with an adaptive control law. Numerical examples are given to verify the theoretical results and to illustrate their applications.
FBFN-based adaptive repetitive control of nonlinearly parameterized systems
Institute of Scientific and Technical Information of China (English)
Wenli Sun; Hong Cai; Fu Zhao
2013-01-01
An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy ba-sis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mecha-nism. Based on the Lyapunov stability theory, an adaptive repeti-tive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the control er singularity problem is solved. The proposed approach does not require an exact structure of the sys-tem dynamics, and the proposed control er is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simula-tion results demonstrate the effectiveness of the proposed method.
Nonlinear System Control Using Neural Networks
Directory of Open Access Journals (Sweden)
Jaroslava Žilková
2006-10-01
Full Text Available The paper is focused especially on presenting possibilities of applying off-linetrained artificial neural networks at creating the system inverse models that are used atdesigning control algorithm for non-linear dynamic system. The ability of cascadefeedforward neural networks to model arbitrary non-linear functions and their inverses isexploited. This paper presents a quasi-inverse neural model, which works as a speedcontroller of an induction motor. The neural speed controller consists of two cascadefeedforward neural networks subsystems. The first subsystem provides desired statorcurrent components for control algorithm and the second subsystem providescorresponding voltage components for PWM converter. The availability of the proposedcontroller is verified through the MATLAB simulation. The effectiveness of the controller isdemonstrated for different operating conditions of the drive system.
Fabri, S.; Kadirkamanathan, V.
1996-01-01
The use of composite adaptive laws for control of the affine class of nonlinear systems having unknown dynamics is proposed. These dynamics are approximated by Gaussian radial basis function neural networks whose parameters are updated by a composite law that is driven by both tracking and estimation errors, combining techniques used in direct and indirect adaptive control. This is motivated by the need to improve the speed of convergence of the unknown parameters, hence resulting in a better...
Zhang, Yuan
2016-01-01
We derive the first law of black hole mechanics from a general nonlinear electrodynamics Lagrangian. Compared with a similar derivation in the literature, our first law is verified by the Bardeen black hole which has been found to possess a nonlinear magnetic monopole. We also propose an alternative first law for the Bardeen black hole, by introducing a new mass formula, which has a simple expression and corresponds to a desired Smarr formula.
Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; An, Ning; Deng, Xuewei; Chen, Xianfeng
2017-04-01
In this article, we demonstrate that the angles at which second-harmonic (SH) waves are generated at ferroelectric domain walls satisfy the Snell law for nonlinear media. Nonlinear reflection and refraction are observed experimentally and the relation is found to be in good agreement with theoretical predictions. The ratio of the intensities of refracted and reflected waves has been measured. Under an anomalous-dispersion-like condition, the forbidden nonlinear reflection and refraction is analyzed and found to have a behavior similar to that of the total internal reflection in linear optics. In the periodic domain structure, the coherent superposition of SH waves has been observed, on the basis of which we have proposed a comprehensive theory to explain nonlinear effects in multilayered structures.
Controller Design of Complex System Based on Nonlinear Strength
Directory of Open Access Journals (Sweden)
Rongjun Mu
2015-01-01
Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.
Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces
Almeida, Euclides; Shalem, Guy; Prior, Yehiam
2016-01-01
Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute an attractive set of materials with a potential for replacing standard bulky optical elements. In recent years, increasing attention has been focused on their nonlinear optical properties, particularly in the context of second and third harmonic generation and beam steering by phase gratings. Here, we harness the full phase control enabled by subwavelength plasmonic elements to demonstrate a unique metasurface phase matching that is required for efficient nonlinear processes. We discuss the difference between scattering by a grating and by subwavelength phase-gradient elements. We show that for such interfaces an anomalous phase-matching condition prevails, which is the nonlinear analogue of the generalized Snell's law. The subwavelength phase control of optical nonlinearities paves the way for the design of ultrathin, flat nonlinear optical elements. We demonstrate nonlinear metasurface lenses, which act both as generators and as manipulators of the frequency-converted signal.
Nonlinear H∞ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation
Directory of Open Access Journals (Sweden)
Zool H. Ismail
2013-01-01
Full Text Available A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV with region tracking function. Within this control scheme, nonlinear H∞ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.
Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem
Directory of Open Access Journals (Sweden)
Xingjian Wang
2013-01-01
Full Text Available Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Lincong Chen; Weiliang Jin; Weiqiu Zhu
2009-01-01
An optimal vibration control strategy for partially observable nonlinear quasi Hamil-tonian systems with actuator saturation is proposed. First, a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Ito stochas-tic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.
Coordinated formation control of multiple nonlinear systems
Institute of Scientific and Technical Information of China (English)
Wei KANG; Ning XI; Jindong TAN; Yiwen ZHAO; Yuechao WANG
2005-01-01
A general method of controller design is developed for the purpose of formation keeping and reconfiguration of nonlinear systems with multiple subsystems,such as the formation of multiple aircraft,ground vehicles,or robot arms.The model consists of multiple nonlinear systems.Controllers are designed to keep the subsystems in a required formation and to coordinate the subsystems in the presence of environmental changes.A step-by-step algorithm of controller design is developed.Sufficient conditions for the stability of formation tracking are proved.Simulations and experiments are conducted to demonstrate some useful coordination strategies such as movement with a leader,simultaneous movement,series connection of formations,and human-machine interaction.
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
Persis, Claudio De; Jayawardhana, Bayu
2012-01-01
The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution o
Persis, Claudio De; Jayawardhana, Bayu
2012-01-01
The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution o
Persis, Claudio De; Jayawardhana, Bayu
2012-01-01
The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution
Wu, Li-Bing; Yang, Guang-Hong
2017-03-01
This paper investigates the problem of adaptive output neural network (NN) control for a class of stochastic nonaffine and nonlinear systems with actuator dead-zone inputs. First, based on the intermediate value theorem, a novel design scheme that converts the nonaffine system into the corresponding affine system is developed. In particular, the priori knowledge of the bound of the derivative of the nonaffine and nonlinear functions is removed; then, by employing NNs to approximate the appropriate nonlinear functions, the corresponding adaptive NN tracking controller with the adjustable parameter updated laws is designed through a backstepping technique. Furthermore, it is shown that all the closed-loop signals are bounded in probability, and the system output tracking error can converge to a small neighborhood in the sense of a mean quartic value. Finally, experimental simulations are provided to demonstrate the efficiency of the proposed adaptive NN tracking control method.
New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case
Wen, John T.; Bayard, David S.
1988-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.
Nonlinear control of ships minimizing the position tracking errors
Directory of Open Access Journals (Sweden)
Svein P. Berge
1999-07-01
Full Text Available In this paper, a nonlinear tracking controller with integral action for ships is presented. The controller is based on state feedback linearization. Exponential convergence of the vessel-fixed position and velocity errors are proven by using Lyapunov stability theory. Since we only have two control devices, a rudder and a propeller, we choose to control the longship and the sideship position errors to zero while the heading is stabilized indirectly. A Virtual Reference Point (VRP is defined at the bow or ahead of the ship. The VRP is used for tracking control. It is shown that the distance from the center of rotation to the VRP will influence on the stability of the zero dynamics. By selecting the VRP at the bow or even ahead of the bow, the damping in yaw can be increased and the zero dynamics is stabilized. Hence, the heading angle will be less sensitive to wind, currents and waves. The control law is simulated by using a nonlinear model of the Japanese training ship Shiojimaru with excellent results. Wind forces are added to demonstrate the robustness and performance of the integral controller.
Approximation law for discrete-time variable structure control systems
Institute of Scientific and Technical Information of China (English)
Yan ZHENG; Yuanwei JING
2006-01-01
Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.
Remote Control Guidance Law Design Using Variable Structure Control
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A method of sliding mode variable structure control for the missile body being a time varying system is presented. A remote control guidance law is designed. The method has strong robustness to target's maneuver. To reduce the chattering phenomena, quasi-sliding mode variable structure control method is used. Simulation results show that the proposed method has small miss distance for any kind of maneuvering targets and requires small control energy.
Internal Decoupling in Nonlinear Process Control
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1988-07-01
Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.
Institute of Scientific and Technical Information of China (English)
钟伟民; 何国龙; 皮道映; 孙优贤
2005-01-01
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
Constrained tracking control for nonlinear systems.
Khani, Fatemeh; Haeri, Mohammad
2017-09-01
This paper proposes a tracking control strategy for nonlinear systems without needing a prior knowledge of the reference trajectory. The proposed method consists of a set of local controllers with appropriate overlaps in their stability regions and an on-line switching strategy which implements these controllers and uses some augmented intermediate controllers to ensure steering the system states to the desired set points without needing to redesign the controller for each value of set point changes. The proposed approach provides smooth transient responses despite switching among the local controllers. It should be mentioned that the stability regions of the proposed controllers could be estimated off-line for a range of set-point changes. The efficiencies of the proposed algorithm are illustrated via two example simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Immersion and Invariance Based Nonlinear Adaptive Flight Control
Sonneveldt, L.; Van Oort, E.R.; Chu, Q.P.; Mulder, J.A.
2010-01-01
In this paper a theoretical framework for nonlinear adaptive flight control is developed and applied to a simplified, over-actuated nonlinear fighter aircraft model. The framework is based on a modular adaptive backstepping scheme with a new type of nonlinear estimator. The nonlinear estimator is
Immersion and Invariance Based Nonlinear Adaptive Flight Control
Sonneveldt, L.; Van Oort, E.R.; Chu, Q.P.; Mulder, J.A.
2010-01-01
In this paper a theoretical framework for nonlinear adaptive flight control is developed and applied to a simplified, over-actuated nonlinear fighter aircraft model. The framework is based on a modular adaptive backstepping scheme with a new type of nonlinear estimator. The nonlinear estimator is co
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.
Sliding Mode Control of PMSG Wind Turbine Based on Enhanced Exponential Reaching Law
DEFF Research Database (Denmark)
Mozayan, Seyed Mehdi; Saad, Maarouf; Vahedi, Hani
2016-01-01
This paper proposes a Sliding Mode Control (SMC) based scheme for a variable speed, direct-driven Wind Energy Conversion Systems (WECS) equipped with Permanent Magnet Synchronous Generator (PMSG) connected to the grid. In this work, diode rectifier, boost converter, Neutral Point Clamped (NPC...... great performance in complicated nonlinear systems control such as WECS. The proposed control strategy modifies Reaching Law (RL) of sliding mode technique to reduce chattering issue and to improve THD property compared to conventional reaching law SMC. The effectiveness of the proposed control strategy...
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Institute of Scientific and Technical Information of China (English)
LI YaoChen
2007-01-01
The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated.Some assumptions are presented based on the published experimental data.The electrical yielding criterion,mechanical yielding criterion and isotropic hardening model are established.The flow theory in incremental forms in polarization procedure is presented.The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically.Finally,the nonlinear constitutive law expressed in a form of matrices and vectors,which is immediately associated with finite element analysis,is formulated.In the example problem of a rectangular specimen subjected to a uniaxial electric field,the procedure from virgin state to fully polarized state is simulated.Afterward,a uniaxial compressive loading is applied to depolarizing the specimen.Results are in agreement with the experimental data.
Institute of Scientific and Technical Information of China (English)
2007-01-01
The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated. Some assumptions are presented based on the published experimental data. The electrical yielding criterion, mechanical yielding criterion and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in a form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. In the example problem of a rectangular specimen subjected to a uniaxial electric field, the procedure from virgin state to fully polarized state is simulated. Afterward, a uniaxial compressive loading is applied to depolarizing the specimen. Results are in agreement with the experimental data.
Control of self-organizing nonlinear systems
Klapp, Sabine; Hövel, Philipp
2016-01-01
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
Synchronization between two different chaotic systems with nonlinear feedback control
Institute of Scientific and Technical Information of China (English)
Lü Ling; Guo Zhi-An; Zhang Chao
2007-01-01
This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.
Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation
Directory of Open Access Journals (Sweden)
Khadijo Rashid Adem
2014-01-01
Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
Arms control and the rule of law
Energy Technology Data Exchange (ETDEWEB)
Tanzman, E.A.
1995-03-01
Many who speak of the end of the Cold War emphasize the warming of international relations when they speak of the momentous consequences of this event. According to this image, the half century since Trinity has been a period of sparse international communication during which the Eastern and Western blocs hibernated in their isolated dens of security alliances. Yet it is equally valid to consider the implications of the end of the war footing that has underlain the policies of all of the major military powers during the last fifty years. While meaningful international dialogue was in a state of relative lethargy during much of this period, the military establishments of the Great Powers were actively engaged in using as much force as possible in their efforts to control world affairs, short of triggering a nuclear holocaust. International discourse, at least in English, was rife with such military images as appeasement, containment, crisis stability, and tripwires. From the military posture of the U.S. and Russia a tense peace ironically emerged, but the terms by which decisions were made about controlling weapons of mass destruction (i.e., nuclear, chemical, and biological weapons) were the terms of war. The thesis of this paper is that the end of the Cold War marks a shift away from reliance on military might toward an international commitment to control weapons of mass destruction through the rule of law developed by John Rawls. The progression of agreements during this century to limit weapons of mass destruction testifies to this new development. A review of arms control agreements that the U.S. is a part of show clear growth of the rule of law as the world has left the Cold War.
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
R. G. SILVA
1999-03-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Nonlinear control of high purity distillation columns
Groebel, Markus; Allgöwer, Frank; Storz, Markus; Gilles, Ernst Dieter
1994-01-01
Two simple models of distillation columns are studied to investigate their suitability for the practical use with exact I/O-linearization. An extension of exact I/O-linearization, the asymptotically exact I/O-linearization is applied to the control of a high purity distillation column, using one of these models to derive the static state feedback law. Simulation studies demonstrate the advantage of asymptotically exact I/O-linearization versus classical exact I/O-linearization techniques. Exp...
Wan, W. M. V.; Lee, H. C.; Hui, P. M.; Yu, K. W.
1996-08-01
The effective response of random media consisting of two different kinds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-field relation of the form J=χ\\|E\\|βE. A simple self-consistent mean-field theory, which leads to a simple way in determining the average local electric field in each constituent, is introduced. Each component is assumed to have a conductivity depending on the averaged local electric field. The averaged local electric field is then determined self-consistently. Numerical simulations of the system are carried out on random nonlinear resistor networks. Theoretical results are compared with simulation data, and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Ponte Castaneda et al. [Phys. Rev. B 46, 4387 (1992)]. It is found that the present theory, at small contrasts of χ between the two components, gives a result identical to that of Ponte Castaneda et al. up to second order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
Adaptive control of nonlinear underwater robotic systems
Directory of Open Access Journals (Sweden)
Thor I. Fossen
1991-04-01
Full Text Available The problem of controlling underwater mobile robots in 6 degrees of freedom (DOF is addressed. Uncertainties in the input matrix due to partly known nonlinear thruster characteristics are modeled as multiplicative input uncertainty. This paper proposes two methods to compensate for the model uncertainties: (1 an adaptive passivity-based control scheme and (2 deriving a hybrid (adaptive and sliding controller. The hybrid controller consists of a switching term which compensates for uncertainties in the input matrix and an on-line parameter estimation algorithm. Global stability is ensured by applying Barbalat's Lyapunovlike lemma. The hybrid controller is simulated for the horizontal motion of the Norwegian Experimental Remotely Operated Vehicle (NEROV.
Design of a robust guidance law via active disturbance rejection control
Institute of Scientific and Technical Information of China (English)
Yanbo Yuan∗; Ke Zhang
2015-01-01
Focusing on the three-dimensional guidance problem in case of target maneuvers and response delay of the autopilot, the missile guidance law utilizing active disturbance rejection control (ADRC) is proposed. Based on the nonlinear three-dimensional missile target engagement kinematics, the guidance model is es-tablished. The target acceleration is treated as a disturbance and the dynamics of the autopilot is considered by using a first-order model. A nonlinear continuous robust guidance law is designed by using a cascaded structure ADRC control er. In this method the disturbance is estimated by using the extended state observer (ESO) and compensated during each sampling period. Simulation results show that the proposed cascaded loop structure is a viable solution to the guidance law design and has strong robustness with respect to target maneuvers and response delay of the autopilot.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Getting inspiration from the constraint forces in the classical mechanics, we presented the nonlinear control method of multiple spacecraft formation flying to accurately keep the desired formation arrays. Considering nonlinearity and perturbation, we changed the question of the formation array control to the Lagrange equations with the holonomic constraints and the differential algebraic equations (DAE), and developed the nonlinear control for design of the follower spacecraft tracking control laws by solving the DAE. Because of using the idea of the constraint forces, this approach can adequately utilize the characteristic of the dynamic equations, i.e., the space natural forces, and accurately keep the arbitrary formation array. Simulation results of the circular formation keeping with the linear and nonlinear dynamical equations were included to illuminate the control performance.
Nonlinear tracking control of a 3-D overhead crane with friction and payload compensations
Directory of Open Access Journals (Sweden)
Anh-Huy Vo
2016-07-01
Full Text Available In this paper, a nonlinear adaptive control of a 3D overhead crane is investigated. A dynamic model of the overhead crane was developed, where the crane system is assumed as a lumped mass model. Under the mutual effects of the sway motions of the payload and the hoisting motion, the nonlinear behavior of the crane system is considered. A nonlinear control model-based scheme was designed to achieve the three objectives: (i drive the crane system to the desired positions, (ii suppresses the vibrations of the payload, and (iii velocity tracking of hoisting motion. The nonlinear control scheme employs adaptation laws that estimate unknown system parameters, friction forces and the mass of the payload. The estimated values were used to compute control forces applied to the trolley of the crane. The asymptotic stability of the crane system is investigated by using the Lyapunov method. The effectiveness of the proposed control scheme is verified by numerical simulation results.
Neuromechanical tuning of nonlinear postural control dynamics
Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.
2009-06-01
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
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Qiang Ma
2011-03-01
Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Ge, Hao; Qian, Hong
2017-01-01
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Directory of Open Access Journals (Sweden)
Juing-Shian Chiou
2013-01-01
Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.
Nonlinear control for dual quaternion systems
Price, William D.
The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is
Marciniak-Czochra, Anna
2013-01-01
We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a non- linear interface law are expected. In this paper we rigorously derive a quadratic effective slip interface law which holds for a range of Reynolds numbers and fracture widths. The porous medium flow is described by the Darcys law. The result shows that the interface slip law can be nonlinear, independently of the regime for the bulk flow. Since most of the interface and boundary slip laws are obtained via upscaling of complex systems, the result indicates that studying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.
Impulse position control algorithms for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Impulse position control algorithms for nonlinear systems
Sesekin, A. N.; Nepp, A. N.
2015-11-01
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays
Institute of Scientific and Technical Information of China (English)
Wei-Sheng Chen; Rui-Hong Li; Jing Li
2010-01-01
An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.
Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
Qudrat Khan; Aamer Iqbal Bhatti; Antonella Ferrara
2014-01-01
An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In c...
Institute of Scientific and Technical Information of China (English)
CHEN Xiang-Jun; HOU Li-Jie; LAM Wa Kun
2005-01-01
@@ Conservation laws for the derivative nonlinear Schr(o)dinger equation with non-vanishing boundary conditions are derived, based on the recently developed inverse scattering transform using the affine parameter technique.
On the exact controllability of a nonlinear stochastic heat equation
Directory of Open Access Journals (Sweden)
Bui An Ton
2006-01-01
Full Text Available The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.
A BPTT-like Min-Max Optimal Control Algorithm for Nonlinear Systems
Milić, Vladimir; Kasać, Josip; Majetić, Dubravko; Šitum, Željko
2010-09-01
This paper presents a conjugate gradient-based algorithm for feedback min-max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer neural network. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation (AD), to provide an effective, novel algorithm for solving numerically optimally min-max control problems. The proposed algorithm is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem with control and state vector constraints.
Passivation and control of partially known SISO nonlinear systems via dynamic neural networks
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Reyes-Reyes J.
2000-01-01
Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.
Dai, Juan; Gao, Ai; Xia, Yuanqing
2017-03-01
A robust entry guidance law based on terminal sliding mode and second-order differentiator is designed for trajectory tracking in this paper. The bank angle is regarded as the control variable. A novel nonlinear compound controller is designed to make the system with the trajectory-tracking error and its rate as states be input-to-state stable (ISS) with respect to uncertainties. The terminal sliding mode controller is designed to the problem of entry guidance by using the second-order differentiator to estimate the total disturbances. The proposed nonlinear compound control law by employing the second-order differentiator and the terminal sliding mode controller, provide robustness, higher control precision. Also, simulation results are presented to illustrate the effectiveness of the control strategy.
Simple robust control laws for robot manipulators. Part 1: Non-adaptive case
Wen, J. T.; Bayard, D. S.
1987-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.
APPROXIMATION LAWS OF DISCRETE-TIME VARIABLE STRUCTURE CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also ...
Robust Nonlinear Control of Tailless Fighter Aircraft
1999-02-01
also resulted in 1 book chapter and 12 refereed conference papers published, to appear and submitted. These papers are listed below. 1. A.R. Teel and L...Verlag, 1999, to appear. 4 Refereed Conference Publications 11. A.R. Teel. "A nonlinear control viewpoint on anti-windup and related problems", Preprints... Drc . TS"ThCH’WCAL R~PORT HAS qSN REViEWMAND IS APPRoVvOR 0 PLnUcBL EASE’WA APR 190-12, DISTRIBUTION I YONNE MASON S7T]NQ1pROORAJMMANAGE
Guidance Law and Neural Control for Hypersonic Missile to Track Targets
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Wenxing Fu
2016-01-01
Full Text Available Hypersonic technology plays an important role in prompt global strike. Because the flight dynamics of a hypersonic vehicle is nonlinear, uncertain, and highly coupled, the controller design is challenging, especially to design its guidance and control law during the attack of a maneuvering target. In this paper, the sliding mode control (SMC method is used to develop the guidance law from which the desired flight path angle is derived. With the desired information as control command, the adaptive neural control in discrete time is investigated ingeniously for the longitudinal dynamics of the hypersonic missile. The proposed guidance and control laws are validated by simulation of a hypersonic missile against a maneuvering target. It is demonstrated that the scheme has good robustness and high accuracy to attack a maneuvering target in the presence of external disturbance and missile model uncertainty.
Featuring Control Power: Corporate Law and Economics Revisited
A.M. Pacces (Alessio)
2008-01-01
textabstractThis dissertation reappraises the existing framework for economic analysis of corporate law. The standard approach to the legal foundations of corporate governance is based on the ‘law matters’ thesis, according to which corporate law promotes separation of ownership and control by prote
Muralidharan, Vijay; Anantharaman, S.; Mahindrakar, Arun D.
2010-06-01
We present a new nonlinear control law to stabilise the ball and beam system at a desired operating point. The control law is based on the interconnection and damping assignment-passivity-based control (IDA-PBC) methodology developed in Ortega, Spong, Gomez-Estern, and Blankenstien (Ortega, R., Spong, M., Gomez-Estern, F., and Blankenstien, G. (2002), 'Stabilization of Underactuated Mechanical Systems via Interconnection and Damping Assignment', IEEE Transactions on Automatic Control, 47, 1218-1233) that guarantees stability in the sense of Lyapunov. We present a novel proof of the asymptotic stability of the desired operating point. The validity of the proposed control law is demonstrated through the experimental results.
Design of nonlinear adaptive steam valve controllers for a turbo-generator system
Energy Technology Data Exchange (ETDEWEB)
Bekiaris-Liberis, N.K.; Paraskevopoulos, P.N. [National Technical Univ. of Athens Zographou, Athens (Greece); Boglou, A.K. [Technology Education Inst. of Kavala Agios Loukas, Kavala (Greece); Arvanitis, K.G.; Pasgianos, G.D. [Agricultural Univ. of Athens, Athens (Greece)
2008-07-01
This paper reported on a study that investigated the control of power systems consisting of interconnected networks of transmission lines linking generators and loads. Improving both small and large perturbation stability and dynamic performance is important because power systems have become less stable in the past 15 years due to the use of controllers that have been designed on the basis of linearized synchronous generators and turbine models. The high nonlinear nature of power system models and the resulting disturbances render conventional linear controller design techniques obsolete for use in power systems control. Power system engineers are becoming aware of the role of turbine steam valves in improving the dynamic stability of power systems and damping low frequency oscillations. Advanced nonlinear control strategies are needed since the conventional steam valve control theory cannot guarantee transient stability in cases where operational conditions and parameters vary considerably. A design approach to a nonlinear adaptive control system with unknown parameters was developed and applied to the turbine main steam valve control of a power system. A fourth order machine model was used along with an adaptive backstepping method to construct the Lyapunov function in order to obtain a nonlinear adaptive controller to solve the turbine fast valving nonlinear control problem. The newly designed nonlinear adaptive controller can make the resulting adaptive system asymptotically stable. The proposed controller is accompanied by a dynamic estimator of parameters and includes nonlinear damping terms, which guarantee input-output stability even without the use of the adaptive law. Simulation results showed that the proposed nonlinear adaptive controller performs better than other turbine main steam valve control techniques. It can face large parametric uncertainty and results in a closed-loop system that is able to face large and smaller disturbances, providing a
Robust Adaptive Neural Control of a Class of MIMO Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
HU Tingliang; ZHU Jihong; SUN Zengqi
2007-01-01
In this paper we present a robust adaptive control for a class of uncertain continuous time multiple input multiple output (MIMO) nonlinear systems. Multiple multi-layer neural networks are employed to approximate the uncertainty of the nonlinear functions,and robustifying control terms are used to compensate for approximation errors.All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semiglobal stability of the closed - loop system is guaranteed, and the tracking error asymptotically converges to zero. Simulations performed on a two-link robot manipulator illustrate the approach and its performance.
New variable structure control for MIMO nonlinear system based on I/O linearization
Institute of Scientific and Technical Information of China (English)
许春山; 孙兴进; 曹广益
2004-01-01
A novel variable structure control (VSC) with new rapid-smooth reaching law (RSRL) and new rapid-convergent sliding mode (FCSM) is proposed, which is based on analysis of normal VSC system. When it is used for an MIMO nonlinear system, we combine the method of Input/Output linearizing (I/O L) with VSC. After analyzing the robustness of the MIMO nonlinear system, we use this novel controller for Precision One Robot position control system. Simulation provides a quite satisfactory performance with uncertainties and external disturbances.
Lyapunov optimal feedback control of a nonlinear inverted pendulum
Grantham, W. J.; Anderson, M. J.
1989-01-01
Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
Lyapunov optimal feedback control of a nonlinear inverted pendulum
Grantham, W. J.; Anderson, M. J.
1989-01-01
Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws
Institute of Scientific and Technical Information of China (English)
DonghaiLI; XuezhiJIANG; 等
1997-01-01
The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.
Singular solutions of a fully nonlinear 2x2 system of conservation laws
Kalisch, Henrik
2011-01-01
Existence and admissibility of $\\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \\pa_t u + \\pa_x \\big(\\Sfrac{u^2+v^2}{2} \\big) &=0 \\pa_t v +\\pa_x(v(u-1))&=0. The system is fully nonlinear, i.e. it is nonlinear with respect to both variables. The latter system does not admit the classical Lax-admissible solution to certain Riemann problems. By introducing complex valued corrections in the framework of the weak asymptotic method, we show that an overcompressive $\\delta$-shock type solution resolves such Riemann problems. By letting the approximation parameter to zero, the corrections become real valued and we obtain a $\\delta$-type solution concept. In the frame of that concept, we can show that every $2\\times 2$ system of conservation laws admits $\\delta$-type solution.
The rigid-flexible nonlinear robotic manipulator: Modeling and control
Fenili, André; Balthazar, José Manoel
2011-05-01
The State-Dependent Riccati Equation (SDRE) control of a nonlinear rigid-flexible two link robotic manipulator is investigated. Different cases are considered assuming small deviations and large deviations from the desired final states. The nonlinear governing equations of motion are coupled, providing considerable excitation of all the nonlinear terms. The results present satisfactory final states but also undesirable overshoot.
Directory of Open Access Journals (Sweden)
Taochang Li
2014-01-01
Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.
Directory of Open Access Journals (Sweden)
Bahita Mohamed
2011-01-01
Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.
Institute of Scientific and Technical Information of China (English)
CHENMou; JIANGChang-sheng; CHENWen-hua
2004-01-01
A new decentralized robust control method is discussed for a class of nonlinear interconnected largescale system with unknown bounded disturbance and unknown nonlinear function term. A decentralized control law is proposed which combines the approximation method of neural network with sliding mode control. The decentralized controller consists of an equivalent controller and an adaptive sliding mode controller. The sliding mode controller is a robust controller used to reduce the track error of the control system. The neural networks are used to approximate the unknown nonlinear functions, meanwhile the approximation errors of the neural networks are applied to the weight value updated law to improve performance of the system. Finally, an example demonstrates the availability of the decentralized control method.
Global satisfactory control for nonlinear integrator processes with long delay
Institute of Scientific and Technical Information of China (English)
Yiqun YANG; Guobo XIANG
2007-01-01
Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control (GSC) of such processes with relay-type nonlinearity. An oscillatory control signal is injected into the nonlinear process; the amplitude and frequency of the oscillatory signal are designed to linearise the nonlinear process in the sense of harmonic analysis; and a state feedback controller is configured to implement GSC over the linearised process. An illustrative example is given to demonstrate the effectiveness of the proposed method.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
Shokef, Yair; Safran, Samuel A.
2012-04-01
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Maxwell's equal area law for black holes with a nonlinear source
Li, Huai-Fan; Zhao, Hui-Hua; Zhao, Ren
2016-01-01
In this paper, we consider the phase transition of black hole in power Maxwell invariant by means of Maxwell's equal area law. First, we review and study the analogy of nonlinear charged black hole solutions with the Van der Waals gas-liquid system in the extended phase space, and obtain isothermal $P$-$v$ diagram. Then, using the Maxwell's equal area law we study the phase transition of AdS black hole with different temperatures. Finally, we extend the method to the black hole in the canonical (grand canonical) ensemble in which charge (potential) is fixed at infinity. Interestingly, we find the phase transition occurs in the both ensembles. We also study the effect of the parameters of the black hole on the two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.
Nonlinear Acoustics FDTD method including Frequency Power Law Attenuation for Soft Tissue Modeling
Jiménez, Noé; Sánchez-Morcillo, Víctor; Camarena, Francisco; Hou, Yi; Konofagou, Elisa E
2014-01-01
This paper describes a model for nonlinear acoustic wave propagation through absorbing and weakly dispersive media, and its numerical solution by means of finite differences in time domain method (FDTD). The attenuation is based on multiple relaxation processes, and provides frequency dependent absorption and dispersion without using computational expensive convolutional operators. In this way, by using an optimization algorithm the coefficients for the relaxation processes can be obtained in order to fit a frequency power law that agrees the experimentally measured attenuation data for heterogeneous media over the typical frequency range for ultrasound medical applications. Our results show that two relaxation processes are enough to fit attenuation data for most soft tissues in this frequency range including the fundamental and the first ten harmonics. Furthermore, this model can fit experimental attenuation data that do not follow exactly a frequency power law over the frequency range of interest. The main...
Institute of Scientific and Technical Information of China (English)
Zongyao SUN; Yungang LIU
2007-01-01
In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper,without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.
Vibration suppression of speed-controlled robots with nonlinear control
Boscariol, Paolo; Gasparetto, Alessandro
2016-06-01
In this paper, a simple nonlinear control strategy for the simultaneous position tracking and vibration damping of robots is presented. The control is developed for devices actuated by speed-controlled servo drives. The conditions for the asymptotic stability of the closed-loop system are derived by ensuring its passivity. The capability of achieving improved trajectory tracking and vibration suppression is shown through experimental tests conducted on a three-axis Cartesian robot. The control is aimed to be compatible with most industrial applications given the simplicity of implementation, the reduced computational requirements, and the use of joint position as the only measured signal.
Steering Law Controlling the Constant Speeds of Control Moment Gyros
KOYASAKO, Y.; TAKAHASHI, M.
2016-09-01
To enable the agile control of satellites, using control moment gyros (CMGs) has become increasingly necessary because of their ability to generate large amounts of torque. However, CMGs have a singularity problem whereby the torque by the CMGs degenerates from three dimensions to two dimensions, affecting spacecraft attitude control performance. This study proposes a new steering control law for CMGs by controlling the constant speed of a CMG. The proposed method enables agile attitude changes, according to the required task, by managing the total angular momentum of the CMGs by considering the distance to external singularities. In the proposed method, the total angular momentum is biased in a specific direction and the angular momentum envelope is extended. The design method can increase the net angular momentum of CMGs which can be exchanged with the satellite. The effectiveness of the proposed method is demonstrated by numerical simulations.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Non-linear power law approach for spatial and temporal pattern analysis of salt marsh evolution
Taramelli, A.; Cornacchia, L.; Valentini, E.; Bozzeda, F.
2013-11-01
Many complex systems on the Earth surface show non-equilibrium fluctuations, often determining the spontaneous evolution towards a critical state. In this context salt marshes are characterized by complex patterns both in geomorphological and ecological features, which often appear to be strongly correlated. A striking feature in salt marshes is vegetation distribution, which can self-organize in patterns over time and space. Self-organized patchiness of vegetation can often give rise to power law relationships in the frequency distribution of patch sizes. In cases where the whole distribution does not follow a power law, the variance of scale in its tail may often be disregarded. To this end, the research aims at how changes in the main climatic and hydrodynamic variables may influence such non-linearity, and how numerical thresholds can describe this. Since it would be difficult to simultaneously monitor the presence and typology of vegetation and channel sinuosity through in situ data, and even harder to analyze them over medium to large time-space scales, remote sensing offers the ability to analyze the scale invariance of patchiness distributions. Here, we focus on a densely vegetated and channelized salt marsh (Scheldt estuary Belgium-the Netherlands) by means of the sub-pixel analysis on satellite images to calculate the non-linearity in the values of the power law exponents due to the variance of scale. The deviation from power laws represents stochastic conditions under climate drivers that can be hybridized on the basis of a fuzzy Bayesian generative algorithm. The results show that the hybrid approach is able to simulate the non-linearity inherent to the system and clearly show the existence of a link between the autocorrelation level of the target variable (i.e. size of vegetation patches), due to its self-organization properties, and the influence exerted on it by the external drivers (i.e. climate and hydrology). Considering the results of the
Recursive design of nonlinear H _∞ excitation controller
Institute of Scientific and Technical Information of China (English)
卢强; 梅生伟; 申铁龙; 胡伟
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization
Energy Technology Data Exchange (ETDEWEB)
Li, Q.; Chen, W. [School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan Province (China); Wang, Y.; Jia, J. [School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue 639798, Singapore (Singapore); Han, M. [School of Engineering, Temasek Polytechnic, Tampines 529757, Singapore (Singapore)
2009-10-20
By utilizing the state feedback exact linearization approach, a nonlinear robust control strategy is designed based on a multiple-input multiple-output (MIMO) dynamic nonlinear model of proton exchange membrane fuel cell (PEMFC). The state feedback exact linearization approach can achieve the global exact linearization via the nonlinear coordinate transformation and the dynamic extension algorithm such that H{sub {infinity}} robust control strategy can be directly utilized to guarantee the robustness of the system. The proposed dynamic nonlinear model is tested by comparing the simulation results with the experimental data in Fuel Cell Application Centre in Temasek Polytechnic. The comprehensive results of simulation manifest that the dynamic nonlinear model with nonlinear robust control law has better transient and robust stability when the vehicle running process is simulated. The proposed nonlinear robust controller will be very useful to protect the membrane damage by keeping the pressure deviations as small as possible during large disturbances and prolong the stack life of PEMFC. (author)
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear c
Formation design and nonlinear control of spacecraft formation flying
Wong, Hong
The fundamental control challenges associated with Spacecraft Formation Flying (SFF) can be classified into two categories: (i) trajectory design and (ii) trajectory tracking. In this research, we address these challenges for several different operating environments. The first part of this research focuses on providing a trajectory generation and an adaptive control design methodology to facilitate SFF missions near the Sun-Earth L2 Lagrange point. Specifically, we create a spacecraft formation by placing a leader spacecraft on a desired Halo orbit and a follower spacecraft on a desired quasi-periodic orbit surrounding the Halo orbit. We develop the nonlinear dynamics of the leader spacecraft and the follower spacecraft relative to the leader spacecraft, wherein the leader spacecraft is assumed to be on a desired Halo orbit trajectory. Finally, we design formation maintenance controllers such that the leader and follower spacecraft track desired trajectories. In particular, we design a set of adaptive position tracking controllers for the leader and follower spacecraft in the presence of unknown spacecraft mass. The proposed control laws are simulated for the case of the leader and follower spacecraft pair and are shown to yield asymptotic convergence of the position tracking errors. The second part of this research focuses on providing nonlinear trajectory tracking control designs for SFF missions near Earth. First, we address output feedback tracking control problems for the coupled translation and attitude motion of a leader and a follower spacecraft. It is assumed that the translation and angular velocity measurements of the two spacecraft are not available for feedback. Second, we address a periodic trajectory tracking problem arising in spacecraft formation flying. In particular, the nonlinear position dynamics of a follower spacecraft relative to a leader spacecraft are utilized to develop a learning controller which learns a periodic, unknown model
A macro-meso constitutive law for concrete having imperfect interface and nonlinear matrix
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The overall behavior of concrete depends on its meso structures such as aggregate shape, interface status, and mortar matrix property. The two key meso structure characters of concrete, bond status of interface and nonlinear property of matrix, are considered in focus. The variational structure principle is adopted to establish the macro-meso constitutive law of concrete. Specially, a linear reference composite material is selected to make its effective behavior approach the nonlinear overall behavior of concrete. And the overall property of linear reference composite can be estimated by classical estimation method such as self-consistent estimates method and Mori-Tanaka method. This variational structure method involves an optimum problem ultimately. Finally, the macro-meso constitutive law of concrete is established by optimizing the shear modulus of matrix of the linear reference composite. By analyzing the constitutive relation of concrete established, we find that the brittleness of concrete stems from the imperfect interface and the shear dilation property of concrete comes from the micro holes contained in concrete.
Uncertain Unified Chaotic Systems Control with Input Nonlinearity via Sliding Mode Control
Directory of Open Access Journals (Sweden)
Zhi-ping Shen
2016-01-01
Full Text Available This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.
Adaptive Control for Nonlinear Systems with Time-Varying Control Gain
Directory of Open Access Journals (Sweden)
Alejandro Rincon
2012-01-01
Full Text Available We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM, and we achieve proper tracking results.
Directory of Open Access Journals (Sweden)
Deyuan Meng
2014-05-01
Full Text Available The dynamics of pneumatic systems are highly nonlinear, and there normally exists a large extent of model uncertainties; the precision motion trajectory tracking control of pneumatic cylinders is still a challenge. In this paper, two typical nonlinear controllers—adaptive controller and deterministic robust controller—are constructed firstly. Considering that they have both benefits and limitations, an adaptive robust controller (ARC is further proposed. The ARC is a combination of the first two controllers; it employs online recursive least squares estimation (RLSE to reduce the extent of parametric uncertainties, and utilizes the robust control method to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. In order to solve the conflicts between the robust control design and the parameter adaption law design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Theoretically, ARC possesses the advantages of the adaptive control and the deterministic robust control, and thus an even better tracking performance can be expected. Extensive comparative experimental results are presented to illustrate the achievable performance of the three proposed controllers and their performance robustness to the parameter variations and sudden disturbance.
A family of asymptotically stable control laws for flexible robots based on a passivity approach
Lanari, Leonardo; Wen, John T.
1991-01-01
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.
Simon, J. S.; Valavani, L.
1991-01-01
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
Simon, J. S.; Valavani, L.
1991-01-01
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System
Institute of Scientific and Technical Information of China (English)
LUO Xiaohui; ZHU Yuquan; HU Junhua
2009-01-01
For the electro-hydraulic servo vibrating system(ESVS) with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control(ILC), is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time's tracking error of the system and then applies the error information to the next time's control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro-hydraulic servo vibrating system.
L1 adaptive controller of nonlinear reference system in presence of unmatched uncertainties
Institute of Scientific and Technical Information of China (English)
宋海涛; 张涛; 张国良
2016-01-01
An extension of L1 adaptive control is proposed for the unmatched uncertain nonlinear system with the nonlinear reference system that defines the performance specifications. The control law adapts fast and tracks the reference system with the guaranteed robustness and transient performance in the presence of unmatched uncertainties. The interval analysis is used to build the quasi-linear parameter-varying model of unmatched nonlinear system, and the robust stability of the proposed controller is addressed by sum of squares programming. The transient performance analysis shows that within the limit of hardware a large adaption gain can improve the asymptotic tracking performance. Simulation results are provided to demonstrate the theoretical findings of the proposed controller.
Robust nonlinear variable selective control for networked systems
Rahmani, Behrooz
2016-10-01
This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Dynamic decoupling nonlinear control method for aircraft gust alleviation
Lv, Yang; Wan, Xiaopeng; Li, Aijun
2008-10-01
A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Directory of Open Access Journals (Sweden)
Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation
Institute of Scientific and Technical Information of China (English)
Rong-hua HUAN; Wei-qiu ZHU; Yong-jun WU
2008-01-01
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged It6 stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged It6 equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.
Control of an under activated unstable nonlinear object
DEFF Research Database (Denmark)
Andersen, Nils Axel; Skovgaard, L.; Ravn, Ole
2001-01-01
This paper presents a comprehensive comparative study of several nonlinear controllers for stabilisation of the under actuated unstable nonlinear object known as the Acrobot in the literature. The object is a two DOF robot arm only actuated at the elbow. The study compares several control...
Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
This paper proposes a fault tolerant control method for input-affine nonlinear systems using a nonlinear reconfiguration block (RB). The basic idea of the method is to insert the RB between the plant and the nominal controller such that fault tolerance is achieved without re-designing the nominal...
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Nonlinear superheat and capacity control of a refrigeration plant
DEFF Research Database (Denmark)
Rasmussen, Henrik; Larsen, Lars F. S.
2009-01-01
This paper proposes a novel method for superheat and capacity control of refrigeration systems. A new low order nonlinear model of the evaporator is developed and used in a backstepping design of a nonlinear controller. The stability of the proposed method is validated theoretically by Lyapunov a...
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Control of an under activated unstable nonlinear object
DEFF Research Database (Denmark)
Andersen, Nils Axel; Skovgaard, L.; Ravn, Ole
2001-01-01
This paper presents a comprehensive comparative study of several nonlinear controllers for stabilisation of the under actuated unstable nonlinear object known as the Acrobot in the literature. The object is a two DOF robot arm only actuated at the elbow. The study compares several control...
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
Energy Technology Data Exchange (ETDEWEB)
Souza de Paula, Aline [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp@ufrj.br; Savi, Marcelo Amorim [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-12-15
Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.
Non-linear controllers in ship tracking control system
Institute of Scientific and Technical Information of China (English)
LESZEK M
2005-01-01
The cascade systems which stabilize the transverse deviation of the ship in relation to the set path is presented. The ship's path is determined as a broken line with specified coordinates of way points. Three controllers are used in the system. The main primary controller is the trajectory controller. The set value of heading for the course control system or angular velocity for the turning control system is generated. The course control system is used on the straight line of the set trajectory while the turning controller is used during a change of the set trajectory segment. The characteristics of the non-linear controllers are selected in such a way that the properties of the control system with the rate of turn controller are modelled by the first-order inertia, while the system with the course keeping controller is modelled by a second-order linear term. The presented control system is tested in computer simulation. Some results of simulation tests are presented and discussed.
Nonlinear control synthesis for electrical power systems using controllable series capacitors
Energy Technology Data Exchange (ETDEWEB)
Manjarekar, N.S.; Banavar, Ravi N. [Indian Institute of Technology Bombay, Mumbai (India). Systems and Control Engineering
2012-07-01
In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector g(x) in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stabilizing controllers for power systems, where the CSC dynamics are included as a first order system. Next, we consider a different control methodology, immersion and invariance (I and I), to synthesize an asymptotically stabilizing control law for the SMIB system with a CSC. The CSC is described by a first order system. As a generalization of I and I, we incorporate the power balance algebraic constraints in the load bus to the SMIB swing equation, and extend the design philosophy to a class of differential algebraic systems. The proposed result is then demonstrated on another example: a two-machine system with two load buses and a CSC. The controller performances are validated through simulations for all cases.
Control mechanisms for a nonlinear model of international relations
Energy Technology Data Exchange (ETDEWEB)
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Saturations-based nonlinear controllers with integral term: validation in real-time
Alatorre, A. G.; Castillo, P.; Mondié, S.
2016-05-01
Popular saturations-based nonlinear controller usually include proportional and derivative components of the state or output. The fact that in many applications, these components do not suffice to insure the convergence to the desired output values, motivate the addition of an integral term. In this paper, three configurations of nonlinear controllers based on saturation functions are improved with an integral component. The stability of the three algorithms is analysed using the Lyapunov theory. Simulation results validate the proposed control laws when they are applied to nonlinear systems with constant and unknown perturbations. Real-time experiments realised with a quad-rotor aerial vehicle and a hovercraft vehicle show that the proposed scheme can follow autonomously some trajectories, and that it could be robust with respect to delays.
Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system
Institute of Scientific and Technical Information of China (English)
Jinkun LIU; Fuchun SUN
2006-01-01
A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.
Nonlinear Economic Model Predictive Control Strategy for Active Smart Buildings
DEFF Research Database (Denmark)
Santos, Rui Mirra; Zong, Yi; Sousa, Joao M. C.
2016-01-01
Nowadays, the development of advanced and innovative intelligent control techniques for energy management in buildings is a key issue within the smart grid topic. A nonlinear economic model predictive control (EMPC) scheme, based on the branch-and-bound tree search used as optimization algorithm...... for solving the nonconvex optimization problem is proposed in this paper. A simulation using the nonlinear model-based controller to control the temperature levels of an intelligent office building (PowerFlexHouse) is addressed. Its performance is compared with a linear model-based controller. The nonlinear...
Longitudinal control laws design for a flying wing aircraft
Zhu, Yan
2012-01-01
This research is concerned with the flight dynamic, pitch flight control and flying qualities assessment for the reference BWB aircraft. It aims to develop the longitudinal control laws which could satisfy the flying and handing qualities over the whole flight envelope with added consideration of centre of gravity (CG) variation. In order to achieve this goal, both the longitudinal stability augmentation system (SAS) and autopilot control laws are studied in this thesis. Usi...
Longitudinal control laws design for a flying wing aircraft
Zhu, Yan
2012-01-01
This research is concerned with the flight dynamic, pitch flight control and flying qualities assessment for the reference BWB aircraft. It aims to develop the longitudinal control laws which could satisfy the flying and handing qualities over the whole flight envelope with added consideration of centre of gravity (CG) variation. In order to achieve this goal, both the longitudinal stability augmentation system (SAS) and autopilot control laws are studied in this thesis. Usi...
The Life-Changing Magic of Nonlinearity in Network Control
Cornelius, Sean
The proper functioning and reliability of many man-made and natural systems is fundamentally tied to our ability to control them. Indeed, applications as diverse as ecosystem management, emergency response and cell reprogramming all, at their heart, require us to drive a system to--or keep it in--a desired state. This process is complicated by the nonlinear dynamics inherent to most real systems, which has traditionally been viewed as the principle obstacle to their control. In this talk, I will discuss two ways in which nonlinearity turns this view on its head, in fact representing an asset to the control of complex systems. First, I will show how nonlinearity in the form of multistability allows one to systematically design control interventions that can deliberately induce ``reverse cascading failures'', in which a network spontaneously evolves to a desirable (rather than a failed) state. Second, I will show that nonlinearity in the form of time-varying dynamics unexpectedly makes temporal networks easier to control than their static counterparts, with the former enjoying dramatic and simultaneous reductions in all costs of control. This is true despite the fact that temporality tends to fragment a network's structure, disrupting the paths that allow the directly-controlled or ``driver'' nodes to communicate with the rest of the network. Taken together, these studies shed new light on the crucial role of nonlinearity in network control, and provide support to the idea we can control nonlinearity, rather than letting nonlinearity control us.
Testing the Law of One Price under Nonlinearity for Egg Market of Selected Provinces of Iran
Directory of Open Access Journals (Sweden)
M. Ghahremanzadeh
2016-05-01
Full Text Available Introduction: Regarding to the ever-increasing consumption of egg and consequently enhancement of its production during recent years, consideration to this output's market integration has special importance. Considering the fact that information on market integration may provide specific evidence as to the competitiveness of market, the effectiveness of arbitrage and the efficiency of pricing could be, likewise, useful to guide subsequent interventions aimed at improving the performance of market. In this context, in present study, validity of Law of One Price (LOP will be tested in the egg market and among selected provinces. Materials and Methods: Nonlinearity naturally extracted from local market due to existence of transportation and other transaction costs, so common cointegration test results are not suitable for market integration. In this study, at first, for being sure that series follow nonlinear behavior, Luukkonen et al. (1988 and BDS nonlinearity tests were used. Then for testing Law of One price in the egg market, nonlinear unit root test proposed by Emmanouilides and Fousekis (2012, which is an auxiliary regression for ESTAR model, was used. The data are daily retail prices of egg with the sample period ranging from April 2006 to march 2014 for north-west provinces of Iran including West Azerbaijan, East Azerbaijan, Ardebil, Tehran and Zanjan, which were obtained from State Live Stock Affairs Logistics Incorporated Company. Results and Discussion: Based on the DF-GLS unit root test, the null hypothesis of unit root for egg price differentials was rejected. So, all series of price differentials are stationary. In the next step nonlinearity of price differentials of egg between two provinces was examined. In BDS test, at the beginning, an ARMA model was estimated then the test was carried out to the residual of estimated model with embedding dimension (m 2-8 and the dimensional distance (ε chosen equals to 0.5 and 2 times of
Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies
Directory of Open Access Journals (Sweden)
Kairui Chen
2016-01-01
Full Text Available This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results.
Nonlinear Differential Geometry Method and Its Application in Induction Motor Decoupling Control
Directory of Open Access Journals (Sweden)
Linyuan Fan
2016-05-01
Full Text Available An alternating current induction motor is a nonlinear, multi-variable, and strong-coupled system that is difficult to control. To address this problem, a novel control strategy based on nonlinear differential geometry theory was proposed. First, a five-order affine mathematical model for an alternating current induction motor was provided. Then, the feedback linearization method was used to realize decoupling and full linearization of the system model. Moreover, a general and simplified control law was adopted to facilitate practical applications. Finally, a controller was designed using the pole assignment method. Simulation results show that the proposed method can decouple the system model into two independent subsystems, and that the closed-loop system exhibits good dynamic and static performances. The proposed decoupling control method is useful to reduce the system complexity of an induction motor and to improve its control performance, thereby providing a new and feasible dynamic decoupling control for an alternating current induction motor.
Nonlinear Adaptive PID Control for Greenhouse Environment Based on RBF Network
Directory of Open Access Journals (Sweden)
Guanghui Li
2012-04-01
Full Text Available This paper presents a hybrid control strategy, combining Radial Basis Function (RBF network with conventional proportional, integral, and derivative (PID controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production.
Nonlinear adaptive PID control for greenhouse environment based on RBF network.
Zeng, Songwei; Hu, Haigen; Xu, Lihong; Li, Guanghui
2012-01-01
This paper presents a hybrid control strategy, combining Radial Basis Function (RBF) network with conventional proportional, integral, and derivative (PID) controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA) to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production.
On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design
Directory of Open Access Journals (Sweden)
Ibraheem Kasim Ibraheem
2016-10-01
Full Text Available This paper presents a new improved nonlinear tracking differentiator (INTD with hyperbolic tangent function in the state-space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. The improved tracking differentiator (INTD has the required filtering features and can cope with the nonlinearities caused by the noise. Through simulations, the INTD is implemented as a signal’s derivative generator for the closed-loop feedback control system with a nonlinear PID controller for the nonlinear Mass-Spring-Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error.
Series-based approximate approach of optimal tracking control for nonlinear systems with time-delay
Institute of Scientific and Technical Information of China (English)
Gongyou Tang; Mingqu Fan
2008-01-01
The optimal output tracking control (OTC) problem for nonlinear systems with time-delay is considered.Using a series-based approx-imate approach,the original OTC problem is transformed into iteration solving linear two-point boundary value problems without time-delay.The OTC law obtained consists of analytical linear feedback and feedforward terms and a nonlinear compensation term with an infinite series of the adjoint vectors.By truncating a finite sum of the adjoint vector series,an approximate optimal tracking control law is obtained.A reduced-order reference input observer is constructed to make the feedforward term physically realizable.Simulation exam-pies are used to test the validity of the series-based approximate approach.
Active Nonlinear Feedback Control for Aerospace Systems. Processor
1990-12-01
Stabilizability of Uncertain Linear Systems: Existence of a Nonlinear Stabilizing Control Does Not Imply Existence of a Linear Stabilizing Control ," IEEE Trans...799-802, 1985. 13. I. R. Petersen, "Quadratic Stabilizability of Uncertain Linear Systems: Existence of a Nonlinear Stabilizing Control Does Not Imply...Existence of a Linear Stabilizing Control ," IEEE Trans. Autom. Contr., Vol. AC-30, pp. 291-293, 1985. 14. B. R. Barmish and A. R. Galimidi
Nonlinear and cooperative control of multiple hovercraft with input constraints
Dunbar, William B.; Olfati-Saber, Reza; Richard M Murray
2003-01-01
In this paper, we introduce an approach for distributed nonlinear control of multiple hovercraft-type underactuated vehicles with bounded and unidirectional inputs. First, a bounded nonlinear controller is given for stabilization and tracking of a single vehicle, using a cascade backstepping method. Then, this controller is combined with a distributed gradient-based control for multi-vehicle formation stabilization using formation potential functions previously constructed. The vehicles are u...
Clarelli, Fabrizio; Inglese, Gabriele
2016-11-01
Heat exchange between a conducting plate and the environment is described here by means of an unknown nonlinear function F of the temperature u. In this paper we construct a method for recovering F by means of polynomial expansion, perturbation theory and the toolbox of thermal inverse problems. We test our method on two examples: In the first one, we heat the plate (initially at 20 ^\\circ {{C}}) from one side, read the temperature on the same side and identify the heat exchange law on the opposite side (active thermography); in the second example we measure the temperature of one side of the plate (initially at 1500 ^\\circ {{C}}) and study the heat exchange while cooling (passive thermography).
Nonlinear Dynamics and Control of Flexible Structures
1991-03-01
Freedom," Ph.D. Thesis, Department of Theoretical and Applied Mechanics, Cornell University, in preparation. 5I I URI Reorts Islam , Saiful and Mircea...Theoretical and Applied Mechanics I S. Islam Civil and Environmental Engineering I 2! I 3 URI Accomplishments 3 -Nonlinear Dynamics and Chaos in Flexible...Structures with Symmetry," 31 (1991) 265-285. Islam , S. and M. Grigoriu, "Nonlinear Random Vibration of Pin-Jointed Trusses with Imperfections," in
Digital adaptive control laws for the F-8
Hartmann, G. L.; Harvey, C. A.
1976-01-01
NASA is conducting a flight control research program in digital fly-by-wire technology using a modified F-8C aircraft. The first phase of this program used Apollo hardware to demonstrate the practicality of digital fly-by-wire in an actual test vehicle. For the second phase, conventional aircraft sensors and a large floating point digital computer are being utilized to test advanced control laws and redundancy concepts. As part of NASA's research in digital fly-by-wire technology, Honeywell developed digital adaptive flight control laws for flight test in the F-8C. Adaptation of the control laws was to be based on information sensed from conventional aircraft sensors excluding air data. The control laws were constrained to use only existing elevator, rudder, and ailerons as control effectors, each powered by existing actuators. Three adaptive control laws were successfully designed using maximum likelihood estimation, a Liapunov stable model tracker and a self-excited limit cycle concept. The maximum likelihood estimation design was selected as the most promising because of its capability to identify more than surface effectiveness parameters. The adaptive concepts, the control laws and comparisons of predicted performance are described.
Nonlinear terahertz metamaterials with active electrical control
Keiser, G. R.; Karl, N.; Liu, P. Q.; Tulloss, C.; Chen, H.-T.; Taylor, A. J.; Brener, I.; Reno, J. L.; Mittleman, D. M.
2017-09-01
We present a study of an electrically modulated nonlinear metamaterial consisting of an array of split-ring resonators fabricated on n-type gallium arsenide. The resonant metamaterial nonlinearity appears as an intensity-dependent transmission minimum at terahertz frequencies and arises from the interaction between local electric fields in the split-ring resonator (SRR) capacitive gaps and charge carriers in the n-type substrate. We investigate the active tuning range of the metamaterial device as the incident terahertz field intensity is increased and conversely the effect of an applied DC bias on the terahertz field-induced nonlinear modulation of the metamaterial response. Applying a DC bias to the metamaterial sample alters the nonlinear response and reduces the net nonlinear modulation. Similarly, increasing the incident terahertz field intensity decreases the net modulation induced by an applied DC bias. We interpret these results in terms of DC and terahertz-field-assisted carrier acceleration, scattering, and multiplication processes, highlighting the unique nature of this DC-field modulated terahertz nonlinearity.
Analysis and design of robust decentralized controllers for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
Nonlinear system identification and control based on modular neural networks.
Puscasu, Gheorghe; Codres, Bogdan
2011-08-01
A new approach for nonlinear system identification and control based on modular neural networks (MNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This is obtained using a partitioning algorithm. Each local nonlinear model is associated with a nonlinear controller. These are also implemented by neural networks. The switching between the neural controllers is done by a dynamical switcher, also implemented by neural networks, that tracks the different operating points. The proposed multiple modelling and control strategy has been successfully tested on simulated laboratory scale liquid-level system.
Impulsive control of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Bao Jing-Fu; Zhang Hong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Sang
2008-01-01
A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.
Directory of Open Access Journals (Sweden)
Sergey Gennadyevich Ol’kov
2015-06-01
Full Text Available Objective to clarify the law of good and evil the function rule of justice and to construct mathematical models of political regimes. Methods 1 observation analysis and synthesis 2 deduction and induction 3 using the laws of formal logic 4 formal legal method 5 mathematical modeling 6 the study of mathematical functions 7 differential calculus 8 plotting. Results the author has deduced 1 the nonlinear law function of good and evil 2 the nonlinear function of justice 3 the law function of political regimes. Scientific novelty the author has calculated and found 1 a nonlinear formula DLcol ndashLcol3 which represents the relationship between the acts of legal public relations subjects D and thecollective freedom Lcol ndash the law of quotgood and evilquot 2 a nonlinear formula YD D3 illustrating the relationship between the acts of legal relations subjects D and responsibility for their actions Y ndash a nonlinear function of justice 3 a nonlinear formulanbsp that shows the relationship between the individual Lind and collective freedom Lcol in the negative area of the function definition collective negative freedom and a formulanbsp reflecting the relationship between the individual and collective freedom in the positive area of the function definition collective positive freedom 4 has given a general classification of political regimes in the world describing their functions showing the types of political systems deformation that occur due to the leftwise and rightwise shifts of collective freedom. Practical value the possibility to use the obtained scientific results in the development of various legal theories. nbsp
Efficient Control Law Simulation for Multiple Mobile Robots
Energy Technology Data Exchange (ETDEWEB)
Driessen, B.J.; Feddema, J.T.; Kotulski, J.D.; Kwok, K.S.
1998-10-06
In this paper we consider the problem of simulating simple control laws involving large numbers of mobile robots. Such simulation can be computationally prohibitive if the number of robots is large enough, say 1 million, due to the 0(N2 ) cost of each time step. This work therefore uses hierarchical tree-based methods for calculating the control law. These tree-based approaches have O(NlogN) cost per time step, thus allowing for efficient simulation involving a large number of robots. For concreteness, a decentralized control law which involves only the distance and bearing to the closest neighbor robot will be considered. The time to calculate the control law for each robot at each time step is demonstrated to be O(logN).
Efficient Control Law Simulation for Multiple Mobile Robots
Energy Technology Data Exchange (ETDEWEB)
Driessen, B.J.; Feddema, J.T.; Kotulski, J.D.; Kwok, K.S.
1998-10-06
In this paper we consider the problem of simulating simple control laws involving large numbers of mobile robots. Such simulation can be computationally prohibitive if the number of robots is large enough, say 1 million, due to the 0(N2 ) cost of each time step. This work therefore uses hierarchical tree-based methods for calculating the control law. These tree-based approaches have O(NlogN) cost per time step, thus allowing for efficient simulation involving a large number of robots. For concreteness, a decentralized control law which involves only the distance and bearing to the closest neighbor robot will be considered. The time to calculate the control law for each robot at each time step is demonstrated to be O(logN).
Eleiwi, Fadi
2015-07-01
This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.
Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems.
Zhao, Xudong; Shi, Peng; Zheng, Xiaolong; Zhang, Jianhua
2016-09-01
This brief is concerned with the problem of intelligent tracking control for a class of high-order nonlinear systems with completely unknown nonlinearities. An intelligent adaptive control algorithm is presented by combining the adaptive backstepping technique with the neural networks' approximation ability. It is shown that the practical output tracking performance of the system is achieved using the proposed state-feedback controller under two mild assumptions. In particular, by introducing a parameter in the derivations, the tracking error between the time-varying target signal and the output can be reduced via tuning the controller design parameters. Moreover, in order to solve the problem of overparameterization, which is a common issue in adaptive control design, a controller with one adaptive law is also designed. Finally, simulation results are given to show the effectiveness of the theoretical approaches and the potential of the proposed new design techniques.
A Space-time Smooth Artificial Viscosity Method For Nonlinear Conservation Laws
Reisner, Jon; Shkoller, Steve
2012-01-01
We introduce the $C$-method, a simple scheme for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities. In particular, we focus our attention on the compressible Euler equations which form a 3x3 system in one space dimension. The novel feature of our approach involves the coupling of a linear scalar reaction diffusion equation to our system of conservation laws, whose solution $C(x,t)$ is the coefficient to an additional (and artificial) term added to the flux, which determines both the location and strength of the added viscosity. Near shock discontinuities, $C(x,t)$ is large and localized, and transitions smoothly in space-time to zero away from the shock. This simple approach has two fundamental features: (1) our regularization is at the continuum level--i.e., the level of he partial differential equations (PDE)-- so that any higher-order numerical discretization scheme can be employed, and ...
L2-gain and passivity techniques in nonlinear control
van der Schaft, Arjan
2017-01-01
This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization...
Tang, Ze; Park, Ju H.; Lee, Tae H.
2016-10-01
This paper is devoted to the cluster synchronization issue of nonlinearly coupled Lur'e networks under the distributed adaptive pinning control strategy. The time-varying delayed networks consisted of identical and nonidentical Lur'e systems are discussed respectively by applying the edge-based pinning control scheme. In each cluster, the edges belonging to the spanning tree are pinned. In view of the nonlinearly couplings of the networks, for the first time, an efficient distributed nonlinearly adaptive update law based on the local information of the dynamical behaviors of node is proposed. Sufficient criteria for the achievement of cluster synchronization are derived based on S-procedure, Kronecker product and Lyapunov stability theory. Additionally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical results.
Explicit Nonlinear Model Predictive Control for a Saucer-Shaped Unmanned Aerial Vehicle
Directory of Open Access Journals (Sweden)
Zhihui Xing
2013-01-01
Full Text Available A lifting body unmanned aerial vehicle (UAV generates lift by its body and shows many significant advantages due to the particular shape, such as huge loading space, small wetted area, high-strength fuselage structure, and large lifting area. However, designing the control law for a lifting body UAV is quite challenging because it has strong nonlinearity and coupling, and usually lacks it rudders. In this paper, an explicit nonlinear model predictive control (ENMPC strategy is employed to design a control law for a saucer-shaped UAV which can be adequately modeled with a rigid 6-degrees-of-freedom (DOF representation. In the ENMPC, control signal is calculated by approximation of the tracking error in the receding horizon by its Taylor-series expansion to any specified order. It enhances the advantages of the nonlinear model predictive control and eliminates the time-consuming online optimization. The simulation results show that ENMPC is a propriety strategy for controlling lifting body UAVs and can compensate the insufficient control surface area.
Robust receding horizon control for networked and distributed nonlinear systems
Li, Huiping
2017-01-01
This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...
Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Xiao-Yuan Luo; Zhi-Hao Zhu; Xin-Ping Guan
2009-01-01
In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globaily uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Advanced Control Law Tuning and Performance Assessment
2006-12-01
range. The Fig. 21 shows the response of the NGMV controller and of two of the PID controllers obtained. The dynamic response of the NGMV controller...is very close to the original one, despite the significant increase in the time delay. It was not possible to obtain, for the PID controllers , both
Nonlinear Control Structure of Grid Connected Modular Multilevel Converters
DEFF Research Database (Denmark)
Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza
2017-01-01
in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab/Simulink...
Nonlinear Control Structure of Grid Connected Modular Multilevel Converters
DEFF Research Database (Denmark)
Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza
2017-01-01
in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab...
To sample or not to sample: Self-triggered control for nonlinear systems
Anta, Adolfo
2008-01-01
Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.
Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control
Domínguez, Luis F.
2011-01-19
In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.
Directory of Open Access Journals (Sweden)
Jing Lei
2013-01-01
Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
Multivariable adaptive control and estimation of a nonlinear wastewater treatment process
Energy Technology Data Exchange (ETDEWEB)
Ben Youssef, C.; Dahhou, B. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France)]|[Institut National des Sciences Appliquees (INSA), 31 - Toulouse (France)
1995-12-31
In this paper, an approach for estimating biological state and parameter variables and for controlling a non linear wastewater treatment process is developed. Combination of a nonlinear estimation procedure and a multivariable reference model control law provides favourable performances for tracking a given model-based reference model despite disturbances and system parameter uncertainties. Convergence of both estimation and control scheme are demonstrated via Lyapunov`s method. Simulation study with additive measurements noises and parameter jumps shows the efficiency and significant robustness of the control methodology developed for this non linear process. (author) 13 refs.
Fuzzy Sliding Mode Controller Design Using Takagi-Sugeno Modelled Nonlinear Systems
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S. Bououden
2013-01-01
Full Text Available Adaptive fuzzy sliding mode controller for a class of uncertain nonlinear systems is proposed in this paper. The unknown system dynamics and upper bounds of the minimum approximation errors are adaptively updated with stabilizing adaptive laws. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. The performance and stability of the proposed control system are achieved analytically using the Lyapunov stability theory. Simulations show that the proposed controller performs well and exhibits good performance.
Robust nonlinear control design with application to a marine cooling system
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2012-01-01
In this paper we consider design of control laws for a class of nonlinear systems with time-varying state delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H-inf controller is designed for the feedback linearized system....... In this context, we apply a bilinear transformation to obtain a well-posed H-inf problem. The design procedure is applied to a marine cooling system with flow dependent delays and performance of the resulting control design is evaluated through a simulation example where a comparison is made to a linear control...
Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series Capacitors
Manjarekar, N S
2012-01-01
In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector $g(x)$ in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stab...
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
Software Considerations for Subscale Flight Testing of Experimental Control Laws
Murch, Austin M.; Cox, David E.; Cunningham, Kevin
2009-01-01
The NASA AirSTAR system has been designed to address the challenges associated with safe and efficient subscale flight testing of research control laws in adverse flight conditions. In this paper, software elements of this system are described, with an emphasis on components which allow for rapid prototyping and deployment of aircraft control laws. Through model-based design and automatic coding a common code-base is used for desktop analysis, piloted simulation and real-time flight control. The flight control system provides the ability to rapidly integrate and test multiple research control laws and to emulate component or sensor failures. Integrated integrity monitoring systems provide aircraft structural load protection, isolate the system from control algorithm failures, and monitor the health of telemetry streams. Finally, issues associated with software configuration management and code modularity are briefly discussed.
A Hybrid Nonlinear Control Scheme for Active Magnetic Bearings
Xia, F.; Albritton, N. G.; Hung, J. Y.; Nelms, R. M.
1996-01-01
A nonlinear control scheme for active magnetic bearings is presented in this work. Magnet winding currents are chosen as control inputs for the electromechanical dynamics, which are linearized using feedback linearization. Then, the desired magnet currents are enforced by sliding mode control design of the electromagnetic dynamics. The overall control scheme is described by a multiple loop block diagram; the approach also falls in the class of nonlinear controls that are collectively known as the 'integrator backstepping' method. Control system hardware and new switching power electronics for implementing the controller are described. Various experiments and simulation results are presented to demonstrate the concepts' potentials.
Khazaee, Mostafa; Markazi, Amir H D; Omidi, Ehsan
2015-11-01
In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.
Primary exploration of nonlinear information fusion control theory
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By introducing information fusion techniques into a control field, a new theory of information fusion control (IFC) is proposed. Based on the theory of information fusion estimation, optimal control of nonlinear discrete control system is investigated. All information on control strategy, including ideal control strategy, expected object trajectory and dynamics of system, are regarded as measuring information of control strategy. Therefore, the problem of optimal control is transferred into the one of information fusion estimation. Firstly, the nonlinear information fusion estimation theorems are described. Secondly, an algorithm of nonlinear IFC theory is detailedly deduced. Finally, the simulation results of manipulator shift control are given, which show the feasibility and effectiveness of the presented algorithm.
Controllable spatiotemporal nonlinear effects in multimode fibres
Wright, Logan G.; Christodoulides, Demetrios N.; Wise, Frank W.
2015-05-01
Multimode fibres are of interest for next-generation telecommunications systems and the construction of high-energy fibre lasers. However, relatively little work has explored nonlinear pulse propagation in multimode fibres. Here, we consider highly nonlinear ultrashort pulse propagation in the anomalous-dispersion regime of a graded-index multimode fibre. Low modal dispersion and strong nonlinear coupling between the fibre's many spatial modes result in interesting behaviour. We observe spatiotemporal effects reminiscent of nonlinear optics in bulk media—self-focusing and multiple filamentation—at a fraction of the usual power. By adjusting the spatial initial conditions, we generate on-demand, megawatt, ultrashort pulses tunable between 1,550 and 2,200 nm dispersive waves over one octave; intense combs of visible light; and a multi-octave-spanning supercontinuum. Our results indicate that multimode fibres present unique opportunities for observing new spatiotemporal dynamics and phenomena. They also enable the realization of a new type of tunable, broadband fibre source that could be useful for many applications.
Directory of Open Access Journals (Sweden)
Long Wei
2014-01-01
Full Text Available In a recent paper (Zhang (2013, the author claims that he has proposed two rules to modify Ibragimov’s theorem on conservation laws to “ensure the theorem can be applied to nonlinear evolution equations with any mixed derivatives.” In this letter, we analysis the paper. Indeed, the so-called “modification rules” are needless and the theorem of Ibragimov can be applied to construct conservation laws directly for nonlinear equations with any mixed derivatives as long as the formal Lagrangian is rewritten in symmetric form. Moreover, the conservation laws obtained by the so-called “modification rules” in the paper under discussion are equivalent to the one obtained by Ibragimov’s theorem.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Long, Lijun; Zhao, Jun
2015-07-01
This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed.
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Yi-Xiang Chen
Full Text Available Two families of Gaussian-type soliton solutions of the (n+1-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically derived. As an example, we discuss some dynamical behaviors of two dimensional soliton solutions. Their phase switches, powers and transverse power-flow densities are discussed. Results imply that the powers flow and exchange from the gain toward the loss regions in the PT cell. Moreover, the linear stability analysis and the direct numerical simulation are carried out, which indicates that spatial Gaussian-type soliton solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media.
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
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Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
Approximate viability for nonlinear evolution inclusions with application to controllability
Directory of Open Access Journals (Sweden)
Omar Benniche
2016-12-01
Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.
Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics
Institute of Scientific and Technical Information of China (English)
LIU Yu-sheng; CHEN Jiang; LI Xing-yuan
2006-01-01
Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties.How to control such systems effectively is one of the most challenging problems.This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems.The controller can be used in cases where there exist parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded disturbances.The design of the controller is based on the control Lyapunov function method.A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics,nonlinear uncertainties and unknown bounded disturbances.The backstepping procedure is employed to overcome the complexity in the design.With the proposed method,the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters.there are.It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system.Furthermore,all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately.Simulation results illustrate the effectiveness of the proposed robust adaptive controller.
Nonlinear Observers for Gyro Calibration Coupled with a Nonlinear Control Algorithm
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The observers are then combined. The convergence properties of all three observers, and the combined observers, are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Optimal nonlinear feedback control of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
1999-01-01
An innovative strategy for optimal nonlinear feedback control of linear or nonlinear stochastic dynamic systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and stochastic dynamic programming principle. Feedback control forces of a system are divided into conservative parts and dissipative parts. The conservative parts are so selected that the energy distribution in the controlled system is as requested as possible. Then the response of the system with known conservative control forces is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are obtained from solving the stochastic dynamic programming equation.
Nonlinear systems techniques for dynamical analysis and control
Lefeber, Erjen; Arteaga, Ines
2017-01-01
This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...
Nonlinear identification and control a neural network approach
Liu, G P
2001-01-01
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies . . . , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series otTers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The time for nonlinear control to enter routine application seems to be approaching. Nonlinear control has had a long gestation period but much ofthe past has been concerned with methods that involve formal nonlinear functional model representations. It seems more likely that the breakthough will come through the use of other more flexible and ame...
Organic Law Of Judicial Guarantees And Constitutional Control
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Ernesto López Freire
2013-01-01
Full Text Available This paper demonstrates the various unconstitutional and fallacies of the Organic Law of Judicial guarantees and Constitutional Control. For that, there will be a comprehensive collation between the mentioned law and the Constitution of the Republic of Ecuador and force. Through this analysis shows a lack of knowledge of Ecuadorian law or legal science by their authors. This study elucidated, inter alia, the inconsistencies in matters relating to the interpretation of constitutional provisions, full compensation, material and integral; challenge administrative acts, judicial unit.
Nonlinear Spectral-Spatial Control and Localization of Supercontinuum Radiation
Neshev, Dragomir N.; Sukhorukov, Andrey A.; Dreischuh, Alexander; Fischer, Robert; Ha, Sangwoo; Bolger, Jeremy; Bui, Lam; Krolikowski, Wieslaw; Eggleton, Benjamin J.; Mitchell, Arnan; Austin, Michael W.; Kivshar, Yuri S.
2007-09-01
We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.
A Unified Pseudospectral Framework for Nonlinear Controller and Observer Design
Gong, Qi; Ross, I. Michael; Kang,Wei
2007-01-01
Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 2007 As a result of significant progress in pseudospectral methods for real-time dynamic optimization, it has become apparent in recent years that it is possible to present a unified framework for both controller and observer design. In this paper, we present such an approach for nonlinear systems. The method can be applied to a wide variety of nonlinear systems....
Research on Robust Control of Nonlinear Fuzzy VSS for Spacecraft
Institute of Scientific and Technical Information of China (English)
DONG Shou-quan; BI Kai-bo
2007-01-01
The nonlinear dynamic system of spacecraft with uncertainty and coupling is analyzed and its general dynamical equation is given. The decoupling-ability and controllability are proved. Aiming at this system, a new nonlinear decoupling controlling method is put forward by synthetically using the variable structure and fuzzy theory. The simulation results show that this method is effective in tracking performances under the existence of uncertainty and outer disturbance.
Nonlinear model-based control algorithm for a distillation column using software sensor.
Jana, Amiya Kumar; Samanta, Amar Nath; Ganguly, Saibal
2005-04-01
This paper presents the design of model-based globally linearizing control (GLC) structure for a distillation process within the differential geometric framework. The model of a nonideal binary distillation column, whose characteristics were highly nonlinear and strongly interactive, is used as a real process. The classical GLC law is comprised of a transformer (input-output linearizing state feedback), a nonlinear state observer, and an external PI controller. The tray temperature based short-cut observer (TTBSCO) has been used as a state estimator within the control structure, in which all tray temperatures were considered to be measured. Accordingly, the liquid phase composition of each tray was calculated online using the derived temperature-composition correlation. In the simulation experiment, the proposed GLC coupled with TTBSCO (GLC-TTBSCO) outperformed a conventional PI controller based on servo performances with and without measurement noise as well as on regulatory behaviors. In the subsequent part, the GLC law has been synthesized in conjunction with tray temperature based reduced-order observer (GLC-TTBROO) where the distillate and bottom compositions of the distillation process have been inferred from top and bottom product temperatures respectively, which were measured online. Finally, the comparative performance of the GLC-TTBSCO and the GLC-TTBROO has been addressed under parametric uncertainty and the GLC-TTBSCO algorithm provided slightly better performance than the GLC-TTBROO. The resulting control laws are rather general and can be easily adopted for other binary distillation columns.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Modular design of adaptive robust controller for strict-feedback stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
WANG Jun; XI Hong-sheng; JI Hai-bo; KANG Yu
2006-01-01
A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters.By using It(o)'s differentiation rule, nonlinear damping and adaptive Backstepping procedure,the input-to-state stable controller of global stabilization in probability is developed,which guarantees that system states are bounded and the system has a robust stabilization.According to Swapping technique,we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.Transient performance of the system is estimated by the norm of error.Results of simulation show the effectiveness of the control algorithms.The modular design,which has a concise hierarchy,is more flexible and versatile than a Lyapunov-based algorithm.
Variable Structure Control for Unmatched MIMO Nonlinear System with Its Application to MCFC Stacks
Institute of Scientific and Technical Information of China (English)
Xu Chunshan(许春山); Sun Xingjin; Cao Guangyi; Zhu Xinjian
2004-01-01
A new Variable Structure Control (VSC) with Rapid-Smooth Reaching Law (RSRL) and Rapid-Convergent Sliding Mode (FCSM) is proposed, which is based on normal VSC system. When it is used to unmatched MIMO nonlinear system, the authors combine the method of Input/Output Linearizing (I/O L) with VSC: they use the I/O L method to solve the "Unmatched" problem and use the new VSC to get good result of control. After analyzing the robustness of the MIMO nonlinear system, they use this novel controller to the temperature and gas pressure control system of Molten Carbonate Fuel Cell (MCFC) Stacks. Simulation provides quite satisfactory performance with unmatched uncertainties and external disturbances. Its future actual application is practical.
Directory of Open Access Journals (Sweden)
Gao Dexin
2012-10-01
Full Text Available This paper concentrates on the solution of state feedback exact linearization zero steady-state error optimal control problem for nonlinear systems affected by external disturbances. Firstly, the nonlinear system model with external disturbances is converted to quasi-linear system model by differential homeomorphism. Using Internal Model Optional Control (IMOC, the disturbances compensator is designed, which exactly offset the impact of external disturbances on the system. Taking the system and the disturbances compensator in series, a new augmented system is obtained. Then the zero steady-state error optimal control problem is transformed into the optimal regulator design problem of an augmented system, and the optimal static error feedback control law is designed according to the different quadratic performance index. At last, the simulation results show the effectiveness of the method.
Volyanskyy, Kostyantyn Y; Haddad, Wassim M; Calise, Anthony J
2009-11-01
This paper develops a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture involving additional terms in the update laws that are constructed using a moving time window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress and cancel system uncertainty without the need for persistency of excitation. A nonlinear parametrization of the system uncertainty is considered and state and output feedback neuroadaptive controllers are developed. To illustrate the efficacy of the proposed approach we apply our results to a spacecraft model with unknown moment of inertia and compare our results with standard neuroadaptive control methods.
Robust Adaptive Backstepping Control Design for a Nonlinear Hydraulic-Mechanical System
DEFF Research Database (Denmark)
Choux, Martin; Karimi, Hamid Reza; Hovland, Geir
2009-01-01
converge to zero despite the uncertainties in the system according to the Barbalat lemma. The resulting controllers are able to take into account the interval uncertainties in Coulomb friction parameters and in the internal leakage parameters in the cylinders. Two adaptation laws are obtained by using......The complex dynamics that characterize hydraulic systems make it difficult for the control design to achieve prescribed goals in an efficient manner. In this paper, we present the design and analysis of a robust nonlinear controller for a nonlinear hydraulic-mechanical (NHM) system. The system...... consists of an electrohydraulic servo valve and two hydraulic cylinders. Specifically, by considering a part of the dynamics of the NHM system as a norm-bounded uncertainty, two adaptive controllers are developed based on the backstepping technique that ensure the tracking error signals asymptotically...
Nonlinear region of attraction analysis for hypersonic flight vehicles’ flight control verification
Directory of Open Access Journals (Sweden)
Jie Chen
2017-05-01
Full Text Available The stability analysis method based on region of attraction is proposed for the hypersonic flight vehicles’ flight control verification in this article. Current practice for hypersonic flight vehicles’ flight control verification is largely dependent on linear theoretical analysis and nonlinear simulation research. This problem can be improved by the nonlinear stability analysis of flight control system. Firstly, the hypersonic flight vehicles’ flight dynamic model is simplified and fitted by polynomial equation. And then the region of attraction estimation method based on V–s iteration is presented to complete the stability analysis. Finally, with the controller law, the closed-loop system stability is analyzed to verify the effectiveness of the proposed method.
Zayed, Elsayed M. E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.
2017-06-01
The (G^'/G)-expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Institute of Scientific and Technical Information of China (English)
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Improved adaptive fuzzy control for MIMO nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents an improved observer-based indirect adaptive fuzzy control scheme for multiinput-multioutput (MIMO) nonlinear time-delay systems.The control scheme synthesizes adaptive fuzzy control with adaptive fuzzy identification.An observer is designed to observe the system state,and an identifier is developed to identify the unknown parts of the system.The update laws for parameters utilize two types of errors in the adaptive time-delay fuzzy logic systems,the observation error and the identificat...
Fuzzy Sliding Mode Control for Discrete Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
F.Qiao.Q.M.Zhu; A.Winfield; C.Melhuish
2003-01-01
Sliding mode control is introduced into classical model free fuzzy logic control for discrete time nonlinear systems with uncertainty to the design of a novel fuzzy sliding mode control to meet the requirement of necessary and sufficient reaching conditions of sliding mode control. The simulation results show that the proposed controller outperforms the original fuzzy sliding mode controller and the classical fuzzy logic controller in stability, convergence and robustness.
Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System
Directory of Open Access Journals (Sweden)
Xie Zheng
2015-01-01
Full Text Available A nonlinear integral sliding-mode control (NISMC scheme is proposed for second order nonlinear systems. The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. In particular, compared with four kinds of sliding mode control (SMC, the proposed control scheme is able to provide better transient performances. Furthermore, the proposed scheme ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance is proved by Lyapunov stability theory and LaSalle invariance principle. Finally, both the theoretical analysis and simulation examples demonstrate the validity of the proposed scheme.
Nonlinear Dynamic Model-Based Adaptive Control of a Solenoid-Valve System
Directory of Open Access Journals (Sweden)
DongBin Lee
2012-01-01
Full Text Available In this paper, a nonlinear model-based adaptive control approach is proposed for a solenoid-valve system. The challenge is that solenoids and butterfly valves have uncertainties in multiple parameters in the nonlinear model; various kinds of physical appearance such as size and stroke, dynamic parameters including inertia, damping, and torque coefficients, and operational parameters especially, pipe diameters and flow velocities. These uncertainties are making the system not only difficult to adjust to the environment, but also further complicated to develop the appropriate control approach for meeting the system objectives. The main contribution of this research is the application of adaptive control theory and Lyapunov-type stability approach to design a controller for a dynamic model of the solenoid-valve system in the presence of those uncertainties. The control objectives such as set-point regulation, parameter compensation, and stability are supposed to be simultaneously accomplished. The error signals are first formulated based on the nonlinear dynamic models and then the control input is developed using the Lyapunov stability-type analysis to obtain the error bounded while overcoming the uncertainties. The parameter groups are updated by adaptation laws using a projection algorithm. Numerical simulation results are shown to demonstrate good performance of the proposed nonlinear model-based adaptive approach and to compare the performance of the same solenoid-valve system with a non-adaptive method as well.
H∞ reference tracking control design for a class of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Mei-qin LIU; Hai-yang CHEN; Sen-lin ZHANG
2015-01-01
This paper investigates the H∞ trajectory tracking control for a class of nonlinear systems with time-varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unifi ed model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor (CSTR), and the standard genetic regulatory network (SGRN). First, the defi nition of the tracking control is given. Second, the H∞ performance analysis of the closed-loop system including this unifi ed model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the H∞ sense. The reference model adopted here is modifi ed to be more fl exible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.
Stochastic control and the second law of thermodynamics
Brockett, R. W.; Willems, J. C.
1979-01-01
The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media (where distortion can be cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
The importance of domestic law to international arms control
Energy Technology Data Exchange (ETDEWEB)
Lehman, R.F. II
1993-11-01
Studies of arms control and disarmament tend to focus on political, military, and diplomatic processes. Recently, in the context of the conversion of defense activities to civilian use, the economic aspects of arms control have also received renewed interest. The legal dimension, however, is in need of fresh examination. Both international and domestic law are sailing increasingly in uncharted waters. Recent arms control agreements and related developments in international peacekeeping have expanded the scope of international law and altered how one perceives certain fundamentals, including the principle of national sovereignty. Still, the nation state is largely unchallenged as the primary actor in international affairs. National governments retain near absolute sovereign rights and responsibilities even in an age of trans-national economic integration and codified international norms for human rights, freedom of the press, and the peaceful resolution of disputes. Indeed, the role of domestic law in arms control and disarmament may be more significant now than ever before. A brief review of relationships between arms control and domestic law should illustrate ways in which ones thinking has been underestimating the importance of domestic law. Hopefully, this survey will set the stage properly for the excellent, more detailed case studies by Elinor Hammarskjold and Alan Crawford. Toward that end, this paper will highlight a number of more general, and sometimes provocative, themes. These themes should be kept in mind when those two complementary presentations are considered.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang
2015-06-01
Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.
Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.
1992-01-01
A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).
Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.
1992-01-01
A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).
Robotic Manipulator Control Performance Evaluation.
1986-08-01
torque technique produces a control law analogous to the mathematically based exact linearization 1951, nonlinear feedback [201, and optimal control...law analogous to the mathematically based exact linearization [951, nonlinear feedback [201, and optimal control methods [651. Therefore the results...control law analogous to the mathematically based exact linearization [951, nonlinear feedback [201, and optimal control methods [65]. Knowledge about
Digital adaptive control laws for VTOL aircraft
Hartmann, G. L.; Stein, G.
1979-01-01
Honeywell has designed a digital self-adaptive flight control system for flight test in the VALT Research Aircraft (a modified CH-47). The final design resulted from a comparison of two different adaptive concepts: one based on explicit parameter estimates from a real-time maximum likelihood estimation algorithm and the other based on an implicit model reference adaptive system. The two designs are compared on the basis of performance and complexity.
Genetic Algorithm Optimizes Q-LAW Control Parameters
Lee, Seungwon; von Allmen, Paul; Petropoulos, Anastassios; Terrile, Richard
2008-01-01
A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
Nonlinear Control of Heart Rate Variability in Human Infants
Sugihara, George; Allan, Walter; Sobel, Daniel; Allan, Kenneth D.
1996-03-01
Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation >= 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A. L., Rigney, D. R. & West, B. J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.
Tracking Control for Switched Cascade Nonlinear Systems
Directory of Open Access Journals (Sweden)
Xiaoxiao Dong
2015-01-01
Full Text Available The issue of H∞ output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.
Nonlinear Predictive Control for PEMFC Stack Operation Temperature
Institute of Scientific and Technical Information of China (English)
LI Xi; CAO Guang-yi; ZHU Xin-jian
2005-01-01
Operating temperature of proton exchange membrane fuel cell stack should be controlled within a special range. The input-output data and operating experiences were used to establish a PEMFC stack model and operating temperature control system. A nonlinear predictive control algorithm based on fuzzy model was presented for a family of complex system with severe nonlinearity such as PEMFC. Based on the obtained fuzzy model, a discrete optimization of the control action was carried out according to the principle of Branch and Bound method. The test results demonstrate the effectiveness and advantage of this approach.
A non-linear UAV altitude PSO-PD control
Orlando, Calogero
2015-12-01
In this work, a nonlinear model based approach is presented for the altitude stabilization of a hexarotor unmanned aerial vehicle (UAV). The mathematical model and control of the hexacopter airframe is presented. To stabilize the system along the vertical direction, a Proportional Derivative (PD) control is taken into account. A particle swarm optimization (PSO) approach is used in this paper to select the optimal parameters of the control algorithm taking into account different objective functions. Simulation sets are performed to carry out the results for the non-linear system to show how the PSO tuned PD controller leads to zero the error of the position along Z earth direction.
Robust stabilization for a class of nonlinear networked control systems
Institute of Scientific and Technical Information of China (English)
Jinfeng GAO; Hongye SU; Xiaofu JI; Jian CHU
2008-01-01
The problem of robust stabilization for a class of uncertain networked control systems(NCSs)with nonlinearities satisfying a given sector condition is investigated in this paper.By introducing a new model of NCSs with parameter uncertainty,network.induced delay,nonlinearity and data packet dropout in the transmission,a strict linear matrix inequality(LMI)criterion is proposed for robust stabilization of the uncenmn nonlinear NCSs based on the Lyapunov stability theory.The maximum allowable transfer interval(MATI)can be derived by solving the feasibility problem of the corresponding LMI.Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.
Control design approaches for nonlinear systems using multiple models
Institute of Scientific and Technical Information of China (English)
Junyong ZHAI; Shumin FEI; Feipeng DA
2007-01-01
It is difficult to realize control for some complex nonlinear systems operated in different operating regions.Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models.The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.
Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints
Fradkov, Alexander L; Evans, Robin J
2007-01-01
Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification Theorem. It is shown that the synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Indirect adaptive control of nonlinear systems based on bilinear neuro-fuzzy approximation.
Boutalis, Yiannis; Christodoulou, Manolis; Theodoridis, Dimitrios
2013-10-01
In this paper, we investigate the indirect adaptive regulation problem of unknown affine in the control nonlinear systems. The proposed approach consists of choosing an appropriate system approximation model and a proper control law, which will regulate the system under the certainty equivalence principle. The main difference from other relevant works of the literature lies in the proposal of a potent approximation model that is bilinear with respect to the tunable parameters. To deploy the bilinear model, the components of the nonlinear plant are initially approximated by Fuzzy subsystems. Then, using appropriately defined fuzzy rule indicator functions, the initial dynamical fuzzy system is translated to a dynamical neuro-fuzzy model, where the indicator functions are replaced by High Order Neural Networks (HONNS), trained by sampled system data. The fuzzy output partitions of the initial fuzzy components are also estimated based on sampled data. This way, the parameters to be estimated are the weights of the HONNs and the centers of the output partitions, both arranged in matrices of appropriate dimensions and leading to a matrix to matrix bilinear parametric model. Based on the bilinear parametric model and the design of appropriate control law we use a Lyapunov stability analysis to obtain parameter adaptation laws and to regulate the states of the system. The weight updating laws guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. Moreover, introducing a method of "concurrent" parameter hopping, the updating laws are modified so that the existence of the control signal is always assured. The main characteristic of the proposed approach is that the a priori experts information required by the identification scheme is extremely low, limited to the knowledge of the signs of the centers of the fuzzy output partitions. Therefore, the proposed scheme is not
Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.
Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G
2016-07-01
We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.
Mathematical Systems Theory : from Behaviors to Nonlinear Control
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Hierarchical robust nonlinear switching control design for propulsion systems
Leonessa, Alexander
1999-09-01
The desire for developing an integrated control system- design methodology for advanced propulsion systems has led to significant activity in modeling and control of flow compression systems in recent years. In this dissertation we develop a novel hierarchical switching control framework for addressing the compressor aerodynamic instabilities of rotating stall and surge. The proposed control framework accounts for the coupling between higher-order modes while explicitly addressing actuator rate saturation constraints and system modeling uncertainty. To develop a hierarchical nonlinear switching control framework, first we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems. Using the generalized Lyapunov and invariant set theorems, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria- dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a
Output Feedback Control for a Class of Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Keylan Alimhan; Hiroshi Inaba
2006-01-01
This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.
Digital set point control of nonlinear stochastic systems
Moose, R. L.; Vanlandingham, H. F.; Zwicke, P. E.
1978-01-01
A technique for digital control of nonlinear stochastic plants is presented. The development achieves a practical digital algorithm with which the closed-loop system behaves in a classical Type I manner even with gross nonlinearities in the plant structure and low signal-to-noise power ratios. The design procedure is explained in detail and illustrated by an example whose simulated responses testify to the practicality of the approach.
Directory of Open Access Journals (Sweden)
Wei-Cheng Wang
2002-06-01
Full Text Available We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear $2imes 2$ conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer.
Nonlinear analysis and control of a continuous fermentation process
DEFF Research Database (Denmark)
Szederkényi, G.; Kristensen, Niels Rode; Hangos, K.M
2002-01-01
open-loop system properties, to explore the possible control difficulties and to select the system output to be used in the control structure. A wide range of controllers are tested including pole placement and LQ controllers, feedback and input–output linearization controllers and a nonlinear...... controller based on direct passivation. The comparison is based on time-domain performance and on investigating the stability region, robustness and tuning possibilities of the controllers. Controllers using partial state feedback of the substrate concentration and not directly depending on the reaction rate...... are recommended for the simple fermenter. Passivity based controllers have been found to be globally stable, not very sensitive to the uncertainties in the reaction rate and controller parameter but they require full nonlinear state feedback....
An energy-saving nonlinear position control strategy for electro-hydraulic servo systems.
Baghestan, Keivan; Rezaei, Seyed Mehdi; Talebi, Heidar Ali; Zareinejad, Mohammad
2015-11-01
The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system.
Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
Cancellation-Based Nonquadratic Controller Design for Nonlinear Systems via Takagi-Sugeno Models.
Gonzalez, Temoatzin; Bernal, Miguel; Sala, Antonio; Aguiar, Braulio
2016-08-12
This paper is concerned with nonquadratic conditions for stabilization of continuous-time nonlinear systems via exact Takagi-Sugeno models and generalized fuzzy Lyapunov functions. The approach hereby proposed feedback to the time derivatives of the membership functions through a multi-index control law that cancels out the terms responsible of former a priori local conditions. Thus, a nonquadratic controller design in the form of linear matrix inequalities is achieved; it does not require bounds on the time derivatives nor any extra parameters. The examples included are shown to outperform former approaches.
Output feedback control for a class of nonlinear systems with actuator degradation and sensor noise.
Ai, Weiqing; Lu, Zhenli; Li, Bin; Fei, Shumin
2016-11-01
This paper investigates the output feedback control problem of a class of nonlinear systems with sensor noise and actuator degradation. Firstly, by using the descriptor observer approach, the origin system is transformed into a descriptor system. On the basis of the descriptor system, a novel Proportional Derivative (PD) observer is developed to asymptotically estimate sensor noise and system state simultaneously. Then, by designing an adaptive law to estimate the effectiveness of actuator, an adaptive observer-based controller is constructed to ensure that system state can be regulated to the origin asymptotically. Finally, the design scheme is applied to address a flexible joint robot link problem.
Institute of Scientific and Technical Information of China (English)
WANG Hui-feng; DU Hong-bin
2008-01-01
In this paper,a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure.The proposed variable structure controller is proved to be C1,thus can be applied for backstepping design,which has extended the scope of previous nonlinear systems in the form of strict-feedback and pure-feedback.With the help of neural network approximator,H-oo performance analysis of stability is given.The effectiveness of proposed control law is verified via simulation.
Nonlinear Robust Control Theory and Applications
1997-01-18
IEEE Transactions on Automatic Control , pp. 228-238...34Robustness in the presence of mixed parametric uncertainty and unmodelled dynamics," IEEE Transactions on Automatic Control , pp. 25-38, 1991. 8 [10...Letter, 1994. [14] B. Moore, "Principal component analysis of linear systems: Controllability, observ- ability and model reduction," IEEE Transactions on Automatic Control ,
Theory, Methods, and Applications of Nonlinear Control
2012-08-29
IEEE Transactions on Automatic Control , Volume...tracking control using input-to-state stability,” IEEE Transactions on Automatic Control , Volume 57, Number 5, May 2012, pp. 1320-1326. [MZ12a... Transactions on Automatic Control , Volume 55, Number 4, April 2010, pp. 841-854. 4 [MM10b] Mazenc, F., and M. Malisoff, “Stabilization of
Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit
Energy Technology Data Exchange (ETDEWEB)
Wang Jinzhi [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)]. E-mail: jinzhiw@pku.edu.cn; Duan Zhisheng [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China); Huang Lin [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)
2006-02-27
In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method.
Nonlinear Control and Discrete Event Systems
Meyer, George; Null, Cynthia H. (Technical Monitor)
1995-01-01
As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.
Active control of chirality in nonlinear metamaterials
Energy Technology Data Exchange (ETDEWEB)
Zhu, Yu; Chai, Zhen; Yang, Hong [State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871 (China); Hu, Xiaoyong, E-mail: xiaoyonghu@pku.edu.cn; Gong, Qihuang [State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter, Beijing 100871 (China)
2015-03-02
An all-optical tunabe chirality is realized in a photonic metamaterial, the metamolecule of which consists of a nonlinear nano-Au:polycrystalline indium-tin oxide layer sandwiched between two L-shaped gold nano-antennas twisted 90° with each other. The maximum circular dichroism reached 30%. Under excitation of a 40 kW/cm{sup 2} weak pump light, the peak in the circular dichroism shifts 45 nm in the short-wavelength direction. An ultrafast response time of 35 ps is maintained. This work not only opens up the possibility for the realization of ultralow-power and ultrafast all-optical tunable chirality but also offers a way to construct ultrahigh-speed on-chip biochemical sensors.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Variable universe stable adaptive fuzzy control of nonlinear system
Institute of Scientific and Technical Information of China (English)
李洪兴; 苗志宏; 王加银
2002-01-01
A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor that is a key tool of variable universe method is defined by means of integral regulation idea, and a kind of adaptive fuzzy controllers is designed by using such a contraction-expansion factor. The simulation on first order nonlinear system is done. Secondly, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on the second order nonlinear system shows that its simulation effect is also quite good. Finally a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the settling time and enhance the robustness of the system.
Controlling chaos based on an adaptive nonlinear compensator mechanism
Institute of Scientific and Technical Information of China (English)
Tian Ling-Ling; Li Dong-Hai; Sun Xian-Fang
2008-01-01
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory.By using a designed nonlinear compensator mechanism,the system deterministic nonlinearity,parametric uncertainty and disturbance effect can be compensated effectively.The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example.From the Lyapunov stability theory,sufficient conditions for choosing control parameters to guarantee chaos control are derived.Several experiments are carried out,including parameter change experiments,set-point change experiments and disturbance experiments.Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
Backstepping Design of Adaptive Neural Fault-Tolerant Control for MIMO Nonlinear Systems.
Gao, Hui; Song, Yongduan; Wen, Changyun
2016-08-24
In this paper, an adaptive controller is developed for a class of multi-input and multioutput nonlinear systems with neural networks (NNs) used as a modeling tool. It is shown that all the signals in the closed-loop system with the proposed adaptive neural controller are globally uniformly bounded for any external input in L[₀,∞]. In our control design, the upper bound of the NN modeling error and the gains of external disturbance are characterized by unknown upper bounds, which is more rational to establish the stability in the adaptive NN control. Filter-based modification terms are used in the update laws of unknown parameters to improve the transient performance. Finally, fault-tolerant control is developed to accommodate actuator failure. An illustrative example applying the adaptive controller to control a rigid robot arm shows the validation of the proposed controller.
Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft
Snell, Antony
1993-01-01
Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.
Neural networks for function approximation in nonlinear control
Linse, Dennis J.; Stengel, Robert F.
1990-01-01
Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.
Post-recession US employment through the lens of a non-linear Okun’s law
Menzie Chinn; Laurent Ferrara; Valérie Mignon
2013-01-01
This paper aims at investigating the relationship between employment and GDP in the United States. We disentangle trend and cyclical employment components by estimating a non-linear Okun's law based on a smooth transition error-correction model that simultaneously accounts for long-term relationships between growth and employment and short-run instability over the business cycle. Our findings based on out-of-sample conditional forecasts show that, since the exit of the 2008-09 recession, US e...
Nonlinear H-infinity control of nuclear steam generators
Ramalho, Fernando Pinto
Motivated by the fact that problems related to the control of steam generators are responsible for a significant amount of downtime in nuclear power plants, this thesis investigates the applicability of linear and nonlinear Hinfinity theory to the control of nuclear steam generators. A nonlinear model based on mass, energy, and momentum balances was developed for a U-tube steam generator, with the water level and steam quality at the exit of the riser considered as state variables. In this model the steam flow to the turbines and the heat flow from the primary to the secondary side are represented as disturbances affecting the system, while the feedwater flow is used to compensate for changes in the water level. The performance specifications for the feedback loop are encoded using weight functions incorporated into an augmented plant, and the control problem is formulated to minimize the effects of disturbances on the controlled variables. The solution of the optimization problem is reduced to the solution of a set of differential equations, which, in the linear case, is equivalent to the solution of Riccati equations. The linear Hinfinity controller and filter were obtained for the U-tube steam generator with and without weight functions, and simulations for a 50 s ramp transient resulting in 50% decrease in the heat and steam flows were performed over 300 s. The use of weights provided less variation in the water level, and an excellent noise rejection capability was observed. For the nonlinear Hinfinity formulation a finite-difference method was used to solve the state and costate equations numerically for optimal feedwater flow minimizing water level variations. The combined solution of the state equation in the forward direction and the costate equations in the backward direction converged in 10 iteractions. The nonlinear controller results in less variation in the water level than the corresponding linear Hinfinity controller, demonstrating the feasibility
Fan, Quan-Yong; Yang, Guang-Hong
2017-01-01
The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies.
Institute of Scientific and Technical Information of China (English)
SU BaiLi; LI ShaoYuan; ZHU QuanMin
2009-01-01
Stabilization of the constrained switched nonlinear systems is an attractive research subject. Predictive control can handle variable constraints well and make the system stable. Its stability is typically based on an assumption of initial feasibility of the optimization problem; however the set of initial conditions, starting from where a given predictive formulation is guaranteed to be feasible, is not explicitly char-acterized. In this paper, a hybrid predictive control method is proposed for a class of switched nonlin-ear systems with input constraints and un-measurable states. The main idea is to design a mixed con-troller using Lyapunov functions and a state observer, which switches appropriately between a bounded feedback controller and a predictive controller, and to give an explicitly characterized set of initial conditions to stabilize each closed-loop subsystem. For the whole switched nonlinear system, a suitable switched law based on the state estimation is designed to orchestrate the transitions between the consistituent modes and their respective controllers, and to ensure the whole closed-loop system's stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Stabilization of the constrained switched nonlinear systems is an attractive research subject. Predictive control can handle variable constraints well and make the system stable. Its stability is typically based on an assumption of initial feasibility of the optimization problem; however the set of initial conditions, starting from where a given predictive formulation is guaranteed to be feasible, is not explicitly characterized. In this paper, a hybrid predictive control method is proposed for a class of switched nonlinear systems with input constraints and un-measurable states. The main idea is to design a mixed controller using Lyapunov functions and a state observer, which switches appropriately between a bounded feedback controller and a predictive controller, and to give an explicitly characterized set of initial conditions to stabilize each closed-loop subsystem. For the whole switched nonlinear system, a suitable switched law based on the state estimation is designed to orchestrate the transitions between the consistituent modes and their respective controllers, and to ensure the whole closed-loop system’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.
Robust Adaptive Control of Multivariable Nonlinear Systems
2011-03-28
IEEE Transactions on Automatic Control , 42(9): 1200-1221, 1997. 6. D. Li, N. Hovakimyan...limitations of performance,” IEEE Transactions on Automatic Control , vol. 52, no. 7, pp. 1604–1615, 2008. 8. X. Wang, N. Hovakimyan, 1L Adaptive...550-564, 2010. 5. C. Cao, N. Hovakimyan, Stability Margins of 1L Adaptive Control Architecture, IEEE Transactions on Automatic Control , vol. 55,
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Exact controllability for a nonlinear stochastic wave equation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The exact controllability for a semilinear stochastic wave equation with a boundary control is established. The target and initial spaces are L 2 ( G × H −1 ( G with G being a bounded open subset of R 3 and the nonlinear terms having at most a linear growth.
Nonlinear Passive Control and Observer Design for Ships
Directory of Open Access Journals (Sweden)
Thor Inge Fossen
2000-07-01
Full Text Available Starting with passivity of the ambient water-ship system this article proceeds with nonlinear observer design, design of dynamic ship positioning systems and weather optimal positioning control systems exploiting the passivity properties of the vessel and the surrounding water. The article gives an overview of methods for passive ship control and observer design.
On a state space approach to nonlinear H∞ control
Schaft, van der A.J.
1991-01-01
We study the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H∞ norm for the syste
Nonlinear Superheat Control of a Refrigeration Plant using Backstepping
DEFF Research Database (Denmark)
Rasmussen, Henrik
2008-01-01
This paper proposes a novel method for superheat and capacity control of refrigeration systems. The main idea is to control the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed and used in a backstepping design...
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
Directory of Open Access Journals (Sweden)
W. L. Chiang
2008-11-01
Full Text Available Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC or an adaptive fuzzy sliding mode controller (AFSMC capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
Dielectric Optical-Controllable Magnifying Lens by Nonlinear Negative Refraction
Cao, Jianjun; Shang, Ce; Zheng, Yuanlin; Feng, Yaming; Chen, Xianfeng; Liang, Xiaogan; Wan, Wenjie
2015-01-01
A simple optical lens plays an important role for exploring the microscopic world in science and technology by refracting light with tailored spatially varying refractive indices. Recent advancements in nanotechnology enable novel lenses, such as, superlens and hyperlens, with sub-wavelength resolution capabilities by specially designed materials’ refractive indices with meta-materials and transformation optics. However, these artificially nano- or micro-engineered lenses usually suffer high losses from metals and are highly demanding in fabrication. Here, we experimentally demonstrate, for the first time, a nonlinear dielectric magnifying lens using negative refraction by degenerate four-wave mixing in a plano-concave glass slide, obtaining magnified images. Moreover, we transform a nonlinear flat lens into a magnifying lens by introducing transformation optics into the nonlinear regime, achieving an all-optical controllable lensing effect through nonlinear wave mixing, which may have many potential applications in microscopy and imaging science. PMID:26149952
Dielectric Optical-Controlled Magnifying Lens by Nonlinear Negative Refraction
Cao, Jianjun; Zheng, Yuanlin; Chen, Xianfeng; Liang, Xiaogan; Wan, Wenjie
2014-01-01
A simple optical lens plays an important role for exploring the microscopic world in science and technology by refracting light with tailored spatially varying refractive index. Recent advancements in nanotechnology enable novel lenses, such as, superlens, hyperlens, Luneburg lens, with sub-wavelength resolution capabilities by specially designing materials' refractive indices with meta-materials and transformation optics. However, these artificially nano/micro engineered lenses usually suffer high losses from metals and are highly demanding in fabrication. Here we experimentally demonstrate for the first time a nonlinear dielectric magnifying lens using negative refraction by degenerate four-wave mixing in a plano-concave glass slide, obtaining magnified images. Moreover, we transform a nonlinear flat lens into a magnifying lens by introducing transformation optics into nonlinear regime, achieving an all-optical controllable lensing effect through nonlinear wave mixing, which may have many potential applicat...
Control Configuration Selection for Multivariable Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; Komareji, Mohammad
2012-01-01
Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of SISO (or block) controllers. This step is an important prerequisite for a successful industrial control strategy. In industrial practices, it is often the case that systems, which...
Mathematical Modeling and Control of Nonlinear Oscillators with Shape Memory Alloys
Bendame, Mohamed
for the system's thermo-mechanical dynamics are constructed using conservation laws of mass, momentum, and energy. Due to the complexity of the derived thermo-mechanical model, and the need to control the nonlinear oscillator, a model reduction based on the Galerkin method is applied to the new system in order to derive a low-dimensional model which is then solved numerically. A linear feedback control strategy for nonlinear systems is then implemented to design a tracking controller that makes the system follow a given reference input signal. The work presented in this thesis demonstrates how SMAs can be modeled by using efficient methodologies in order to capture their behavior, and how SMAs can be made stable and their chaotic behavior can be controlled by using linear and nonlinear control methods.
Klein, S. B.
1980-01-01
Twenty states, the District of Columbia, and the Virgin Islands enacted erosion and sediment control legislation during the past decade to provide for the implementation or the strengthening of statewide erosion and sediment control plans for rural and/or urban lands. That legislation and the state programs developed to implement these laws are quoted and reviewed. The natural resource data requirements of each program are also extracted. The legislation includes amendments to conservation district laws, water quality laws, and erosion and sediment control laws. Laws which provides for legislative review of administrative regulations and LANDSAT applications and/or information systems that were involved in implementing or gathering data for a specific soil erosion and sediment control program are summarized as well as principal concerns affecting erosion and sediment control laws.
Non-linear laws of echoic memory and auditory change detection in humans
Directory of Open Access Journals (Sweden)
Takeshima Yasuyuki
2010-07-01
Full Text Available Abstract Background The detection of any abrupt change in the environment is important to survival. Since memory of preceding sensory conditions is necessary for detecting changes, such a change-detection system relates closely to the memory system. Here we used an auditory change-related N1 subcomponent (change-N1 of event-related brain potentials to investigate cortical mechanisms underlying change detection and echoic memory. Results Change-N1 was elicited by a simple paradigm with two tones, a standard followed by a deviant, while subjects watched a silent movie. The amplitude of change-N1 elicited by a fixed sound pressure deviance (70 dB vs. 75 dB was negatively correlated with the logarithm of the interval between the standard sound and deviant sound (1, 10, 100, or 1000 ms, while positively correlated with the logarithm of the duration of the standard sound (25, 100, 500, or 1000 ms. The amplitude of change-N1 elicited by a deviance in sound pressure, sound frequency, and sound location was correlated with the logarithm of the magnitude of physical differences between the standard and deviant sounds. Conclusions The present findings suggest that temporal representation of echoic memory is non-linear and Weber-Fechner law holds for the automatic cortical response to sound changes within a suprathreshold range. Since the present results show that the behavior of echoic memory can be understood through change-N1, change-N1 would be a useful tool to investigate memory systems.
Nonlinear vibration with control for flexible and adaptive structures
Wagg, David
2015-01-01
This book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader ...
Nonlinear control for a class of hydraulic servo system
Institute of Scientific and Technical Information of China (English)
余宏; 冯正进; 王旭永
2004-01-01
The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.
Nonlinear control for a class of hydraulic servo system
Institute of Scientific and Technical Information of China (English)
余宏; 冯正进; 王旭永
2004-01-01
The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening,friction,etc. Aside from the nonlinear nature of hydraulic dynamics,hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues,a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well,and all signals in the closed-loop system remain bounded. Moreover,a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers,this paper's robust controller based on backstepping recursive design method is easier to design,and is more suitable for implementation.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
Robust adaptive output feedback control of nonlinearly parameterized systems
Institute of Scientific and Technical Information of China (English)
LIU Yusheng; LI Xingyuan
2007-01-01
The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded disturbances.The high-gain observer was used to estimate the state of the system.A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by inputoutput models.The scheme does not need to estimate the unknown parameters nor add a dynamical signal to dominate the effects of unmodeled dynamics.It is proven that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.Simulation results have illustrated the effectiveness of the proposed robust adaptive control scheme.
Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.
Zhang, Yanjun; Tao, Gang; Chen, Mou
2016-09-01
This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.
Parameterized design of nonlinear feedback controllers for servo positioning systems
Institute of Scientific and Technical Information of China (English)
Cheng Guoyang; Jin Wenguang
2006-01-01
To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology.
Law-Aware Access Control and its Information Model
Stieghahn, Michael
2010-01-01
Cross-border access to a variety of data such as market information, strategic information, or customer-related information defines the daily business of many global companies, including financial institutions. These companies are obliged by law to keep a data processing legal for all offered services. They need to fulfill different security objectives specified by the legislation. Therefore, they control access to prevent unauthorized users from using data. Those security objectives, for example confidentiality or secrecy, are often defined in the eXtensible Access Control Markup Language that promotes interoperability between different systems. In this paper, we show the necessity of incorporating the requirements of legislation into access control. Based on the work flow in a banking scenario we describe a variety of available contextual information and their interrelations. Different from other access control systems our main focus is on law-compliant cross-border data access. By including legislation dir...
F-8C digital CCV flight control laws
Hartmann, G. L.; Hauge, J. A.; Hendrick, R. C.
1976-01-01
A set of digital flight control laws were designed for the NASA F-8C digital fly-by-wire aircraft. The control laws emphasize Control Configured Vehicle (CCV) benefits. Specific pitch axis objectives were improved handling qualities, angle-of-attack limiting, gust alleviation, drag reduction in steady and maneuvering flight, and a capability to fly with reduced static stability. The lateral-directional design objectives were improved Dutch roll damping and turn coordination over a wide range in angle-of-attack. An overall program objective was to explore the use of modern control design methodilogy to achieve these specific CCV benefits. Tests for verifying system integrity, an experimental design for handling qualities evaluation, and recommended flight test investigations were specified.
Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
Luo, Biao; Wu, Huai-Ning; Li, Han-Xiong
2015-04-01
Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.
Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
Nonlinear Dynamics and Control of Flexible Structures
1990-10-10
control problem is to drive the outputs asymptotically to zero. Since output regulation problem seeks to enforce the set of constraints I hi() = , i = 1...K an m x m constant matrix, solves the output regulation problem if sliding can be achieved. In sliding the equivalent control is, Uq = -B(x)-KAz - B
Motor Control Research Requires Nonlinear Dynamics
Guastello, Stephen J.
2006-01-01
The author comments on the original article "The Cinderella of psychology: The neglect of motor control in the science of mental life and behavior," by D. A. Rosenbaum. Rosenbaum draws attention to the study of motor control and evaluates seven possible explanations for why the topic has been relatively neglected. The point of this comment is that…
Motor Control Research Requires Nonlinear Dynamics
Guastello, Stephen J.
2006-01-01
The author comments on the original article "The Cinderella of psychology: The neglect of motor control in the science of mental life and behavior," by D. A. Rosenbaum. Rosenbaum draws attention to the study of motor control and evaluates seven possible explanations for why the topic has been relatively neglected. The point of this comment is that…
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Evans, Denis J; Williams, Stephen R; Rondoni, Lamberto
2012-11-21
What is now known as the zeroth "law" of thermodynamics was first stated by Maxwell in 1872: at equilibrium, "Bodies whose temperatures are equal to that of the same body have themselves equal temperatures." In the present paper, we give an explicit mathematical proof of the zeroth "law" for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will in the course of time (subject to some simple conditions) relax to isothermal equilibrium where all parts of the system will have the same temperature in accord with the zeroth "law." As part of the derivation we give for the first time, an exact expression for the far from equilibrium thermal conductivity. We also give a general proof that the infinite-time integral, of transient and equilibrium autocorrelation functions of fluxes of non-conserved quantities vanish. This constitutes a proof of what was called the "heat death of the Universe" as was widely discussed in the latter half of the 19th century.
Adaptive Fuzzy Containment Control for Uncertain Nonlinear Multiagent Systems
Directory of Open Access Journals (Sweden)
Yang Yu
2014-01-01
Full Text Available This paper considers the containment control problem for uncertain nonlinear multiagent systems under directed graphs. The followers are governed by nonlinear systems with unknown dynamics while the multiple leaders are neighbors of a subset of the followers. Fuzzy logic systems (FLSs are used to identify the unknown dynamics and a distributed state feedback containment control protocol is proposed. This result is extended to the output feedback case, where observers are designed to estimate the unmeasurable states. Then, an output feedback containment control scheme is presented. The developed state feedback and output feedback containment controllers guarantee that the states of all followers converge to the convex hull spanned by the dynamic leaders. Based on Lyapunov stability theory, it is proved that the containment control errors are uniformly ultimately bounded (UUB. An example is provided to show the effectiveness of the proposed control method.
INTERVAL ROBUST CONTROL FOR NONLINEAR FLAT SYSTEMS
2013-01-01
Esta tesis se enfoca principalmente en el control robusto de sistemas no lineales planos. El objetivo principal es determinar una familia de controladores robustos con la finalidad de asegurar el cumplimiento de un conjunto de especificaciones deseadas bajo incertidumbre paramétrica en el proceso. La familia de controladores robustos se determina con un nuevo enfoque de control robusto posibilistico conjuntamente con la teoría de los sistemas planos. Las especificaciones e incertidumbre param...
Robust Integral of Neural Network and Error Sign Control of MIMO Nonlinear Systems.
Yang, Qinmin; Jagannathan, Sarangapani; Sun, Youxian
2015-12-01
This paper presents a novel state-feedback control scheme for the tracking control of a class of multi-input multioutput continuous-time nonlinear systems with unknown dynamics and bounded disturbances. First, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced. The NN in the control law learns the system dynamics in an online manner, while the NN residual reconstruction errors and the bounded disturbances are overcome by the error sign signal. Since both of the NN output and the error sign signal are included in the integral, the continuity of the control input is ensured. The controller structure and the NN weight update law are novel in contrast with the previous effort, and the semiglobal asymptotic tracking performance is still guaranteed by using the Lyapunov analysis. In addition, the NN weights and all other signals are proved to be bounded simultaneously. The proposed approach also relaxes the need for the upper bounds of certain terms, which are usually required in the previous designs. Finally, the theoretical results are substantiated with simulations.
Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot
Reyhanoglu, Mahmut; Rubio Hervas, Jaime
2013-06-01
This paper studies the point-to-point liquid container transfer control problem for a PPR robot. The robot manipulator is represented as three rigid links, and the liquid slosh dynamics are included using a multi-mass-spring model. It is assumed that two forces and a torque applied to the prismatic joints and the revolute joint, respectively, are available as control inputs. The objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these assumptions is first introduced. Then, Lyapunov-based feedback controllers are designed to achieve the control objective. Two cases are considered: partial-state feedback that does not use slosh state information and full-state feedback that uses both robot state and slosh state measurements or estimations. Computer simulations are included to illustrate the effectiveness of the proposed control laws.
Souza, Luiz C. G.; Bigot, P.
2016-10-01
One of the most well-known techniques of optimal control is the theory of Linear Quadratic Regulator (LQR). This method was originally applied only to linear systems but has been generalized for non-linear systems: the State Dependent Riccati Equation (SDRE) technique. One of the advantages of SDRE is that the weight matrix selection is the same as in LQR. The difference is that weights are not necessarily constant: they can be state dependent. Then, it gives an additional flexibility to design the control law. Many are applications of SDRE for simulation or real time control but generally SDRE weights are chosen constant so no advantage of this flexibility is taken. This work serves to show through simulation that state dependent weights matrix can improve SDRE control performance. The system is a non-linear flexible rotatory beam. In a brief first part SDRE theory will be explained and the non-linear model detailed. Then, influence of SDRE weight matrix associated with the state Q will be analyzed to get some insight in order to assume a state dependent law. Finally, these laws are tested and compared to constant weight matrix Q. Based on simulation results; one concludes showing the benefits of using an adaptive weight Q rather than a constant one.
Model algorithm control using neural networks for input delayed nonlinear control system
Institute of Scientific and Technical Information of China (English)
Yuanliang Zhang; Kil To Chong
2015-01-01
The performance of the model algorithm control method is partial y based on the accuracy of the system’s model. It is diffi-cult to obtain a good model of a nonlinear system, especial y when the nonlinearity is high. Neural networks have the ability to“learn”the characteristics of a system through nonlinear mapping to rep-resent nonlinear functions as wel as their inverse functions. This paper presents a model algorithm control method using neural net-works for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one pro-duces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to il ustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.
Grid-connected of photovoltaic module using nonlinear control
DEFF Research Database (Denmark)
El Fadil, H.; Giri, F.; Guerrero, Josep M.
2012-01-01
The problem of controlling single-phase grid connected photovoltaic (PV) system is considered. The control objective is fourfold: (i) asymptotic stability of the closed loop system, (ii) maximum power point tracking (MPPT) of PV module (iii) tight regulation of the DC bus voltage, and (iv) unity......, for the nonlinear characteristic of PV panel. It is formally shown, through theoretical analysis and simulation results, that the proposed controller does achieve its objectives....
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Nonlinear Control of Induction Motors: A Performance Study
DEFF Research Database (Denmark)
Rasmussen, Henrik; Vadstrup, P.; Børsting, H.
1998-01-01
A novel approach to control of induction motors based on nonlinear state feedback has previously been presented by the authors. The resulting scheme gives a linearized input-output decoupling of the torque and the amplitude of the field. The proposed approach is used to design controllers...... for the field amplitude and the motor torque. The method is compared with the traditional Rotor Field Oriented Control method as regards variations in rotor resistance an magnetizing inductance...
Controller Design of High Order Nonholonomic System with Nonlinear Drifts
Institute of Scientific and Technical Information of China (English)
Xiu-Yun Zheng; Yu-Qiang Wu
2009-01-01
A controller design is proposed for a class of high order nonholonomic systems with nonlinear drifts. The purpose is to ensure a solution for the closed-loop system regulated to zero. Adding a power integrator backstepping technique and the switching control strategy are employed to design the controller. The state scaling is applied to the recursive manipulation. The simulation example demonstrates the effectiveness and robust features of the proposed method.
Neuro-fuzzy predictive control for nonlinear application
Institute of Scientific and Technical Information of China (English)
CHEN Dong-xiang; WANG Gang; LV Shi-xia
2008-01-01
Aiming at the unsatisfactory dynamic performances of conventional model predictive control (MPC) in a highly nonlinear process, a scheme employed the fuzzy neural network to realize the nonlinear process is proposed. The neuro-fuzzy predictor has the capability of achieving high predictive accuracy due to its nonlinear mapping and interpolation features, and adaptively updating network parameters by a learning procedure to re-duce the model errors caused by changes of the process under control. To cope with the difficult problem of non-linear optimization, Pepanaqi method was applied to search the optimal or suboptimal solution. Comparisons were made among the objective function values of alternatives in initial space. The search was then confined to shrink the smaller region according to results of comparisons. The convergent point was finally approached to be considered as the optimal or suboptimal solution. Experimental results of the neuro-fuzzy predictive control for drier application reveal that the proposed control scheme has less tracking errors and can smooth control actions, which is applicable to changes of drying condition.
Rudra, Shubhobrata; Barai, Ranjit Kumar; Maitra, Madhubanti
2014-03-01
This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.
Input-output-controlled nonlinear equation solvers
Padovan, Joseph
1988-01-01
To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.
Rigatos, Gerasimos G
2016-06-01
It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.
Control of nonlinear systems represented in quasilinear form. Ph.D. Thesis, 1994 Final Report
Coetsee, Josef A.
1993-01-01
Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Bounded Nonlinear Control of a Rotating Pendulum System
Luyckx, L.; Loccufier, M.; Noldus, E.
2004-08-01
We are interested in the output feedback control of mechanical systems governed by the Euler-Lagrange formalism. The systems are collocated actuator-sensor controlled and underactuated. We present a design method by means of a specific example : the set point control of a rotating pendulum. We use constrained output feedback, whereby the control inputs satisfy a priori imposed upper bounds. The closed loop stability analysis relies on the direct method of Liapunov. This results in a frequency criterion on the controller's linear dynamic component and some restrictions on its nonlinearities. The control parameters are tuned for maximizing closed loop damping.
Nonlinear system PID-type multi-step predictive control
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Zhuzhi YUAN
2004-01-01
A compound neural network was constructed during the process of identification and multi-step prediction. Under the PlD-type long-range predictive cost function, the control signal was calculated based on gradient algorithm. The nonlinear controller' s structure was similar to the conventional PID controller. The parameters of this controller were tuned by using a local recurrent neural network on-line. The controller has a better effect than the conventional PID controller. Simulation study shows the effectiveness and good performance.
Nonlinear H-ininity state feedback controllers:
DEFF Research Database (Denmark)
Cromme, Marc; Møller-Pedersen, Jens; Pagh Petersen, Martin
1997-01-01
From a general point of view the state feedback H∞ suboptimal control problem is reasonably well understood. Important problems remain with regard to a priori information of the size of the neighbourhood where the local state feedback H∞ problem is solvable. This problem is solved regionally (sem...
Nonlinear Modeling and Neuro-Fuzzy Control of PEMFC
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The proton exchange membrane generation technology is highly efficient, and clean and is considered as the most hopeful "green" power technology. The operating principles of proton exchange membrane fuel cell (PEMFC) system involve thermodynamics, electrochemistry, hydrodynamics and mass transfer theory, which comprise a complex nonlinear system, for which it is difficult to establish a mathematical model and control online.This paper analyzed the characters of the PEMFC; and used the approach and self-study ability of artificial neural networks to build the model of nonlinear system, and adopted the adaptive neural-networks fuzzy infer system to build the temperature model of PEMFC which is used as the reference model of the control system, and adjusted the model parameters to control online. The model and control were implemented in SIMULINK environment.The results of simulation show the test data and model have a good agreement. The model is useful for the optimal and real time control of PEMFC system.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
Use of ILTV Control Laws for LaNCETS Flight Research
Moua, Cheng
2010-01-01
A report discusses the Lift and Nozzle Change Effects on Tail Shock (LaNCETS) test to investigate the effects of lift distribution and nozzle-area ratio changes on tail shock strength of an F-15 aircraft. Specific research objectives are to obtain inflight shock strength for multiple combinations of nozzle-area ratio and lift distribution; compare results with preflight prediction tools; and update predictive tools with flight results. The objectives from a stability and control perspective are to ensure adequate aircraft stability for the changes in lift distribution and plume shape, and ensure manageable transient from engaging and disengaging the ILTV research control laws. In order to change the lift distribution and plume shape of the F-15 aircraft, a decade-old Inner Loop Thrust Vectoring (ILTV) research control law was used. Flight envelope expansion was performed for the test configuration and flight conditions prior to the probing test points. The approach for achieving the research objectives was to utilize the unique capabilities of NASA's NF-15B-837 aircraft to allow the adjustment of the nozzle-area ratio and/or canard positions by engaging the ILTV research control laws. The ILTV control laws provide the ability to add trim command biases to canard positions, nozzle area ratios, and thrust vectoring through the use of datasets. Datasets consist of programmed test inputs (PTIs) that define trims to change the nozzle-area ratio and/or canard positions. The trims are applied as increments to the normally commanded positions. A LaNCETS non-linear, six-degrees-of-freedom simulation capable of realtime pilot-in-the-loop, hardware-in-the-loop, and non-real-time batch support was developed and validated. Prior to first flight, extensive simulation analyses were performed to show adequate stability margins with the changes in lift distribution and plume shape. Additionally, engagement/disengagement transient analysis was also performed to show manageable
Incremental approximate dynamic programming for nonlinear flight control design
Zhou, Y.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
A self-learning adaptive flight control design for non-linear systems allows reliable and effective operation of flight vehicles in a dynamic environment. Approximate dynamic programming (ADP) provides a model-free and computationally effective process for designing adaptive linear optimal
Networked control of nonlinear systems under Denial-of-Service
De Persis, C.; Tesi, P.
2016-01-01
We investigate the analysis and design of a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time that feedback information can be lost without resulting in instability of th
Identification of uncertain nonlinear systems for robust fuzzy control.
Senthilkumar, D; Mahanta, Chitralekha
2010-01-01
In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.
On global asymptotic controllability of planar affine nonlinear systems
Institute of Scientific and Technical Information of China (English)
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Distributed control design for nonlinear output agreement in convergent systems
Weitenberg, Erik; De Persis, Claudio
2015-01-01
This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived,
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2011-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design ...
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2014-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also inc...
Multiple nonlinear parameter estimation using PI feedback control
Lith, van P. F.; Witteveen, H.; Betlem, B.H.L.; Roffel, B.
2001-01-01
Nonlinear parameters often need to be estimated during the building of chemical process models. To accomplish this, many techniques are available. This paper discusses an alternative view to parameter estimation, where the concept of PI feedback control is used to estimate model parameters. The appr
Institute of Scientific and Technical Information of China (English)
Juming CHEN; Feng LIU; Shengwei MEI
2006-01-01
Active power filter (APF) based on voltage source inverter (VSI) is one of the important measures for handling the power quality problem. Mathematically, the APF model in a power grid is a typical nonlinear one. The idea of passivity is a powerful tool to study the stabilization of such a nonlinear system. In this paper, a state-space model of the four-leg APF is derived, based on which a new H-infinity controller for current tracking is proposed from the passivity point of view. It can achieve not only asymptotic tracking, but also disturbance attenuation in the sense of L2-gain. Subsequently,a sufficient condition to guarantee the boundedness and desired mean of the DC voltage is also given. This straightforward condition is consistent with the power-balancing law of electrical circuits. Simulations performed on PSCAD platform verify the validity of the new approach.
Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control.
On-Line Approximation Control of Uncertain Nonlinear Systems: Issues With Control Input Saturation
2005-01-01
stability properties of the proposed feedback control law are obtained via Lyapunov analysis. Particular emphasis is given to aircraft longitudinal control, which extends the results to the backstepping feedback control procedure.
Direct Lyapunov-based control law design for spacecraft attitude maneuvers
Institute of Scientific and Technical Information of China (English)
HU Likun; ANG Qingchao
2006-01-01
A direct Lyapunov-based control law is presented to perform on-orbit stability for spacecraft attitude maneuvers. Spacecraft attitude kinematic equations and dynamic equations are coupled, nonlinear, multi-input multi-output(MIMO), which baffles controller design. Orbit angular rates are taken into account in kinematic equations and influence of gravity gradient moments and disturbance moments on the spacecraft attitude in dynamic equations is considered to approach the practical environment, which enhance the problem complexity to some extent. Based on attitude tracking errors and angular rates, a Lyapunov function is constructed, through which the stabilizing feedback control law is deduced via Lie derivation of the Lyapunov function. The proposed method can deal with the case that the spacecraft is subjected to mass property variations or centroidal inertia matrix variations due to fuel assumption or flexibility, and disturbance moments, which shows the proposed controller is robust for spacecraft attitude maneuvers. The unlimited controller and the limited controller are taken into account respectively in simulations. Simulation results are demonstrated to validate effectiveness and feasibility of the proposed method.
Impacts of Deflection Nose on Ballistic Trajectory Control Law
Directory of Open Access Journals (Sweden)
Bo Zhang
2014-01-01
Full Text Available The deflection of projectile nose is aimed at changing the motion of the projectile in flight with the theory of motion control and changing the exterior ballistics so as to change its range and increase its accuracy. The law of external ballistics with the deflectable nose is considered as the basis of the design of a flight control system and an important part in the process of projectile development. Based on the existing rigid external ballistic model, this paper establishes an external ballistic calculation model for deflectable nose projectile and further establishes the solving programs accordingly. Different angle of attack, velocity, coefficients of lift, resistance, and moment under the deflection can be obtained in this paper based on the previous experiments and emulation researches. In the end, the author pointed out the laws on the impaction of external ballistic trajectory by the deflection of nose of the missile.
Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator.
Nguyen, Sy Dzung; Vo, Hoang Duy; Seo, Tae-Il
2017-09-01
It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Zhang, Ruikun; Hou, Zhongsheng; Ji, Honghai; Yin, Chenkun
2016-04-01
In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.
Non-linear controls on the persistence of La Nina
Di Nezio, P. N.; Deser, C.
2013-12-01
Non-linear controls on the persistence of La Nina Pedro DiNezio and Clara Deser Up to half of the observed La Nina events last for two years or more. Most El Nino events, in contrast, last no longer than one year. The physical processes causing this asymmetry in the duration of warm and cold ENSO events is unknown. The persistence of La Nina, not only exacerbates the climate impacts, especially in regions prone to drought, but also is highly unpredictable. In this talk we will explore the nonlinear processes that generate the persistence of La Nina in observations and in CCSM4 - a coupled climate model that simulates this feature realistically. First, we develop a non-linear delayed-oscillator model (nonlinDO) based on CCSM4's heat budget. All positive and negative feedbacks of nonlinDO capture the nonlinear and seasonal dependence exhibited by CCSM4. The nonlinear behavior is due to: 1) weaker atmospheric damping of cold events with respect to warm events, 2) stronger wind response for large warm events, and 3) weaker coupling between thermocline and sea-surface temperature anomalies when the thermocline deepens. We force the simple model with white Gaussian noise resulting in seasonal modulation of variance and skewness, and a spectral peak, that are in agreement with CCSM4. Sensitivity experiments with nonlinDO show that the thermocline nonlinearity (3) is the sole process controlling the duration of La Nina events. Linear ENSO theory indicates that La Nina events drive a delayed thermocline deepening that leads to their demise. However, the thermocline nonlinearity (3) renders this response ineffective as La Nina events become stronger. This diminishing of the delayed-thermocline feedback prevents the equatorial Pacific from returning to neutral or warm conditions and cold conditions persist for a second year. Observations show evidence for this thermocline nonlinearity suggesting that this process could be at work in the real world. Last, we show evidence that
Nonlinear time-series-based adaptive control applications
Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.
1991-01-01
A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.
Nonlinear Feedforward Control for Wind Disturbance Rejection on Autonomous Helicopter
DEFF Research Database (Denmark)
Bisgaard, Morten; la Cour-Harbo, Anders; A. Danapalasingam, Kumeresan
2010-01-01
for the purpose. The model is inverted for the calculation of rotor collective and cyclic pitch angles given the wind disturbance. The control strategy is then applied on a small helicopter in a controlled wind environment and flight tests demonstrates the effectiveness and advantage of the feedforward controller.......This paper presents the design and verification of a model based nonlinear feedforward controller for wind disturbance rejection on autonomous helicopters. The feedforward control is based on a helicopter model that is derived using a number of carefully chosen simplifications to make it suitable...
Nonlinear control techniques for an atomic force microscope system
Institute of Scientific and Technical Information of China (English)
Yongchun FANG; Matthew FEEMSTER; Darren DAWSON; Nader M.JALILI
2005-01-01
Two nonlinear control techniques are proposed for an atomic force microscope system.Initially,a learning-based control algorithm is developed for the microcantilever-sample system that achieves asymptotic cantilever tip tracking for periodic trajectories.Specifically,the control approach utilizes a learning-based feedforward term to compensate for periodic dynamics and high-gain terms to account for non-periodic dynamics.An adaptive control algorithm is then developed to achieve asymptotic cantilever tip tracking for bounded tip trajectories despite uncertainty throughout the system parameters.Simulation results are provided to illustrate the efficacy and performance of the control strategies.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
From linear to nonlinear control means: a practical progression.
Gao, Zhiqiang
2002-04-01
With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology.
Nonlinear model predictive control of a packed distillation column
Energy Technology Data Exchange (ETDEWEB)
Patwardhan, A.A.; Edgar, T.F. (Univ. of Texas, Austin, TX (United States). Dept. of Chemical Engineering)
1993-10-01
A rigorous dynamic model based on fundamental chemical engineering principles was formulated for a packed distillation column separating a mixture of cyclohexane and n-heptane. This model was simplified to a form suitable for use in on-line model predictive control calculations. A packed distillation column was operated at several operating conditions to estimate two unknown model parameters in the rigorous and simplified models. The actual column response to step changes in the feed rate, distillate rate, and reboiler duty agreed well with dynamic model predictions. One unusual characteristic observed was that the packed column exhibited gain-sign changes, which are very difficult to treat using conventional linear feedback control. Nonlinear model predictive control was used to control the distillation column at an operating condition where the process gain changed sign. An on-line, nonlinear model-based scheme was used to estimate unknown/time-varying model parameters.
Structure-based control of complex networks with nonlinear dynamics
Zañudo, Jorge G T; Albert, Réka
2016-01-01
Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure? Over a century of research in control theory has given us tools to answer this question, which were widely applied in science and engineering. Yet the current tools do not always consider the inherently nonlinear dynamics of real systems and the naturally occurring system states in their definition of "control", a term whose interpretation varies across disciplines. Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system. We use this framework on several real networks, compar...
Backstepping tracking control for nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Weisheng; Li Junmin
2006-01-01
Two design approaches of state feedback and output feedback tracking controllers are proposed for a class of strict feedback nonlinear time-delay systems by using backstepping technique. When the states of system cannot be observed, the time-delay state observer is designed to estimate the system states. Domination method is used to deal with nonlinear time-delay function under the assumption that the nonlinear time-delay functions of systems satisfy Lipschitz condition. The global asymptotical tracking of the references signal is achieved and the bound of all signals of the resultant closed-loop system is also guaranteed. By constructing a Lyapunov-Krasoviskii functional, the stability of the closed-loop system is proved. The feasibility of the proposed approach is illustrated by a simulation example.
Fitts' law with an isometric controller: effects of order of control and control-display gain.
Kantowitz, B H; Elvers, G C
1988-03-01
Twenty-four male subjects performed a discrete positioning task using an isometric controller. Two levels of order of control (position and velocity) were factorially crossed with two levels of control-display gain. Fitts' law functions were found for each of the four conditions. The velocity control conditions had significantly steeper slopes than the corresponding position control conditions, but there was no main effect for gain. A predicted interaction between control-display gain and order of control was found, indicating that the relative benefit of high gain is greater for velocity control than for position control. The reaction time (RT) regression lines had steeper negative slopes than those attained by Jagacinski, Repperger, Moran, Ward, and Glass (1980), who used an isotonic controller. This is in agreement with the results of Falkenberg and Newell (1980), who found that as average velocity increases, RT decreases. The components of Fitts' law were investigated, and this showed that the RT finding was due to the amplitude of the target, which covaried with average velocity, but was not due to the width.
Nonlinear burn condition control in tokamaks using isotopic fuel tailoring
Boyer, Mark D.; Schuster, Eugenio
2015-08-01
One of the fundamental problems in tokamak fusion reactors is how to control the plasma density and temperature in order to regulate the amount of fusion power produced by the device. Control of these parameters will be critical to the success of burning plasma experiments like ITER. The most previous burn condition control efforts use either non-model based control designs or techniques based on models linearized around particular operating points. Such strategies limit the potential operational space and must be carefully retuned or redesigned to accommodate changes in operating points or plasma parameters. In this work, a nonlinear dynamic model of the spatial averages of energy and ion species densities is used to synthesize a nonlinear feedback controller for stabilizing the burn condition. The nonlinear model-based control strategy guarantees a much larger operational space than previous linear controllers. Because it is not designed around a particular operating point, the controller can be used to move from one burn condition to another. The proposed scheme first attempts to use regulation of the auxiliary heating power to reject temperature perturbations, then, if necessary, uses isotopic fuel tailoring as a way to reduce fusion heating during positive temperature perturbations. A global model of hydrogen recycling is incorporated into the model used for design and simulation, and the proposed control scheme is tested for a range of recycling model parameters. As we find the possibility of changing the isotopic mix can be limited for certain unfavorable recycling conditions, we also consider impurity injection as a back-up method for controlling the system. A simple supervisory control strategy is proposed to switch between the primary and back-up control schemes based on stability and performance criteria. A zero-dimensional simulation study is used to study the performance of the control scheme for several scenarios and model parameters. Finally, a one
Fault detection and fault-tolerant control for nonlinear systems
Li, Linlin
2016-01-01
Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...
Energy Technology Data Exchange (ETDEWEB)
Narain, R; Kara, A H, E-mail: Abdul.Kara@wits.ac.z [School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg (South Africa)
2010-02-26
The construction of conserved vectors using Noether's theorem via a knowledge of a Lagrangian (or via the recently developed concept of partial Lagrangians) is well known. The formulas to determine these for higher order flows are somewhat cumbersome but peculiar and become more so as the order increases. We carry out these for a class of high-order partial differential equations from mathematical physics and then consider some specific ones with mixed derivatives. In the latter set of examples, our main focus is that the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives. Overall, we consider a large class of equations of interest and construct some new conservation laws.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator
Institute of Scientific and Technical Information of China (English)
Han Songshan; Jiao Zongxia; Wang Chengwen; Shang Yaoxing
2015-01-01
A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion sim-ulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simula-tors. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO) fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decom-position of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the control-ler theoretically can guarantee asymptotic tracking performance in the presence of the above uncer-tainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.
Control law design to meet constraints using SYNPAC-synthesis package for active controls
Adams, W. M., Jr.; Tiffany, S. H.
1982-01-01
Major features of SYNPAC (Synthesis Package for Active Controls) are described. SYNPAC employs constrained optimization techniques which allow explicit inclusion of design criteria (constraints) in the control law design process. Interrelationships are indicated between this constrained optimization approach, classical and linear quadratic Gaussian design techniques. Results are presented that were obtained by applying SYNPAC to the design of a combined stability augmentation/gust load alleviation control law for the DAST ARW-2.
Numerical Study on Nonlinear Semiactive Control of Steel-Concrete Hybrid Structures Using MR Dampers
Directory of Open Access Journals (Sweden)
Long-He Xu
2013-01-01
Full Text Available Controlling the damage process, avoiding the global collapse, and increasing the seismic safety of the super high-rise building structures are of great significance to the casualties’ reduction and seismic losses mitigation. In this paper, a semiactive control platform based on magnetorheological (MR dampers comprising the Bouc-Wen model, the semi-active control law, and the shear wall damage criteria and steel damage material model is developed in LS-DYNA program, based on the data transferring between the main program and the control platform; it can realize the purpose of integrated modeling, analysis, and design of the nonlinear semi-active control system. The nonlinear seismic control effectiveness is verified by the numerical example of a 15-story steel-concrete hybrid structure; the results indicate that the control platform and the numerical method are stable and fast, the relative displacement, shear force, and damage of the steel-concrete structure are largely reduced using the optimal designed MR dampers, and the deformations and shear forces of the concrete tube and frame are better consorted by the control devices.
Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
Nonlinear Control of a Reusable Rocket Engine for Life Extension
Lorenzo, Carl F.; Holmes, Michael S.; Ray, Asok
1998-01-01
This paper presents the conceptual development of a life-extending control system where the objective is to achieve high performance and structural durability of the plant. A life-extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel (H2) and oxidizer (O2) turbines while achieving high performance for transient responses of the combustion chamber pressure and the O2/H2 mixture ratio. The design procedure makes use of a combination of linear and nonlinear controller synthesis techniques and also allows adaptation of the life-extending controller module to augment a conventional performance controller of the rocket engine. The nonlinear aspect of the design is achieved using non-linear parameter optimization of a prescribed control structure. Fatigue damage in fuel and oxidizer turbine blades is primarily caused by stress cycling during start-up, shutdown, and transient operations of a rocket engine. Fatigue damage in the turbine blades is one of the most serious causes for engine failure.
Central suboptimal H ∞ control design for nonlinear polynomial systems
Basin, Michael V.; Shi, Peng; Calderon-Alvarez, Dario
2011-05-01
This article presents the central finite-dimensional H ∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H ∞ control problem to the corresponding optimal H 2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H 2 and H ∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H ∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H 2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H ∞ regulator available for the corresponding linearised system.
A nonlinear robust PI controller for an uncertain system
Aguilar-Ibañez, Carlos; Mendoza-Mendoza, Julio A.; Suarez-Castanon, Miguel S.; Davila, Jorge
2014-05-01
This paper presents a smooth control strategy for the regulation problem of an uncertain system, which assures uniform ultimate boundedness of the closed-loop system inside of the zero-state neighbourhood. This neighbourhood can be made arbitrarily small. To this end, a class of nonlinear proportional integral controllers or PI controllers was designed. The behaviour of this controller emulates very close a sliding mode controller. To accomplish this behaviour saturation functions were combined with traditional PI controller. The controller did not need a high-gain controller or a sliding mode controller to accomplish robustness against unmodelled persistent perturbations. The obtained closed-solution has a finite time of convergence in a small vicinity. The corresponding stability convergence analysis was done applying the traditional Lyapunov method. Numerical simulations were carried out to assess the effectiveness of the obtained controller.
Kun, David William
Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external
Evaluation of Tobacco Control Law at Cafe’ and Restaurants
Directory of Open Access Journals (Sweden)
Hilal Özcebe
2015-04-01
Full Text Available Objective: This study was conducted in order to evaluate ideas of some cafe and restaurants’ clients and workers about the tobacco control law three years after entering into force in a central district in Ankara in 2008. Methods: In the descriptive study;105 management, 113 worker and 386 client was visited, face to face interviews were done using two different questionnaire form and another form for managements’ evaluation. SPSS 15.0 statistical package program, Chi-square and t-tests were used. Administrative leave was taken. Results: Mean age of workers was 30.1±8.32 years; 82.3% were men, 54.0% smoker; with clients the values are 27.7±8.61 years; 53.6% women and 39.4% were smokers. There’s a difference between smokers and non- smokers’ ideas about the hazards; death due to second-hand smoking (p=0.024; p<0.01. 80.3% of smokers and 74.3% of non-smokers knew the law in restaurants serving alcoholic beverages. Acceptance of the idea of the law could help to quit smoking was significantly different between smoker/non smoker workers and smoker/non smoker clients (p=0.004;p<0.001. According to observations, 7.6% of the managements didn’t have law related plaque, 94.1% had smoking free areas, 57.1% had show window, 22.7% had smoking individuals and 12.6% had ashtray. Conclusion: Tobacco use is an individualistic reality but also a public health issue. Publicly acceptance of 45 law and implementations are needed besides individual perceptions. Implementations must be inspected and Smokers’ observance of the rules must be supplied in order to decrease tobacco use and related health complications.
Krishnan, Hariharan; Reyhanoglu, Mahmut; McClamroch, Harris
1994-06-01
The attitude stabilization problem of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. If the uncontrolled principal axis of the spacecraft is not an axis of symmetry, then the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to any equilibrium attitude. If the uncontrolled principal axis of the spacecraft is an axis of symmetry, the complete spacecraft dynamics are not even assessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between several feedback functions which are selected to accomplish a sequence of spacecraft maneuvers. The results of the paper show that although standard nonlinear control techniques are not applicable, it is possible to construct a nonlinear discontinuous control law based on the dynamics of the particular physical system.
Sliding mode control based guidance law with impact angle constraint
Institute of Scientific and Technical Information of China (English)
Zhao Yao; Sheng Yongzhi; Liu Xiangdong
2014-01-01
The terminal guidance problem for an unpowered lifting reentry vehicle against a sta-tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control (SMC)-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effec-tiveness of the proposed guidance law is verified by the simulation results in various scenarios.
Directory of Open Access Journals (Sweden)
Mahmood Pervaiz
2014-01-01
Full Text Available We present a control strategy for nonlinear nontriangular uncertain systems. The proposed control method is a synergy between the dynamic adaptive backstepping (DAB and integral sliding mode (ISM and is referred to as DAB-ISMC. Our main objective is to find a recursive procedure to transform a nontriangular system into an implementable form that enables designing a control law which almost eliminates the reaching-phase. The proposed method further facilitates minimization of chattering which is believed to be a shortcoming of the sliding mode control. In this methodology, the ISM, as an integrated subsystem of DAB, is introduced at the final stage of backstepping. This strategy works very well to obtain a system that is robust against model imperfections, matching and unmatching uncertainties. The DAB-ISMC method is applied on a continuous stirred tank reactor (CSTR and simulation results obtained on Matlab are found to be very promising.
A Nonlinear Flow Control Scheme Under Capacity Constraints
Institute of Scientific and Technical Information of China (English)
Yi Fan; Zhong-Ping Jiang
2005-01-01
We present a nonlinear flow control scheme based on a buffer management model with physical constraints. It extends previous result of Pitsillides et al. in [6] by improving the queue length regulation for better service of network traffics. Besides a single node system, we also address the decentralized control of many cascaded nodes. The proposed discontinuous controller asymptotically regulates the buffer queue length at the output port of a router/switch to a constant reference value, under unknown time varying interfering traffics and saturation constraints on control input and states. Its continuous approximation achieves practical regulation with an ultimate bound on the regulation error tunable by a design parameter.