A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >

Variable structure control: a survey

The design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented. Using the Utkin-Drazenovic method of equivalent control and generalized Lyapunov stability concepts, the VSC design is described in a unified manner. Complications that arise due to multiple inputs are examined, and several approaches useful in overcoming them are developed. Recent developments are investigated, as is the kinship of VSC and the deterministic approach to the control of uncertain systems. All points are illustrated by numerical examples. The recent literature on VSC applications is surveyed. >

Variable structure control of nonlinear multivariable systems: a tutorial

A new approach for the design of variable structure control (VSC) of nonlinear systems is presented. It is based on a new method called the reaching law method, and is complemented by a sliding-mode equivalence technique. They facilitate the design of the system dynamics in all three modes of a VSC system including the sliding, reaching, and steady-state modes. Invariance and robustness properties are discussed. The approach is applied to a robot manipulator to demonstrate its effectiveness. >

Variable structure control of nonlinear systems: a new approach

1. Introduction: An Overview of Classical Sliding Mode Control 2. Differential Inclusions and Sliding Mode Control 3. Higher-Order Sliding Modes 4. Sliding Mode Observers 5. Dynamic Sliding Mode Control and Output Feedback 6. Sliding Modes, Passivity, and Flatness 7. Stability and Stabilization 8. Discretization Issues 9. Adaptive and Sliding Mode Control 10. Steady Modes in Relay Systems with Delay 11. Sliding Mode Control for Systems with Time Delay 12. Sliding Mode Control of Infinite-Dimensional Systems 13. Application of Sliding Mode Control to Robotic Systems 14. Sliding Modes Control of the Induction Motor: A Benchmark Experimental Test

Sliding Mode Control in Engineering

Sliding-mode control (SMC) has been studied extensively for over 50 years and widely used in practical applications due to its simplicity and robustness against parameter variations and disturbances. Despite the extensive research activities carried out, the key technical problems associated with SMC remain as challenging research questions due to demands for new industrial applications and technological advances. In this respect, soft computing (SC) is a rather recent development in intelligent systems which has provided alternative means for adaptive learning and control to overcome the key SMC technical problems. Substantial efforts in integration of SMC with SC have been placed in recent years with various successes. In this paper, we provide the state of the art of recent developments in SMC systems with SC, examining key technical research issues and future perspectives.

Sliding-Mode Control With Soft Computing: A Survey

Multivariate variable structure systems in the sliding mode are studied using a geometric approach. The properties of system order reduction and disturbance rejection are proved using projector the...

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Analysis and design of variable structure systems using a geometric approach

The analysis of variable-structure systems in the sliding mode yields the concept of equivalent control, which leads naturally to a new method for determining the zeros and zero directions of square linear multivariable systems. The analysis presented is conceptually easy and computationally attractive.

Variable-structure systems and system zeros

A new geometric method of calculating multivariable system zeros and zero directions is presented by considering a particular choice of state feedback control law. This control law has been motivated by the study of variable structure systems in the sliding mode. The cases of singular and non-singular CB have been treated separately.

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Computation of the zeros and zero directions of linear multivariable systems

Linear model-following control (LMFC) is an efficient control method that avoids the difficulty of specifying a performance index which is usually encountered in the application of optimal control ti multivariable control systems

Variable Structure Control of Adaptive Model Following Systems

The celebrated method of Ackermann for eigenvalue assignment of single-input controllable systems is revisited in this paper, contributing an elegant proof. The new proof facilitates a compact formula which consequently permits an extension of the method to what we call incomplete assignment of eigenvalues. The inability of Ackermann’s formula to deal with uncontrollable systems is considered a weakness inherent in the method. The notion of incomplete assignment leads to a straightforward generalization of our method to eigenvalue assignment of uncontrollable systems, thus mitigating such a drawback of a popular method. Further results concerning the incomplete assignment are stated, verified, and commented. Such results reveal the trace of the state matrix $A$ a worthy feature pertinent to an open loop system. Finally, four numerical examples are worked out to demonstrate cases of incomplete, and uncontrollable eigenvalues assignment. The examples consider a case where the structure of the feedback matrix can be easily simplified. The paper ends with a commentary brief concerning some commonly used MATLAB commands for eigenvalue assignment.

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O.M.E. El-Ghezawi

Papers

Analysis and design of variable structure systems using a geometric approach

Variable-structure systems and system zeros

Computation of the zeros and zero directions of linear multivariable systems

Variable Structure Control of Adaptive Model Following Systems

Ackermann’s Method: Revisited, Extended, and Generalized to Uncontrollabe Systems