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.
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'.
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.
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.
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.
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.
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.
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
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
Directory of Open Access Journals (Sweden)
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.
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.
An hp symplectic pseudospectral method for nonlinear optimal control
Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong
2017-01-01
An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.
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
Energy Technology Data Exchange (ETDEWEB)
Etchepareborda, Andres [Department of Nuclear Engineering, Argentine National Atomic Energy Commission, Centro Atomico Bariloche, Av. E. Bustillo 9500, Bariloche 8400 (Argentina)]. E-mail: etche@cab.cnea.gov.ar; Lolich, Jose [INVAP S.E., Moreno 1089, Bariloche 8400 (Argentina)
2007-02-15
A constrained, output feedback nonlinear receding horizon control (NRHC) method is applied to design a research reactor power controller. The method uses a nonlinear plant model subject to state, control and terminal set constraints; a nonlinear cost function; and a high gain observer. The controller regulates reactor power from 1% to 100% of full power; considers known disturbances, such as reactivity insertions and changes in core inlet flow and temperature; and includes upper limits constraints on neutron flux, neutron flux rate, core outlet temperature and core inlet-outlet temperature difference. Simulation results show an excellent performance for power regulation and known disturbances rejection: all process variables are kept within the admissible limits avoiding the actuation of the safety systems.
Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method
Institute of Scientific and Technical Information of China (English)
Chen Yimei; Han Zhengzhi; Tang Houjun
2006-01-01
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
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.
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.
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.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Control design for the nonlinear benchmark problem via the output regulation method
Institute of Scientific and Technical Information of China (English)
Jie HUANG; Guoqiang HU
2004-01-01
The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.
An extended harmonic balance method based on incremental nonlinear control parameters
Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.
2017-02-01
A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
Robust control methods for nonlinear systems with uncertain dynamics and unknown control direction
Ton, Chau T.
Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly aects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special
H∞ Synthesis Method for Control of Non-linear Flexible Joint Models
Axelsson, Patrik; Pipeleers, Goele; Helmersson, Anders; Norrlöf, Mikael
2014-01-01
An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a con...
Directory of Open Access Journals (Sweden)
Mahsa Khoeiniha
2012-01-01
Full Text Available This paper investigated study of dynamics of nonlinear electrical circuit by means of modern nonlinear techniques and the control of a class of chaotic system by using backstepping method based on Lyapunov function. The behavior of such nonlinear system when they are under the influence of external sinusoidal disturbances with unknown amplitudes has been considered. The objective is to analyze the performance of this system at different amplitudes of disturbances. We illustrate the proposed approach for controlling duffing oscillator problem to stabilize this system at the equilibrium point. Also Genetic Algorithm method (GA for computing the parameters of controller has been used. GA can be successfully applied to achieve a better controller. Simulation results have shown the effectiveness of the proposed method.
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.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-01-01
Full Text Available Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to the conventional methods in terms of prediction accuracy.
Optimal Parameter Tuning in a Predictive Nonlinear Control Method for a Mobile Robot
Directory of Open Access Journals (Sweden)
D. Hazry
2006-01-01
Full Text Available This study contributes to a new optimal parameter tuning in a predictive nonlinear control method for stable trajectory straight line tracking with a non-holonomic mobile robot. In this method, the focus lies in finding the optimal parameter estimation and to predict the path that the mobile robot will follow for stable trajectory straight line tracking system. The stability control contains three parameters: 1 deflection parameter for the traveling direction of the mobile robot 2 deflection parameter for the distance across traveling direction of the mobile robot and 3 deflection parameter for the steering angle of the mobile robot . Two hundred and seventy three experimental were performed and the results have been analyzed and described herewith. It is found that by using a new optimal parameter tuning in a predictive nonlinear control method derived from the extension of kinematics model, the movement of the mobile robot is stabilized and adhered to the reference posture
A comparative analysis of efficiency of nonlinear dynamics control methods for a buck converter
Andriyanov, A. I.
2017-02-01
The paper presents a comparative analysis of efficiency of methods of nonlinear dynamics control with feedback: a method of linearization of Poincaré map, a method of time-delay feedback, a method of target-oriented control. Efficiency of each method is evaluated on basis of the achieved domain of the desired dynamic mode. Dynamics modes maps and diagrams allowing evaluation of a particular method efficiency are given. It is shown that a target-oriented control has the greatest efficiency, and when it is applied in the selected range of system parameters, undesired dynamic modes do not exist. The method of Poincaré map linearization and the method of time-delay feedback control have approximately equal efficiency. A comparative analysis is performed for the first time, and the obtained results are of great importance for practice.
Waveform control method for mitigating harmonics of inverter systems with nonlinear load
DEFF Research Database (Denmark)
Wang, Haoran; Zhu, Guorong; Fu, Xiaobin;
2015-01-01
DC power systems connecting to single-phase DC/AC inverters with nonlinear loads will have their DC sources being injected with AC ripple currents containing a low-frequency component at twice the output voltage frequency of the inverter and also other current harmonics. Such a current may create...... instability in the DC power system, lower its efficiency, and shorten the lifetime of the DC source. This paper presents a general waveform control method that can mitigate the injection of the low-frequency ripple current by the single-phase DC/AC inverter into the DC source. It also discusses the inhibiting...... ability of the waveform control method on other coexisting harmonics, while the DC source delivers AC power to a nonlinear load. With the application of the waveform control, the average DC output power is supplied by the DC source, while the other harmonics pulsation power can be confined to the AC side...
Feedback control of nonlinear differential algebraic systems using Hamiltonian function method
Institute of Scientific and Technical Information of China (English)
LIU Yanhong; LI Chunwen; WU Rebing
2006-01-01
The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR) structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.
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.
Combined indirect and direct method for adaptive fuzzy output feedback control of nonlinear system
Institute of Scientific and Technical Information of China (English)
Ding Quanxin; Chen Haitong; Jiang Changsheng; Chen Zongji
2007-01-01
A novel control method for a general class of nonlinear systems using fuzzy logic systems (FLSs) is presertted.Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.
Attitude Control Synthesis for Small Satellites Using Gradient Method. Part I - Nonlinear Equations
Directory of Open Access Journals (Sweden)
Teodor-Viorel CHELARU
2012-12-01
Full Text Available The paper presents some aspects for synthesis of small satellites attitude control. Thesatellite nonlinear model presented here will be with six degrees of freedom. After movement equationlinearization the stability and command matrixes will be established and the controller will beobtained using gradient and gradient method. Two attitude control cases will be analysed: thereaction wheels and the micro thrusters. The results will be used in the project European Space MoonOrbit - ESMO founded by European Space Agency in which the University POLITEHNICA ofBucharest is involved.
ISS method for coordination control of nonlinear dynamical agents under directed topology.
Wang, Xiangke; Qin, Jiahu; Yu, Changbin
2014-10-01
The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.
A new analytic method with a convergence-control parameter for solving nonlinear problems
Zhang, Xiaolong
2016-01-01
In this paper, a new analytic method with a convergence-control parameter $c$ is first proposed. The parameter $c$ is used to adjust and control the convergence region and rate of the resulting series solution. It turns out that the convergence region and rate can be greatly enlarged by choosing a proper value of $c$. Furthermore, a numerical approach for finding the optimal value of the convergence-control parameter is given. At the same time, it is found that the traditional Adomian decomposition method is only a special case of the new method. The effectiveness and applicability of the new technique are demonstrated by several physical models including nonlinear heat transfer problems, nano-electromechanical systems, diffusion and dissipation phenomena, and dispersive waves. Moreover, the ideas proposed in this paper may offer us possibilities to greatly improve current analytic and numerical techniques.
A new adaptive backstepping method for nonlinear control of turbine main steam valve
Institute of Scientific and Technical Information of China (English)
Jun FU; Jun ZHAO
2007-01-01
A new approach for nonlinear adaptive control of turbine main steam valve is developed.In comparison with the existing controller based on "classical" adaptive backstepping.this method does not follow the classical certaintyequivalence principle in the design of adaptive control law.We introduce this approach,for the first time,to power systems and present a novel parameter estimator and dynamic feedback controller for a single machine infinite bus(SMIB)system with steam valve contral.This system contains unknown parameters such as reactance of transmission lines.Besides preserving useful nonlinearities and the real-time estimation of uncertain parameters,the proposed approach possesses better performances with respect to the response of the system and the speed of adaptation.The simulation results demonstrate that the proposed approach is better than the design based on "classical" adaptive backstepping in terms of properties of stability and parameter estimation,and recovers the performance of the "full-information" controller.Hence.the proposed method provides an alternative for engineers in applications.
Chaos control in a nonlinear pendulum using a semi-continuous method
Energy Technology Data Exchange (ETDEWEB)
Pereira-Pinto, Francisco Heitor I. E-mail: heitor@epq.ime.eb.br; Ferreira, Armando M. E-mail: armando@epq.ime.eb.br; Savi, Marcelo A. E-mail: savi@ufrj.br
2004-11-01
Chaotic behavior of dynamical systems offers a rich variety of orbits, which can be controlled by small perturbations in either a specific parameter of the system or a dynamical variable. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs) that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. At first, it is considered signals generated by numerical integration of the mathematical model. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method is employed with this aim. Finally, an analysis related to the effect of noise in controlling chaos is of concern. Results show situations where these techniques may be used to control chaos in mechanical systems.
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.
Output feedback adaptive control of multivariable nonlinear systems using Nussbaum gain method
Institute of Scientific and Technical Information of China (English)
Zhou Ying; Wu Yuqiang
2006-01-01
A new output feedback adaptive control scheme for multi-input and multi-output nonlinear systems with parametric uncertainty is presented based on the Nussbaum gain method and the backstepping approach. The high frequency gain matrix of the linear part of the system is not necessarily positive definite, but can be transformed into a lower or upper triangular matrix whose signs of diagonal elements are unknown. The new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. The global stability of the closed loop systems is guaranteed through this control scheme, at the same time the tracking error converges to zero.
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...
Directory of Open Access Journals (Sweden)
Ćosić Mladen
2014-01-01
Full Text Available This paper presents the original method of controlled building damage mechanisms based on Nonlinear Static Pushover Analysis (NSPA-DMBD. The optimal building damage mechanism is determined based on the solution of the Capacity Design Method (CDM, and the response of the building is considered in incremental situations. The development of damage mechanism of a system in such incremental situations is being controlled on the strain level, examining the relationship of current and limit strains in concrete and reinforcement steel. Since the procedure of the system damage mechanism analysis according to the NSPA-DMBD method is being iteratively implemented and designing checked after the strain reaches the limit, for this analysis a term Iterative-Interactive Design (IID has been introduced. By selecting, monitoring and controlling the optimal damage mechanism of the system and by developed NSPA-DMBD method, damage mechanism of the building is being controlled and the level of resistance to an early collapse is being increased. [Projekat Ministarstva nauke Republike Srbije, br. TR 36043
Non-local and nonlinear background suppression method controlled by multi-scale clutter metric
Gong, Jinnan; Hou, Qingyu; Zhang, Wei; Zhi, Xiyang
2015-07-01
To improve the detection performance for non-morphological multi-scale target in IR image containing complex cloud clutter, on basis of cloud scenario self-similarity feature, a non-local and nonlinear background suppression algorithm controlled by multi-scale clutter metric is presented. According to the classical achievements on cloud structure, self-similarity and relativity of cloud clutter on image for target detection is deeply analyzed by classical indicators firstly. Then we establish multi-scale clutter metric method based on LoG operator to describe scenes feature for controlled suppression method. After that, non-local means based on optimal strength similarity metric as non-local processing, and multi-scale median filter and on minimum gradient direction as local processing are set up. Finally linear fusing principle adopting clutter metric for local and non-local processing is put forward. Experimental results by two kinds of infrared imageries show that compared with classical and similar methods, the proposed method solves the existing problems of targets energy attenuation and suppression degradation in strongly evolving regions in previous methods. By evaluating indicators, the proposed method has a superior background suppression performance by increasing the BSF and ISCR 2 times at least.
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi; Atena Pasban; Kilicman, A.; S. Lotfi Noghabi
2013-01-01
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover,...
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
Institute of Scientific and Technical Information of China (English)
WANG Zi-yang; WU Gang; CHEN Wei
2007-01-01
A new model predictive control (MPC) algorithm for nonlinear systems is presented, its stabilizing property is proved, and its attractive regions are estimated. The presented method is based on the feasible solution,which makes the attractive regions much larger than those of the normal MPC controller that is based on the optimal solution.
hp-Pseudospectral method for solving continuous-time nonlinear optimal control problems
Darby, Christopher L.
2011-12-01
In this dissertation, a direct hp-pseudospectral method for approximating the solution to nonlinear optimal control problems is proposed. The hp-pseudospectral method utilizes a variable number of approximating intervals and variable-degree polynomial approximations of the state within each interval. Using the hp-discretization, the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP). The differential-algebraic constraints of the optimal control problem are enforced at a finite set of collocation points, where the collocation points are either the Legendre-Gauss or Legendre-Gauss-Radau quadrature points. These sets of points are chosen because they correspond to high-accuracy Gaussian quadrature rules for approximating the integral of a function. Moreover, Runge phenomenon for high-degree Lagrange polynomial approximations to the state is avoided by using these points. The key features of the hp-method include computational sparsity associated with low-order polynomial approximations and rapid convergence rates associated with higher-degree polynomials approximations. Consequently, the hp-method is both highly accurate and computationally efficient. Two hp-adaptive algorithms are developed that demonstrate the utility of the hp-approach. The algorithms are shown to accurately approximate the solution to general continuous-time optimal control problems in a computationally efficient manner without a priori knowledge of the solution structure. The hp-algorithms are compared empirically against local (h) and global (p) collocation methods over a wide range of problems and are found to be more efficient and more accurate. The hp-pseudospectral approach developed in this research not only provides a high-accuracy approximation to the state and control of an optimal control problem, but also provides high-accuracy approximations to the costate of the optimal control problem. The costate is approximated by
Fast numerical methods for mixed-integer nonlinear model-predictive control
Kirches, Christian
2011-01-01
Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
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
Energy Technology Data Exchange (ETDEWEB)
Duan Zhisheng [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: duanzs@pku.edu.cn; Wang Jinzhi; Yang Ying; Huang Lin [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)
2009-04-30
This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur'e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the convergence of solutions are presented. Some latest results on analysis and control of nonlinear systems with multiple equilibria and applications to chaos control are reviewed. Finally, new chaotic oscillating phenomena are shown in a pendulum-like system and a new nonlinear system with an attraction/repulsion function.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
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.-
Institute of Scientific and Technical Information of China (English)
2011-01-01
In this paper mathematical model of single inverted pendulum established based on Lagrange method. Stability of the inverted pendulum system is analyzed. Single inverted pendulum can be controlled by modem control theory, pole assignment method and Linear-quadratic regulator theory, effectually but only in small angle range. In order to obtain the larger controllable angle, the fuzzy method has been accepted to treat with this system. The idea behind of fuzzy control method in this paper is to divide the operating region of nonlinear system into small area, and treated as a collection of local linear systems which can be controlled. Global bounded property of the fuzzy method has been proven success, and according the simulation results of fuzzy servo system controllable angle is extended.
Computer-Aided Design Methods for Model-Based Nonlinear Engine Control Systems Project
National Aeronautics and Space Administration — Traditional design methods for aircraft turbine engine control systems have relied on the use of linearized models and linear control theory. While these controllers...
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→.
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 Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
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...
Institute of Scientific and Technical Information of China (English)
宋浩; 蔡遵生; 赵学庄; 李勇军; 习保民; 李燕妮
1999-01-01
A new method of controlling chemical chaos to attain the stabilized unstable periodic orbit (UPO) is proposed. It is an extension of the occasional proportional feedback (OPF) control strategy which spans the limitations of OPF, i.e. the linear region of the control rule, and extends to the whole chaotic region. It also expresses the nonlinear control rule with the back propogation-artificial neural network (BP-ANN) in order to increase the robustness of the control. Its effectiveness is examined through controlling an autocatalytic chaotic reaction model numerically.
Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong
2011-12-01
In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Identification of Stiction Nonlinearity for Pneumatic Control Valve using ANFIS Method
Directory of Open Access Journals (Sweden)
Srinivasan Arumugam
2014-05-01
Full Text Available Valve stiction is one of the prominent stand-alone reasons for oscillatory behavior in process industry. Stiction is a common problem in spring diaphragm type valves, which are widely used in the process industry. This behavior leads control valves to deliver accurate feed and thereby allowing wastage of utility. Recently, there have been many attempts to understand, define, model and detect stiction in control valves. Most of the available methods cannot simultaneously detect and quantify stiction. The paper presents an Adaptive Neuro-Fuzzy methodology for identification of stiction. For a vertical two tank level process with Kano’s model of stiction is considered to obtain necessary required data to formulate objective function. The proposed methods for detecting and quantifying stiction are applied on the flow control valve using MATLAB/Simulink platform.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
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
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.
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.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
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.
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
Boutalis, Yiannis; Theodoridis, Dimitris C; Christodoulou, Manolis A
2009-04-01
The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.
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.
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.
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.
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.
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.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
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.
Gómez-Estern, F.; Schaft, A.J. van der
2004-01-01
Energy shaping and passivity-based control designs have proven to be effective in solving control problems for underactuated mechanical systems. In recent works, Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) has been successfully applied to open loop conservative models, i
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
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...
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....
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
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
Halo轨道的ASRE非线性留位控制方法%ASRE nonlinear station-keeping control method of Halo orbits
Institute of Scientific and Technical Information of China (English)
蔡志勤; 赵军; 彭海军
2011-01-01
针对Halo轨道的留位控制问题,提出一种跟踪名义参考轨道的非线性最优跟踪控制策略.首先得到日-地系统第二平动点附近的有控制力作用下的轨道动力学方程,其次利用微分修正法得到要跟踪的名义参考轨道,然后将ASRE非线性最优跟踪控制方法与精细积分法相结合,针对Halo轨道的留位设计非线性控制器,最后利用数值算例验证了本文方法的有效性.%A new nonlinear optimal tracking control scheme is proposed to remain close to nominal paths for the station-keeping problem of Halo orbits. Firstly, the orbital dynamics equations with control force of the spacecraft near the second librafion point of the Sun-Earth system are developed. Then the nominal orbits are obtained by differential correction process. In combination with the nonlinear optimal tracking control method based on the ASRE and precise integration method, the station-keeping controller of the Halo orbit is designed. The simulations illustrating the effectiveness of the nonlinear tracking controller arc-performed.
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.
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...
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...
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.
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
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.
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.
Gavryushin, S. S.; Nikolaeva, A. S.
2016-05-01
The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes of nonlinear deformation of thin-walled axisymmetric shells by the solution parametric continuation method is generalized to solving the practical problem of design of mechanical actuators of discrete action. The synthesis algorithm is based on the method of changing the subspace of control parameters, which is supplemented with the procedure of smooth transition in changing the subspaces. The efficiency of the proposed algorithm is illustrated by an example of synthesis of a thermobimetallic actuator of discrete action. The procedure of determining an isolated solution, whose existencewas predicted byV. I. Feodosiev, is considered in the framework of studying the process of nonlinear deformation of a corrugated membrane loaded by an external pressure.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.
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.
Directory of Open Access Journals (Sweden)
Syam Syafiie
2014-06-01
Full Text Available A comparative study of Model Predictive Control (MPC using active-set method and interior point methods is proposed as a control technique for highly non-linear pH process. The process is a strong acid-strong base system. A strong acid of hydrochloric acid (HCl and a strong base of sodium hydroxide (NaOH with the presence of buffer solution sodium bicarbonate (NaHCO3 are used in a neutralization process flowing into reactor. The non-linear pH neutralization model governed in this process is presented by multi-linear models. Performance of both controllers is studied by evaluating its ability of set-point tracking and disturbance-rejection. Besides, the optimization time is compared between these two methods; both MPC shows the similar performance with no overshoot, offset, and oscillation. However, the conventional active-set method gives a shorter control action time for small scale optimization problem compared to MPC using IPM method for pH control.
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.
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.
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
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.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
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.
Convergence of some asynchronous nonlinear multisplitting methods
Szyld, Daniel B.; Xu, Jian-Jun
2000-09-01
Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach.
Optimal Variational Method for Truly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
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.
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.
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.
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....
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...
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.
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.
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
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.
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.
一种非线性航迹自适应跟踪控制方法%Adaptive tracking control method for nonlinear trajectory
Institute of Scientific and Technical Information of China (English)
缪存孝; 房建成; 盛蔚
2012-01-01
For flight trajectory tracking accuracy and quality problem of small unmanned aerial vehicle（SUAV）,an adaptive tracking control method for nonlinear trajectory was proposed.Waypoints were fitted utilizing five-order B-spline to built nonlinear desired trajectory.The location and crossing heading error equations were established within the Serret-Frenet coordinates.The asymptotically stable convergence adaptive crossing heading law was designed based on the error formulations.The flight experimental results show that the proposed adaptive tracking control method are effective and can improve the tracking accuracy.%针对小型无人飞行器航迹跟踪精度和飞行品质问题,提出了一种基于非线性航迹的自适应跟踪控制方法.应用五阶B样条拟合航点,构建非线性期望航迹;建立基于非线性期望航迹Serret-Frenet坐标系下的位置和运动航向误差方程;根据误差方程设计渐近稳定收敛的自适应运动航向控制律.并应用此方法进行了外场飞行实验,实验结果表明自适应航迹跟踪控制方法有效且能保证航迹跟踪精度.
Directory of Open Access Journals (Sweden)
Gaosheng Luo
2014-01-01
Full Text Available A robust adaptive control method with full-state feedback is proposed based on the fact that the elbow joint of a seven-function hydraulic manipulator with double-screw-pair transmission features the following control characteristics: a strongly nonlinear hydraulic system, parameter uncertainties susceptible to temperature and pressure changes of the external environment, and unknown outer disturbances. Combined with the design method of the back-stepping controller, the asymptotic stability of the control system in the presence of disturbances from uncertain systematic parameters and unknown external disturbances was demonstrated using Lyapunov stability theory. Based on the elbow joint of the seven-function master-slave hydraulic manipulator for the 4500 m Deep-Sea Working System as the research subject, a comparative study was conducted using the control method presented in this paper for unknown external disturbances. Simulations and experiments of different unknown outer disturbances showed that (1 the proposed controller could robustly track the desired reference trajectory with satisfactory dynamic performance and steady accuracy and that (2 the modified parameter adaptive laws could also guarantee that the estimated parameters are bounded.
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.
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.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
Ho, K. K.; Moody, G. B.; Peng, C. K.; Mietus, J. E.; Larson, M. G.; Levy, D.; Goldberger, A. L.
1997-01-01
BACKGROUND: Despite much recent interest in quantification of heart rate variability (HRV), the prognostic value of conventional measures of HRV and of newer indices based on nonlinear dynamics is not universally accepted. METHODS AND RESULTS: We have designed algorithms for analyzing ambulatory ECG recordings and measuring HRV without human intervention, using robust methods for obtaining time-domain measures (mean and SD of heart rate), frequency-domain measures (power in the bands of 0.001 to 0.01 Hz [VLF], 0.01 to 0.15 Hz [LF], and 0.15 to 0.5 Hz [HF] and total spectral power [TP] over all three of these bands), and measures based on nonlinear dynamics (approximate entropy [ApEn], a measure of complexity, and detrended fluctuation analysis [DFA], a measure of long-term correlations). The study population consisted of chronic congestive heart failure (CHF) case patients and sex- and age-matched control subjects in the Framingham Heart Study. After exclusion of technically inadequate studies and those with atrial fibrillation, we used these algorithms to study HRV in 2-hour ambulatory ECG recordings of 69 participants (mean age, 71.7+/-8.1 years). By use of separate Cox proportional-hazards models, the conventional measures SD (Psurvival over a mean follow-up period of 1.9 years; other measures, including ApEn (P>.3), were not. In multivariable models, DFA was of borderline predictive significance (P=.06) after adjustment for the diagnosis of CHF and SD. CONCLUSIONS: These results demonstrate that HRV analysis of ambulatory ECG recordings based on fully automated methods can have prognostic value in a population-based study and that nonlinear HRV indices may contribute prognostic value to complement traditional HRV measures.
DEFF Research Database (Denmark)
Lu, Kaiyuan; Lei, Xiao; Blaabjerg, Frede
2013-01-01
The back EMF-based sensorless control method is very popular for permanent magnet synchronous machines (PMSMs) in the medium- to high-speed operation range due to its simple structure. In this speed range, the accuracy of the estimated position is mainly affected by the inductance, which varies...... on the estimated position error, and gives a deep insight into this problem. It also provides a simple approach to achieve a globally minimized position error. A proper choice of the artificial machine inductance may reduce the maximum position error by 50% without considering the actual inductance variation...
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.
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guang-wei Yuan; Xu-deng Hang
2006-01-01
This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.
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.
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.
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...
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.
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.
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.
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-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.
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...
LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
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.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Method for conducting nonlinear electrochemical impedance spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
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...
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
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.
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.
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.
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.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
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.
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 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.
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.
反激变换器的原边非线性电流控制方法%Primary-side nonlinear current control method for flyback converter
Institute of Scientific and Technical Information of China (English)
廖鸿飞; 帅定新; 梁奇峰
2013-01-01
反激变换器是 LED 驱动的常用拓扑，为了降低成本，减小光耦对于 LED 电源可靠性的影响，提高系统的控制性能，同时避免线性控制方式在启动时的输出过冲造成 LED 损坏，提出了一种通过控制原边电流间接控制输出恒流的非线性控制策略。根据无源性控制理论建立了反激变换器的欧拉⁃拉格朗日模型，验证了系统的无源性，获得反激变换器原副边电流关系，然后基于无源性理论和 Layapunov 稳定性理论，推导出系统的无源性控制规律。这里所提出的控制方法结构简单，成本低，可靠性高，控制性能良好。实验结果验证了该控制方法的正确性，采用原边非线性电流控制方法的反激变换器具有稳定的输出电流，恒流精度高，启动无过冲并且具有良好的动态响应。%Flyback converter is the common topology for LED driver. In order to reduce costs,reduce the influence of opti⁃calcoupler on the reliability of LED power supply,improve the control property of the system and avoid the LED damage caused by output overshoot when the linear control mode is started,a nonlinear control strategy which can indirectly control output con⁃stant current by controlling the primary current is proposed. Euler⁃Lagrange model of the flyback converter was established to ver⁃ify the passivity of the system based on passivity⁃based control theory,the relationship between the primary current and output current was obtained,and then the passivity⁃based control rule was deduced base on passivity theory and Layapunov stability theory. The control method proposed in this paper has advantages of simple controller structure,low cost,high reliability and good control performance. The validity of the control scheme was verified by test result. The flyback converter controlled by pri⁃mary nonlinear current control method has a stable output,high precision and exellent transient
Gauthier, Daniel J.; Hall, G. Martin; Oliver, Robert A.; Dixon-Tulloch, Ellen G.; Wolf, Patrick D.; Bahar, Sonya
2002-09-01
We describe preliminary experiments on controlling in vivo atrial fibrillation using a closed-loop feedback protocol that measures the dynamics of the right atrium at a single spatial location and applies control perturbations at a single spatial location. This study allows investigation of control of cardiac dynamics in a preparation that is physiologically close to an in vivo human heart. The spatial-temporal response of the fibrillating sheep atrium is measured using a multi-channel electronic recording system to assess the control effectiveness. In an attempt to suppress fibrillation, we implement a scheme that paces occasionally the cardiac muscle with small shocks. When successful, the inter-activation time interval is the same and electrical stimuli are only applied when the controller senses that the dynamics are beginning to depart from the desired periodic rhythm. The shock timing is adjusted in real time using a control algorithm that attempts to synchronize the most recently measured inter-activation interval with the previous interval by inducing an activation at a time projected by the algorithm. The scheme is "single-sided" in that it can only shorten the inter-activation time but not lengthen it. Using probability distributions of the inter-activation time intervals, we find that the feedback protocol is not effective in regularizing the dynamics. One possible reason for the less-than-successful results is that the controller often attempts to stimulate the tissue while it is still in the refractory state and hence it does not induce an activation.
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.
Energy Technology Data Exchange (ETDEWEB)
Nayfeh, A.H.; Burns, J.A.; Cliff, E.M.
1990-05-18
The report summarizes results of experimental and theoretical investigations into the nonlinear response and control of structural elements. Methods for the analysis and design of control procedures applicable to certain nonlinear distributed parameter systems were investigated. Analytical and computational techniques were developed for evaluating the nonlinear effects on control designs. Bench-type experiments were conducted for validating some of the theoretical results.
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
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.
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Review of Nonlinear Methods and Modelling
Borg, F G
2005-01-01
The first part of this Review describes a few of the main methods that have been employed in non-linear time series analysis with special reference to biological applications (biomechanics). The second part treats the physical basis of posturogram data (human balance) and EMG (electromyography, a measure of muscle activity).
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.
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.
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.
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.
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.
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.
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...
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.
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...
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
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...
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
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.
Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor
Vojtesek, Jiri; Dostal, Petr
2015-01-01
Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878
Application of homotopy analysis method for solving nonlinear Cauchy problem
Directory of Open Access Journals (Sweden)
V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
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.
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.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Hierarchical robust nonlinear switching control design for propulsion systems
Leonessa, Alexander
1999-09-01
rigorous alternative to designing gain scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems. Furthermore, the hierarchical switching control framework is extended to include inverse optimality notions. Specifically, the hierarchical controller is parameterized with respect to a given system equilibrium manifold wherein an inverse optimal morphing strategy is constructed to coordinate the hierarchical switching. The overall approach is quite different from the quasivariational inequality methods for optimal switching systems developed in the literature in that our results provide hierarchical homotopic feedback controllers guaranteeing closed-loop stability via an underlying Lyapunov function. Finally, the proposed control framework is extended to account for system parametric uncertainty wherein the hierarchical switching architecture is parameterized over a set of moving nominal system equilibria.
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.
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 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.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Nonlinear Field Oriented Control of Induction Motors using the Backstepping Design
DEFF Research Database (Denmark)
Rasmussen, Henrik; Vadstrup, P.; Børsting, H.
1999-01-01
Using backstepping, which is a recursive nonlinear design method, a novel approach to control of induction motors is developed. The resulting scheme leads to a nonlinear controller for the torque and the amplitude of the field. A combination of nonlinear damping and observer backstepping with a s......Using backstepping, which is a recursive nonlinear design method, a novel approach to control of induction motors is developed. The resulting scheme leads to a nonlinear controller for the torque and the amplitude of the field. A combination of nonlinear damping and observer backstepping...... with a simple flux observer is used in the design. Assuming known motor parameters the design achieves stabilioty with garanteed region of attraction. It is also shown how a conventional field oriented controller may be obtained by omitting parts of the nonlinear controller....
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.
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.
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
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.
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
Nonlinear modal methods for crack localization
Sutin, Alexander; Ostrovsky, Lev; Lebedev, Andrey
2003-10-01
A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.
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.
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 calculating method of pile settlement
Institute of Scientific and Technical Information of China (English)
贺炜; 王桂尧; 王泓华
2008-01-01
To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.
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.
Institute of Scientific and Technical Information of China (English)
郭亚红; 吴保奎
2011-01-01
Studying control theory of induction motor nonlinear control method is the development direction. For nonlinear control method of induction motor, there are mainly three forms-feedback linearization method, passivity-based control method and backstepping method. Based on the introduction the basic control principle, and comparisons among the different control methods were made through simulation experiments, the results show that the passivity-based control method with stronger robustness is more beneficial to design.%非线性控制方法是感应电机控制理论研究的发展方向.感应电机的非线性控制方法主要有反馈线性化法、无源性控制法和反步法三种,在介绍其基本控制原理的基础上,通过仿真实验对不同的控制方法进行比较,结果表明无源性控制方法有较强的鲁棒性,更利于设计.
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.
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.
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
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.
NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation.However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process.Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis.A nonlinear data reconciliation method based on KPCA is proposed.The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space.Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel.The data reconciliation method based on KPCA is applied to ternary distillation column.Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.
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...
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 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.
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.
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.
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.
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.
Stabilization and utilization of nonlinear phenomena based on bifurcation control for slow dynamics
Yabuno, Hiroshi
2008-08-01
Mechanical systems may experience undesirable and unexpected behavior and instability due to the effects of nonlinearity of the systems. Many kinds of control methods to decrease or eliminate the effects have been studied. In particular, bifurcation control to stabilize or utilize nonlinear phenomena is currently an active topic in the field of nonlinear dynamics. This article presents some types of bifurcation control methods with the aim of realizing vibration control and motion control for mechanical systems. It is also indicated through every control method that slowly varying components in the dynamics play important roles for the control and the utilizations of nonlinear phenomena. In the first part, we deal with stabilization control methods for nonlinear resonance which is the 1/3-order subharmonic resonance in a nonlinear spring-mass-damper system and the self-excited oscillation (hunting motion) in a railway vehicle wheelset. The second part deals with positive utilizations of nonlinear phenomena by the generation and the modification of bifurcation phenomena. We propose the amplitude control method of the cantilever probe of an atomic force microscope (AFM) by increasing the nonlinearity in the system. Also, the motion control of a two link underactuated manipulator with a free link and an active link is considered by actuating the bifurcations produced under high-frequency excitation. This article is a discussion on the bifurcation control methods presented by the author and co-researchers by focusing on the actuation of the slowly varying components included in the original dynamics.
A simplified NARMAX method using nonlinear input-output data
Institute of Scientific and Technical Information of China (English)
Jie CHEN; Sheng FENG
2007-01-01
A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.
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...
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.
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.
Shuttle entry guidance revisited using nonlinear geometric methods
Mease, Kenneth D.; Kremer, Jean-Paul
1994-11-01
The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.
Method of guiding functions in problems of nonlinear analysis
Obukhovskii, Valeri; Van Loi, Nguyen; Kornev, Sergei
2013-01-01
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
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.
... Home A-Z Health Topics Birth control methods Birth control methods > A-Z Health Topics Birth control methods ... To receive Publications email updates Enter email Submit Birth control methods Birth control (contraception) is any method, medicine, ...
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. E-mail: wajdi@sharjah.ac.ae; Harb, Ahmad M. E-mail: aharb@just.edu.jo
2003-11-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
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.
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.
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
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
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...
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
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.
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.
Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities
Directory of Open Access Journals (Sweden)
Linna Zhou
2013-01-01
Full Text Available This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.
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.
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 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
Nonlinear model predictive control of managed pressure drilling.
Nandan, Anirudh; Imtiaz, Syed
2017-07-01
A new design of nonlinear model predictive controller (NMPC) is proposed for managed pressure drilling (MPD) system. The NMPC is based on output feedback control architecture and employs offset-free formulation proposed in [1]. NMPC uses active set method for computing control inputs. The controller implements an automatic switching from constant bottom hole pressure (CBHP) regulation to flow control mode in the event of a reservoir kick. In the flow control mode the controller automatically raises the bottom hole pressure setpoint, and thereby keeps the reservoir fluid flow to the surface within a tunable threshold. This is achieved by exploiting constraint handling capability of NMPC. In addition to kick mitigation the controller demonstrated good performance in containing the bottom hole pressure (BHP) during the pipe connection sequence. The controller also delivered satisfactory performance in the presence of measurement noise and uncertainty in the system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
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....
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.
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.
Comparative study of homotopy continuation methods for nonlinear algebraic equations
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
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.
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.
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects
Non-linear and adaptive control of a refrigeration system
DEFF Research Database (Denmark)
Rasmussen, Henrik; Larsen, Lars F. S.
2011-01-01
In a refrigeration process heat is absorbed in an evaporator by evaporating a flow of liquid refrigerant at low pressure and temperature. Controlling the evaporator inlet valve and the compressor in such a way that a high degree of liquid filling in the evaporator is obtained at all compressor...... are capable of adapting to variety of systems. This paper proposes a novel method for superheat and capacity control of refrigeration systems; namely by controlling the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed...
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.
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.
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.
H∞ Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise
Directory of Open Access Journals (Sweden)
Ming Gao
2015-01-01
Full Text Available This paper studies the infinite horizon H∞ control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean square H∞ control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Institute of Scientific and Technical Information of China (English)
张家树; 肖先赐; 万继宏
2001-01-01
An adaptive nonlinear feedback-control method is proposed to control continuous-time chaotic dynamical systems,where the adaptive nonlinear controller acts on only one-dimensional error signals between the desired state and the observed chaotic state of a system. The reduced parameter adaptive quadratic predictor used in adaptive feedback cancellation of the nonlinear terms can control the system at any desired state. Computer simulation results on the Lorenz system are shown to demonstrate the effectiveness of this feedback-control method.
Control of an extending nonlinear elastic cable with an active vibration control strategy
Dai, L.; Sun, L.; Chen, C.
2014-10-01
An active control strategy based on the fuzzy sliding mode control (FSMC) is developed in this research for controlling the large-amplitude vibrations of an extending nonlinear elastic cable. The geometric nonlinearity of the cable and the fixed-fixed boundary of the cable are considered. For effectively and accurately control the motion of the cable with the active control strategy developed, the governing equation of the elastic cable is established and transformed into a multi-dimensional dynamic system with the 3rd order Galerkin method. The active control strategy is developed on the basis of the dynamic system, and the control strategy is applicable to multi-dimensional dynamic systems. In the numerical simulation, large-amplitude vibrations of the cable are effectively controlled with the control strategy. The results of the research demonstrate significances for controlling the cable vibrations of an elevator in practice.
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...
Directory of Open Access Journals (Sweden)
Shuiqing Yu
2013-01-01
Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.
Kvitko, Alexander
2016-06-01
By constructing a Luenberger-type asymptotic observer, a method of finding the control function, that ensures the translation of a class of nonlinear stationary control systems of ordinary differential equations from the initial state to a given final state taking into account the actual measured values, was developed. A constructive criterion guaranteeing the existence of solution of this problem was found. An algorithm is proposed for constructing a control function that transfer wide class of nonlinear systems of ordinary differential equations from an initial state to an fixed state. The algorithm is convenient for numerical implementation. A constructive condition is obtained for which this transfer is possible.
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.
Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
On discrete control of nonlinear systems with applications to robotics
Eslami, Mansour
1989-01-01
Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.
Nonlinear Ultrasonic Characterization Using the Noncollinear Method
Croxford, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2011-06-01
The measurement of material non-linearity using ultrasound is an attractive concept, offering the potential to detect fatigue damage earlier than is possible with conventional techniques. Despite this advantage and much work in the field the currently developed approaches are primarily limited to the lab environment. This is due to the difficulty in separating the material nonlinearity from that generated by equipment. This paper reports on an approach that eliminates this problem. When two shear waves interact a third wave is generated due to the material nonlinearity. This paper shows how this interaction can be used to measure material properties in damaged specimens. It goes on to show that this approach can be used to make measurements of material non-linearity both across a specimen.
Numerical solution of control problems governed by nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Heinkenschloss, M. [Virginia Polytechnic Institute and State Univ., Blacksburg, VA (United States)
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Multiple-model-and-neural-network-based nonlinear multivariable adaptive control
Institute of Scientific and Technical Information of China (English)
Yue FU; Tianyou CHAI
2007-01-01
A multivariable adaptive controller feasible for implementation on distributed computer systems (DCS) is presented for a class of uncertain nonlinear multivariable discrete time systems. The adaptive controller is composed of a linear adaptive controller, a neural network nonlinear adaptive controller and a switching mechanism. The linear controller can provide boundedness of the input and output signals, and the nonlinear controller can improve the performance of the system. The purpose of using the switching mechanism is to obtain the improved system performance and stability simultaneously. Theory analysis and simulation results are presented to show the effectiveness of the proposed method.
Observer-Based Nonlinear Control of A Torque Motor with Perturbation Estimation
Institute of Scientific and Technical Information of China (English)
J Chen; E Prempain; Q H Wu
2006-01-01
This paper presents an observer-based nonlinear control method that was developed and implemented to provide accurate tracking control of a limited angle torque motor following a 50Hz reference waveform. The method is based on a robust nonlinear observer, which is used to estimate system states and perturbations and then employ input-output feedback linearization to compensate for the system nonlinearities and uncertainties. The estimation of system states and perturbations allows input-output linearization of the nonlinear system without an accurate mathematical model of nominal plant. The simulation results show that the observer-based nonlinear control method is superior in comparison with the conventional model-based state feedback linearizing controller.
A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Nonlinear Control of Large Disturbances in Magnetic Bearing Systems
Jiang, Yuhong; Zmood, R. B.
1996-01-01
In this paper, the nonlinear operation of magnetic bearing control methods is reviewed. For large disturbances, the effects of displacement constraints and power amplifier current and di/dt limits on bearing control system performance are analyzed. The operation of magnetic bearings exhibiting self-excited large scale oscillations have been studied both experimentally and by simulation. The simulation of the bearing system has been extended to include the effects of eddy currents in the actuators, so as to improve the accuracy of the simulation results. The results of these experiments and simulations are compared, and some useful conclusions are drawn for improving bearing system robustness.
Nonlinear fault diagnosis method based on kernel principal component analysis
Institute of Scientific and Technical Information of China (English)
Yan Weiwu; Zhang Chunkai; Shao Huihe
2005-01-01
To ensure the system run under working order, detection and diagnosis of faults play an important role in industrial process. This paper proposed a nonlinear fault diagnosis method based on kernel principal component analysis (KPCA). In proposed method, using essential information of nonlinear system extracted by KPCA, we constructed KPCA model of nonlinear system under normal working condition. Then new data were projected onto the KPCA model. When new data are incompatible with the KPCA model, it can be concluded that the nonlinear system isout of normal working condition. Proposed method was applied to fault diagnosison rolling bearings. Simulation results show proposed method provides an effective method for fault detection and diagnosis of nonlinear system.
Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter
Institute of Scientific and Technical Information of China (English)
Ashfaq Ahmad Mian; Wang Daobo
2008-01-01
In this article,a nonlinear model of an underactuated six degrees of freedom (6 DOF) quadrotor helicopter is derived on the basis of the Newton-Euler formalism.The derivation comprises determining equations of the motion of the quadrotor in three dimensions andapproximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics.The derived modelcomposed of translatioual and rotational subsystems is dynamically unstable,so a sequential nonlinear control strategy is used.The con-trol strategy includes feedback linearization coupled with a PD controller for the translational subsystem and a backstepping-based PID nonlinear controller for the rotational subsystem of the quadrotor.The performances of the nonlinear control method are evaluated by nonlinear simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter inquasi-stationary flights.
Institute of Scientific and Technical Information of China (English)
王庆林; 陈悦
1999-01-01
Aim To present a simple and effective method for the design of nonlinear and time-varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time-varying control system.%目的给出一种简单有效的非线性时变控制系统设计方法.方法提出了动平衡态及其稳定性的概念.指出控制系统输入直接控制的是系统的动平衡态而不是系统的状态.在此基础上,给出了一种基于李雅普诺夫直接方法的非线性时变系统反馈线性方法并进行了仿真研究.结果实例和仿真表明采用这一方法不仅使控制系统的设计变得简单,同时其控制效果也是令人满意的.结论新方法将控制系统设计的调节问题与跟踪问题统一起来,是一种简单和有效的非线性时变控制系统设计方法.
EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM
Institute of Scientific and Technical Information of China (English)
XU Zi-xiang; ZHOU De-yun; DENG Zi-chen
2006-01-01
To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control,multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
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
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.
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; �...
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.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
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...
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...
NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL CONTROLLABILITY OF A CLASS OF AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yimin SUN; Shengwei MEI; Qiang LU
2007-01-01
In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n - 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore,we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure.Finally, we will give three examples to show the applications of our results.
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.
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.
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have been...
Nonlinear modal method of crack localization
Ostrovsky, Lev; Sutin, Alexander; Lebedev, Andrey
2004-05-01
A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have be...
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.
Directory of Open Access Journals (Sweden)
Yacouba Simporé
2016-01-01
Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Universal construction of control Lyapunov functions for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically.Based on the control Lyapunov function,a feedback control is obtained to stabilize the closed-loop system.In addition,this method is applied to stabilize the Benchmark system.A simulation shows the effectiveness of the method.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis
Institute of Scientific and Technical Information of China (English)
WEI Rui-xuan; WU Li-xun; WANG Yong-chang; HAN Chong-zhao
2005-01-01
The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.
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 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...
J. Lang; J.G. Verwer (Jan)
2013-01-01
htmlabstractThis paper addresses consistency and stability of W-methods up to order three for nonlinear ODE-constrained control problems with possible restrictions on the control. The analysis is based on the transformed adjoint system and the control uniqueness property. These methods can also be
Institute of Scientific and Technical Information of China (English)
柴天佑; 张亚军
2011-01-01
针对一类不确定的离散时间零动态不稳定的单输入-单输出(Single-input single-output,SISO)非线性系统,提出了一种基于未建模动态补偿的非线性控制器.采用自适应神经模糊推理系统(Adaptive-network-based fuzzy inference system,ANFIS)和一一映射相结合的方法估计未建模动态在此基础上,提出了由线性自适应控制器、非线性自适应空制器以及切换机制组成的自适应切换控制方法该方法通过对上述两种控制器的切换,保证闭环系统输入输出信号有界的同时,改善系统性能.本文将要求未建模动态全局有界的条件放宽为线性增长,建立了所提自适应控制方法的稳定性和收敛性分析.通过仿真比较和水箱的液位控制实验,验证了所提方法的有效性.%This paper presents a nonlinear controller based on unmodeled dynamics compensation for a class of uncertain and discrete-time single-input single-output (SISO) nonlinear systems with unstable zero-dynamics. By combining an adaptive-network-based fuzzy inference system (ANFIS) with "one-to-one mapping", a compensator for unmodeled dynamics is constructed. With the above development, an adaptive switching control method is proposed that consists of a linear adaptive controller, a nonlinear adaptive controller and a switching mechanism. By using switching between the above two controllers, it has been shown that both an improved performance and stability can be achieved simultaneously. The paper assumes the unmodeled dynamics of the systems to satisfy a linear growth condition, which relaxes the widely used global bounded ness condition on the unmodeled dynamics. The analysis on stability and convergence of the adaptive control method are established. Finally, through the simulation based comparative study and the experiment of the proposed control on a tank level adaptive control system, the effectiveness of the proposed method is justified.
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.
Hyperbolic function method for solving nonlinear differential-different equations
Institute of Scientific and Technical Information of China (English)
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
1989-10-30
In this Phase I SBIR study, new methods are developed for the system identification and stochastic filtering of nonlinear controlled Markov processes...state space Markov process models and canonical variate analysis (CVA) for obtaining optimal nonlinear procedures for system identification and stochastic
Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control
Institute of Scientific and Technical Information of China (English)
Xiao-Bing Hu; Wen-Hua Chen
2007-01-01
This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods,this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion (LDI)and linear matrix inequality (LMI) techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
Nonlinear platoon control of Arduino cars with range-limited sensors
Yue, Wei; Guo, Ge; Wang, Liyuan; Wang, Wei
2015-05-01
This paper investigates the problem of platoon control with sensor range limitation. A nonlinear vehicular platoon model is established, in which the sensing range constraint described by a piecewise nonlinear function is involved. Then a robust nonlinear control design method is proposed based on a disturbance observer and the backstepping technique. The results are obtained in the context of both individual vehicle stability and platoon string stability analysis, which can lead to substantially enhanced platoon control performance with a guaranteed level of attenuation of the disturbance caused by lead vehicle acceleration and wind gust. The effectiveness of the method has been shown by numerical simulations and experiments carried out with Arduino cars.
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.
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.
Tip position control of a two-link flexible robot manipulator based on nonlinear deflection feedback
Energy Technology Data Exchange (ETDEWEB)
Oke, G. E-mail: oke@boun.edu.tr; Istefanopulos, Y
2003-07-01
The control of flexible link manipulators has gained an increasing importance in robotics, in recent years. To control the tip of a flexible manipulator, the joint angles should converge to the desired positions fast and elastic deflections must be effectively suppressed. In this study, a two-link flexible manipulator is controlled by three methods and the results are compared. These methods are, Pd control, PD control augmented by a nonlinear correction term feedback, where the correction term is a function of the deflection of each link, and an adaptive fuzzy controller with the nonlinear correction term feedback. Simulations have been carried out to compare the performances of all three methods.
Nonlinear system identification and control using state transition algorithm
Yang, Chunhua; Gui, Weihua
2012-01-01
This paper presents a novel optimization method named state transition algorithm (STA) to solve the problem of identification and control for nonlinear system. In the proposed algorithm, a solution to optimization problem is considered as a state, and the updating of a solution equates to the process of state transition, which makes the STA easy to understand and convenient to be implemented. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results demonstrate the validity of the methodology, and comparison to STA with other optimization algorithms confirms that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence speed and more stable performance.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
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
Study of Super-Twisting sliding mode control for U model based nonlinear system
Directory of Open Access Journals (Sweden)
Jianhua ZHANG
2016-08-01
Full Text Available The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is carried out to verify the feasibility and effectiveness of the described method. The result shows that the output of the controlled system can be tracked in a very short time by using the designed Super-Twisting controller, and the robustness of the controlled system is significantly improved as well.
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
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.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo
2015-01-01
In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.
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.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
Recent advance in nonlinear aeroelastic analysis and control of the aircraft
Directory of Open Access Journals (Sweden)
Xiang Jinwu
2014-02-01
Full Text Available A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different nonlinearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Various structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are discussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long-endurance (HALE and fight aircrafts are studied separately. Finally, conclusions and the challenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.
Recent advance in nonlinear aeroelastic analysis and control of the aircraft
Institute of Scientific and Technical Information of China (English)
Xiang Jinwu; Yan Yongju; Li Daochun
2014-01-01
A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different non-linearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Var-ious structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are dis-cussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long-endurance (HALE) and fight aircrafts are studied separately. Finally, conclusions and the chal-lenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.
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.
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.
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.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
2015-01-01
In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small ...
State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
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.
Position control of nonlinear hydraulic system using an improved PSO based PID controller
Ye, Yi; Yin, Chen-Bo; Gong, Yue; Zhou, Jun-jing
2017-01-01
This paper addresses the position control of valve-controlled cylinder system employed in hydraulic excavator. Nonlinearities such as dead zone, saturation, discharge coefficient and friction existed in the system are highlighted during the mathematical modeling. On this basis, simulation model is established and then validated against experiments. Aim for achieving excellent position control performances, an improved particle swarm optimization (PSO) algorithm is presented to search for the optimal proportional-integral-derivative (PID) controller gains for the nonlinear hydraulic system. The proposed algorithm is a hybrid based on the standard PSO algorithm but with the addition of selection and crossover operators from genetic algorithm in order to enhance the searching efficiency. Furthermore, a nonlinear decreasing scheme for the inertia weight of the improved PSO algorithm is adopted to balance global exploration and local exploration abilities of particles. Then a co-simulation platform combining the simulation model with the improved PSO tuning based PID controller is developed. Comparisons of the improved PSO, standard PSO and Phase Margin (PM) tuning methods are carried out with three position references as step signal, ramp signal and sinusoidal wave using the co-simulation platform. The results demonstrated that the improved PSO algorithm can perform well in PID control for positioning of nonlinear hydraulic system.
Nonlinear adaptive control using the Fourier integral and its application to CSTR systems.
Zhang, Huaguang; Cai, Lilong
2002-01-01
This paper presents a new nonlinear adaptive tracking controller for a class of general time-variant nonlinear systems. The control system consists of an inner loop and an outer loop. The inner loop is a fuzzy sliding mode control that is used as the feedback controller to overcome random instant disturbances. The stability of the inner loop is designed by the sliding mode control method. The other loop is a Fourier integral-based control that is used as the feedforward controller to overcome the deterministic type of uncertain disturbance. The asymptotic convergence condition of the nonlinear adaptive control system is guaranteed by the Lyapunov direct method. The effectiveness of the proposed controller is illustrated by its application to composition control in a continuously stirred tank reactor system.
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...
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 ...
Nonlinear Magnetic Circuit Analysis of SMART Control Rod Drive Actuator
Energy Technology Data Exchange (ETDEWEB)
Noh, Myounggyu; Gi, Myung Ju; Kim, Myounggon; Park, Youngwoo [Chungnam Nat' l Univ., Daejeon (Korea, Republic of); Lee, Jaeseon; Kim, Jongwook [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
In this paper, we derive a nonlinear magnetic circuit model of an electromagnetic control-rod actuator in the SMART. The results of the nonlinear model are compared with those by linear circuit model and finite-element analyses. gnetic circuit modeling is a useful tool when designing an electromagnetic actuator, as it allows fast calculations and enables parametric studies. It is particularly essential when the actuator is to be used in a very complex system such as a nuclear reactor. Important design parameters must be identified at the early stage of the design process. Once the design space is narrowed down, more accurate methods such finite-element analyses (FEA) can be employed for detailed design. Magnetic circuit modeling is based on the assumption that a flux path consists of sections in each of which field quantities are constant with linear constitutive relations. This assumption fails to hold when portions of the flux path become saturated. The magnetic circuit must be modified in order to accurately describe the nonlinear behavior of saturation.
Institute of Scientific and Technical Information of China (English)
常乃超; 陈来军; 侯云鹤
2014-01-01
分析了电力系统非线性的数学性质,指出电力系统非线性是一种有界非线性。在此基础上,将反馈主导方法(feedback domination method, FDM)引入多机电力系统非线性控制。该方法与反馈线性化方法不同；反馈线性化方法是通过反馈将原非线性系统转化为线性系统,反馈主导方法则是通过反馈将原非线性系统转换为特定形式的非线性系统,该特定形式的非线性系统的动态由反馈引入的非线性部分主导。以多机系统非线性汽门控制问题为例,设计了反馈主导非线性汽门控制器,该控制器仅包含本地量测量,易于实现。数值仿真表明,多机系统反馈主导非线性汽门控制器可显著提高电力系统暂态稳定性。%Mathematical characteristics of power system nonlinearity are analyzed. It is shown that the nonlinearity between generator output power and node voltage is a kind of bounded nonlinearity. According to the bounded nonlinearity, we introduce the feedback domination method (FDM) for controlling the nonlinear multi-machine power systems. Being different from the feedback linearization method (FLM) which transforms a nonlinear system into a linear system through nonlinear feedback, FDM transforms a nonlinear system into another nonlinear system with a particular form through nonlinear feedback. The dynamics of the transformed nonlinear system is dominated by the nonlinear part in the feedback loop. As an example, feedback domination method (FDM) is applied to design the nonlinear turbine valve control in multi-machine power systems. The nonlinear valve control law constructed for generators only includes local measurements, so that it is easy to be implemented. Numerical simulations demonstrate that the nonlinear valve control law based on FDM effectively improves transient stability in power system.
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...
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes
Directory of Open Access Journals (Sweden)
Qi-Zhi Zhang
2005-01-01
Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
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.
Nonlinear Model Predictive Control for Oil Reservoirs Management
DEFF Research Database (Denmark)
Capolei, Andrea
. With this objective function we link the optimization problem in production optimization to the Markowitz portfolio optimization problem in finance or to the the robust design problem in topology optimization. In this study we focus on open-loop configuration, i.e. without measurement feedback. We demonstrate......, the research community is working on improving current feedback model-based optimal control technologies. The topic of this thesis is production optimization for water flooding in the secondary phase of oil recovery. We developed numerical methods for nonlinear model predictive control (NMPC) of an oil field....... Further, we studied the use of robust control strategies in both open-loop, i.e. without measurement feedback, and closed-loop, i.e. with measurement feedback, configurations. This thesis has three main original contributions: The first contribution in this thesis is to improve the computationally...
Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.
Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong
2016-12-13
In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Energy Technology Data Exchange (ETDEWEB)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Computer-aided Nonlinear Control System Design Using Describing Function Models
Nassirharand, Amir
2012-01-01
A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mecha...
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.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Institute of Scientific and Technical Information of China (English)
Jean-Michel CORON; Jesús Ildefonso D（I）AZ; Abdelmalek DRICI; Tommaso MINGAZZINI
2013-01-01
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control.They assume that the internal control is only time dependent.The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
DEFF Research Database (Denmark)
Yang, Z.; Izadi-Zamanabadi, Roozbeh; Blanke, M.
2000-01-01
Based on the model-matching strategy, an adaptive control reconfiguration method for a class of nonlinear control systems is proposed by using the multiple-model scheme. Instead of requiring the nominal and faulty nonlinear systems to match each other directly in some proper sense, three sets of ...... corresponding to the updating of local LTI models, which validations are determined by the model approximation errors and the optimal index of local design. The test on a nonlinear ship propulsion system shows the promising potential of this method for system reconfiguration...
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
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.
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
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
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.
Institute of Scientific and Technical Information of China (English)
唐立军; 刘友宽; 杜景琦; 罗恩博
2014-01-01
水轮发电机组是一个典型的非线性系统，不同的导叶开度下其简化线性模型不同。本文分析了水电机组功率波动的原因，提出一种针对不同导叶开度下简化线性模型的自适应校正PID比例增益的控制方法，给出了导叶开度非线性自适应校正控制方法的参数整定方法，并在石门坎水电厂＃2机组进行了现场实施，现场实施和试验表明：该方法实施后机组静态调节误差、功率波动周期、功率波动幅度、调节稳定时间明显改善，有效的提高了机组的调节性能。%Hydro generating plant is a typical nonlinear system,the simplified linear model is different under different guide glade o-pening� This paper analyzes the cause of power oscillation of hydropower plant and proposes an adaptive control method of PID pro-portional gain correction for simplified linear model under different guide glade opening� A parameter setting method of the nonlinear adaptive control method for the guide glade opening is then present and has conducted in field implementation in#2 unit of Shimen-kan hydropower plant� The results of the field implementation indicate that this method has effectively enhanced the regulating per-formance of units and the static regulation error,power oscillation cycle,power fluctuations,adjusting and stabilizing time of units has significantly improved.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement.
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
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.
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.
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 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.
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.
Bai, Cheng; Huang, Jin
2015-07-01
Fast settling, accurate positioning, and a large tilt angle range are important for MEMS mirrors. Here, residual vibration and the pull-in phenomenon-both major problems affecting the performance of an electrostatically actuated mirror-are investigated. Based on the analysis of a nonlinear proportional-derivative (PD) control with parametric uncertainties, a closed-loop feedback control strategy with a combined control scheme is proposed. This method, combining nonlinear PD control and sliding mode control (SMC), not only inherits the virtue of a good dynamic performance from the nonlinear PD control, but also further improves the robustness with SMC for such MEMS mirrors. Furthermore, this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate. Numerical simulation results show that with this combined control scheme not only the transient response of the MEMS mirror is improved but the influence of parametric uncertainties and external disturbance is also reduced.
Institute of Scientific and Technical Information of China (English)
臧强; 张凯锋; 戴先中; 周颖
2012-01-01
For a class of nonlinear differential - algebraic equations ( DAE) subsystems: whose index is one and interconnection is local measurable, the inverse system control method is studied in this paper. The result is applied to the components control of power systems. At first the background and the particularities of such systems are expatiated. Then the definition of - order right inverse system is put forward. A recursive algorithm is given, with which to identify whether the nonlinear DAE subsystems are invertible. An - order right inverse system is realized by both state - feedback and dynamic compensation, with which the nonlinear DAE subsystems are decoupled and linearized. Finally, an excitation controller is designed for one of the synchronous generators in the multi - machine power systems based on the proposed method in this paper. The simulation is conducted and the results demonstrate the effectiveness of the proposed control scheme.%对于指数1且关联可测的非线性微分-代数子系统,研究其逆系统控制方法,并将结果应用于电力系统元件分散控制.首先描述了此类非线性微分-代数子系统的物理背景和系统特性,并给出了非线性微分-代数子系统的α阶积分右逆系统和可逆的定义;然后给出了一种递归算法,以此来判别被控系统的可逆性,并构造出由状态反馈和动态补偿实现的α阶积分右逆系统,实现了复合系统的线性化解耦；最后针对多机电力系统中的一台同步发电机,应用所提出的方法研究其励磁控制电压问题.仿真结果验证了所提出方法的有效性.
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.
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
Ross, Ian
2008-01-01
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mappin...
Robust Control Design for Uncertain Nonlinear Dynamic Systems
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
An improved impulsive control approach to nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Zhang Hua-Guang; Fu Jie; Ma Tie-Dong; Tong Shao-Cheng
2009-01-01
A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Improved Stability Analysis of Nonlinear Networked Control Systems over Multiple Communication Links
Delavar, Rahim; Tavassoli, Babak; Beheshti, Mohammad Taghi Hamidi
2015-01-01
In this paper, we consider a nonlinear networked control system (NCS) in which controllers, sensors and actuators are connected via several communication links. In each link, networking effects such as the transmission delay, packet loss, sampling jitter and data packet miss-ordering are captured by time-varying delays. Stability analysis is carried out based on the Lyapunov Krasovskii method to obtain a condition for stability of the nonlinear NCS in the form of linear matrix inequality (LMI...
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.
Electrostatic Suspension System Nonlinear Character Analysis and Its Internal Model Control
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nonlinearity is an important characteristic in electrostatic suspension system (ESS). This paper concludes the nonlinear parts in ESS, which generally result from the relationships between rotor displacement and capacitance, rotor displacement and electrostatic force, and control voltage and electrostatic force. In terms of the nonlinearities, a new control method with modified internal model control (IMC) was proposed to analyze the ESS, deduce the transfer function of the modified IMC controller in ESS, and simulate this new application in ESS. Comparing with proportional integral derivative (PID)control, IMC has only a parameter, and has better performance. As a result, IMC solves nonlinearity error well in ESS with only one uncertain parameter, and performs well when the rotor has large displacement.
Dynamic modeling and nonlinear control strategy for an underactuated quad rotor rotorcraft
Institute of Scientific and Technical Information of China (English)
Ashfaq Ahmad MIAN; Dao-bo WANG
2008-01-01
In this paper, a nonlinear dynamic MIMO model of a 6-DOF underactuated quad rotor rotorcraft is derived based on Newton-Euler formalism. The derivation comprises determining equations of motion of the quad rotor in three dimensions and seeking to approximate the actuation forces through modeling of the aerodynamic coefficients and electric motor dynamics. The derived model is dynamically unstable, so a sequential nonlinear control strategy is implemented for the quad rotor. The control strategy includes exact feedback linearization technique, using the geometric methods of nonlinear control. The performance of the nonlinear control algorithm is evaluated using simulation and the results show the effectiveness of the proposed control strategy for the quad rotor rotorcraft near quasi-stationary flight.
A new method for parameter estimation in nonlinear dynamical equations
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
An adaptive model-free predictive control method of nonlinear system%一种非线性系统的自适应无模型预测控制方法
Institute of Scientific and Technical Information of China (English)
张洁; 张广辉; 苏成利
2014-01-01
In order to avoid modeling difficulties and model mismatch problems of control method based on model which control the nonlinear system , an adaptive model-free predictive control algorithm of nonlinear sysytem is proposed .In the algorithm , nonlinear systems are converted into linear systems which are described by a series of pseudo-partial-derivatives.Then a novel project algorithm is used to estimate the pseudo-partial-derivatives , and the general model of the controlled object is given .By sol-ving quadratic objective function through the receding horizon optimization strategy , the optimized control law is obtained .Simulation result of CSTR process shows that the proposed algorithm is an effective strat -egy with excellent tracking ability and strong robustness .%为了避免基于模型的控制方法在控制非线性系统时存在建模困难和模型失配的问题，提出一种非线性系统的自适应无模型预测控制方法。该方法首先将非线性系统转化为由一组伪偏导数描述的线性系统，然后利用一种改进的投影算法在线估计这组伪偏导数，得到被控系统的泛模型。根据得到的泛模型，推导出预测模型，在此基础上根据预测控制滚动的优化策略求解二次目标函数得出最优控制律。通过对CSTR过程进行仿真验证，结果表明该方法具有良好的跟踪性能和较强的鲁棒性。
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.
Directory of Open Access Journals (Sweden)
Yu-Chi Wang
2015-01-01
Full Text Available This paper presents a unified approach to nonlinear dynamic inversion control algorithm with the parameters for desired dynamics determined by using an eigenvalue assignment method, which may be applied in a very straightforward and convenient way. By using this method, it is not necessary to transform the nonlinear equations into linear equations by feedback linearization before beginning control designs. The applications of this method are not limited to affine nonlinear control systems or limited to minimum phase problems if the eigenvalues of error dynamics are carefully assigned so that the desired dynamics is stable. The control design by using this method is shown to be robust to modeling uncertainties. To validate the theory, the design of a UAV control system is presented as an example. Numerical simulations show the performance of the design to be quite remarkable.
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
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.
Directory of Open Access Journals (Sweden)
Pedro A. Galvani
2016-08-01
Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
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.
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
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.
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 phononics and structural control of strongly correlated materials
Energy Technology Data Exchange (ETDEWEB)
Mankowsky, Roman
2016-01-20
Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal
Online prediction and control in nonlinear stochastic systems
DEFF Research Database (Denmark)
Nielsen, Torben Skov
2002-01-01
of systems which are inherently non-stationary. The third part concerns the issue of predicting the power production from wind turbines in the presence of Numerical Weather Predictions (NWP) of selected climatical variables. Here the transformation through the wind turbines from (primarily) wind speed....... The papers G , H and J investigate models and methods for predicting wind power from a wind farm on basis of observations and numerical weather predictions. All three papers consider multistep prediction models, but uses di erent estimation methods as well as dierent models for the diurnal variation of wind......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...
CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai
2001-01-01
This paper proves that a simplified Armijo-type line search can ensure the global con vergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for un constrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.
Improved HPC method for nonlinear wave tank
DEFF Research Database (Denmark)
Zhu, Wenbo; Greco, Marilena; Shao, Yanlin
2017-01-01
The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance...
Directory of Open Access Journals (Sweden)
Chaojiao Sun
2016-01-01
Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.
Nonlinear analysis of vehicle control actuations based on controlled invariant sets
Directory of Open Access Journals (Sweden)
Németh Balázs
2016-03-01
Full Text Available In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant sets of the steering and braking control systems at various velocities and road conditions. Illustration examples show that, depending on the environments, different vehicle dynamic regions can be reached and stabilized by these controllers. The results can be applied to the theoretical basis of their interventions into the vehicle control system.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
The optical nonlinearity of gold nanoparticles prepared by bioreduction method
Balbuena Ortega, A.; Arroyo Carrasco, M. L.; Gayou, V. L.; Orduña Díaz, A.; Delgado Macuil, R.; Rojas López, Marlon
2013-11-01
Nonlinear optical and electronic properties of nanosized metal particles have drawn considerable attention because of their strong and size-dependent plasmon resonance absorption. In a metal nanoparticle system such as gold dispersed in a transparent matrix, an absorption peak due to surface plasmon resonance is usually observed in the visible spectral region. Metal nanoparticles are of special interest as nonlinear materials for optical switching and computing because of their relatively large third-order nonlinearity (χ3) and ultrafast response time. The purpose of this study was to analyze the nonlinear optical properties of biosynthesized gold nanoparticles. The samples were prepared by biosynthesis method using yeast extract as reducing agent and the nonlinear optical properties of the nanoparticles were investigated using a single beam Z-scan technique with a beam power of 20 mW and operated at wavelength of 514 nm. The reaction between metal ions and yeast extracts were monitored by UV-visible spectra of Au nanoparticles in aqueous solution with different pH (3-6). The surface plasmon peak position was shifted from 528 nm to 573 nm, according to of pH variation 4 to 6. The average particle size was calculated by the absorption peak position using the Fernig method, from 42 to 103 nm. The z-scan curves showed a negative nonlocal nonlinear refractive index with a magnitude dependent on the nanoparticle size.
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.
DEFF Research Database (Denmark)
Yang, Z.; Izadi-Zamanabadi, Roozbeh; Blanke, M.
2000-01-01
Based on the model-matching strategy, an adaptive control reconfiguration method for a class of nonlinear control systems is proposed by using the multiple-model scheme. Instead of requiring the nominal and faulty nonlinear systems to match each other directly in some proper sense, three sets...... of LTI models are employed to approximate the faulty, reconfigured and nominal nonlinear systems respectively with respect to the on-line information of the operating system, and a set of compensating modules are proposed and designed so as to make the local LTI model approximating to the reconfigured...
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
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.
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
Analysis of Nonlinear Discrete Time Active Control System with Boring Chatter
Directory of Open Access Journals (Sweden)
Shujing Wu
2014-03-01
Full Text Available In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS was proposed by Okubo (1985. In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k║&le&alpha+&betaβ║v (k║&gamma, where &alpha&ge0, &beta&ge0, 0&le&gamma&le1. When 0&le&gamma&le1. It is easy to extend the method to discrete time systems. But in the case &gamma = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.
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.
New Efficient Fourth Order Method for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Farooq Ahmad
2013-12-01
Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.
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.
Koo, Min-Sung; Choi, Ho-Lim
2016-04-01
We consider the global regulation problem of uncertain systems with both triangular and non-triangular nonlinearities. For the global regulation in the presence of non-triangular nonlinearities, we propose a dynamic gain controller designed by using power order conditions and a matrix inequality condition imposed on non-triangular nonlinearities. Compared with the existing results, the proposed control method allows a class of nonlinear systems that have not been treated before. Analysis and examples are given to prove the general applicability of our control method.
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.
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.
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 $\\mathbb{S}^2$.
Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients.
Ge, Shuzhi Sam; Hong, Fan; Lee, Tong Heng
2004-02-01
In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.
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.
APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
G.I. Melnikov
2015-01-01
Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.
An averaging method for nonlinear laminar Ekman layers
DEFF Research Database (Denmark)
Andersen, Anders Peter; Lautrup, B.; Bohr, T.
2003-01-01
We study steady laminar Ekman boundary layers in rotating systems using,an averaging method similar to the technique of von Karman and Pohlhausen. The method allows us to explore nonlinear corrections to the standard Ekman theory even at large Rossby numbers. We consider both the standard self...
Tensor methods for large sparse systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Application of Nonlinear Predictive Control Based on RBF Network Predictive Model in MCFC Plant
Institute of Scientific and Technical Information of China (English)
CHEN Yue-hua; CAO Guang-yi; ZHU Xin-jian
2007-01-01
This paper described a nonlinear model predictive controller for regulating a molten carbonate fuel cell (MCFC). A detailed mechanism model of output voltage of a MCFC was presented at first. However, this model was too complicated to be used in a control system. Consequently, an off line radial basis function (RBF) network was introduced to build a nonlinear predictive model. And then, the optimal control sequences were obtained by applying golden mean method. The models and controller have been realized in the MATLAB environment. Simulation results indicate the proposed algorithm exhibits satisfying control effect even when the current densities vary largely.
Institute of Scientific and Technical Information of China (English)
Zhou Di; Zhou Jingyang
2007-01-01
The slewing motion control of a truss arm driven by a V-gimbaled control-moment-gyro (CMG) is a nonlinear control problem.The V-gimbaled CMG consists of a pair of gyros that must precess synchronously. The moment of inertia of the system, the angular momentum of the gyros and the external disturbances are not exactly known. With the help of feedback linearization and recursive Lyapunov design method, an adaptive nonlinear controller is designed to deal with the unknown items. Performance of the proposed controller is verified by simulation.
Distributed Cooperative Control of Nonlinear and Non-identical Multi-agent Systems
DEFF Research Database (Denmark)
Bidram, Ali; Lewis, Frank; Davoudi, Ali
2013-01-01
to the synchronization problem for an identical linear multi-agent system. The controller for each agent is designed to be fully distributed, such that each agent only requires its own information and the information of its neighbors. The proposed control method is exploited to implement the secondary voltage control......This paper exploits input-output feedback linearization technique to implement distributed cooperative control of multi-agent systems with nonlinear and non-identical dynamics. Feedback linearization transforms the synchronization problem for a nonlinear and heterogeneous multi-agent system...... for electric power microgrids. The effectiveness of the proposed control is verified by simulating a microgrid test system....
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....
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Institute of Scientific and Technical Information of China (English)
吴雨珊; 江驹; 甄子洋; 顾臣风
2016-01-01
In this paper, an intelligence nonlinear control scheme is proposed based on the backstepping method to solve the difficulty of the stable tracking control of the hypersonic morphing vehicle, considering compound disturb⁃ances as well as the influence of model uncertainties and unknown outside disturbances. First, the aerodynamic pa⁃rameters of the morphing vehicle are replaced with a curve⁃fitted approximation in order to build an accurate hyper⁃sonic model. Then, the feedback linearization approach is used to transform the nonlinear vehicle model into a strict feedback multi⁃input/multi⁃output nonlinear system. The nonlinear system is divided into three subsystems accord⁃ing to the features of the state variables and the virtual control signals are calculated for every subsystem. Next, the radial basis function ( RBF) is proved to have excellent capability in restraining unknown disturbances, and a dy⁃namic surface control strategy is employed to eliminate the explosion terms. The simulation results show that the pro⁃posed method can ensure the integral stability of the closed⁃loop system, as well as can have excellent tracing per⁃formance and robustness.%针对可变翼高超声速飞行器的外环稳定跟踪控制问题，考虑可变翼对建模的影响、模型参数不确定和外界未知干扰对跟踪控制性能的影响，提出基于回馈递推的智能非线性控制策略。本文首先利用巡航段气动参数的插值数据建立精确的纵向模型；然后采用输入－输出反馈线性化方法对飞行器纵向模型进行非线性映射，并根据状态变量特性将飞行器划分为三个子系统，利用回馈递推依次求取控制信号，采用RBF神经网络对未知干扰进行逼近，保证鲁棒性能。针对回馈递推设计过程中微分膨胀的问题，加入动态面控制思想进行改进。通过仿真表明，该方法可以保证闭环系统的全局稳定，并且拥有良好的跟踪性能和鲁棒性能。
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 ,
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
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.
Nonlinear Control of Electrodynamic Tether in Equatorial or Somewhat Inclined Orbits
DEFF Research Database (Denmark)
Larsen, Martin Birkelund; Blanke, Mogens
2007-01-01
feedback designed for the controllable subspace of the system, a feedback linearization design and a sliding mode control. The controllers are evaluated by their ability to suppress variations in the B-field and their robustness with respect to the internal dynamics.......This paper applies different control design methods to a tethered satellite system (TSS) to investigate essential control properties of this under-actuated and nonlinear system. When the tether position in the orbit plane is controlled by the tether current, out of orbit plane motions occur...... as an unwanted side effect, due to nonlinear interaction with the Earth’s magnetic field. This paper focus on the uncontrollable out-of-plane motions and the robustness against B-field uncertainty associated with each of three popular controller design methodologies for nonlinear systems: linear quadratic...
Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum
Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton
2017-01-01
The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.
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.
A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes.
Savran, Aydogan; Kahraman, Gokalp
2014-03-01
We develop a novel adaptive tuning method for classical proportional-integral-derivative (PID) controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in industry, to the control of nonlinear processes, we introduce a method which can readily be used by the industry. In this method, controller design does not require a first principal model of the process which is usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from the measured input-output data of the process. A soft limiter is used to impose industrial limits on the control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear process involving instabilities. Several tests showed the method's success in tracking, robustness to noise, and adaptation properties. We as well compared our system's performance to those of a plant with altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude, we present a novel adaptive control method that is built upon the well-known PID architecture that successfully controls highly nonlinear industrial processes, even under conditions such as strong parameter variations, noise, and instabilities.
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.
Institute of Scientific and Technical Information of China (English)
Yun Li; Hiroshi Kashiwagi
2005-01-01
Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
Lakshmanan, M
1997-01-01
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.
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.
Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.
Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping
2017-01-31
In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.
Chattering-Free Sliding-Mode Control for Electromechanical Actuator with Backlash Nonlinearity
Directory of Open Access Journals (Sweden)
Dongqi Ma
2017-01-01
Full Text Available Considering the backlash nonlinearity and parameter time-varying characteristics in electromechanical actuators, a chattering-free sliding-mode control strategy is proposed in this paper to regulate the rudder angle and suppress unknown external disturbances. Different from most existing backlash compensation methods, a special continuous function is addressed to approximate the backlash nonlinear dead-zone model. Regarding the approximation error, unmodeled dynamics, and unknown external disturbances as a disturbance-like term, a strict feedback nonlinear model is established. Based on this nonlinear model, a chattering-free nonsingular terminal sliding-mode controller is proposed to achieve the rudder angle tracking with a chattering elimination and tracking dynamic performance improvement. A Lyapunov-based proof ensures the asymptotic stability and finite-time convergence of the closed-loop system. Experimental results have verified the effectiveness of the proposed method.
Nonlinear Multiscale Transformations: From Synchronization to Error Control
2001-07-01
Donat Dept. Matematica Aplicada, University of Valencia, Spain. arandiga@uv. es donat uv. es Abstract Data-dependent interpolatory techniques can be used...Numer. Algorith. 23, 175-216, 2000. 5. F. Arhndiga, R. Donat, and A. Harten. Multiresolution based on weighted averages of the hat function II : Nonlinear...transforms for image coding via lifting scheme. submitted to IEEE Trans. on Image Nonlinear multiscale transformations 313 Method II ’ 1 I ŕ, 11蕀 r
A practical nonlinear robust control approach of electro-hydraulic load simulator
Institute of Scientific and Technical Information of China (English)
Wang Chengwen; Jiao Zongxia; Wu Shuai; Shang Yaoxing
2014-01-01
This paper studies a nonlinear robust control algorithm of the electro-hydraulic load simulator (EHLS). The tracking performance of the EHLS is mainly limited by the actuator’s motion disturbance, flow nonlinearity, and friction, etc. The developed controller is developed based on the nonlinear motion loading model. The problems of the actuator’s disturbance and flow nonlinearity are considered. To address the friction problem, the friction model of the loading motor is identified experimentally. The friction disturbance is compensated using the obtained friction model. Therefore, this paper considers the main three factors comprehensively. The devel-oped algorithm is easy to apply since the controller can be obtained just with one step back-stepping design. The stability of the developed algorithm is proven via Lyapunov analysis. Both co-simula-tion and experiments are performed to verify the effectiveness of this method.
Observer-based robust control of one-sided Lipschitz nonlinear systems.
Ahmad, Sohaira; Rehan, Muhammad; Hong, Keum-Shik
2016-11-01
This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young's inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.
Data-based identification and control of nonlinear systems via piecewise affine approximation.
Lai, Chow Yin; Xiang, Cheng; Lee, Tong Heng
2011-12-01
The piecewise affine (PWA) model represents an attractive model structure for approximating nonlinear systems. In this paper, a procedure for obtaining the PWA autoregressive exogenous (ARX) (autoregressive systems with exogenous inputs) models of nonlinear systems is proposed. Two key parameters defining a PWARX model, namely, the parameters of locally affine subsystems and the partition of the regressor space, are estimated, the former through a least-squares-based identification method using multiple models, and the latter using standard procedures such as neural network classifier or support vector machine classifier. Having obtained the PWARX model of the nonlinear system, a controller is then derived to control the system for reference tracking. Both simulation and experimental studies show that the proposed algorithm can indeed provide accurate PWA approximation of nonlinear systems, and the designed controller provides good tracking performance.
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.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
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.
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.
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.
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
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
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...
Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying
Directory of Open Access Journals (Sweden)
Inseok Yang
2014-01-01
Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.
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.
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 model predictive control with guaraneed stability based on pesudolinear neural networks
Institute of Scientific and Technical Information of China (English)
WANG Yongji; WANG Hong
2004-01-01
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor. It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems.
Li, Zhaoying; Zhou, Wenjie; Liu, Hao
2016-09-01
This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach.
Lai, Guanyu; Liu, Zhi; Zhang, Yun; Chen, Chun Lung Philip; Xie, Shengli
2015-12-24
This paper mainly aims at the problem of adaptive quantized control for a class of uncertain nonlinear systems preceded by asymmetric actuator backlash. One challenging problem that blocks the construction of our control scheme is that the real control signal is wrapped in the coupling of quantization effect and nonsmooth backlash nonlinearity. To resolve this challenge, this paper presents a two-stage separation approach established on two new technical components, which are the approximate asymmetric backlash model and the nonlinear decomposition of quantizer, respectively. Then the real control is successfully separated from the coupling dynamics. Furthermore, by employing the neural networks and adaptation method in control design, a quantized controller is developed to guarantee the asymptotic convergence of tracking error to an adjustable region of zero and uniform ultimate boundedness of all closed-loop signals. Eventually, simulations are conducted to support our theoretical results.
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.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
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 ...
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.
Nonlinear Burn Control and Operating Point Optimization in ITER
Boyer, Mark; Schuster, Eugenio
2013-10-01
Control of the fusion power through regulation of the plasma density and temperature will be essential for achieving and maintaining desired operating points in fusion reactors and burning plasma experiments like ITER. In this work, a volume averaged model for the evolution of the density of energy, deuterium and tritium fuel ions, alpha-particles, and impurity ions is used to synthesize a multi-input multi-output nonlinear feedback controller for stabilizing and modulating the burn condition. Adaptive control techniques are used to account for uncertainty in model parameters, including particle confinement times and recycling rates. The control approach makes use of the different possible methods for altering the fusion power, including adjusting the temperature through auxiliary heating, modulating the density and isotopic mix through fueling, and altering the impurity density through impurity injection. Furthermore, a model-based optimization scheme is proposed to drive the system as close as possible to desired fusion power and temperature references. Constraints are considered in the optimization scheme to ensure that, for example, density and beta limits are avoided, and that optimal operation is achieved even when actuators reach saturation. Supported by the NSF CAREER award program (ECCS-0645086).
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.
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.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
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)
Institute of Scientific and Technical Information of China (English)
尹新权; 李新勇; 王珺
2013-01-01
T-S fuzzy model of four Degree-of-freedom semi-active suspension frame of half-vehicle was established and described as a combination of several local linear systems.The state feedback controller was designed for each local linear subsystem with parallel-distributed compensation(PDC),the parameters of controller was obtained by means of solving linear matrix inequalities(LMIs),and the validity of T-S fuzzy model and the stability of dosed-loop system were verified.The simulation result showed that,comparing the semi-active suspension frame designed with the control method presented in this paper to passive suspension frames,the attenuation of system vibration became faster in the former and the stability could be quickly realized.The proposed control method was effective for deal with complicated nonlinear system.%建立1/2车四自由度半主动悬架的T-S模糊模型,将其描述成多个局部线性系统的组合.运用并行分布补偿方法设计各个子系统的状态反馈控制器,通过求解线性矩阵不等式族等方法获得控制器参数,验证T-S模糊模型的有效性和闭环系统的稳定性.仿真结果表明,采用本文控制方法设计的半主动悬架与被动悬架相比,系统振动能快速衰减,趋于稳定速度更快.
An Agent Interaction Based Method for Nonlinear Process Plan Scheduling
Institute of Scientific and Technical Information of China (English)
GAO Qinglu; WU Bo; GUO Guang
2006-01-01
This article puts forward a scheduling method for nonlinear process plan shop floor. Task allocation and load balance are realized by bidding mechanism. Though the agent interaction process, the execution of tasks is determined and the coherence of manufacturing decision is verified. The employment of heuristic index can help to optimize the system performance.
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
An iterative regularization method for nonlinear problems based on Bregman projections
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237-62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
Method for Measuring Small Nonlinearities of Electric Characteristics
DEFF Research Database (Denmark)
Guldbrandsen, Tom; Meyer, Niels I; Schjær-Jacobsen, Jørgen
1965-01-01
A method is described for measuring very small deviations from linearity in electric characteristics. The measurement is based on the harmonics generated by the nonlinear element when subjected to a sine wave signal. A special bridge circuit is used to balance out the undesired harmonics...... of the signal generator together with the first harmonic frequency. The set-up measures the small-signal value and the first and second derivative with respect to voltage. The detailed circuits are given for measuring nonlinearities in Ohmic and capacitive components. In the Ohmic case, a sensitivity...
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…
Rodríguez, Hugo; Schaft, Arjan J. van der; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the “control by interconnection” method provides a simple and elegant procedure for stab
Rodríguez, Hugo; Schaft, van der Arjan J.; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the "control by interconnection" method provides a simple and elegant procedure for stab
Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.
2002-01-01
The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the nonl
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.
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.
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 ...
Institute of Scientific and Technical Information of China (English)
Changshui Feng; Weiqiu Zhu
2008-01-01
A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Ito equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged Ito equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.
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.
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....
Design New Intelligent-Base Chattering Free Nonlinear Control of Spherical Motor
Directory of Open Access Journals (Sweden)
Mohammad Ali Tayebi
2014-09-01
Full Text Available The main four objectives to design controllers are: stability, robust, minimum error and reliability. Linear PID controller is model-free controller and this controller is not reliable. One of the robust nonlinear controller to control of nonlinear systems is sliding mode controller (SMC. Sliding mode controller (SMC is robust conventional nonlinear controller in a partly uncertain dynamic system’s parameters. Sliding mode controller is divided into two main sub parts: discontinues controller〖(τ〗_dis and equivalent controller〖(τ〗_eq. Discontinues controller is used to design suitable tracking performance based on very fast switching. Fast switching or discontinuous part have essential role to achieve to good trajectory following, but it is caused system instability and chattering phenomenon. Chattering phenomenon is one of the main challenges in conventional sliding mode controller and it can causes some important mechanical problems such as saturation and heats the mechanical parts of robot manipulators or drivers. To reduce or eliminate the chattering two methods are used in many researches which these methods are: boundary layer saturation method and artificial intelligence based method. In this research fuzzy switching methodology is used to eliminate the chattering in presence of uncertainty to increase the robust of this controller with application to three dimensions of spherical motor.