Variable Structure Control Problem Research Articles

Picking Robot Visual Servo Control Based on Modified Fuzzy Neural Network Sliding Mode Algorithms

Through an analysis of the kinematics and dynamics relations between the target positioning of manipulator joint angles of an apple-picking robot, the sliding-mode control (SMC) method is introduced into robot servo control according to the characteristics of servo control. However, the biggest problem of the sliding-mode variable structure control is chattering, and the speed, inertia, acceleration, switching surface, and other factors are also considered when approaching the sliding die surface. Meanwhile, neural network has the characteristics of approaching non-linear function and not depending on the mechanism model of the system. Therefore, the fuzzy neural network control algorithm can effectively solve the chattering problem caused by the variable structure of the sliding mode and improve the dynamic and static performances of the control system. The comparison experiment is carried out through the application of the PID algorithm, the sliding mode control algorithm, and the improved fuzzy neural network sliding mode control algorithm on the picking robot system in the laboratory environment. The result verified that the intelligent algorithm can reduce the complexity of parameter adjustments and improve the control accuracy to a certain extent.

The Research Based on Fuzzy Sliding Mode Control for Linear Double Inverted Pendulum

This paper involves a linear double inverted pendulum system whose the state space model is established by Lagrange function. In order to solve the chattering problem of the conventional quasi-sliding mode variable structure control, this linear double inverted pendulum system applies the fuzzy control theory to adjust the parameterwhich is in the sliding mode variable structure control law. Then the fuzzy theory is utilized to design the sliding mode and deduce the fuzzy sliding mode reaching law. The significance of this method is that it diffuses the control signal, reduces or avoids the chattering phenomenon of sliding mode control. For the most, the simulation results show that the linear double inverted pendulum system based on fuzzy sliding mode variable structure control not only retains the strong robustness of sliding mode variable structure control, but also improves the dynamic quality of the system and weakens the buffeting of the system. Thus the method is proved to have certain research.

Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.

Variable Structure Control Based Wavelet Transforms for Linear Time-Invariant Distributed Parameter Systems

The distributed parameter systems(DPS) are usually described by the partial differential equations(PDEs). Compared the variable structure control problem of DPS with that of the lumped parameter systems(LPS) , it is more complicated because the problem of variable structure control for DPS is often closely related to the theory of the differential operator or integral operator. Based on Haar wavelets transform, the operational matrixes and their characteristics, this paper attempts to propose a new approach for the variable structure control problem of a class linear time-invariant DPS by converting it into that of lumped parameter systems(LPS) and then makes use of the mature research methods of LPS to design the variable structure control problem so as to solve the variable structure control problem of DPS. The proposed method in this paper has the advantages of the simpler algorithm, less computation and better control effect. The simulation results also prove that it is an efficient algorithm for DPS.

Sliding Mode Variable Structure Control Design for a Kind of Nonlinear Discrete Singular Uncertain Systems with Time-Delay

In this paper, the quasi-sliding mode variable structure control problem for interval coefficients nonlinear discrete singular uncertain systems with time-delay is researched, and it can be decomposed to two lower dimension systems with ordinary coefficients. According to some results on robust stability of discrete singular systems with time-delay, the quasi-switching manifold with difference compensator are designed, then with the quasi-sliding mode variable structure control law, the system comes to stability. At last, the feasibility and effectiveness of the results are explained by a numerical example.

Optimal Sliding Mode Control for Linear Singualr System with Input and State Time-Delays

Synthetic problem of variable structure control (VSC) for linear singular system with input and state time-delays is studied. Firstly, the original system with both input and state time-delays is written into a form without time-delay by a linear transformation. Secondly, the system without time-delay is decomposed into two low dimensional subsystems by a restricted system equivalent decomposed method. Thirdly, the quadratic performance index optimal control technique is introduced to design the optimal sliding mode for the restricted equivalent subsystems. By applying reaching law approach, the selected control law ensures that the solution trajectories of the system reach the switching manifold in finite time and have low chattering in the sliding motion. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed method.

Design of adaptive variable structure controllers for T–S fuzzy time‐delay systems

AbstractIn this paper, the adaptive variable structure control problem is presented for Takagi–Sugeno (T–S) fuzzy time‐delay systems with uncertainties and external disturbances. The fuzzy sliding surfaces for the T–S fuzzy time‐delay system are proposed by using a Lyapunov function, and we design the adaptive variable structure controllers such that the global T–S fuzzy time‐delay system confined on the fuzzy sliding surfaces is asymptotically stable. One example is given to illustrate the effectiveness of our proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.

Sliding mode variable structure control for parameter uncertain stochastic systems with time-varying delay

In this paper, the variable structure control problem for a class uncertain of stochastic system with time-varying delay is investigated. Firstly, a new concept of the subordinated reachability of the sliding motion is introduced to approach approximately the specified sliding surface. The variable structure control law is then proposed to ensure that the sliding motion is subordinated reachable. Furthermore, a sufficient condition for mean-square asymptotical stability of the sliding motion is given. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained results.

Output feedback variable structure control for a class of uncertain switched systems

AbstractThis paper considers the output feedback variable structure control problem for a class of uncertain switched systems. A single sliding surface is constructed using only output information. Robust stability of the sliding motion restricted to the sliding surface is achieved and complete invariance to the matched and the mismatched uncertainties is guaranteed via a hysteresis switching law based on a reduced order observer. Output feedback variable structure controllers are given to guarantee that the redefined sliding surface is reached in finite time. A numerical example illustrates the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Variable Structure Control of Uncontrollable Quantum Systems

This paper formulates and solves a variable structure control problem for the state control of quantum systems. Following the concept of wavefunction controllability, we first present a specific quantum system which is wavefunction uncontrollable under the action of any one of two controllers with different fixed structures. However, we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers. An extension and the potential applications of the proposed control strategy are briefly discussed and the general steps of variable structure control design for this class of quantum systems are also presented. The variable structure control scheme provides an alternative quantum engineering approach for the manipulation of quantum systems.

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi-Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T-S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T-S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.

A Model Reference Variable Structure Controller Design for Time-Delay Systems with Input Nonlinearities.

The problem of model reference variable structure control for a class of perturbed time-delay systems with input nonlinearities is investigated. In this paper, the variable structure control is incorporated with an adaptive law to drive the state error between the desired model state and the controlled plant state to zero. The adaptive law is utilized for adapting the unknown upper bounds of the perturbations, and variable structure control is used for enhancing the robustness of the controlled systems. Hence, the information of the upper bounds of the perturbations is not required beforehand. It also shows that the proposed method ensures the property of globally asymptotically stable or uniformly ultimate boundness for the overall controlled system. Finally, a practical example is given to illustrate the feasibility of the proposed control methodology.

Variable Structure Control for a Class of Systems with Mismatched Uncertainties

AbstractThe problem of Variable Structure Control (VSC) for a class of systems with mismatched uncertainties is studied in this paper. The systems considered in this paper can be transformed into two staged sub‐systems. The first subsystem is a linear system with uncertainties U1, and its inputs are the state variables of the second subsystem. The second sub‐system, having the same dimension as the inputs, is a nonlinear system with uncertainties U2 and its inputs are the control inputs for the original system. In fact, U1 and U2 are the mismatched uncertainties and matched uncertainties of the original system, respectively. Based on the quadratic stabilization for the first sub‐system, the desired values of the second state variables are synthesized by Linear Matrix Inequality (LMI) technique, and the switching function vector is constructed based on the errors between the values of the second state variables and their desired values. Furthermore, the variable structure controller is derived by the reachable condition for the sliding‐mode such that the closed‐loop system can enter and retain the sliding‐mode. Meanwhile, the closed‐loop system has the stable sliding‐mode motion.

Variable Structure Control of Uncertain Dynamical Systems with Time-Varying Delay

The problem of variable structure control of uncertain time-delay dynamical systems is discussed. Two types of sliding surfaces are considered, and a class of variable structure control strategies are proposed. It is shown that for the uncertainties satisfying the matching conditions, the resulting variable structure control systems are invariant, i.e. the systems are completely insensitive to such uncertainties. Some sufficient conditions are also derived such that the robust stability of the resulting variable structure control systems with unmatched uncertainties can be guaranteed. In addition, the time-varying delay is assumed only to be any bounded and continuous function, and all of the control laws, the sliding surfaces, and the sufficient conditions are independent of the delay. Therefore, the results obtained in the paper are also applicable to the systems with perturbed time-delay.

Variable structure control of stochastic systems

In this paper, the problem of variable structure control of stochastic (SVSC) systems is proposed and the corresponding variable structure control strategies with complete and incomplete state information are established. The concepts of stochastic sliding mode and sliding motion band are introduced which may be regarded as the basic characteristics of SVSC systems. Robustness of SVSC systems is considered and a general design procedure for SVSC systems is presented. The effectiveness of the proposed control method is shown by simulation results.

Penalty method and maximum principle for nonsmooth variable-structure control problems

We consider the penalty method for a nonsmooth minimax control problem with interdependent variables. A scheme for the derivation of necessary optimality conditions and their application for the analysis of a particular technological process is described.