Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

Compensation for secondary uncertainty in electro-hydraulic servo system by gain adaptive sliding mode variable structure control

Based on consideration of the differential relations between the immeasurable variables and measurable variables in electro-hydraulic servo system,adaptive dynamic recurrent fuzzy neural networks(ADRFNNs) were employed to identify the primary uncertainty and the mathematic model of the system was turned into an equivalent linear model with terms of secondary uncertainty.At the same time,gain adaptive sliding mode variable structure control(GASMVSC) was employed to synthesize the control effort.The results show that the unrealization problem caused by some system's immeasurable state variables in traditional fuzzy neural networks(TFNN) taking all state variables as its inputs is overcome.On the other hand,the identification by the ADRFNNs online with high accuracy and the adaptive function of the correction term's gain in the GASMVSC make the system possess strong robustness and improved steady accuracy,and the chattering phenomenon of the control effort is also suppressed effectively.

Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-varying Delays and Unknown Dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

Sliding Mode Variable Structure Control for Visual Servoing System

A visual servoing tracking controller is proposed based on the sliding mode control theory in order to achieve strong robustness against parameter variations and external disturbances. A sliding plane with time delay compensation is presented by the pre-estimate of states. To reduce the chattering of the sliding mode controller, a modified exponential reaching law and hyperbolic tangent function are applied to the design of visual controller and robot joint controller. Simulation results show that the visual servoing control scheme is robust and has good tracking performance.

An Approach to Polynomial NARX/NARMAX Systems Identification in a Closed-loop with Variable Structure Control

Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model. The identification of such models has been widely explored in literature. The majority of these approaches are for the open-loop identification. However, for reasons such as safety and production restrictions, open-loop identification cannot always be done. In such cases, closed-loop identification is necessary. This paper presents a two-step approach to closed-loop identification of the polynomial NARX/NARMAX systems with variable structure control （VSC）. First, a genetic algorithm （GA） is used to maximize the similarity of VSC signal to white noise by tuning the switching function parameters. Second, the system is simulated again and its parameters are estimated by an algorithm of the least square （LS） family. Finally, simulation examples are given to show the validity of the proposed approach.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

Nonlinear and Variable Structure Excitation Controller for Power System Stability

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 affme 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.

VARIABLE STRUCTURE CONTROL APPLIED IN ELECTRO-HYDRAULIC SERVO SYSTEM WITH ANN

The variable structure control （VSC） theory is applied to the electro-hydraulic servo system here. The VSC control law is achieved using Lyapunov method and pole placement. To eliminate the chattering phenomena, a saturation function is adopted. The proposed VSC approach is fairly robust to load disturbance and system parameter variation. Since the distortion. including phase lag and amplitude attenuation occurs in the system sinusoid response, the amplitude and phase control （APC） algorithm, based on Adaline neural network and using LMS algorithm, is developed for distortion cancellation. The APC controller is simple and can on-line adjust, thus it gives accurate tracking.

Adaptive variable structure control for large-scale time-delayed systems with unknown nonlinear dead-zone

The problem of adaptive fuzzy control for a class of large-scale, time-delayed systems with unknown nonlinear dead-zone is discussed here. Based on the principle of variable structure control, a design scheme of adaptive, decentralized, variable structure control is proposed. The approach removes the conditions that the dead-zone slopes and boundaries are equal and symmetric, respectively. In addition, it does not require that the assumptions that all parameters of the nonlinear dead-zone model and the lumped uncertainty are known constants. The adaptive compensation terms of the approximation errors axe adopted to minimize the influence of modeling errors and parameter estimation errors. By theoretical analysis, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, with tracking errors converging to zero. Simulation results demonstrate the effectiveness of the approach.

Decentralized Variable Structure Control of Complex Giant Singular Uncertainty Systems

This paper, at the first time, considers the problem of decentralized variable structure control of complex giant singular uncertainty systems by using the property of diagonally dominant matrix and Frobenius-Person theorem. The splendid selection of switching manifold for each subsystem makes the design relatively straightforward and can be easily realized. An illustrate example is given.

PREDICTIVE VARIABLE STRUCTURE CONTROL FOR A CLASS OF NONLINEAR SYSTEM

Nonlinear sliding m ode predictive controller is designed for a class of nonlinear system w ith unm odeled dynam ic characteristics and nonlinear term . The m ethod is based on nonlinear opti- m alpredictive control. The variable structure controllaw m inim izes the quadratic index ofa predic- tive sliding m ode, w hich contains thecostfunction ofcontrolpreventing the controleffectfrom satu- ration for in m ostpracticalim plem entation the controlinputs are bounded by physicalconstraints and energy constraints. According to the im m easurable states, the variable structure observer for nonlin- ear system sisadapted. The variablestructure system m ethod isaptto therealization ofobserverw ith variable param eters and uncertainty. The proofshow s thatthe states ofthe observer asym ptotically convergence to the realstates ofthe system although itisofuncertainty and nonlinear term s. Final- ly, the digitalsim ulation results prove the effectiveness ofthe proposed m ethod.

Design of variable structure controller for uncertain time-delay singular system

To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control,and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circumstances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear state feedback. The design guarantees the asymptotical stablity of switching manifolds,and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifolds in limited time. A numerical example is given to demonstrate the feasibility and simplicity of the design method.

Coordinating optimization-based sliding mode variable structure control for electro-hydraulic servo system

A sliding mode variable structure control （SMVSC） based on a coordinating optimization algorithm has been developed. Steady state error and control switching frequency are used to constitute the system performance indexes in the coordinating optimization, while the tuning rate of boundary layer width （BLW） is employed as the optimization parameter. Based on the mathematical relationship between the BLW and steady-state error, an optimized BLW tuning rate is added to the nonlinear control term of SMVSC. Simulation experiment results applied to the positioning control of an electro-hydraulic servo system show the comprehensive superiority in dynamical and static state performance by using the proposed controller is better than that by using SMVSC without optimized BLW tuning rate. This succeeds in coordinately considering both chattering reduction and high-precision control realization in SMVSC.

Stabilization Variable Structure Control for Singular Decoupling Motor System

This paper describes the important application of variable structure control (VSC) theory on induction motor (IM) decoupling control system. A design scheme using singular system variable structure control method for a decoupling IM system is presented. The scheme is shown to be robust to parametric variations and external disturbances. Simulation results show the stability and effectiveness of the proposed scheme

Nonlinear variable structure excitation and steam valving controllers for power system stability

A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper. On the basis of the classical dynamic equations of a generator, excitation control and steam valving control are simultaneously considered. Design of these controllers combines the differential geometry theory with the variable structure controlling theory. The mathematical model in the form of ＂an affine nonlinear system＂ is set up for the control design of a large-scale power plant. The dynamic performance of the nonlinear variable structure controllers proposed for a single machine connected to an infinite bus power system is simulated. Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.

Variable structure control for descriptor Markovian jump systems subject to partially unknown transition probabilities

The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.

Adaptive synchronization of a class of chaotic systems via variable structure control

The synchronization problem under two cases is considered. One is that the bound on the uncertainty existing in the controller is known, the other is that the bound is unknown. In the latter case, the simple adaptation laws for upper bound on the norm of the uncertainty is proposed. Using this adaptive upper bound, a variable structure control is designed. The proposed method does not guarantee the convergence of the adaptive upper bound to the real one but makes the system asymptotically stable.

VARIABLE STRUCTURE CONTROL OF INDEFINITE-DIMENSIONAL SYSTEMS

In lhis paper, we study the variable structure control of indefinite-dimensionalcontrol systems with the functional analysis method. The reaching conditions, stabilityconditions and the approximating conditions of sliding mode, as well as the generalform of the variable structure control law are given. and the elementary frame of thevariable structure control of indefinite-dimensional systems is built.

APPROXIMATION LAWS OF DISCRETE-TIME VARIABLE STRUCTURE CONTROL SYSTEMS

Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also considered,which is very important in practical systems. Finally two simulation examples showing the effectiveness of the approximation laws are proposed.