Nonlinear resonances in a class of multi-degree-of-freedom systems
Sridhar, S.; Nayfeh, A. H.; Mook, D. T.
1975-01-01
An analysis is presented of the superharmonic, subharmonic, and combination resonances in a multi-degree-of-freedom system which has cubic nonlinearity and modal viscous damping and is subject to harmonic excitation. It is shown that, in the absence of internal resonances, the steady-state response contains only the modes which are directly excited. It is shown that, in the presence of internal resonances, modes other than those that are directly excited can appear in the response. The strong influence of internal resonances is exhibited in numerical examples involving hinged-clamped beams. It is shown that when a multimode solution exists the lowest mode can dominate the response, even when it is not directly excited.
Institute of Scientific and Technical Information of China (English)
ZHANG; Yimin; (张义民); WANG; Shun; (王; 顺); LIU; Qiaoling; (刘巧伶); WEN; Bangchun; (闻邦椿)
2003-01-01
Based on the generalized probabilistic finite element method, this paper presents an approximate solution technique for general multi-degree-of-freedom nonlinear random vibration systems with random parameters. The fourth-moment technique, maximum entropy theory and incomplete probability information theory are employed to systematically develop a reliability analysis method for dynamic random structural systems with correlation failure modes under unavailable joint probability density functions of basic random variables. The first passage problem of multi-degree-of-freedom nonlinear random vibration systems is solved.
Institute of Scientific and Technical Information of China (English)
姜剑; 王兆清; 庄美玲
2015-01-01
The nonlinear vibration of multi-degree-of-freedom systems can be modeled by initial value problem of nonlinear differential equation,this paper mainly studied the application of barycentric rational interpolation iterative collocation method to solve nonlinear vibration of multi-degree-of-freedom systems. A linear iterative scheme is constructed for approximating nonlinear differential equations. The linear differential equations are discretized into algebraic equations by applying Barycentric rational interpolation differential matrixes. Then, the numerical results of nonlinear vibration problem can be obtained by solving the algebraic equations with iteration method. The examples of nonlinear vibration of coupled systems demonstrated the proposed method is simple, effective and excellent stability and can accurately simulate various physical quantities of the nonlinear vibration.%多自由度非线性振动的数学模型为非线性微分方程组的初值问题。文章运用重心有理插值迭代配点法研究了求解多自由度非线性振动的问题；通过构造一个逼近非线性微分方程组的线性化迭代格式，采用重心有理插值微分矩阵离散线性化微分方程组，由线性化迭代计算最终得到非线性方程组的数值解。结果表明：依据算例的解析解和数值解比较，重心有理插值迭代配点法能够高精度计算模拟多自由度非线性振动的各项物理量，并且简单有效，具有优异的计算稳定性。
Semi-active optimal control of linearized systems with multi-degree of freedom and application
Ying, Z. G.; Ni, Y. Q.; Ko, J. M.
2005-01-01
A semi-active optimal control method for non-linear multi-degree-of-freedom systems and its application to a building structure for random response reduction are presented in this paper. A structural system with semi-active control devices under random loading is modelled as a controlled, randomly excited and dissipated Hamiltonian system of multi-degree of freedom. The control force produced by a semi-active control device is split into semi-active part and passive part incorporated in the uncontrolled system. Applying the statistical linearization method to the non-linear multi-degree-of-freedom system with passive control force components yields quasi-linear equations of motion, which can tend to corresponding linear ones with system response reduction. By applying the dynamical programming principle to the controlled linearized system, a dynamical programming equation is established and in particular, for a non-filtering white noise excitation, is solved as an optimal regulation problem to determine the quasi-linear quadratic optimal control law and furthermore semi-active optimal control law according to the variational principle. Then the semi-active optimal control of a tall building structure with magnetorheological-tuned liquid column damper (MR-TLCD) under random wind excitation is performed by using the proposed method. The non-linear model of the structural system with semi-active MR-TLCD is formulated in structural mode space and uncoupled between structural and MR fluid accelerations. The quasi-linear equations for system states are derived from the model and the dynamical programming equation for the system is obtained. In the case that the random wind excitation with the Davenport power spectrum cannot be modelled as a linear filtering white noise, the dynamical programming equation is solved as an optimal regulation problem to obtain the semi-active optimal control force, on which the clipping treatment may be performed to ensure the control force
A New Method of Shock Dynamic Analysis of Multi-degree-of-freedom Systems
Institute of Scientific and Technical Information of China (English)
ZOU Guang-rong; WU Hui
2008-01-01
A new method is presented to analyze multi-degree-of-freedom (MDOF) dynamic systems subjected to an external shock excitation. A two-degree-of-freedom theoretical system with linear characteristics is exemplified to illustrate the procedure of this method. The equations of motion of the dynamic system are established via matrix method. The dynamic responses of the dynamic system under an external shock excitation of a half-sine type are obtained by MATLAB and ANSYS. It is proved that the new method is helpful to analyze MDOF dynamic systems.
Vibration control of multi-degrees-of-freedom system with dynamic absorbers based on power flow
Institute of Scientific and Technical Information of China (English)
WANG Quanjuan; HUANG Wenhua; XIA Songbo; LI Jimin; SUN Zhizhuo
2003-01-01
In accordance with a multiple degrees of freedom vibration system with dynamicvibration absorbers (DVAs), an equivalent admittance matrix and the power flows input majorstructure and minor structure are deduced on the basis of the theories of structure mobility.Furthermore, regarding the net power flow of main vibration system as the controlled object,probed into are the single and multiple model controls of multi-degrees-of-freedom system withone or several absorbers attached. And the control mechanism and effect of dynamic vibrationabsorbers are revealed.
Particle Damping with Granular Materials for Multi Degree of Freedom System
Directory of Open Access Journals (Sweden)
Masanobu Inoue
2011-01-01
Full Text Available A particle damper consists of a bed of granular materials moving in cavities within a multi degree-of-freedom (MDOF structure. This paper deals with the damping effects on forced vibrations of a MDOF structure provided with the vertical particle dampers. In the analysis, the particle bed is assumed to be a single mass, and the collisions between the granules and the cavities are completely inelastic, i.e., all energy dissipation mechanisms are wrapped into zero coefficient of restitution. To predict the particle damping effect, equations of motion are developed in terms of equivalent single degree-of-freedom (SDOF system and damper mass with use made of modal approach. In this report, the periodic vibration model comprising sustained contact on or separation of the damper mass from vibrating structure is developed. A digital model is also formulated to simulate the damped motion of the physical system, taking account of all vibration modes. Numerical and experimental studies are made of the damping performance of plural dampers located at selected positions throughout a 3MDOF system. The experimental results confirm numerical prediction that collision between granules and structures is completely inelastic as the contributing mechanism of damping in the vertical vibration. It is found that particle dampers with properly selected mass ratios and clearances effectively suppress the resonance peaks over a wide frequency range.
A VHDL application for kinematic equation solutions of multi-degree-of-freedom systems
Institute of Scientific and Technical Information of China (English)
Hseyin Oktay ERKOL; Hseyin DEMREL
2014-01-01
As kinematic calculations are complicated, it takes a long time and is difficult to get the desired accurate result with a single processor in real-time motion control of multi-degree-of-freedom (MDOF) systems. Another calculation unit is needed, especially with the increase in the degree of freedom. The main central processing unit (CPU) has additional loads because of numerous motion elements which move independently from each other and their closed-loop controls. The system designed is also complicated because there are many parts and cabling. This paper presents the design and implementation of a hardware that will provide solutions to these problems. It is realized using the Very High Speed Integrated Circuit Hardware Description Language (VHDL) and field-programmable gate array (FPGA). This hardware is designed for a six-legged robot and has been working with servo motors controlled via the serial port. The hardware on FPGA calculates the required joint angles for the feet positions received from the serial port and sends the calculated angels to the servo motors via the serial port. This hardware has a co-processor for the calculation of kinematic equations and can be used together with the equipment that would reduce the elec-tromechanical mess. It is intended to be used as a tool which will accelerate the transition from design to application for robots.
Ferri, A. A.; Dowell, E. H.
1985-01-01
The anticipated low damping level in large space structures (LSS) has been a major concern for the designers of these structures. Low damping degrades the free response and complicates the design of shape and attitude controllers for flexible spacecraft. Dry friction damping has been considered as a means of increasing the passive damping of LSS, by placing it in the joints and connecting junctures of structures. However, dry friction is highly nonlinear and, hence, analytical investigations are difficult to perform. Here, a multi-harmonic, frequency domain solution technique is developed and applied to a multi-DOF, dry friction damped system. It is seen that the multi-harmonic method is much more accurate than traditional, one harmonic solution methods. The method also compares well with time integration. Finally, comparisons are made with experimental results.
Jaensch, M.; Lampérth, M. U.
2007-04-01
This paper describes the design and performance testing of a micropositioning, vibration isolation and suppression system, which can be used to position a piece of equipment with sub-micrometre accuracy and stabilize it against various types of external disturbance. The presented demonstrator was designed as part of a novel extremely open pre-polarization magnetic resonance imaging (MRI) scanner. The active control system utilizes six piezoelectric actuators, wide-bandwidth optical fibre displacement sensors and a very fast digital field programmable gate array (FPGA) controller. A PID feedback control algorithm with emphasis on a very high level of integral gain is employed. Due to the high external forces expected, the whole structure is designed to be as stiff as possible, including a novel hard mount approach with parallel passive damping for the suspension of the payload. The performance of the system is studied theoretically and experimentally. The sensitive equipment can be positioned in six degrees of freedom with an accuracy of ± 0.2 µm. External disturbances acting on the support structure or the equipment itself are attenuated in three degrees of freedom by more than -20 dB within a bandwidth of 0-200 Hz. Excellent impulse rejection and input tracking are demonstrated as well.
2011-07-21
cowork- ers in the Mechanical Systems Lab. Thanks to Mauro, Dino, Clay, Eric, Debbie, Jens, and Marca for their discussions and assistance with...through static equilibrium simultaneously. iii. Displacement of one mass uniquely defines the displacements of all masses. These criteria are analogous to...be greater. Shaw and Pierre [10, 11] present an alternative definition of nonlinear normal modes, defined for both conservative and dissipative systems
Multi-degree-of-freedom coupling dynamic characteristic of TBM disc cutter under shock excitation
Institute of Scientific and Technical Information of China (English)
霍军周; 孙晓龙; 李广庆; 李涛; 孙伟
2015-01-01
When the tunneling boring machine (TBM) cutterhead tunnels, the excessive vibration and damage are a severe engineering problem, thereby the anti-vibration design is a key technology in the disc cutter system. The structure of disc cutter contains many joint interfaces among cutter ring, cutter body, bearings and cutter shaft. On account of the coupling for dynamic contact and the transfer path among joint interface, mechanical behavior of disc cutter becomes extremely complex under the impact of heavy-duty, which puts forward higher requirements for disc cutter design. A multi-degree-of-freedom coupling dynamic model, which contains a cutter ring, a cutter body, two bearings and cutter shaft, is established, considering the external stochastic excitations, bearing nonlinear contact force, multidirectional mutual coupling vibration, etc. Based on the parameters of an actual project and the strong impact external excitations, the modal properties and dynamic responses are analyzed, as well as the cutter shaft and bearings’ loads and load transmission law are obtained. Numerical results indicate the maximum radial and axial cutter ring amplitudes of dynamic responses are 0.568 mm and 0.112 mm;the maximum radial and axial vibration velocities are 41.1 mm/s and 38.9 mm/s;the maximum radial and axial vibration accelerations are 94.7 m/s2 and 58.6 m/s2;the maximum swing angle and angular velocity of cutter ring are 0.007° and 0.0074 rad/s, respectively. Finally, the maximum load of bearing roller is 40.3 kN. The proposed research lays a foundation for structure optimization design of disc cutter and cutter base, as well as model selection, modification and fatigue life of the cutter bearing.
Critical earthquake load inputs for multi-degree-of-freedom inelastic structures
Moustafa, Abbas
2009-08-01
The problem of modeling earthquake ground motions as design inputs for multi-degree-of-freedom inelastic structures is studied. The earthquake acceleration is expressed as a Fourier series modulated by an envelope function. The coefficients of the series representation are calculated such that the structure inelastic deformation is maximized subjected to predefined constraints. These constraints are taken to reflect known characteristics of recorded earthquakes such as upper bounds on the energy and peak values of the ground acceleration, velocity and displacement and upper and lower limits on the Fourier spectra of the ground acceleration. The material stress-strain behavior is modeled using bilinear and elastic-plastic relations. The resulting nonlinear optimization problem is solved by using the sequential quadratic optimization method. Issues related to various forms of energy dissipated by the inelastic structure are explored. The study also examines the effect of nonlinear damping models and the influence of the strain hardening ratio (ratio of the post-yield stiffness to the pre-yield stiffness) on the derived optimal earthquake and associated inelastic deformation. The formulation is demonstrated for a two-storey inelastic building frame with nonlinear damping.
Bandwidth optimization design of a multi degree of freedom MEMS gyroscope.
Si, Chaowei; Han, Guowei; Ning, Jin; Yang, Fuhua
2013-08-14
A new robust multi-degree of freedom (multi-DOF) MEMS gyroscope is presented in this paper. The designed gyroscope has its bandwidth and amplification factor of the sense mode adjusted more easily than the previous reported multi-DOF MEMS gyroscopes. Besides, a novel spring system with very small coupling stiffness is proposed, which helps achieve a narrow bandwidth and a high amplification factor for a 2-DOF vibration system. A multi-DOF gyroscope with the proposed weak spring system is designed, and simulations indicate that when the operating frequency is set at 12.59 kHz, the flat frequency response region of the sense mode can be designed as narrow as 80 Hz, and the amplification factor of the sense mode at the operating frequency is up to 91, which not only protects the amplification factor from instability against process and temperature variations, but also sacrifices less performance. An experiment is also carried out to demonstrate the validity of the design. The multi-DOF gyroscope with the proposed weak coupling spring system is capable of achieving a good tradeoff between robustness and the performance.
Bandwidth Optimization Design of a Multi Degree of Freedom MEMS Gyroscope
Directory of Open Access Journals (Sweden)
Fuhua Yang
2013-08-01
Full Text Available A new robust multi-degree of freedom (multi-DOF MEMS gyroscope is presented in this paper. The designed gyroscope has its bandwidth and amplification factor of the sense mode adjusted more easily than the previous reported multi-DOF MEMS gyroscopes. Besides, a novel spring system with very small coupling stiffness is proposed, which helps achieve a narrow bandwidth and a high amplification factor for a 2-DOF vibration system. A multi-DOF gyroscope with the proposed weak spring system is designed, and simulations indicate that when the operating frequency is set at 12.59 kHz, the flat frequency response region of the sense mode can be designed as narrow as 80 Hz, and the amplification factor of the sense mode at the operating frequency is up to 91, which not only protects the amplification factor from instability against process and temperature variations, but also sacrifices less performance. An experiment is also carried out to demonstrate the validity of the design. The multi-DOF gyroscope with the proposed weak coupling spring system is capable of achieving a good tradeoff between robustness and the performance.
Virtual laparoscopic surgical skills practice using a multi-degree of freedom joystick.
Huang, Chun-Kai; Head, Michael J; Nelson, Carl A; Oleynikov, Dmitry; Siu, Ka-Chun
2014-01-01
The objective of this study was to compare three different surgical skills practice environments while performing a virtual laparoscopic surgical training task using a multi-degree of freedom joystick, a commercial manipulator or a training box. Nine subjects performed a virtual peg transfer task and their upper extremity muscle effort and fatigue were measured. The results demonstrated a similar muscle effort and fatigue of the upper extremity among the three training environments. Subjects with medical backgrounds used significantly higher muscle effort when they performed the training task using the joystick than the manipulator, but used similar muscle effort between the joystick and the training box. This study suggests that the multi-degree of freedom joystick could provide more options to practice virtual laparoscopic surgical training tasks with muscle effort and fatigue similar to other traditional training boxes.
Analytic Solution to Nonlinear Dynamical System of Dragon Washbasin
Institute of Scientific and Technical Information of China (English)
贾启芬; 李芳; 于雯; 刘习军; 王大钧
2004-01-01
Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region.
Institute of Scientific and Technical Information of China (English)
宋宝成; 刘初升; 彭利平; 李珺
2015-01-01
A feasible method was proposed to improve the vibration intensity of screen surface via application of a new type elastic screen surface with multi degree of freedom (NTESSMDF). In the NTESSMDF, the primary robs were coupled to the main screen structure with ends embedded into the elastomers, and the secondary robs were attached to adjacent two primary robs with elastic bands. The dynamic model of vibrating screen with NTESSMDF was established based on Lagrange’s equation and the equivalent stiffnesses of the elastomer and elastic band were calculated. According to numerical simulation using the 4th order Runge-Kutta method, the vibration intensity of screen surface can be enhanced substantially with an averaged acceleration amplitude increasing ratio of 72.36%. The primary robs and secondary robs vibrate inversely in steady state, which would result in the friability of materials and avoid stoppage. The experimental results validate the dynamic characteristics with acceleration amplitude rising by 62.93%on average, which demonstrates the feasibility of NTESSMDF.
A novel multi-degree-of-freedom thick-film ultrasonic motor.
Aoyagi, Manaba; Beeby, Steve P; White, Neil M
2002-02-01
This paper describes a new multi-degree-of-freedom (MDOF) ultrasonic motor that comprises few parts and is based on low-cost thick-film technology. Conventional ultrasonic motors using bulk lead zirconate titanate (PZT) or thin-film PZT layers are relatively expensive at the present time. Thick-film printed PZT technology provides the opportunity to reduce the costs of ultrasonic motors. To demonstrate the feasibility of this approach, an ultrasonic motor was fabricated from alumina using thick-film printed PZT actuators. The thick-film PZT and electrode layers were printed on a thin alumina plate, and a tiny cylinder was mounted at its center. This cylinder magnifies the lateral displacement of the stator, holds the spherical rotor, and transmits the driving force to the sphere. Three bending vibrations, B22, B30, B03, of the plate were applied to rotate the sphere. Sufficient displacements for rotating the sphere were obtained near the resonance of B22 by applying an excitation voltage of 200 V peak-to-peak via a three-phase drive circuit. Rotations in three orthogonal directions have been observed by controlling the phase of the driving signal to the PZT electrodes, and a MDOF ultrasonic motor was successfully realized.
Cho, Hyunok; Park, Jongcheol; Park, Jae Yeong
2016-05-01
A piezoelectric vibration energy harvester with interdigital shaped cantilever was developed by using silicon bulk micromachining technology. The proposed energy harvester was designed to obtain multi degree-of-freedom (m-DOF). Most of the piezoelectric vibration energy harvesters are comprised of mass-loaded cantilever beams having several resonant frequencies. The second resonant frequency of such a device has lower amplitude compared to its first resonant frequency (fundamental frequency). Therefore, the interdigital shaped cantilever has been proposed for multiple fundamental resonant frequencies. The fabricated piezoelectric vibration energy harvester is composed of main cantilever (MC), sub-main cantilever (SMC), and secondary cantilevers (SC). MC surrounds SMC and SC which have same dimension of 5600 x 800 x 10 μm3. The fabricated piezoelectric energy harvester can generate 51.4 mV(p-p) and 11 mV(p-p) of output voltages at 24.2 Hz and 33 Hz of its resonant frequencies by MC. Moreover, it can generate 8 mV(p-p) and 6.6 mV(p-p) of output voltages at 24.2 Hz and 33.2 Hz of its resonant frequencies by SMC; and 364 mV(p-p) of output voltage at 33.6 Hz of its resonant frequency by SC.
Nonlinear identification of MDOF systems using Volterra series approximation
Prawin, J.; Rao, A. Rama Mohan
2017-02-01
Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Meanwhile, the presence of non-linearity in the system can lead to a wide range of structural behavior, for example, jumps, limit cycles, internal resonances, modal coupling, super and sub-harmonic resonances, etc. In this paper, we present a Volterra series approximation approach based on the adaptive filter concept for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach. The effectiveness of the proposed approach is demonstrated using two classical single degrees of freedom systems (breathing crack problem and Duffing Holmes oscillator) and later we extend to multi-degree of freedom systems.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises
Deng, Mao-Lin; Zhu, Wei-Qiu
2016-08-01
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises
Energy Technology Data Exchange (ETDEWEB)
Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)
2016-08-15
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises.
Deng, Mao-Lin; Zhu, Wei-Qiu
2016-08-01
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
Institute of Scientific and Technical Information of China (English)
卢煜海; 曾昭文; 马俊生; 马桂香
2016-01-01
Due to the lack of research and development for large banana planting base of banana harvesting equipment, a multi degree of freedom and self-locking banana harvester was designed.The machine is mainly composed of a power system, a feeding system and a harvesting system.Manual and electric mixed mode of operation.It not only can be used as a harvester, also can be used as a small transport or traction machine.Using three-dimensional modeling software SolidWorks to establish model and simulate the motion of key structure, the results show that the design meets the re-quirements.Design of banana harvester with multi degree of freedom and self locking can be provided as a reference to other similar crop harvesting machinery.%针对大规模香蕉种植基地香蕉收割机具的研发比较缺乏的现状，设计了一种多自由度自锁式香蕉收割机。该机主要由动力系统、进给系统及收割系统等组成，手动与电动混合操作方式，既可作为收割机，同时又可作为小型运输机及牵引机使用。采用三维造型软件 SolidWorks 对其建立模型，并对关键结构进行相应的运动仿真。结果表明：该机设计满足工作要求，可为其他类似农作物收割机具的设计提供参考。
Waalkens, H.; Wiggins, S.
2004-01-01
The fundamental assumption of transition state theory is the existence of a dividing surface having the property that trajectories originating in reactants (resp. products) must cross the surface only once and then proceed to products (resp. reactants). Recently it has been shown how to construct a
Sensor fusion and computer vision for context-aware control of a multi degree-of-freedom prosthesis
Markovic, Marko; Dosen, Strahinja; Popovic, Dejan; Graimann, Bernhard; Farina, Dario
2015-12-01
Objective. Myoelectric activity volitionally generated by the user is often used for controlling hand prostheses in order to replicate the synergistic actions of muscles in healthy humans during grasping. Muscle synergies in healthy humans are based on the integration of visual perception, heuristics and proprioception. Here, we demonstrate how sensor fusion that combines artificial vision and proprioceptive information with the high-level processing characteristics of biological systems can be effectively used in transradial prosthesis control. Approach. We developed a novel context- and user-aware prosthesis (CASP) controller integrating computer vision and inertial sensing with myoelectric activity in order to achieve semi-autonomous and reactive control of a prosthetic hand. The presented method semi-automatically provides simultaneous and proportional control of multiple degrees-of-freedom (DOFs), thus decreasing overall physical effort while retaining full user control. The system was compared against the major commercial state-of-the art myoelectric control system in ten able-bodied and one amputee subject. All subjects used transradial prosthesis with an active wrist to grasp objects typically associated with activities of daily living. Main results. The CASP significantly outperformed the myoelectric interface when controlling all of the prosthesis DOF. However, when tested with less complex prosthetic system (smaller number of DOF), the CASP was slower but resulted with reaching motions that contained less compensatory movements. Another important finding is that the CASP system required minimal user adaptation and training. Significance. The CASP constitutes a substantial improvement for the control of multi-DOF prostheses. The application of the CASP will have a significant impact when translated to real-life scenarious, particularly with respect to improving the usability and acceptance of highly complex systems (e.g., full prosthetic arms) by amputees.
Faster Simulation Methods for the Non-Stationary Random Vibrations of Non-Linear MDOF Systems
DEFF Research Database (Denmark)
Askar, A.; Köylüoglu, H. U.; Nielsen, Søren R. K.;
In this paper semi-analytical forward-difference Monte Carlo simulation procedures are proposed for the determination of the lower order statistics and the Joint Probability Density Function (JPDF) of the stochastic response of geometrically nonlinear multi-degree-of-freedom structural systems....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.
there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte Carlo......A method for computing the lower-order moments of randomly-excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random...
Institute of Scientific and Technical Information of China (English)
卢煜海; 曾昭文; 马桂香; 马俊生
2016-01-01
Due to the lack of research and development for large banana planting base of banana harvesting equipment , a multi degree of freedom and self-locking banana harvester was designed .The machine can harvest the various types of bananas .It has the characteristics of self-locking , multi degree of freedom movement , small transport etc .Through the analysis of the working principle of the machine , the finite element model is established for the key parts , and finite ele-ment analysis based on ANSYS is done .The results show that: the stiffness and strength of the harvester key parts can meet the requirements of the job .Design of banana harvester with multi degree of freedom and self locking can be provid-ed as a reference to other similar crop harvesting machinery .%针对大规模香蕉种植基地香蕉收割机具的研发比较缺乏，研制了一种多自由度自锁式香蕉收割机。该机可收割各型株高的香蕉，具有自锁、多自由度动作及小型运输等特点。通过分析该机的工作原理，对其关键零部件建立有限元模型，进行基于ANSYS的有限元分析。结果表明：收割机关键零部件的刚度和强度满足工作要求。自锁式多自由度香蕉收割机的研制可为其他类似农作物收割机具的研制提供参考。
SEISMIC RANDOM RESPONSE ANALYSIS OF HYSTERETIC SYSTEMS WITH PSEUDO EXCITATION METHOD
Institute of Scientific and Technical Information of China (English)
Wang Jun; Lin Jiahao
2000-01-01
The stationary random responses of nonlinear shear-type Multi-Degrees-of-Freedom(MDOF) hysteretic system are analyzed by nsing the Pseudo Excitation Method (PEM) combined with the Equivalent Linearization Method (ELM). The solution of the equivalent linear system is obtained by iteratively solving complex algebraic equations instead of the Lyapunov equations. The efficiency of this method is much higher for practical engineering systems with many degrees-of-freedom.
QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu
2005-01-01
Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal beatings with nonlinear suspensionare are determined.
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.;
A method for computing the lower-order moments of randomly-excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random...... structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficient and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random...... initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases...
Institute of Scientific and Technical Information of China (English)
王化明; 吕俊; 陈林; 吴宝山; 赵春慧
2016-01-01
计及多自由度运动的船舶斜航水动力预报对船舶航行安全具有重要意义。文章通过耦合求解船舶运动方程和雷诺平均N-S方程，并采用VOF方法和高精度自由面捕捉技术对作多自由度斜航运动船舶的粘性绕流场进行数值模拟。船舶动态平衡位置根据计算出的力和力矩来决定，得到包括升沉、纵倾和横倾在内的船舶浮态。文中采用的算例与爱荷华大学进行的模型试验相同，通过比较数值计算结果和试验值验证了该方法的有效性。对船模在受约束和自由运动两种状态下的船舶运动和流场进行模拟，通过比较分析船舶升沉、纵倾和横倾的影响。文中计算获得的详细流场细节特征，包括前体和舭部的涡以及船体表面上的压力，有助于理解船舶斜航运动浮态变化的机理。%It is of significance for the safety of ship to predict the hydrodynamic forces on ship in oblique motion with multi-degree of freedom. In this work, the free-surface viscous flow around ship in oblique motion with multi-degree of freedom is simulated by coupling the equations of ship mo-tion with the Reynolds Averaged Navier-Stokes (RANS) equations. The free surface is modeled by using Volume-of-Fluid (VOF) approach and a high-resolution interface-capturing scheme. The cal-culated forces and moments are used to determine the dynamic equilibrium position of the ship at the specified speed. Hereby, the running attitudes including the sinkage, trim and heel are obtained. The computations presented here are an effort to numerically simulate the cases as the same as the experiments reported by IWOA (The University of Iowa), and validation of the present method is veri-fied by comparing the present numerical results and measurements. Two sets of simulations are per-formed, including the model-fixed condition and the model-free condition. Comparisons between the model-fixed condition and model-free condition
多自由度超声波电机的研究进展和展望%Recent development and prospect of multi-degree-of-freedom ultrasonic motors
Institute of Scientific and Technical Information of China (English)
郭吉丰; 白洋; 王剑
2013-01-01
Ultrasonic motors (USM) have the advantages of low speed,high torque,quick response,high resolution and anti-electromagnetic interference capability,which bring them broad application prospect in fields of robots,industrial instruments and security technologies.Multi-degree-of-freedom (MDOF) motor is one of the most cutting-edge aspects in the ultrasonic motor researches.Several typical MDOF ultrasonic motors of different types were introduced.The structure,working principle and characteristics were mainly discussed.Some typical examples were given and the key achievements were summarized,as well as their applications.The research and development trends were proposed.%超声波电机具有低速大力矩、响应快、分辨率高和抗电磁干扰等优点,能直接驱动,使其在机器人、工业仪器仪表、安防等领域有着广阔的应用前景.多自由度是超声波电机研究领域的前沿课题.分类探讨了近年来出现的几种多自由度超声电机的结构、机理、性能及其特点,给出一些具有代表性的实例,总结了多自由度超声波电机的主要研究成果和应用状况,对多自由度超声波电机的今后研究重点和发展方向提出了建议.
Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearities
Padmanabhan, C.; Singh, R.
1992-06-01
In an earlier study [14], the frequency response characteristics of a multi-degree-of-freedom system with clearance non-linearities were presented. The current study is an extension of this prior work and deals specifically with the issue of dynamic interactions between resonances. The harmonic balance method, digital solutions and analog computer simulation are used to investigate a two-degree-of-freedom system under a mean load, when subjected to sinusoidal excitations. The existence of harmonic, periodic and chaotic solutions is demonstrated using digital simulation. The method of harmonic balance is employed to construct approximate solutions at the excitation frequency which are then used to classify weak, moderate and strong non-linear spectral interactions. The effects of parameters such as damping ratio, mean load, alternating load and frequency spacing between the resonances have been quantified. The applicability of the methodology is demonstrated through the following practical examples: (i) neutral gear rattle in an automotive transmission system; and (ii) steady state characteristics of a spur gear pair with backlash. In the second case, measured dynamic transmission error data at the gear mesh frequency are used to investigate spectral interactions. Limitations associated with solution methods and interaction classification schemes are also discussed.
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
Kahraman, A.; Singh, R.
1991-02-01
Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.
Kougioumtzoglou, I. A.; Fragkoulis, V. C.; Pantelous, A. A.; Pirrotta, A.
2017-09-01
A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based frequency response function (FRF) is determined for a linear structural system with singular matrices. Next, relying on the M-P FRF a spectral input-output (excitation-response) relationship is derived in the frequency domain for determining the linear system response power spectrum. Further, the above methodology is extended via statistical linearization to account for nonlinear systems. This leads to an iterative determination of the system response mean vector and covariance matrix. Furthermore, to account for singular matrices, the generalization of a widely utilized formula that facilitates the application of statistical linearization is proved as well. The formula relates to the expectation of the derivatives of the system nonlinear function and is based on a Gaussian response assumption. Several linear and nonlinear MDOF structural systems with singular matrices are considered as numerical examples for demonstrating the validity and applicability of the developed frequency domain methodology.
Institute of Scientific and Technical Information of China (English)
李晓玮; 施卫星
2012-01-01
A developed method of optimal parameter select method of Multiple Tuned Mass Damper ( MTMD ) is presented in the article. This method can be used to choose the optimal parameter by comparing the transfer function as well as H2 norm. It is constructed on SDOF systems;and can be applied to MDOF systems by a little promotion. The analysis of vibration suppression of a pedestrian bridge shows that the bridge will drastically resonate under crowd walking load by setting MTMD system;whose parameters are definded upon the former method. The vibration of the bridge can be significantly improved to meet the demand of comfort.%介绍了一种MTMD系统最优参数的选取方法,即通过比较传递函数以及它的H2泛函来评价参数的优劣.这种方法建立于主体结构为单自由度的基础之上,但很容易推广到多自由度体系中.随后对某人行天桥进行了MTMD消能减振分析,人行荷载采用三阶简谐波分量进行模拟,用两种方法评价其舒适度.结果表明采用该方法选取的MTMD最优参数可以对天桥起到较好的减振效果.
Institute of Scientific and Technical Information of China (English)
王大鹏; 田石柱
2013-01-01
In order to set up pseudo-dynamic testing system suitable for any control system of testing equipment, the external command control method is put forward. The testing program is compiled using hybrid program control method with Visual C++ and MATLAB. Using MTS FlexTest GT controller as example, the acquisition boards are connected to FlexTest GT controller. Visual C + + is used to compile the acquisition board program to control the I/O channels of GT controller, which enables external command to control the actuator. MATLAB is used to compile the calculation program. By calling MATLAB engine in Visual C + + , the interface between control program and calculation program is implemented. Three degrees-of-freedom pseudo-dynamic testing about full-scale three-story masonry structure is carried out. The results indicate that testing system not only enables three actuators to load harmoniously and stably, but ensures control precision; MATLAB programs simply and flexibly, which enables calculation program to be expanded easily; the external command control method can be extended and applied in structural seismic testing research associating numerical simulation with physical testing because of simple hardware connection and control program independent on control software of testing equipment.%为了建立对任何试验设备控制系统均通用的拟动力试验系统,提出外部命令控制方法,并应用Visual C++和MATLAB混合编程控制的方法编制试验程序.以MTS FlexTest GT控制系统为例,在GT控制器上连接采集卡,应用Visual C++编制采集卡控制程序,控制GT控制器的I/O通道,实现外部命令对作动器的控制.应用MATLAB语言编制计算程序,通过VisualC++调用MATLAB引擎的方法,完成了控制程序和计算程序的接口.进行了一个3层砌体结构足尺模型的三自由度结构拟动力试验.试验结果表明,试验系统能够保证3个作动器之间协调地稳定加载,并且保证控制精度
Multi-degree of freedom joystick for virtual reality simulation.
Head, M J; Nelson, C A; Siu, K C
2013-11-01
A modular control interface and simulated virtual reality environment were designed and created in order to determine how the kinematic architecture of a control interface affects minimally invasive surgery training. A user is able to selectively determine the kinematic configuration of an input device (number, type and location of degrees of freedom) for a specific surgical simulation through the use of modular joints and constraint components. Furthermore, passive locking was designed and implemented through the use of inflated latex tubing around rotational joints in order to allow a user to step away from a simulation without unwanted tool motion. It is believed that these features will facilitate improved simulation of a variety of surgical procedures and, thus, improve surgical skills training.
A review of development and implementation of an active nonlinear vibration absorber
Energy Technology Data Exchange (ETDEWEB)
Oueini, S.S.; Nayfeh, A.H. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Engineering Science and Mechanics; Pratt, J.R. [Manufacturing Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899-001 (United States)
1999-10-01
We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the saturation phenomenon that is known to occur in quadratically-coupled multi-degree-of-freedom systems subjected to primary excitation and possessing a two-to-one internal resonance. The technique is based on introducing an absorber and coupling it with the structure through a sensor and an actuator, where the feedback and control signals are quadratic. First, we consider the case of controlling the vibrations of a single-degree-of-freedom system. We develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigate the performance of the control strategy by studying its steady-state and transient characteristics. Additionally, we compare the performance of the quadratic absorber with that of a linear absorber. Then, we present theoretical and experimental results that demonstrate the versatility of the technique. We design an electronic circuit to emulate the absorber and use a variety of sensors and actuators to implement the active control strategy. First, we use a motor and a potentiometer to control the vibration of a rigid beam. We develop a plant model that includes Coulomb friction and demonstrate that the closed-loop system exhibits the saturation phenomenon. Second, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of flexible steel beams when subjected to single- and simultaneous two-mode excitations. Third, we employ Terfenol-D, a nonlinear actuator, and accelerometers to control the vibrations of flexible beams. In all instances, the technique is successful in reducing the response amplitude of the structures. (orig.)
Non-Stationary Random Response of MDOF Duffing Systems
Directory of Open Access Journals (Sweden)
J.H. Lin
2004-01-01
Full Text Available This paper presents a method to solve non-stationary random responses of nonlinear multi-degrees-of-freedom (MDOF Duffing systems subjected to evolutionary random excitations. Specific phase-lags between the excitations can also be taken into account. The power spectral density (PSD of the input excitations is not confined to simple white noise or filtered white noise, in fact it can also take more complicated forms. The MDOF nonlinear random differential equations are iteratively solved by means of the Equivalent Linearization Method (ELM combined with the Pseudo Excitation Method (PEM. This combined method is easy and efficient. Two examples are given in which this method is well justified by the Monte-Carlo numerical simulations. Although only a Duffing model is dealt with in this paper for computational simplicity, the proposed method is in fact quite general, e.g. it can also deal with nonlinear hysteretic structures that will be dealt with in a separate paper.
Advances in simulated modeling of vibration systems based on computational intelligence
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Computational intelligence is the computational simulation of the bio-intelligence, which includes artificial neural networks, fuzzy systems and evolutionary computations. This article summarizes the state of the art in the field of simulated modeling of vibration systems using methods of computational intelligence, based on some relevant subjects and the authors' own research work. First, contributions to the applications of computational intelligence to the identification of nonlinear characteristics of packaging are reviewed. Subsequently, applications of the newly developed training algorithms for feedforward neural networks to the identification of restoring forces in multi-degree-of-freedom nonlinear systems are discussed. Finally, the neural-network-based method of model reduction for the dynamic simulation of microelectromechanical systems (MEMS) using generalized Hebbian algorithm (GHA) and robust GHA is outlined. The prospects of the simulated modeling of vibration systems using techniques of computational intelligence are also indicated.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.;
This paper contains an analyses of the error induced by applying the method of the equivalent statistical linearzation (ESL) to randomly-exited multi-degree-of-freedom (MDOF) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases. The quantity that is analyzed...
Energy Technology Data Exchange (ETDEWEB)
Huan, Ronghua; Zhu, Weiqiu [Zhejiang University, Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Hangzhou (China); Wu, Yongjun [East China University of Science and Technology, School of Information Science and Engineering, Shanghai (China)
2009-02-15
A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Ito stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang-bang control strategy. (orig.)
Ondra, V.; Sever, I. A.; Schwingshackl, C. W.
2017-01-01
This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
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.
Energy Technology Data Exchange (ETDEWEB)
Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in
2017-07-15
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Tuneable, non-degenerated, nonlinear, parametrically-excited amplifier
Dolev, Amit; Bucher, Izhak
2016-01-01
The proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator. Parametric amplifiers had been studied extensively, although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier's natural frequency. These amplifiers are confined to amplifying predetermined frequencies. The proposed parametric amplifier's bandwidth is indeed tuneable to nearly any input frequency, not bound to be an integer multiple of a natural frequency. In order to tune the stiffness and induce a variable frequency parametric excitation, a digitally controlled electromechanical element must be incorporated in the realization. We introduce a novel parametric amplifier with nonlinearity, Duffing type hardening, that bounds the otherwise unlimited amplitude. Moreover, we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system, and thus to transform external excitations to a frequency band where signal levels are considerably higher. Using the method of multiple scales, analytical expressions for the responses have been retrieved and verified numerically. Parametric studies of the amplifiers' gain, sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically. The results demonstrate the advantage of the proposed approach over existing schemes. Practical applications envisaged for the proposed method will be outlined.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
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.-
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
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Campbell, David K.
2010-03-01
In 1953, Enrico Fermi, John Pasta, and Stan Ulam initiated a series of computer studies aimed at exploring how simple, multi-degree of freedom nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time to an equilibrium state describable by statistical mechanics. Their expectation was that this would occur by mixing behavior among the many linear modes. Their intention was then to study more complex nonlinear systems, with the hope of modeling turbulence computationally. The results of this first study of the so-called Fermi-Pasta-Ulam (FPU) problem, which were published in 1955 and characterized by Fermi as a ``little discovery,'' showed instead of the expected mixing of linear modes a striking series of (near) recurrences of the initial state and no evidence of equipartition. This work heralded the beginning of both computational physics and (modern) nonlinear science. In particular, the work marked the first systematic study of a nonlinear system by digital computers (``experimental mathematics'') and led directly to the discovery of ``solitons,'' as well as to deep insights into deterministic chaos and statistical mechanics. In this talk, I will review the original FPU studies and show how they led to the understanding of two key paradigms of nonlinear science. Specifically, I will show how a continuum approximation to the original discrete system led to the discovery of ``solitions'' whereas a low-mode approximation led to an early example of ``deterministic chaos.'' I will close with a brief indication of how the recurrence phenomenon observed by behavior by FPU can be reconciled with mixing, equipartition, and statistical mechanics.
Robust and Transparent Multi-Degree-of-Freedom Bilateral Teleoperation with Time-Delay
Pinto Rebelo, J.L.
2015-01-01
Robots are particularly well suited for executing tasks that take place in locations which are too dangerous or inaccessible to human operators. For robot manipulators to execute complex activities in unknown, unstructured environments, despite the recent increases in computation power, human input
Controlling a multi-degree of freedom upper limb prosthesis using foot controls: user experience.
Resnik, Linda; Klinger, Shana Lieberman; Etter, Katherine; Fantini, Christopher
2014-07-01
The DEKA Arm, a pre-commercial upper limb prosthesis, funded by the DARPA Revolutionizing Prosthetics Program, offers increased degrees of freedom while requiring a large number of user control inputs to operate. To address this challenge, DEKA developed prototype foot controls. Although the concept of utilizing foot controls to operate an upper limb prosthesis has been discussed for decades, only small-sized studies have been performed and no commercial product exists. The purpose of this paper is to report amputee user perspectives on using three different iterations of foot controls to operate the DEKA Arm. Qualitative data was collected from 36 subjects as part of the Department of Veterans Affairs (VA) Study to Optimize the DEKA Arm through surveys, interviews, audio memos, and videotaped sessions. Three major, interrelated themes were identified using the constant comparative method: attitudes towards foot controls, psychomotor learning and physical experience of using foot controls. Feedback about foot controls was generally positive for all iterations. The final version of foot controls was viewed most favorably. Our findings indicate that foot controls are a viable control option that can enable control of a multifunction upper limb prosthesis (the DEKA Arm). Multifunction upper limb prostheses require many user control inputs to operate. Foot controls offer additional control input options for such advanced devices, yet have had minimal study. This study found that foot controls were a viable option for controlling multifunction upper limb prostheses. Most of the 36 subjects in this study were willing to adopt foot controls to control the multiple degrees of freedom of the DEKA Arm. With training and practice, all users were able to develop the psychomotor skills needed to successfully operate food controls. Some had initial difficulty, but acclimated over time.
Foundations for learning and adaptation in a multi-degree-of-freedom unmanned ground vehicle
Blackburn, Michael R.; Bailey, Richard
2004-04-01
The real-time coordination and control of a many motion degrees of freedom (dof) unmanned ground vehicle under dynamic conditions in a complex environment is nearly impossible for a human operator to accomplish. Needed are adaptive on-board mechanisms to quickly complete sensor-effector loops to maintain balance and leverage. This paper contains a description of our approach to the control problem for a small unmanned ground vehicle with six dof in the three spatial dimensions. Vehicle control is based upon seven fixed action patterns that exercise all of the motion dof of which the vehicle is capable, and five basic reactive behaviors that protect the vehicle during operation. The reactive behaviors demonstrate short-term adaptations. The learning processes for long-term adaptations of the vehicle control functions that we are implementing are composed of classical and operant conditionings of novel responses to information available from distance sensors (vision and audition) built upon the pre-defined fixed action patterns. The fixed action patterns are in turn modulated by the pre-defined low-level reactive behaviors that, as unconditioned responses, continuously serve to maintain the viability of the robot during the activations of the fixed action patterns, and of the higher-order (conditioned) behaviors. The sensors of the internal environment that govern the low-level reactive behaviors also serve as the criteria for operant conditioning, and satisfy the requirement for basic behavioral motivation.
Bayesian robot system identification with input and output noise.
Ting, Jo-Anne; D'Souza, Aaron; Schaal, Stefan
2011-01-01
For complex robots such as humanoids, model-based control is highly beneficial for accurate tracking while keeping negative feedback gains low for compliance. However, in such multi degree-of-freedom lightweight systems, conventional identification of rigid body dynamics models using CAD data and actuator models is inaccurate due to unknown nonlinear robot dynamic effects. An alternative method is data-driven parameter estimation, but significant noise in measured and inferred variables affects it adversely. Moreover, standard estimation procedures may give physically inconsistent results due to unmodeled nonlinearities or insufficiently rich data. This paper addresses these problems, proposing a Bayesian system identification technique for linear or piecewise linear systems. Inspired by Factor Analysis regression, we develop a computationally efficient variational Bayesian regression algorithm that is robust to ill-conditioned data, automatically detects relevant features, and identifies input and output noise. We evaluate our approach on rigid body parameter estimation for various robotic systems, achieving an error of up to three times lower than other state-of-the-art machine learning methods.
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Motion control and vibration suppression of flexible lumped systems via sensorless LQR control
Çelebi, Beşir; Celebi, Besir; Çevik, Gülnihal; Cevik, Gulnihal; Mehmet, Berkem; Shoukry Mohammed Khalil, Islam; ŞABANOVIÇ, Asif; SABANOVIC, Asif
2011-01-01
This work attempts to achieve motion control along with vibration suppression of flexible systems by developing a sensorless closed loop LQR controller. Vibration suppression is used as a performance index that has to be minimized so that motion control is achieved with zero residual vibration. An estimation algorithm is combined with the regular LQR to develop sensorless motion and vibration controller that is capable of positioning multi degrees of freedom flexible system point of interest ...
Directory of Open Access Journals (Sweden)
Amin Jalali
2013-09-01
Full Text Available The increasing demand for multi-degree-of-freedom (DOF continuum robot in presence of highly nonlinear dynamic parameters in a number of industries has motivated a flurry of research in the development of soft computing nonlinear methodology. This robot is capable of providing smooth and isotropic three-dimensional motion in each joint. Compared to conventional robotic manipulators that offer the same motion capabilities, the innovative spherical motor possesses several advantages. Not only can the spherical motor combine 3-DOF motion in a single joint, it has a large range of motion with no singularities in its workspace. This research contributes to the on-going research effort by exploring alternate methods for controlling the continuum robot manipulator. This research addresses two basic issues related to the control of a continuum robots; (1 a more accurate representation of the dynamic model of an existing prototype, and (2 the design of a robust feedback controller. The robust backstepping controller proposed in this research is used to further demonstrate the appealing features exhibited by the continuum robot. Robust feedback controller is used to position control of continuum robot in presence of uncertainties. Using Lyapunov type stability arguments, a robust backstepping controller is designed to achieve this objective. The controller developed in this research is designed in two steps. Firstly, a robust stabilizing torque is designed for the nominal continuum robot dynamics derived using the constrained Lagrangian formulation. Next, the fuzzy logic methodology applied to it to solution uncertainty problem. The fuzzy model free problem is formulated to minimize the nonlinear formulation of continuum robot. The eventual stability of the controller depends on the torque generating capabilities of the continuum robots.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
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
Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Maolin Deng; Weiqiu Zhu
2007-01-01
A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems (multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximiza-tion of reliability and mean first-passage time are formulated.The optimal control law is derived from the dynamical pro-gramming equations and the control constraints. The final dynamical programming equations for these control prob-lems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynami-cal programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illus-trate the application and effectiveness of the proposed control strategy.
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.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Nonlinear input-output systems
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Simulation of the oscillation regimes of bowed bars: a non-linear modal approach
Inácio, Octávio; Henrique, Luís.; Antunes, José
2003-06-01
It is still a challenge to properly simulate the complex stick-slip behavior of multi-degree-of-freedom systems. In the present paper we investigate the self-excited non-linear responses of bowed bars, using a time-domain modal approach, coupled with an explicit model for the frictional forces, which is able to emulate stick-slip behavior. This computational approach can provide very detailed simulations and is well suited to deal with systems presenting a dispersive behavior. The effects of the bar supporting fixture are included in the model, as well as a velocity-dependent friction coefficient. We present the results of numerical simulations, for representative ranges of the bowing velocity and normal force. Computations have been performed for constant-section aluminum bars, as well as for real vibraphone bars, which display a central undercutting, intended to help tuning the first modes. Our results show limiting values for the normal force FN and bowing velocity ẏbow for which the "musical" self-sustained solutions exist. Beyond this "playability space", double period and even chaotic regimes were found for specific ranges of the input parameters FN and ẏbow. As also displayed by bowed strings, the vibration amplitudes of bowed bars also increase with the bow velocity. However, in contrast to string instruments, bowed bars "slip" during most of the motion cycle. Another important difference is that, in bowed bars, the self-excited motions are dominated by the system's first mode. Our numerical results are qualitatively supported by preliminary experimental results.
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
On balanced truncation for symmetric nonlinear systems
Fujimoto, K.; Scherpen, Jacqueline M.A.
2014-01-01
This paper is concerned with model order reduction based on balanced realization for symmetric nonlinear systems. A new notion of symmetry for nonlinear systems was characterized recently. It plays an important role in linear systems theory and is expected to provide new insights to nonlinear system
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
An Adaptive Nonlinear Filter for System Identification
Directory of Open Access Journals (Sweden)
Tokunbo Ogunfunmi
2009-01-01
Full Text Available The primary difficulty in the identification of Hammerstein nonlinear systems (a static memoryless nonlinear system in series with a dynamic linear system is that the output of the nonlinear system (input to the linear system is unknown. By employing the theory of affine projection, we propose a gradient-based adaptive Hammerstein algorithm with variable step-size which estimates the Hammerstein nonlinear system parameters. The adaptive Hammerstein nonlinear system parameter estimation algorithm proposed is accomplished without linearizing the systems nonlinearity. To reduce the effects of eigenvalue spread as a result of the Hammerstein system nonlinearity, a new criterion that provides a measure of how close the Hammerstein filter is to optimum performance was used to update the step-size. Experimental results are presented to validate our proposed variable step-size adaptive Hammerstein algorithm given a real life system and a hypothetical case.
Energy Technology Data Exchange (ETDEWEB)
Han, Dong Ki; Chang, Pyung Hun [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2010-08-15
We propose an enhanced controller to improve the robustness of Time Delay Control (TDC) for a robot manipulator in the presence of nonlinear friction, such as Coulomb friction. The problem of TDC is first analyzed with TDC as a trajectory control for a robot manipulator in the presence of nonlinear friction. Gradient estimation is used to solve this problem. The proposed controller is called TDC with Gradient Estimator (TDCGE). Comparing with a prior research to improve the robustness of TDC, named TDCSA, the TDCGE is much simpler to design. Through 1 DOF linear motor experiment, it is verified that the TDCGE is more robust against nonlinear friction than TDC and the TDCGE has a similar robustness to the TDCSA. In addition, it is confirmed that the TDCGE is easily implemented in the multi degree-of-freedom robot manipulator through a 3 DOF spatial robot manipulator experiment
Nonlinearity of colloid systems oxyhydrate systems
Sucharev, Yuri I
2008-01-01
The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J.M.A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Han...
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.
Computing abstractions of nonlinear systems
Reißig, Gunther
2009-01-01
We present an efficient algorithm for computing discrete abstractions of arbitrary memory span for nonlinear discrete-time and sampled systems, in which, apart from possibly numerically integrating ordinary differential equations, the only nontrivial operation to be performed repeatedly is to distinguish empty from non-empty convex polyhedra. We also provide sufficient conditions for the convexity of attainable sets, which is an important requirement for the correctness of the method we propose. It turns out that requirement can be met under rather mild conditions, which essentially reduce to sufficient smoothness in the case of sampled systems. Practicability of our approach in the design of discrete controllers for continuous plants is demonstrated by an example.
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J. M. A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Stability of fractional positive nonlinear systems
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2015-12-01
Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
DISTURBANCE ATTENUATION FOR UNCERTAIN NONLINEAR CASCADED SYSTEMS
Institute of Scientific and Technical Information of China (English)
BI Weiping; MU Xiaowu; SUN Yuqiang
2004-01-01
In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the disturbance attenuation problem is constructed for uncertain nonlinear cascaded systems with internal stability.
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
Xiang, Kui; Wang, Wen; Zhang, Min; Lu, Keqing; Fan, Zongwei; Chen, Zichen
2015-02-01
A novel cylindrical capacitive sensor (CCS) with differential, symmetrical and integrated structure was proposed to measure multi-degree-of-freedom rotation errors of high precision spindle simultaneously and to reduce impacts of multiple sensors installation errors on the measurement accuracy. The nonlinear relationship between the output capacitance of CCS and the radial gap was derived using the capacitance formula and was quantitatively analyzed. It was found through analysis that the thickness of curved electrode plates led to the existence of fringe effect. The influence of the fringe effect on the output capacitance was investigated through FEM simulation. It was found through analysis and simulation that the CCS could be optimized to improve the measurement accuracy.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
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
Nonlinear identification of power electronic systems
Chau, KT; Chan, CC
1995-01-01
This paper presents a new approach to modelling power electronic systems using nonlinear system identification. By employing the nonlinear autoregressive moving average with exogenous input (NARMAX) technique, the parametric model of power electronic systems can be derived from the time-domain data. This approach possesses some advantages over available circuit-oriented modelling approaches, such as no small-signal approximation, no circuit idealization and no detailed knowledge of system ope...
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
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...
Linearization of Systems of Nonlinear Diffusion Equations
Institute of Scientific and Technical Information of China (English)
KANG Jing; QU Chang-Zheng
2007-01-01
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
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.
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Chaotification for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Liu Na; Guan Zhi-Hong
2009-01-01
More and more attention has been focused on effectively generating chaos via simple physical devices. The problem of creating chaotic attractors is considered for a class of nonlinear systems with backlash function in this paper. By utilizing the Silnikov heteroclinic and homoclinic theorems, some sufficient conditions are established to guarantee that the nonlinear system has horseshoe-type chaos. Examples and simulations are given to verify the effectiveness of the theoretical results.
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Qualitative stability of nonlinear networked systems
Angulo, Marco Tulio; Slotine, Jean-Jacques
2016-01-01
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
Nonlinear Differential Systems with Prescribed Invariant Sets
DEFF Research Database (Denmark)
Sandqvist, Allan
1999-01-01
We present a class of nonlinear differential systems for which invariant sets can be prescribed.Moreover,we show that a system in this class can be explicitly solved if a certain associated linear homogeneous system can be solved.As a simple application we construct a plane autonomous system having...
Hyperchaos in fractional order nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. [Electrical and Computer Engineering Department, University of Sharjah, P.O. Box 27272 Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-12-01
We numerically investigate hyperchaotic behavior in an autonomous nonlinear system of fractional order. It is demonstrated that hyperchaotic behavior of the integer order nonlinear system is preserved when the order becomes fractional. The system under study has been reported in the literature [Murali K, Tamasevicius A, Mykolaitis G, Namajunas A, Lindberg E. Hyperchaotic system with unstable oscillators. Nonlinear Phenom Complex Syst 3(1);2000:7-10], and consists of two nonlinearly coupled unstable oscillators, each consisting of an amplifier and an LC resonance loop. The fractional order model of this system is obtained by replacing one or both of its capacitors by fractional order capacitors. Hyperchaos is then assessed by studying the Lyapunov spectrum. The presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos. Using the appropriate system control parameters, it is demonstrated that hyperchaotic attractors are obtained for a system order less than 4. Consequently, we present a conjecture that fourth-order hyperchaotic nonlinear systems can still produce hyperchaotic behavior with a total system order of 3 + {epsilon}, where 1 > {epsilon} > 0.
Nonlinear characteristics of an autoparametric vibration system
Yan, Zhimiao; Taha, Haithem E.; Tan, Ting
2017-03-01
The nonlinear characteristics of an autoparametric vibration system are investigated. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales (MMS) is used to determine an approximate analytical solution of the nonlinear governing equations and, hence, analyze the stability and bifurcation of the system. Compared with the numerical simulation, the first-order MMS is not sufficient. A Lagrangian-based approach is proposed to perform a second-order analysis, which is applicable to a large class of nonlinear systems. The effects of the amplitude and frequency of the external force, damping and frequency of the attached cantilever beam, and the tip mass on the nonlinear responses of the autoparametric vibration system are determined. The results show that this system exhibits many interesting nonlinear phenomena including saturation, jumps, hysteresis and different kinds of bifurcations, such as saddle-node, supercritical pitchfork and subcritical pitchfork bifurcations. Power spectra, phase portraits and Poincare maps are employed to analyze the unstable behavior and the associated Hopf bifurcation and chaos. Depending on the application of such a system, its dynamical behaviors could be exploited or avoided.
Nonlinear vibrating system identification via Hilbert decomposition
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
Modal analysis of nonlinear mechanical systems
2014-01-01
The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
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
Damage detection in initially nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Bornn, Luke [Los Alamos National Laboratory; Farrar, Charles [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
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 System Identification and Behavioral Modeling
Huq, Kazi Mohammed Saidul; Kabir, A F M Sultanul
2010-01-01
The problem of determining a mathematical model for an unknown system by observing its input-output data pair is generally referred to as system identification. A behavioral model reproduces the required behavior of the original analyzed system, such as there is a one-to-one correspondence between the behavior of the original system and the simulated system. This paper presents nonlinear system identification and behavioral modeling using a work assignment.
Dynamic Response of Linear Mechanical Systems Modeling, Analysis and Simulation
Angeles, Jorge
2012-01-01
Dynamic Response of Linear Mechanical Systems: Modeling, Analysis and Simulation can be utilized for a variety of courses, including junior and senior-level vibration and linear mechanical analysis courses. The author connects, by means of a rigorous, yet intuitive approach, the theory of vibration with the more general theory of systems. The book features: A seven-step modeling technique that helps structure the rather unstructured process of mechanical-system modeling A system-theoretic approach to deriving the time response of the linear mathematical models of mechanical systems The modal analysis and the time response of two-degree-of-freedom systems—the first step on the long way to the more elaborate study of multi-degree-of-freedom systems—using the Mohr circle Simple, yet powerful simulation algorithms that exploit the linearity of the system for both single- and multi-degree-of-freedom systems Examples and exercises that rely on modern computational toolboxes for both numerical and symbolic compu...
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.
Theoretical aspects of nonlinear echo image system
Institute of Scientific and Technical Information of China (English)
ZHANG Ruiquan; FENG Shaosong
2003-01-01
In order to develop the nonlinear echo image system to diagnose pathological changes in biological tissue , a simple physical model to analyse the character of nonlinear reflected wave in biological medium is postulated. The propagation of large amplitude plane sound wave in layered biological media is analysed for the one dimensional case by the method of successive approximation and the expression for the second order wave reflected from any interface of layered biological media is obtained. The relations between the second order reflection coefficients and the nonlinear parameters of medium below the interface are studied in three layers interfaces. Finally, the second order reflection coefficients of four layered media are calculated numerically. The results indicate that the nonlinear parameter B/A of each layer of biological media can be determined by the reflection method.
Nonlinear system identification in offshore structural reliability
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corporation, Houston, TX (United States)
1995-08-01
Nonlinear forces acting on offshore structures are examined from a system identification perspective. The nonlinearities are induced by ocean waves and may become significant in many situations. They are not necessarily in the form of Morison`s equation. Various wave force models are examined. The force function is either decomposed into a set of base functions or it is expanded in terms of the wave and structural kinematics. The resulting nonlinear system is decomposed into a number of parallel no-memory nonlinear systems, each followed by a finite-memory linear system. A conditioning procedure is applied to decouple these linear sub-systems; a frequency domain technique involving autospectra and cross-spectra is employed to identify the linear transfer functions. The structural properties and those force transfer parameters are determine with the aid of the coherence functions. The method is verified using simulated data. It provides a versatile and noniterative approach for dealing with nonlinear interaction problems encountered in offshore structural analysis and design.
BINARY NONLINEARIZATION FOR THE DIRAC SYSTEMS
Institute of Scientific and Technical Information of China (English)
MAWENXIU
1997-01-01
A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Linuville integrable Hamiltonian system and that under the control of the spatial part, the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a hierarchy of commutative, finite dimensional Linuville integrable Hamiltoian systems whose Hamiltonian functions consist of a series of integrals of motion for the spatial part. Moreover an invaiutive representation of solutions of the Dirac systems exhibits their integrability by quadratures. This kind of symmetry constraint procedure involving thespectral problem and the adjoint spectral problem is referred to as a binary nonlinearization technique like a binary Darhoux transformation.
Ontology of Earth's nonlinear dynamic complex systems
Babaie, Hassan; Davarpanah, Armita
2017-04-01
As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.
Robustness analysis for a class of nonlinear descriptor systems
Institute of Scientific and Technical Information of China (English)
吴敏; 张凌波; 何勇
2004-01-01
The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient conditions to guarantee that the nonlinear descriptor systems have robust disturbance attenuation performance, which avoids the computational difficulties in conversing nonlinear matrix and Hamilton-Jacobi inequality. The computation property of convex feasibility of nonlinear matrix inequality makes it possible to apply the results of nonlinear robust control to practice.
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.
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
Dynamic disturbance decoupling for nonlinear systems
Huijberts, H.J.C.; Nijmeijer, H.; Wegen, van der L.L.M.
1992-01-01
In analogy with the dynamic input-output decoupling problem the dynamic disturbance decoupling problem for nonlinear systems is introduced. A local solution of this problem is obtained in the case that the system under consideration is invertible. The solution is given in algebraic as well as in geo
Fault detection for nonlinear systems - A standard problem approach
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, Hans Henrik
1998-01-01
The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...
Network science, nonlinear science and infrastructure systems
2007-01-01
Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .
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.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.
Workshop on Nonlinear Phenomena in Complex Systems
1989-01-01
This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Exploring Nonlinearities in Financial Systemic Risk
Wolski, M.
2013-01-01
We propose a new methodology of assessing the effects of individual institution's risk on the others and on the system as a whole. We build upon the Conditional Value-at-Risk approach, however, we introduce the explicit Granger causal linkages and we account for possible nonlinearities in the
Oscillatority Conditions for Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
Denis V. Efimov
2007-01-01
Full Text Available Sufficient conditions for oscillatority in the sense of Yakubovich for a class of time delay nonlinear systems are proposed. Under proposed conditions, upper and lower bounds for oscillation amplitude are given. Examples illustrating analytical results by computer simulation are presented.
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
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Optimized spectral estimation for nonlinear synchronizing systems.
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Statistical mechanics of a discrete nonlinear system
Rasmussen; Cretegny; Kevrekidis; Gronbech-Jensen
2000-04-24
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
Nonlinear dynamics in distributed systems
Adjali, I; Gell-Mann, Murray; Iqbal Adjali; Jose-Luis Fernandez-Villacanas; Michael Gell
1994-01-01
formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.
Variable Separation Approach to Solve Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
SHEN Shou-Feng; PAN Zu-Liang; ZHANG Jun
2004-01-01
The variable separation approach method is very useful to solving (2+ 1 )-dimensional integrable systems. But the (1+1)-dimensional and (3+ 1 )-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1+1) dimensions by taking the Redekopp system as a simple example and (3+1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3+ 1 )-dimensional universal formula obtained from many (2+ 1 )-dimensional systems is extended.
Variable Separation Approach to Solve Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
SHENShou-Feng; PANZu-Liang; ZHANGJun
2004-01-01
The variable separation approach method is very useful to solving (2+1)-dimensional integrable systems.But the (1+1)-dimensional and (3+1)-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1+1) dimensions by taking the Redekopp system as a simp!e example and (3+1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3+1)-dimensional universal formula obtained from many (2+1)-dimensional systems is extended.
Spectral decomposition of nonlinear systems with memory.
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
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.
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 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.
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
Consensus tracking for multiagent systems with nonlinear dynamics.
Dong, Runsha
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Model reduction of systems with localized nonlinearities.
Energy Technology Data Exchange (ETDEWEB)
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Nonlinear Filtering Preserves Chaotic Synchronization via Master-Slave System
Directory of Open Access Journals (Sweden)
J. S. González-Salas
2013-01-01
Full Text Available We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.
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.
Nonlinear Energy Collimation System for Linear Colliders
Resta-Lopez, Javier
2011-01-01
The post-linac energy collimation system of multi-TeV linear colliders is designed to fulfil an important function of protection of the Beam Delivery System (BDS) against miss-steered beams likely generated by failure modes in the main linac. For the case of the Compact Linear Collider (CLIC), the energy collimators are required to withstand the impact of a full bunch train in case of failure. This is a very challenging task, assuming the nominal CLIC beam parameters at 1.5 TeV beam energy. The increase of the transverse spot size at the collimators using nonlinear magnets is a potential solution to guarantee the survival of the collimators. In this paper we present an alternative nonlinear optics based on a skew sextupole pair for energy collimation. Performance simulation results are also presented.
Adaptive stabilization for cascade nonlinear systems
Institute of Scientific and Technical Information of China (English)
陈岚萍; 王洪元; 吴波
2004-01-01
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF)techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
Ba82]. For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2...linear part generates a linear semigroup as in [BBu1, BBu2, BKap]. One then uses the linear semigroup in a vari- ation of parameters implicit...BBu2, BKap] (for the linear semigroup ) plus a Gronwall inequality. An alternative (and more general) approach given in [Ba82] eschews use of the Trotter
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
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.
Sabanovic, Asif
2011-01-01
"Presents a unified approach to the fundamental issues in motion control, starting from the basics and moving through single degree of freedom and multi-degree of freedom systems In Motion Control Systems, Šabanovic and Ohnishi present a unified approach to very diverse issues covered in motion control systems, offering know-how accumulated through work on very diverse problems into a comprehensive, integrated approach suitable for application in high demanding high-tech products. It covers material from single degree of freedom systems to complex multi-body non-redundant and redundant systems. The discussion of the main subject is based on original research results and will give treatment of the issues in motion control in the framework of the acceleration control method with disturbance rejection technique. This allows consistent unification of different issues in motion control ranging from simple trajectory tracking to topics related to haptics and bilateral control without and with delay in the measure...
Nonlinear dynamics analysis of a new autonomous chaotic system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nuchaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
Identification of Nonlinear Systems Using Neurofuzzy Networks
Institute of Scientific and Technical Information of China (English)
LI Ying; JIAO Licheng
2001-01-01
This paper presents a compound neu-ral network model, I.e., adaptive neurofuzzy network(ANFN), which can be used for identifying the com-plicated nonlinear system. The proposed ANFN has asimple structure and exploits a hybrid algorithm com-bining supervised learning and unsupervised learning.In addition, ANFN is capable of overcoming the errorof system identification due to the existence of somechanging points and improving the accuracy of identi-fication of the whole system. The effectiveness of themodel and its algorithm are tested on the identifica-tion results of missile attacking area.
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.
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
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.
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...
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.
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
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
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.
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.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Institute of Scientific and Technical Information of China (English)
SUN WeiJie; HUANG Jie
2009-01-01
In this paper,we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems.By employing the internal model approach,we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form,the solution of which will lead to the solution of the global robust output regulation problem.An example shows the effectiveness of the proposed approach.
Observability and Information Structure of Nonlinear Systems,
1985-10-01
defined by Shannon and used as a measure of mut.:al infor-mation between event x. and y4. If p(x.l IY.) I I(x., y.) xil -in (1/p(x.)) =- JInp (x.) (2...entropy H(x,y) in a similar way as H(x,y) = - fx,yp(xiy)lnp(x,y)cdlY, = -E[ JInp (x,y)]. (3-13) With the above definitions, mutual information between x...Observabiity of Nonlinear Systems, Eng. Cybernetics, Volume 1, pp 338-345, 1972. 18. Sen , P., Chidambara, M.R., Observability of a Class of Nonli-.ear
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.
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....
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.
Nonlinear Systems of Second-Order ODEs
Directory of Open Access Journals (Sweden)
Patricio Cerda
2008-02-01
Full Text Available We study existence of positive solutions of the nonlinear system Ã¢ÂˆÂ’(p1(t,u,vuÃ¢Â€Â²Ã¢Â€Â²=Ã¢Â€Â…h1(tf1(t,u,v in (0,1; Ã¢ÂˆÂ’(p2(t,u,vvÃ¢Â€Â²Ã¢Â€Â²=h2(tf2(t,u,v in (0,1; u(0=u(1=v(0=v(1=0, where p1(t,u,v=1/(a1(t+c1g1(u,v and p2(t,u,v=1/(a2(t+c2g2(u,v. Here, it is assumed that g1, g2 are nonnegative continuous functions, a1(t, a2(t are positive continuous functions, c1,c2Ã¢Â‰Â¥0, h1,h2Ã¢ÂˆÂˆL1(0,1, and that the nonlinearities f1,Ã¢Â€Â…f2 satisfy superlinear hypotheses at zero and +Ã¢ÂˆÂž. The existence of solutions will be obtained using a combination among the method of truncation, a priori bounded and Krasnosel'skii well-known result on fixed point indices in cones. The main contribution here is that we provide a treatment to the above system considering differential operators with nonlinear coefficients. Observe that these coefficients may not necessarily be bounded from below by a positive bound which is independent of u and v.
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.
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.
Deterministic nonlinear systems a short course
Anishchenko, Vadim S; Strelkova, Galina I
2014-01-01
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Nonlinear Mixing in Optical Multicarrier Systems
Hameed, Mahmood Abdul
Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the...
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.
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Numerical Analysis of Nonlinear Rotor-bearing-seal System
Institute of Scientific and Technical Information of China (English)
CHENG Mei; MENG Guang; JING Jian-ping
2008-01-01
The system state trajectory, Poincaré maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor system. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodicmotion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.
Periodicity of a class of nonlinear fuzzy systems with delays
Energy Technology Data Exchange (ETDEWEB)
Yu Jiali [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: yujiali@uestc.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; Zhang Lei [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: leilazhang@uestc.edu.cn
2009-05-15
The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V; Zezyulin, Dmitry A
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\\cal PT$-symmetric systems arising from various physical disciplines ...
A nonlinear variable structure stabilizer for power system stability
Energy Technology Data Exchange (ETDEWEB)
Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)
1994-09-01
A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
Three positive doubly periodic solutions of a nonlinear telegraph system
Institute of Scientific and Technical Information of China (English)
Fang-lei WANG; Yu-kun AN
2009-01-01
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
Design of a data acquisition system of articulated arm coordinate measuring machines
Yang, Huiping; Gao, Guanbin; Wang, Wen
2015-02-01
A novel cylindrical capacitive sensor (CCS) with differential, symmetrical and integrated structure was proposed to measure multi-degree-of-freedom rotation errors of high precision spindle simultaneously and to reduce impacts of multiple-sensors installation errors on the measurement accuracy. The nonlinear relationship between the output capacitance of CCS and the radial gap was derived using the capacitance formula and was quantitatively analyzed. It was found through analysis that the thickness of curved electrode plates led to the existence of fringe effect. The influence of the fringe effect on the output capacitance was investigated through FEM simulation. It was found through analysis and simulation that the CCS could be optimized to improve the measurement accuracy.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Stabilization of a class of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) ByrnesIsidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented.Finally, as an application the stability of switched lorenz systems is investigated.
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.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
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
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
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Exact solutions for some nonlinear systems of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com
2009-04-30
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.
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.
Experimental Identification of Concentrated Nonlinearity in Aeroelastic System
Directory of Open Access Journals (Sweden)
Nayfeh Ali H
2012-07-01
Full Text Available Identification of concentrated nonlinearity in the torsional spring of an aeroelastic system is performed. This system consists of a rigid airfoil that is supported by a linear spring in the plunge motion and a nonlinear spring in the pitch motion. Quadratic and cubic nonlinearities in the pitch moment are introduced to model the concentrated nonlinearity. The representation of the aerodynamic loads by the Duhamel formulation yielded accurate values for the flutter speed and frequency. The results show that the use of the Duhamel formulation to represent the aerodynamic loads yields excellent agreement between the experimental data and the numerical predictions.
Optimal Transmission Power in a Nonlinear VLC System
Institute of Scientific and Technical Information of China (English)
ZHAO Shuang; CAI Sunzeng; KANG Kai; QIAN Hua
2016-01-01
In a visible light communication (VLC) system, the light emitting diode (LED) is nonlinear for large signals, which limits the trans⁃mission power or equivalently the coverage of the VLC system. When the input signal amplitude is large, the nonlinear distortion creates harmonic and intermodulation distortion, which degrades the transmission error vector magnitude (EVM). To evaluate the impact of nonlinearity on system performance, the signal to noise and distortion ratio (SNDR) is applied, defined as the linear sig⁃nal power over the thermal noise plus the front end nonlinear distortion. At a given noise level, the optimal system performance can be achieved by maximizing the SNDR, which results in high transmission rate or long transmission range for the VLC system. In this paper, we provide theoretical analysis on the optimization of SNDR with a nonlinear Hammerstein model of LED. Simula⁃tion results and lab experiments validate the theoretical analysis.
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima
2017-07-10
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.
Nonlinear phase noise in coherent optical OFDM transmission systems.
Zhu, Xianming; Kumar, Shiva
2010-03-29
We derive an analytical formula to estimate the variance of nonlinear phase noise caused by the interaction of amplified spontaneous emission (ASE) noise with fiber nonlinearity such as self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in coherent orthogonal frequency division multiplexing (OFDM) systems. The analytical results agree very well with numerical simulations, enabling the study of the nonlinear penalties in long-haul coherent OFDM systems without extensive numerical simulation. Our results show that the nonlinear phase noise induced by FWM is significantly larger than that induced by SPM and XPM, which is in contrast to traditional WDM systems where ASE-FWM interaction is negligible in quasi-linear systems. We also found that fiber chromatic dispersion can reduce the nonlinear phase noise. The variance of the total phase noise increases linearly with the bit rate, and does not depend significantly on the number of subcarriers for systems with moderate fiber chromatic dispersion.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Identification of the nonlinear vibration system of power transformers
Jing, Zheng; Hai, Huang; Pan, Jie; Yanni, Zhang
2017-01-01
This paper focuses on the identification of the nonlinear vibration system of power transformers. A Hammerstein model is used to identify the system with electrical inputs and the vibration of the transformer tank as the output. The nonlinear property of the system is modelled using a Fourier neural network consisting of a nonlinear element and a linear dynamic block. The order and weights of the network are determined based on the Lipschitz criterion and the back-propagation algorithm. This system identification method is tested on several power transformers. Promising results for predicting the transformer vibration and extracting system parameters are presented and discussed.
Parameter Identification of Weakly Nonlinear Vibration System in Frequency Domain
Directory of Open Access Journals (Sweden)
Jiehua Peng
2004-01-01
Full Text Available A new method of identifying parameters of nonlinearly vibrating system in frequency domain is presented in this paper. The problems of parameter identification of the nonlinear dynamic system with nonlinear elastic force or nonlinear damping force are discussed. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of perturbation method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new parameters. Then, based on this function and with the least square method, physical parameters of the system are identified. Finally, the applicability of the proposed technique is confirmed by numerical simulation.
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.
Berry phase in a generalized nonlinear two-level system
Institute of Scientific and Technical Information of China (English)
Liu Ji-Bing; Li Jia-Hua; Song Pei-Jun; Li Wei-Bin
2008-01-01
In this paper,we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field.Both the field nonlinearity and the atom-field coupling nonlinearity are considered.We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case.In addition,we also find that the geometric phase may be easily observed when the field nonlinearity is not considered.The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered.We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
RANJU KANWAR; SAMEKSHA BHASKAR
2013-01-01
In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through th...
Identification of systems containing nonlinear stiffnesses using backbone curves
Londoño, Julián M.; Cooper, Jonathan E.; Neild, Simon A.
2017-02-01
This paper presents a method for the dynamic identification of structures containing discrete nonlinear stiffnesses. The approach requires the structure to be excited at a single resonant frequency, enabling measurements to be made in regimes of large displacements where nonlinearities are more likely to be significant. Measured resonant decay data is used to estimate the system backbone curves. Linear natural frequencies and nonlinear parameters are identified using these backbone curves assuming a form for the nonlinear behaviour. Numerical and experimental examples, inspired by an aerospace industry test case study, are considered to illustrate how the method can be applied. Results from these models demonstrate that the method can successfully deliver nonlinear models able to predict the response of the test structure nonlinear dynamics.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
A new, challenging benchmark for nonlinear system identification
Tiso, Paolo; Noël, Jean-Philippe
2017-02-01
The progress accomplished during the past decade in nonlinear system identification in structural dynamics is considerable. The objective of the present paper is to consolidate this progress by challenging the community through a new benchmark structure exhibiting complex nonlinear dynamics. The proposed structure consists of two offset cantilevered beams connected by a highly flexible element. For increasing forcing amplitudes, the system sequentially features linear behaviour, localised nonlinearity associated with the buckling of the connecting element, and distributed nonlinearity resulting from large elastic deformations across the structure. A finite element-based code with time integration capabilities is made available at https://sem.org/nonlinear-systems-imac-focus-group/. This code permits the numerical simulation of the benchmark dynamics in response to arbitrary excitation signals.
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
XXIII International Conference on Nonlinear Dynamics of Electronic Systems
Stoop, Ruedi; Stramaglia, Sebastiano
2017-01-01
This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.
Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
This paper proposes a fault tolerant control method for input-affine nonlinear systems using a nonlinear reconfiguration block (RB). The basic idea of the method is to insert the RB between the plant and the nominal controller such that fault tolerance is achieved without re-designing the nominal...
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Breather compactons in nonlinear Klein-Gordon systems.
Dinda, P T; Remoissenet, M
1999-11-01
We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.
Characterization of nonlinear dynamic systems using artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
Urbina, A. [Univ. of Texas, El Paso, TX (United States); Hunter, N.F. [Los Alamos National Lab., NM (United States). Engineering Science and Analysis Div.; Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States). Experimental Structural Dynamics Dept.
1998-12-01
The efficient characterization of nonlinear systems is an important goal of vibration and model testing. The authors build a nonlinear system model based on the acceleration time series response of a single input, multiple output system. A series of local linear models are used as a template to train artificial neutral networks (ANNs). The trained ANNs map measured time series responses into states of a nonlinear system. Another NN propagates response states in time, and a third ANN inverts the original map, transforming states into acceleration predictions in the measurement domain. The technique is illustrated using a nonlinear oscillator, in which quadratic and cubic stiffness terms play a major part in the system`s response. Reasonable maps are obtained for the states, and accurate, long-term response predictions are made for data outside the training data set.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
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.
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
Nonlinear system identification and control based on modular neural networks.
Puscasu, Gheorghe; Codres, Bogdan
2011-08-01
A new approach for nonlinear system identification and control based on modular neural networks (MNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This is obtained using a partitioning algorithm. Each local nonlinear model is associated with a nonlinear controller. These are also implemented by neural networks. The switching between the neural controllers is done by a dynamical switcher, also implemented by neural networks, that tracks the different operating points. The proposed multiple modelling and control strategy has been successfully tested on simulated laboratory scale liquid-level system.
Impulsive control of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Bao Jing-Fu; Zhang Hong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Sang
2008-01-01
A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
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.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
Robust Fault Diagnosis Algorithm for a Class of Nonlinear Systems
Directory of Open Access Journals (Sweden)
Hai-gang Xu
2015-01-01
Full Text Available A kind of robust fault diagnosis algorithm to Lipschitz nonlinear system is proposed. The novel disturbances constraint condition of the nonlinear system is derived by group algebra method, and the novel constraint condition can meet the system stability performance. Besides, the defined robust performance index of fault diagnosis observer guarantees the robust. Finally, the effectiveness of the algorithm proposed is proved in the simulations.
Dynamic Analysis of Vibrating Systems with Nonlinearities
M. Kalami, Yazdi; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.
2012-02-01
The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
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...
Dimensional reduction of nonlinear time delay systems
Directory of Open Access Journals (Sweden)
M. S. Fofana
2005-01-01
infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.
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.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
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.
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.
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 ...
Optimal beamforming in MIMO systems with HPA nonlinearity
Qi, Jian
2010-09-01
In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.
Synchronization of two different chaotic systems via nonlinear ...
African Journals Online (AJOL)
ADOWIE PERE
Keyword: Synchronization, nonlinear control, chaos, attractors, controllers, secure communications ... the drive system and the other one is taken as the .... active network. Phys ... adaptive sliding mode control. J. Sound and. Vibration. 331:501-9.
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.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
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.
HYPERBOLIC-PARABOLIC CHEMOTAXIS SYSTEM WITH NONLINEAR PRODUCT TERMS
Institute of Scientific and Technical Information of China (English)
Chen Hua; Wu Shaohua
2008-01-01
We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.
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.
A Robust Fault Detection Approach for Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Min-Ze Chen; Qi Zhao; Dong-Hua Zhou
2006-01-01
In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method,a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided,and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
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.
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.
Nonlinear H∞ filtering for interconnected Markovian jump systems
Institute of Scientific and Technical Information of China (English)
Zhang Xiaomei; Zheng Yufan
2006-01-01
The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities(LMIs). A simulation example is presented to demonstrate the effectiveness of the proposed design approach.
Equivalence of Nonlinear Systems to Input-Output Prime Forms
Marino, R.; Respondek, W.; van der Schaft, A. J.
1994-01-01
The problem of transforming nonlinear control systems into input-output prime forms is dealt with, using state space, static state feedback, and also output space transformations. Necessary and sufficient geometric conditions for the solvability of this problem are obtained. The results obtained generalize well-known results both on feedback linearization as well as input-output decoupling of nonlinear systems. It turns out that, from a computational point of view, the output space transforma...
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
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
Adaptive synchronization of uncertain Liu system via nonlinear input
Institute of Scientific and Technical Information of China (English)
Hu Jia; Zhang Qun-Jiao
2008-01-01
This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input.By using a single nonlinear controller,the approach is utilized to implement the synchronization of Liu system with total parameters unknown.This method is simple and can be easily designed.What is more,it improves the existing conclusions in Ref [12].Simulation results prove that the controller is effective and feasible in the end.
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.
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...
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
Partially Linearizable Class of Nonlinear System with Uncertainty
Energy Technology Data Exchange (ETDEWEB)
Joo, Sung Jun [Samsung Electronics Coporation (Korea, Republic of); Seo, Jin H. [Seoul National University (Korea, Republic of)
1998-03-01
In this paper the problem of robust stabilizing control for nonlinear SISO systems in the presence of uncertainties is studied and we give some geometric conditions for this problem. We also show that if and only if the systems satisfy the proposed conditions it can be transformed into a partially linearized system with unknown parameter using the nominal transformation and nominal feedback linearizing controller. In this paper, we call the above considered class of nonlinear system as partially linearizable system. We design the robust controller which stabilizes the partially linearizable system. (author). 14 refs.
Self-characterization of linear and nonlinear adaptive optics systems
Hampton, Peter J.; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan
2008-01-01
We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.
Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
Constantine, Paul G
2010-01-01
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the dynamical system. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. We prove some interesting characteristics of the scheme including uniqueness and an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and groundwater modeling - a nonlinear parabolic PDE w...
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Fernando; Goulart, Érico; Reula, Oscar
2015-01-01
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
Online identification of nonlinear spatiotemporal systems using kernel learning approach.
Ning, Hanwen; Jing, Xingjian; Cheng, Li
2011-09-01
The identification of nonlinear spatiotemporal systems is of significance to engineering practice, since it can always provide useful insight into the underlying nonlinear mechanism and physical characteristics under study. In this paper, nonlinear spatiotemporal system models are transformed into a class of multi-input-multi-output (MIMO) partially linear systems (PLSs), and an effective online identification algorithm is therefore proposed by using a pruning error minimization principle and least square support vector machines. It is shown that many benchmark physical and engineering systems can be transformed into MIMO-PLSs which keep some important physical spatiotemporal relationships and are very helpful in the identification and analysis of the underlying system. Compared with several existing methods, the advantages of the proposed method are that it can make full use of some prior structural information about system physical models, can realize online estimation of the system dynamics, and achieve accurate characterization of some important nonlinear physical characteristics of the system. This would provide an important basis for state estimation, control, optimal analysis, and design of nonlinear distributed parameter systems. The proposed algorithm can also be applied to identification problems of stochastic spatiotemporal dynamical systems. Numeral examples and comparisons are given to demonstrate our results.
Scattering in the nonlinear Lamb system
Energy Technology Data Exchange (ETDEWEB)
Komech, A.I. [Faculty of Mathematics of Vienna University, Vienna (Austria); Institute for the Information Transmission Problems of RAS, Moscow (Russian Federation)], E-mail: alexander.komech@univie.ac.at; Merzon, A.E. [Institute of Physics and Mathematics, University of Michoacan of San Nicolas de Hidalgo, Morelia, Michoacan (Mexico)], E-mail: anatoli@ifm.imich.mx
2009-03-09
We obtain long time asymptotics for the solutions to a string coupled to a nonlinear oscillator: each finite energy solution decays to a sum of a stationary state and a dispersive wave. The asymptotics hold in global energy norm. The dispersive waves are expressed via initial data and solution to an ordinary differential equation. The asymptotics give a mathematical model for the Bohr's transitions between quantum stationary states.
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.
Parametric characteristic of the random vibration response of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Xing-Jian Dong; Zhi-Ke Peng; Wen-Ming Zhang; Guang Meng; Fu-Lei Chu
2013-01-01
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of non-linear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density (PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
Nonlinear feedback synchronization of hyperchaos in higher dimensional systems
Institute of Scientific and Technical Information of China (English)
FangJin－Qing; AliMK
1997-01-01
Nonlinear feedback functional method is presented to realize synchronization of hyperchaos in higher dimensional systems,New nonlinear feedback functions and superpositions of linear and nonlinear feedback functions are also introduced to synchronize hyperchaos.The robustness of the method based on the flexibility of choices of feedback functions is discussed.By coupling well-known chaotic or chaotic-hyperchaotic systems in low-dimensional systems,such as Lorenz system,Van der Pol oscillator,Duffing oscillator and Roessler system,ten dimensional hyperchaotic systems are formed as the model systems.It can be found that there is not any noticeable difference in synchronization based on the numbers of positive Lyapunov exponents and of dimensions.
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.
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques
Institute of Scientific and Technical Information of China (English)
LIU Minzhong; KANG Lishan
2006-01-01
We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems ). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.
Modelling and Estimation of Hammerstein System with Preload Nonlinearity
Directory of Open Access Journals (Sweden)
Khaled ELLEUCH
2010-12-01
Full Text Available This paper deals with modelling and parameter identification of nonlinear systems described by Hammerstein model having asymmetric static nonlinearities known as preload nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the generalized orthonormal bases leads to a particular form of Hammerstein model containing a minimal parameters number. The employ of orthonormal bases for the description of the linear dynamic block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD technique has been applied to separate the coupled parameters. To demonstrate the feasibility of the identification method, an illustrative example is included.
Nonlinear Galerkin Optimal Truncated Low—dimensional Dynamical Systems
Institute of Scientific and Technical Information of China (English)
ChuijieWU
1996-01-01
In this paper,a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems(LDDSs) directly from partial differential equations has been developed.Applying the new theory to the nonlinear Burgers' equation,it is shown that a nearly perfect LDDS can be gotten,and the initial-boundary conditions are automatically included in the optimal bases.The nonlinear Galerkin method does not have advantages within the optimization process,but it can significantly improve the results,after the Galerkin optimal bases have been gotten.
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.
Haar basis and nonlinear modeling of complex systems
García, P.; Merlitti, A.
2007-04-01
In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.
A new extended H∞ filter for discrete nonlinear systems
Institute of Scientific and Technical Information of China (English)
张永安; 周荻; 段广仁
2004-01-01
Nonlinear estimation problem is investigated in this paper. By extension of a linear H∞ estimation with corrector-predictor form to nonlinear cases, a new extended H∞ filter is proposed for time-varying discretetime nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H∞ bound performs better than the EKF.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Practical compensation for nonlinear dynamic thrust measurement system
Directory of Open Access Journals (Sweden)
Chen Lin
2015-04-01
Full Text Available The real dynamic thrust measurement system usually tends to be nonlinear due to the complex characteristics of the rig, pipes connection, etc. For a real dynamic measuring system, the nonlinearity must be eliminated by some adequate methods. In this paper, a nonlinear model of dynamic thrust measurement system is established by using radial basis function neural network (RBF-NN, where a novel multi-step force generator is designed to stimulate the nonlinearity of the system, and a practical compensation method for the measurement system using left inverse model is proposed. Left inverse model can be considered as a perfect dynamic compensation of the dynamic thrust measurement system, and in practice, it can be approximated by RBF-NN based on least mean square (LMS algorithms. Different weights are set for producing the multi-step force, which is the ideal input signal of the nonlinear dynamic thrust measurement system. The validity of the compensation method depends on the engine’s performance and the tolerance error 0.5%, which is commonly demanded in engineering. Results from simulations and experiments show that the practical compensation using left inverse model based on RBF-NN in dynamic thrust measuring system can yield high tracking accuracy than the conventional methods.
Fault detection and fault-tolerant control for nonlinear systems
Li, Linlin
2016-01-01
Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...
Applications of nonlinear system identification to structural health monitoring.
Energy Technology Data Exchange (ETDEWEB)
Farrar, C. R. (Charles R.); Sohn, H. (Hoon); Robertson, A. N. (Amy N.)
2004-01-01
The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.
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...
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
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.
Damage detection in structures through nonlinear excitation and system identification
Hajj, Muhammad R.; Bordonaro, Giancarlo G.; Nayfeh, Ali H.; Duke, John C., Jr.
2008-03-01
Variations in parameters representing natural frequency, damping and effective nonlinearities before and after damage initiation in a beam carrying a lumped mass are assessed. The identification of these parameters is performed by exploiting and modeling nonlinear behavior of the beam-mass system and matching an approximate solution of the representative model with quantities obtained from spectral analysis of measured vibrations. The representative model and identified coefficients are validated through comparison of measured and predicted responses. Percentage variations of the identified parameters before and after damage initiation are determined to establish their sensitivities to the state of damage of the beam. The results show that damping and effective nonlinearity parameters are more sensitive to damage initiation than the system's natural frequency. Moreover, the sensitivity of nonlinear parameters to damage is better established using a physically-derived parameter rather than spectral amplitudes of harmonic components.
A Study of Thermal Contact using Nonlinear System Identification Models
Directory of Open Access Journals (Sweden)
M. H. Shojaeefard
2008-01-01
Full Text Available One interesting application of system identification method is to identify and control the heat transfer from the exhaust valve to the seat to keep away the valve from being damaged. In this study, two co-axial cylindrical specimens are used as exhaust valve and its seat. Using the measured temperatures at different locations of the specimens and with a semi-analytical method, the temperature distribution of the specimens is calculated and consequently, the thermal contact conductance is calculated. By applying the system identification method and having the temperatures at both sides of the contact surface, the temperature transfer function is calculated. With regard to the fact that the thermal contact has nonlinear behavior, two nonlinear black-box models called nonlinear ARX and NLN Hammerstein-Wiener models are taken for accurate estimation. Results show that the NLN Hammerstein-Wiener models with wavelet network nonlinear estimator is the best.
Nonlinear Mixed-Effects Models for Repairable Systems Reliability
Institute of Scientific and Technical Information of China (English)
TAN Fu-rong; JIANG Zhi-bin; KUO Way; Suk Joo BAE
2007-01-01
Mixed-effects models, also called random-effects models, are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject, but also to describe the variation among different subjects. Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data. In this paper, nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies. By using this type of models, statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance. Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.
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.
Hierarchical robust nonlinear switching control design for propulsion systems
Leonessa, Alexander
1999-09-01
The desire for developing an integrated control system- design methodology for advanced propulsion systems has led to significant activity in modeling and control of flow compression systems in recent years. In this dissertation we develop a novel hierarchical switching control framework for addressing the compressor aerodynamic instabilities of rotating stall and surge. The proposed control framework accounts for the coupling between higher-order modes while explicitly addressing actuator rate saturation constraints and system modeling uncertainty. To develop a hierarchical nonlinear switching control framework, first we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems. Using the generalized Lyapunov and invariant set theorems, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria- dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
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.
Grobner Bases for Nonlinear DAE Systems of Analog Circuits
Directory of Open Access Journals (Sweden)
Silke J. Spang
2008-04-01
Full Text Available Systems of differential equations play an important role in modelling and analysis of many complex systems e.g. in electronics and mechanics. The following article is concerned with a symbolic analysis approach for reduction of the differential index of nonlinear differential algebraic equation (DAE systems, which occur in the modelling and simulation of analog circuits.
Nonlinear system identification based on internal recurrent neural networks.
Puscasu, Gheorghe; Codres, Bogdan; Stancu, Alexandru; Murariu, Gabriel
2009-04-01
A novel approach for nonlinear complex system identification based on internal recurrent neural networks (IRNN) 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 approach employs internal state estimation when no measurements coming from the sensors are available for the system states. A modified backpropagation algorithm is introduced in order to train the IRNN for nonlinear system identification. The performance of the proposed design approach is proven on a car simulator case study.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Chaotic and hyperchaotic attractors of a complex nonlinear system
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M; Al-Kashif, M A; Farghaly, A A [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)
2008-02-08
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
Asymptotic analysis of a coupled nonlinear parabolic system
Institute of Scientific and Technical Information of China (English)
Lan QIAO; Sining ZHENG
2008-01-01
This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorption-independent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorption-related blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.
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.
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.
Nonlinear switching and solitons in PT-symmetric photonic systems
Suchkov, Sergey V; Huang, Jiahao; Dmitriev, Sergey V; Lee, Chaohong; Kivshar, Yuri S
2015-01-01
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonl...
DEFF Research Database (Denmark)
Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.
1994-01-01
perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...... for multi-degree-of-freedom (MDOF) systems and the method is illustrated for a single-degree-of-freedom (SDOF) oscillator. The results are compared to those of exact results for a random oscillator subject to white noise excitation with random intensity....
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
Directory of Open Access Journals (Sweden)
RANJU KANWAR
2013-04-01
Full Text Available In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through this work, it is investigated that for longer transmission distance, 40-Gb/s systems are more sensitive to nonlinear phase noise as compared to 50-Gb/s systems. Also, when transmitting the data through the fiber optic link, bit errors are produced due to various effects such as noise from optical amplifiers and nonlinearity occurring in fiber. On the basis of the simulation results , we have compared the bit error rate based on 8-PSK with theoretical results, and result shows that in real time approach, the bit error rate is high for the same signal to noise ratio. MATLAB software is used to validate the analytical expressions for the variance of nonlinear phase noise.
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.
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.
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.
Interval standard neural network models for nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design approach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.
Nonlinear dynamical system identification using unscented Kalman filter
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
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.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
Directory of Open Access Journals (Sweden)
Bo Wang
2012-10-01
Full Text Available In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
General difference schemes with intrinsic parallelism for nonlinear parabolic systems
Institute of Scientific and Technical Information of China (English)
周毓麟; 袁光伟
1997-01-01
The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.
Finite-time disturbance attenuation of nonlinear systems
Institute of Scientific and Technical Information of China (English)
MO LiPo; JIA YingMin; ZHENG ZhiMing
2009-01-01
This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.
Stability properties of a general class of nonlinear dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br
2001-05-04
We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)
Nonlinear Impairment Compensation Using Expectation Maximization for PDM 16-QAM Systems
DEFF Research Database (Denmark)
Zibar, Darko; Winther, Ole; Franceschi, Niccolo
2012-01-01
We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth.......We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth....
Observer Design for a Class of MIMO Nonlinear Systems (Preprint)
2006-06-01
without control), because it covers an important class of dynamic systems such as the Van der Pol equation and Duffing oscillator [5], [13] — both of...1992. [5] J. Guckenheimer and P. Holmes, Nonlinear oscillations , dynamical systems, and bifurcations of vector fields, Springer, NY, 1983. [6] A
A bias identification and state estimation methodology for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
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.
Distributed control design for nonlinear output agreement in convergent systems
Weitenberg, Erik; De Persis, Claudio
2015-01-01
This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived,
Stable Solution of Nonlinear Age-structuredForest Evolution System
Institute of Scientific and Technical Information of China (English)
WANGDing-jiang; ZHAOTing-fang
2004-01-01
This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Sturm-Picone type theorems for nonlinear differential systems
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2015-06-01
Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.
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
Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena
Institute of Scientific and Technical Information of China (English)
WU Shaohua; CHEN Hua
2011-01-01
In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
Adaptive Observer-Based Fault Estimate for Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
ZONG Qun; LIU Wenjing; LIU Li
2006-01-01
An approach for adaptive observer-based fault estimate for nonlinear system is proposed.H-infinity theory is applied to analyzing the design method and stable conditions of the adaptive observer,from which both system state and fault can be estimated.It is proved that the fault estimate error is related to the given H-infinity track performance indexes,as well as to the changing rate of the fault and the Lipschitz constant of the nonlinear item.The design steps of the adaptive observer are proposed.The simulation results show that the observer has good performance for fault estimate even when the system includes nonlinear terms,which confirms the effectiveness of the method.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Numerical studies of identification in nonlinear distributed parameter systems
Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.
1989-01-01
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
Applications of equivalent linearization approaches to nonlinear piping systems
Energy Technology Data Exchange (ETDEWEB)
Park, Y.; Hofmayer, C. [Brookhaven National Lab., Upton, NY (United States); Chokshi, N. [Nuclear Regulatory Commission, Washington, DC (United States)
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
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.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Chen, Gui-Qiang; Zhang, Yongqian
2012-01-01
We establish an $L^1$-estimate to validate the weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws with arbitrary initial data of small bounded variation. This implies that the simpler geometric optics expansion function can be employed to study the properties of general entropy solutions to hyperbolic systems of conservation laws. Our analysis involves new techniques which rely on the structure of the approximate equations, besides the properties of the wave-front tracking algorithm and the standard semigroup estimates.
Nonlinear system guidance in the presence of transmission zero dynamics
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi......-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better than estimators based on Taylor approximations. Nevertheless, the implementation is significantly simpler as no derivatives are required. Thus, it is believed that the new state estimators can replace well...
Observer-based Fault Detection and Isolation for Nonlinear Systems
DEFF Research Database (Denmark)
Lootsma, T.F.
. Then the geometric approach is applied to a nonlinear ship propulsion system benchmark. The calculations and application results are presented in detail to give an illustrative example. The obtained subsystems are considered for the design of nonlinear observers in order to obtain FDI. Additionally, an adaptive...... for the observers designed for the ship propulsion system. Furthermore, it stresses the importance of the time-variant character of the linearization along a trajectory. It leads to a different stability analysis than for linearization at one operation point. Finally, the preliminary concept of (actuator) fault...
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.
Analytical approach to robust design of nonlinear mechanical systems
Institute of Scientific and Technical Information of China (English)
Jian ZHANG; Nengsheng BAO; Guojun ZHANG; Peihua GU
2009-01-01
The robustness of mechanical systems is influenced by various factors. Their effects must be understood for designing robust systems. This paper proposes a model for describing the relationships among functional requirements, structural characteristics, design parameters and uncontrollable variables of nonlinear systems. With this model, the ensitivity of systems was analyzed to formulate a system sensitivity index and robust sensitivity matrix to determine the importance of the factors in relation to the robustness of systems. Based on the robust design principle, an optimization model was developed. Combining this optimization model and the Taguchi method for robust design, annalysis as carried out to reveal the characteristics of the systems. For a nonlinear mechanical system, relationships among structural characteristics of the system, design parameters, and uncontrollable variables can be formulated as a mathematical function. The characteristics of the system determine how design parameters affect the functional equirements of the system. Consequently, they affect the distribution of system performance functions. Nonlinearity of the system can facilitate the selection of design parameters to achieve the required functional requirements.
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Accelerator-feasible N -body nonlinear integrable system
Danilov, V.; Nagaitsev, S.
2014-12-01
Nonlinear N -body integrable Hamiltonian systems, where N is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.
Directory of Open Access Journals (Sweden)
Chuanjing Hou
2015-01-01
Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.
Federated nonlinear predictive filtering for the gyroless attitude determination system
Zhang, Lijun; Qian, Shan; Zhang, Shifeng; Cai, Hong
2016-11-01
This paper presents a federated nonlinear predictive filter (NPF) for the gyroless attitude determination system with star sensor and Global Positioning System (GPS) sensor. This approach combines the good qualities of both the NPF and federated filter. In order to combine them, the equivalence relationship between the NPF and classical Kalman filter (KF) is demonstrated from algorithm structure and estimation criterion. The main features of this approach include a nonlinear predictive filtering algorithm to estimate uncertain model errors and determine the spacecraft attitude by using attitude kinematics and dynamics, and a federated filtering algorithm to process measurement data from multiple attitude sensors. Moreover, a fault detection and isolation algorithm is applied to the proposed federated NPF to improve the estimation accuracy even when one sensor fails. Numerical examples are given to verify the navigation performance and fault-tolerant performance of the proposed federated nonlinear predictive attitude determination algorithm.
Hybrid simulation theory for a classical nonlinear dynamical system
Drazin, Paul L.; Govindjee, Sanjay
2017-03-01
Hybrid simulation is an experimental and computational technique which allows one to study the time evolution of a system by physically testing a subset of it while the remainder is represented by a numerical model that is attached to the physical portion via sensors and actuators. The technique allows one to study large or complicated mechanical systems while only requiring a subset of the complete system to be present in the laboratory. This results in vast cost savings as well as the ability to study systems that simply can not be tested due to scale. However, the errors that arise from splitting the system in two requires careful attention, if a valid simulation is to be guaranteed. To date, efforts to understand the theoretical limitations of hybrid simulation have been restricted to linear dynamical systems. In this work we consider the behavior of hybrid simulation when applied to nonlinear dynamical systems. As a model problem, we focus on the damped, harmonically-driven nonlinear pendulum. This system offers complex nonlinear characteristics, in particular periodic and chaotic motions. We are able to show that the application of hybrid simulation to nonlinear systems requires a careful understanding of what one expects from such an experiment. In particular, when system response is chaotic we advocate the need for the use of multiple metrics to characterize the difference between two chaotic systems via Lyapunov exponents and Lyapunov dimensions, as well as correlation exponents. When system response is periodic we advocate the use of L2 norms. Further, we are able to show that hybrid simulation can falsely predict chaotic or periodic response when the true system has the opposite characteristic. In certain cases, we are able to show that control system parameters can mitigate this issue.
Adaptive Output Regulation for Nonlinear Systems with Unknown Periodic Disturbances
Tsuruoka, Hidenobu; Ohmori, Hiromitsu
Many mechanical systems are subjected to periodic disturbances which may adversely influence control performance. When the plants are nonlinear systems with unknown parameters, this disturbance compensation problem has been considered as adaptive output regulation problem. This paper discusses the problem about adaptive output regulation for nonlinear systems with arbitrary relative degree, which can be transformed into the output feedback form. The nonlinear plant is affected by unknown constant parameters and periodic disturbances with unknown frequencies, magnitudes and phases. The periodic disturbances are considered as signals generated from a linear time invariant exosystem. It is not assumed that the disturbances meet the matching condition for the control input. The design method of the adaptive controller and its parameter update law is based on adaptive backstepping manner for the coordinates-changed extended system, which is generated from the nonlinear plant and the exosystem. Then, it can be achieved that the output asymptotically converges to the output reference and that all signals in the closed-loop system are bounded.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Energy Technology Data Exchange (ETDEWEB)
Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. Thats why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.
Stabilization of switched nonlinear systems with unstable modes
Yang, Hao; Cocquempot, Vincent
2014-01-01
This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...
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.
A generalization error estimate for nonlinear systems
DEFF Research Database (Denmark)
Larsen, Jan
1992-01-01
models of linear and simple neural network systems. Within the linear system GEN is compared to the final prediction error criterion and the leave-one-out cross-validation technique. It was found that the GEN estimate of the true generalization error is less biased on the average. It is concluded...
Hankel Operators and Gramians for Nonlinear Systems
Gray, W. Steven; Scherpen, Jacquelien M.A.
1998-01-01
In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-t
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....
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Long term structural dynamics of mechanical systems with local nonlinearities
Fey, R.H.B.; Campen, D.H. van; Kraker, A. de
1996-01-01
This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to iden
THE HAMILTONIAN SYSTEMS OF THE LCZ HIERARCHY BY NONLINEARIZATION
Institute of Scientific and Technical Information of China (English)
Li Lu
2000-01-01
In this paper, we first search for the Hamiltonian structure of LCZ hierarchy by use of a trace identity. Then we determine a higher-order constraint condition between the potentials and the eigenfunctions of the LCZ spectral problem, and under this constraint condition, the Lax pairs of LCZ hierarchy are all nonlinearized into the finite-dimensional integrable Hamiltonian systems in Liouville sense.
PERMANENCE OF A NONLINEAR DISCRETE PREDATOR-PREY SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we study a nonlinear discrete predator-prey model. We obtain a set of suffcient conditions which guarantee the permanence of the system. And an example together with its numeric simulation is presented to show the feasibility of our result.
Nonlinear System Design: Adaptive Feedback Linearization with Unmodeled Dynamics
1991-09-30
First, we address severe restrictions of the two currently available types of the regulation problem . In Section 11 we characterize the schemes: the...existence of such a Lyapunov II. THE CLASS OF NONLINEAR SYSTEMS function cannot be aserned a priori. fa . The adaptive regulation problem will first be
Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations
Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der
1998-01-01
Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general framework
Equivalence of nonlinear systems to input-output prime forms
Marino, R.; Respondek, W.; Schaft, van der A.J.
1994-01-01
The problem of transforming nonlinear control systems into input-output prime forms is dealt with, using state space, static state feedback, and also output space transformations. Necessary and sufficient geometric conditions for the solvability of this problem are obtained. The results obtained gen
Nonlinear dynamics of a parametrically driven sine-Gordon system
DEFF Research Database (Denmark)
Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm
1993-01-01
We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Preliminary Test for Nonlinear Input Output Relations in SISO Systems
DEFF Research Database (Denmark)
Knudsen, Torben
2000-01-01
This paper discusses and develops preliminary statistical tests for detecting nonlinearities in the deterministic part of SISO systems with noise. The most referenced method is unreliable for common noise processes as e.g.\\ colored. Therefore two new methods based on superposition and sinus input...
Networked control of nonlinear systems under Denial-of-Service
De Persis, C.; Tesi, P.
2016-01-01
We investigate the analysis and design of a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time that feedback information can be lost without resulting in instability of th
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
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.
Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
of container ships. The purpose of the model is to describe the important dynamics of the system, such as nonlinearities, transport delays and closed circuit flow dynamics to enable the model to be used for control design and simulation. The control challenge is related to the highly non-standard type of step...
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.
Observability analysis of nonlinear systems using pseudo-linear transformation
Kawano, Yu; Ohtsuka, Toshiyuki
2013-01-01
In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear system
PERMANENCE OF A NONLINEAR DISCRETE PREDATOR-PREY SYSTEM
Institute of Scientific and Technical Information of China (English)
Yaoping Chen; Fengde Chen
2009-01-01
In this paper,we study a nonlinear discrete predator-prey model. We obtain a set of sufficient conditions which guarantee the permanence of the system. And an example together with its numeric simulation is presented to show the feasibility of our result.
Non-linear Systems and Educational Development in Europe.
Reilly, David H.
1999-01-01
European educational systems are under immense pressure to change, develop, improve, and satisfy many conflicting demands. Educational development and improvement in these countries is unlikely to progress in a neat, orderly, and linear fashion. Applying nonlinear (chaos) theory to development theory may aid understanding of educational…
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Existence of solutions for a nonlinear degenerate elliptic system
Directory of Open Access Journals (Sweden)
Nguyen Minh
2004-07-01
Full Text Available In this paper, we study the existence of solutions for degenerate elliptic systems. We use the sub-super solution method, and the existence of classical and weak solutions. Some sub-supersolutions are constructed explicitly, when the nonlinearities have critical or supercritical growth.
Equivalence of Nonlinear Systems to Input-Output Prime Forms
Marino, R.; Respondek, W.; Schaft, A.J. van der
1994-01-01
The problem of transforming nonlinear control systems into input-output prime forms is dealt with, using state space, static state feedback, and also output space transformations. Necessary and sufficient geometric conditions for the solvability of this problem are obtained. The results obtained gen
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
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.
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.
The Youla Parameterization for Nonlinear Feedback Systems with Additive Disturbances
Paice, A.D.B.; Schaft, A.J. van der
1995-01-01
Building on the work presented previously, a construction of the Youla Parameterization for nonlinear feedback systems is presented in which the feedback loop is disturbed by additive disturbances. The construction of the Youla parameterization may then be shown to be stable and well-posed in the
Solidification of ternary systems with a nonlinear phase diagram
Alexandrov, D. V.; Dubovoi, G. Yu.; Malygin, A. P.; Nizovtseva, I. G.; Toropova, L. V.
2017-02-01
The directional solidification of a ternary system with an extended phase transition region is theoretically studied. A mathematical model is developed to describe quasi-stationary solidification, and its analytical solution is constructed with allowance for a nonlinear liquidus line equation. A deviation of the liquidus equation from a linear function is shown to result in a substantial change in the solidification parameters.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping
Institute of Scientific and Technical Information of China (English)
ZHU Changjiang; JIANG Mina
2006-01-01
In this paper, we study the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (-v(x, t), -u(x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (w0(x), z0(x))lies in (H3 × H2) (R) and |v+ - v-| + ‖w0‖3 + ‖z0‖2 is sufficiently small.Furthermore, the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions are also obtained.
Directory of Open Access Journals (Sweden)
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
Leader-Based Consensus of Heterogeneous Nonlinear Multiagent Systems
Directory of Open Access Journals (Sweden)
Tairen Sun
2014-01-01
Full Text Available This paper considers the leader-based consensus of heterogeneous multiple agents with nonlinear uncertain systems. Based on the information obtained from the following agents’ neighbors, leader observers are designed by the following agents to estimate the leader’s states and nonlinear dynamics. Then, to achieve leader-based consensus, adaptive distributed controllers are designed for the following agents to track the designed corresponding leader observers. The effectiveness of the leader observers and distributed consensus controllers are illustrated by formal proof and simulation results.
Hybrid quantum systems for enhanced nonlinear optical susceptibilities
Sullivan, Dennis; Kuzyk, Mark G
2016-01-01
Significant effort has been expended in the search for materials with ultra-fast nonlinear-optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinear-optical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.
Looking Back at the Gifi System of Nonlinear Multivariate Analysis
Directory of Open Access Journals (Sweden)
Peter G. M. van der Heijden
2016-09-01
Full Text Available Gifi was the nom de plume for a group of researchers led by Jan de Leeuw at the University of Leiden. Between 1970 and 1990 the group produced a stream of theoretical papers and computer programs in the area of nonlinear multivariate analysis that were very innovative. In an informal way this paper discusses the so-called Gifi system of nonlinear multivariate analysis, that entails homogeneity analysis (which is closely related to multiple correspondence analysis and generalizations. The history is discussed, giving attention to the scientific philosophy of this group, and links to machine learning are indicated.
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Directory of Open Access Journals (Sweden)
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
Random perturbations of nonlinear parabolic systems
Beck, Lisa
2011-01-01
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.
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.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
An introduction to complex systems society, ecology, and nonlinear dynamics
Fieguth, Paul
2017-01-01
This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...
Nonlinear dynamics and quantum entanglement in optomechanical systems.
Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2014-03-21
To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.
Nonlinear Analyses of the Dynamic Properties of Hydrostatic Bearing Systems
Institute of Scientific and Technical Information of China (English)
LIU Wei(刘伟); WU Xiujiang(吴秀江); V.A. Prokopenko
2003-01-01
Nonlinear analyses of hydrostatic bearing systems are necessary to adequately model the fluid-solid interaction. The dynamic properties of linear and nonlinear analytical models of hydrostatic bearings are compared in this paper. The analyses were based on the determination of the aperiodic border of transient processes with external step loads. The results show that the dynamic properties can be most effectively improved by increasing the hydrostatic bearing crosspiece width and additional pocket volume in a bearing can extend the load range for which the transient process is aperiodic, but an additional restrictor and capacitor (RC) chain must be introduced for increasing damping. The nonlinear analyses can also be used to predict typical design parameters for a hydrostatic bearing.
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.
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.
Stabilization of nonlinear systems by similarity transformations
Directory of Open Access Journals (Sweden)
Irina E. Zuber
1998-01-01
Full Text Available For a system x˙=A(x+b(xu, u(x=s∗(xx, x∈ℝn, where the pair (A(x,b(x is given, we obtain the feedback vector s(x to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T(A(x,b(x,g is established. The latter transforms matrix A(x into the Frobenius matrix, vector b(x into g, and an unknown feedback vector s(x into the first unit vector. The boundaries of A˜(y,g are determined by the boundaries of {∂kA(x∂xk,∂kb(x∂xk}, k=0,n−1¯. The stabilization of the transformed system is subject to the choice of the constant vector g.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Chaotic motion in nonlinear feedback systems
Energy Technology Data Exchange (ETDEWEB)
Baillieul, J. (Scientific Systems, Inc., Cambridge, MA); Brockett, R.W.; Washburn, R.B.
1980-11-01
New criteria are found which imply the existence of chaos in R/sup n/. These differ significantly from criteria previously reported in the mathematics literature, and in fact our methods apply to a class of systems which do not satisfy the hypotheses of the usual theorems on chaos in R/sup n/. The results are stated in such a way as to preserve the flavor of many well-known frequency-domain stability techniques. The results provide easily verifiable criteria for the existence of chaos in systems which are of dimension greater than one.
Interplay between dissipation and driving in nonlinear quantum systems
Energy Technology Data Exchange (ETDEWEB)
Vierheilig, Carmen
2011-07-01
In this thesis we investigate the interplay between dissipation and driving in nonlinear quantum systems for a special setup: a flux qubit read out by a DC-SQUID - a nonlinear quantum oscillator. The latter is embedded in a harmonic bath, thereby mediating dissipation to the qubit. Two different approaches are elaborated: First we consider a composite qubit-SQUID system and add the bath afterwards. We derive analytical expressions for its eigenstates beyond rotating wave approximation (RWA), by applying Van Vleck perturbation theory (VVPT) in the qubit-oscillator coupling. The second approach is an effective bath approach based on a mapping procedure, where SQUID and bath form an effective bath seen by the qubit. Here the qubit dynamics is obtained by applying standard procedures established for the spin-boson problem. This approach requires the knowledge of the steady-state response of the dissipative Duffing oscillator, which is studied within a resonant and an offresonant approach: The first is applicable near and at an N-photon resonance using VVPT beyond a RWA. The second is based on the exact Floquet states of the nonlinear driven oscillator. The dissipative qubit dynamics is described analytically for weak system-bath coupling and agrees well for both approaches. We derive the effect of the nonlinearity on the qubit dynamics, on the Bloch-Siegert shift and on the vacuum Rabi splitting. (orig.)
Computationally Efficient Nonlinearity Compensation for Coherent Fiber-Optic Systems
Institute of Scientific and Technical Information of China (English)
Likai Zhu; Guifang Li
2012-01-01
Split-step digital backward propagation (DBP) can be combined with coherent detection to compensate for fiber nonlinear impairments. A large number of DBP steps is usually needed for a long-haul fiber system, and this creates a heavy computational load. In a trade-off between complexity and performance, interchannel nonlinearity can be disregarded in order to simplify the DBP algorithm. The number of steps can also be reduced at the expense of performance. In periodic dispersion-managed long-haul transmission systems, optical waveform distortion is dominated by chromatic dispersion. As a result, the nonlinearity of the optical signal repeats in every dispersion period. Because of this periodic behavior, DBP of many fiber spans can be folded into one span. Using this distance-folded DBP method, the required computation for a transoceanic transmission system with full inline dispersion compensation can be reduced by up to two orders of magnitude with negligible penalty. The folded DBP method can be modified to compensate for nonlinearity in fiber links with non-zero residua dispersion per span.
On the power amplifier nonlinearity in MIMO transmit beamforming systems
Qi, Jian
2012-03-01
In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT. © 2012 IEEE.
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.
Observer Based Compensators for Nonlinear Systems
1989-03-31
coordinate change that achieves exact linearization could as well be calculated using the Hunt-Su linearization method. However, in our approach, we...the above, we obtain the exact linearization (implying that the development by the authors. system (52) satisfies the Hunt--Su condition): The multi
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...
Bifurcation criterion of faults in complex nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yagang, E-mail: yagangzhang@gmail.com [State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206 (China); Department of Mathematics and Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, SC 29208 (United States); Wang, Zengping [State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206 (China)
2014-03-01
In this paper, we introduce bifurcation theory into complex nonlinear systems. We adopt a novel approach to identify faults in electric circuit systems. After accidents occur without warning, with large numbers of complicated and high-precision calculations, we use bifurcation results of corresponding amplitude and frequency (period) to analyze their universal characteristics. Based on super attractive parameters, we have got the universal constant 4.6692… . The results from the present investigation imply that each fault in an electric circuit system must correspond to one or more bifurcation locations, which will provide a bifurcation criterion of faults in complex nonlinear systems. This research will have a significant theoretical value and engineering practical significance.
An intelligent online fault diagnostic scheme for nonlinear systems
Institute of Scientific and Technical Information of China (English)
Hing Tung MOK; Che Wai CHAN; Zaiyue YANG
2008-01-01
An online fault diagnostic scheme for nonlinear systems based on neurofuzzy networks is proposed in this paper.The scheme involves two stages.In the first stage,the nonlinear system is approximated by a neurofuzzy network,which is trained offline from data obtained during the normal operation of the system.In the second stage,residual is generated online from this network and is modelled by another neurofuzzy network trained online.Fuzzy rules are extracted from this network,and are compared with those in the fault database obmined under different faulty operations,from which faults are diagnosed.The performance of the proposed intelligent fault scheme is illustrated using a two.tank water level control system under different faulty conditions.
Robust nonlinear system identification using neural-network models.
Lu, S; Basar, T
1998-01-01
We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural-network models. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural-network literature, e.g., the backpropagation scheme and the genetic algorithms-based scheme, with slight modifications, can ensure the identification of the system nonlinearity. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information (FSDI) and noise-perturbed full-state-information (NPFSI), it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity. Results from several simulation studies have been included to demonstrate the effectiveness of these algorithms.
Global solution for coupled nonlinear Klein-Gordon system
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2007-01-01
The global solution for a coupled nonlinear Klein-Gordon system in twodimensional space was studied.First,a sharp threshold of blowup and global existenoe for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
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.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Robust fault diagnosis for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Zhanshan WANG; Huaguang ZHANG
2006-01-01
Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Robust Stabilization of a Class of passive Nonlinear Systems
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
OUTPUT FEEDBACK CONTROL FOR MIMO NONLINEAR SYSTEMS WITH EXOGENOUS SIGNALS
Institute of Scientific and Technical Information of China (English)
Ying ZHOU; Yuqiang WU
2006-01-01
The paper addresses the global output tracking of a class of multi-input multi-output(MIMO) nonlinear systems affected by disturbances, which are generated by a known exosystem. An adaptive controller is designed based on the proposed observer and the backstepping approach to asymptotically track arbitrary reference signal and to guarantee the boundedness of all the signals in the closed loop system. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme.
Adaptive practical output tracking of a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Qiangde WANG; Yuanwei JING; Siying ZHANG
2004-01-01
Focus is laid on the adaptive practical output-tracking problem of a class of nonlinear systems with high-order lower-triangular structure and uncontrollable unstable linearization. Using the modified adaptive addition of a power integrator technique as a basic tool, a new smooth adaptive state feedback controller is designed. This controller can ensure all signals of the closed-loop systems are globally bounded and output tracking error is arbitrary small.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The nat...
A Particle Filtering Approach to Change Detection for Nonlinear Systems
Directory of Open Access Journals (Sweden)
P. S. Krishnaprasad
2004-11-01
Full Text Available We present a change detection method for nonlinear stochastic systems based on particle filtering. We assume that the parameters of the system before and after change are known. The statistic for this method is chosen in such a way that it can be calculated recursively while the computational complexity of the method remains constant with respect to time. We present simulation results that show the advantages of this method compared to linearization techniques.
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.
Iterative Solution for Systems of Nonlinear Two Binary Operator Equations
Institute of Scientific and Technical Information of China (English)
ZHANGZhi-hong; LIWen-feng
2004-01-01
Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are imnroved and generalized.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
Predicting catastrophes in nonlinear dynamical systems by compressive sensing.
Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-04-15
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wang, Wen-Xu; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-01-01
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
Reduced-size kernel models for nonlinear hybrid system identification.
Le, Van Luong; Bloch, Grard; Lauer, Fabien
2011-12-01
This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.
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.
Novel procedure for characterizing nonlinear systems with memory: 2017 update
Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.
2017-05-01
The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.
Nonlinear analysis of green house systems
Directory of Open Access Journals (Sweden)
Ashraf Mohamed Mahmoud
2012-12-01
Full Text Available A numerical procedure based on energy minimization has been extended herein to analyze a system of two dimensional cable trusses called green houses. The joint displacements and member forces results are obtained and compared with a finite element computer program and previously published thesis. This study was done on three cases of span lengths. It was found that the effect of increasing the pylon height (H on the displacements and member forces is less than the case when reducing the value of (H. It was found also that the choice of the span length L = 16 m is more preferable than the others, because the rate of change of displacements and end forces was minimal compared with the others. It was also observed that when the number of spans is increased, the effect of the variation of the pylon height on the cable truss total weight will be vanished.
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Interpolation inequalities for weak solutions of nonlinear parabolic systems
Directory of Open Access Journals (Sweden)
Floridia Giuseppe
2011-01-01
Full Text Available Abstract The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type ∑ | α | ≤ m ( - 1 | α | D α a α X , D u + ∂ u ∂ t = 0 . The achieved results are inspired by the paper of Marino and Maugeri 2008, and the methods there applied. This note can be viewed as a continuation of the study of regularity properties for solutions of systems started in Ragusa 2002, continued in Ragusa 2003 and Floridia and Ragusa 2012 and also as a generalization of the paper by Capanato and Cannarsa 1981, where regularity properties of the solutions of nonlinear elliptic systems with quadratic growth are reached. Mathematics Subject Classification (2000 Primary 35K41, 35K55. Secondary 35B65, 35B45, 35D10
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.
Positive Solutions and Eigenvalue Intervals for Nonlinear Systems
Indian Academy of Sciences (India)
Jifeng Chu; Donal O'Regan; Meirong Zhang
2007-02-01
This paper deals with the existence of positive solutions for the nonlinear system $$(q(t)(p(t){u'}_i(t)))'+f^i(t,u)=0, \\quad 0 < t < 1, \\quad i=1,2,\\ldots,n.$$ This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here $u=(u_1,...,u_n)$ and $f^i,i=1,2,\\ldots,n$ are continuous and nonnegative functions, $p(t), q(t):[0, 1]→(0,∞)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for $$(q(t)(p(t){u'}_i(t)))'+ h_i(t)g^i(u)=0,\\quad 0 < t < 1, \\quad i=1,2,\\ldots,n.$$ The proof is based on a well-known fixed point theorem in cones.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Central suboptimal H ∞ control design for nonlinear polynomial systems
Basin, Michael V.; Shi, Peng; Calderon-Alvarez, Dario
2011-05-01
This article presents the central finite-dimensional H ∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H ∞ control problem to the corresponding optimal H 2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H 2 and H ∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H ∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H 2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H ∞ regulator available for the corresponding linearised system.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
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.
Spatio-temporal modeling of nonlinear distributed parameter systems
Li, Han-Xiong
2011-01-01
The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s
Nonlinear noninteger order circuits and systems an introduction
Arena, P; Fortuna, L; Porto, D
2001-01-01
In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic
Keesman, K.J.
2006-01-01
In this short paper for the panel discussion on ¿Experience and challenges in identification of non-linear systems¿ some major issues with respect to identification of non-linear biochemical and environmental systems are presented.
Thermostatistics of small nonlinear systems: Gaussian thermal bath.
Morgado, Welles A M; Duarte Queirós, Sílvio M
2014-08-01
We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Fast recursive filters for simulating nonlinear dynamic systems.
van Hateren, J H
2008-07-01
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities may depend on system variables, and the topology of the system may be complex, including feedback. Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the Hodgkin-Huxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. On a fairly complex model of the macaque retinal horizontal cell, it computes, for a given level of accuracy, one to two orders of magnitude faster than the fourth-order Runge-Kutta. The computational scheme has minimal memory requirements and is also suited for computation on a stream processor, such as a graphical processing unit.
Output tracking and regulation of nonlinear system based on Takagi-Sugeno fuzzy model.
Ma, X J; Sun, Z Q
2000-01-01
On the basis of the Takagi-Sugeno (TS) fuzzy model, this paper discusses in detail the following three problems: (1) output tracking of the nonlinear system; (2) output regulation of the nonlinear system via a state feedback; (3) output regulation of the nonlinear system via a error feedback. Numerical simulations are given to illustrate the soundness of these results and the effectiveness of the new methodology solving the output tracking and regulation problem of the nonlinear system.
Adaptive control of Hammerstein-Wiener nonlinear systems
Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong
2016-07-01
The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.
The relative degree enhancement problem for MIMO nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering
1995-07-01
The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for a completely decentralized feedback linearization result for at least one input-output channel.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet the implemen......In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...... the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace well-known filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state...
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Application of dynamic recurrent neural networks in nonlinear system identification
Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang
2006-11-01
An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.
On a mixed problem for a coupled nonlinear system
Directory of Open Access Journals (Sweden)
Marcondes R. Clark
1997-03-01
Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.
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.
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...
Extinction in Two-Species Nonlinear Discrete Competitive System
Directory of Open Access Journals (Sweden)
Liqiong Pu
2016-01-01
Full Text Available We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.
Lazy global feedbacks for quantized nonlinear event systems
Jerg, Stefan
2012-01-01
We consider nonlinear event systems with quantized state information and design a globally stabilizing controller from which only the minimal required number of control value changes along the feedback trajectory to a given initial condition is transmitted to the plant. In addition, we present a non-optimal heuristic approach which might reduce the number of control value changes and requires a lower computational effort. The constructions are illustrated by two numerical examples.
An efficient algorithm for solving nonlinear system of differential equations and applications
Directory of Open Access Journals (Sweden)
Mustafa GÜLSU
2015-10-01
Full Text Available In this article, we apply Chebyshev collocation method to obtain the numerical solutions of nonlinear systems of differential equations. This method transforms the nonlinear systems of differential equation to nonlinear systems of algebraic equations. The convergence of the numerical method are given and their applicability is illustrated with some examples.
Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
Zhang, Ruoxun; Tian, Gang; Yang, Shiping; Cao, Hefei
2015-05-01
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
Chaos in fractional-order autonomous nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M.; Sprott, J.C
2003-03-01
We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0,1], based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, and a mechanical chaotic 'jerk' model. In both models, numerical simulations are used to demonstrate that for different types of model nonlinearities, and using the proper control parameters, chaotic attractors are obtained with system orders as low as 2.1. Consequently, we present a conjecture that third-order chaotic nonlinear systems can still produce chaotic behavior with a total system order of 2+{epsilon}, 1>{epsilon}>0, using the appropriate control parameters. The effect of fractional order on the chaotic range of the control parameters is studied. It is demonstrated that as the order is decreased, the chaotic range of the control parameter is affected by contraction and translation. Robustness against model order reduction is demonstrated.
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Bandlimited computerized improvements in characterization of nonlinear systems with memory
Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.
2016-05-01
The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.
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 control techniques for an atomic force microscope system
Institute of Scientific and Technical Information of China (English)
Yongchun FANG; Matthew FEEMSTER; Darren DAWSON; Nader M.JALILI
2005-01-01
Two nonlinear control techniques are proposed for an atomic force microscope system.Initially,a learning-based control algorithm is developed for the microcantilever-sample system that achieves asymptotic cantilever tip tracking for periodic trajectories.Specifically,the control approach utilizes a learning-based feedforward term to compensate for periodic dynamics and high-gain terms to account for non-periodic dynamics.An adaptive control algorithm is then developed to achieve asymptotic cantilever tip tracking for bounded tip trajectories despite uncertainty throughout the system parameters.Simulation results are provided to illustrate the efficacy and performance of the control strategies.
Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics
Institute of Scientific and Technical Information of China (English)
Xin Yu; Na Duan
2009-01-01
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).
Nonlinearity and Chaos in the Magnetopause Shear System
Institute of Scientific and Technical Information of China (English)
傅绥燕; 濮祖荫; 刘振兴
1994-01-01
Chaotic phenomena in the magnetopause boundary region are studied in the MHD framework by using the Fourier truncation method. The MHD system is considered as a one-dimensional current sheet with a co-existing velocity shear and continuous energy transfer. The nonlinearity of the system, the evolution processes and properties of its different attractors are analysed. The possible routs and parameter conditions for chaos onset are also investigated. Numerical solutions show that when the Reynolds number (R) and the magnetic Reynolds number (Km) are very large, chaos appears in the system and its onset may provide a physical mechanism leading to turbulent reconnection at the magnetopause.
Synchronization in Complex Networks of Nonlinear Dynamical Systems
Wu, Chai Wah
2007-01-01
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ide
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.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
On Hamiltonian realization of time-varying nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Miyamoto, Hiroyuki; Ohmori, Hiromitsu
This work considers an adaptive servosystem design for a class of nonlinear systems that can be transformed into a canonical form. Although our proposed compensator is based on nonlinear internal model principle, overall control system structure adopts plug-in manner, i.e. the compensator to achieve tracking and disturbance rejection is placed outside the existed feedback controller. Moreover such compensator can be designed by solving error feedback nonlinear regulation problem and by using recursive procedure. An adaptation mechanism is introduced to cope with the unknown parameters of exosystem.
Nonlinear dynamical systems for theory and research in ergonomics.
Guastello, Stephen J
2017-02-01
Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.
On properties of nonlinear second order systems under nonlinear impulse perturbations
Directory of Open Access Journals (Sweden)
John R. Graef
1998-11-01
Full Text Available In this paper, we consider the impulsive second order system [ ddot{x}+f(x=0quad (teq t_{n};quad dot{x}(t_{n}+0=b_{n}dot{x}(t_{n} quad (t=t_{n} ] where $t_n=t_0+n,p$ $(p>0, n=1,2dots $. In a previous paper, the authors proved that if $f(x$ is strictly nonlinear, then this system has infinitely many periodic solutions. The impulses account for the main differences in the attractivity properties of the zero solution. Here, we prove that these periodic solutions are attractive in some sense, and we give good estimates for the attractivity region.
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.
Design for robust stabilization of nonlinear systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
赖旭芝; 文静; 吴敏
2004-01-01
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics
DEFF Research Database (Denmark)
True, Hans
1999-01-01
We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed....
Study of Super-Twisting sliding mode control for U model based nonlinear system
Zhang, Jianhua; Li, Yang; Xueli WU; Jianan HUO; Shenyang ZHUANG
2016-01-01
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 car...
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Nonlinear optimization of load allocation in a manufacturing system
Institute of Scientific and Technical Information of China (English)
GUO Cai-fen; WANG Ning-sheng
2006-01-01
Based on the queuing theory, a nonlinear optimization model is proposed in this paper. A novel transformation of optimization variables is devised and the constraints are properly combined so as to make this model into a convex one, from which the Lagrangian function and the KKT conditions are derived. The interiorpoint method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are drawn that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method for convex optimization needs fewer iterations with significant computational savings. It appears that many non-linear optimization problems in the industrial engineering field would be amenable to this method of solution.
Autonomous Navigation System Using a Fuzzy Adaptive Nonlinear H∞ Filter
Directory of Open Access Journals (Sweden)
Fariz Outamazirt
2014-09-01
Full Text Available Although nonlinear H∞ (NH∞ filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞ filter is proposed for the Unmanned Aerial Vehicle (UAV localization problem. Based on a real-time Fuzzy Inference System (FIS, the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter.
Nonlinear relaxation field in charged systems under high electric fields
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K
2000-07-01
The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - On-Sager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared. (author)
Swarming behaviors in multi-agent systems with nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Yu, Wenwu, E-mail: wenwuyu@gmail.com [Department of Mathematics, Southeast University, Nanjing 210096 (China); School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001 (Australia); Chen, Guanrong [Department of Electronic Engineering, City University of Hong Kong, Hong Kong (China); Cao, Ming [Faculty of Mathematics and Natural Sciences, ITM, University of Groningen (Netherlands); Lü, Jinhu [Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China); Zhang, Hai-Tao [Department of Control Science and Engineering, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074 (China)
2013-12-15
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Nonlinear problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed.
Swarming behaviors in multi-agent systems with nonlinear dynamics.
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao
2013-12-01
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Nonlinear Dynamics of Controlled Synchronizations of Manipulator System
Directory of Open Access Journals (Sweden)
Qingkai Han
2014-01-01
Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.