TABLE OF CONTENTS

Page

ABSTRACT i

TABLE OF CONTENTS ii

LIST OF FIGURES iii

CHAPTER

1. INTRODUCTION

2. VARIABLE STRUCTURE SYSTEMS

3. SLIDING MODE CONTROL (SMC)

4. MODEL FOLLOWING SMC

5. CHATTERING PROBLEM IN SMC AND REMEDIES

6. BOUNDS OF UNCERTAINTY - ADAPTIVE CONTROL

7. NEED FOR FULL STATE VECTOR AND USE OF OBSERVER

8. INVARIANCE AND MATCHING CONDITIONS - BACKSTEPPING

9. CURRENT DEVELOPMENTS IN SMC APPLICATIONS

10. CONCLUSION

REFERENCES

ABSTRACT

Variable structure control was first proposed and elaborated in the early 1950’s in the Soviet Union by Emelyanov and several co-researchers. Variable structure systems has been a subject of intense theoretical research at the Institute of Control Sciences of the erstwhile USSR Academy of Sciences since the beginning of 1960s. In their pioneer works, the plant considered was a linear second-order system modeled in phase variable form. Since then, VSC has developed into a general design method being examined for a wide spectrum of system types including nonlinear systems, multi-input/multi-output systems, discrete-time models, large-scale and infinite-dimensional systems, and stochastic systems. The most distinguished feature of VSC is its ability to result in very robust control systems; the system is completely insensitive to parametric uncertainty and external disturbances or “invariant”. The sliding mode (SMC) is the major mode of operation in variable structure systems.

Most of the real life processes in mechanical, electrical, aerospace engineering and other areas when characterised by differential equations have discontinuity. The discontinuity is due to certain peculiarities in the system behavior. The simplest case is the Coulomb friction in mechanical systems which is not defined in points where velocity equals zero. If such discontinuities are deliberately introduced on certain surfaces in the system state space, then motions is a sliding mode may occur in the system. The discontinuous nature of the control action in the feedback channels results in switching between two distinctively different system structures (or components) such that a new type of system motion, called sliding mode, exists in a manifold. This results in superb system performance which includes insensitivity to parameter variations, and complete rejection of disturbances. The variations of dynamic characteristics of the control plant pose a central problem in automatic control. Thus, discontinuous control systems provides an effective tool for solving control problems for complex dynamic plants. This means unlike continuous systems with non-measurable disturbances where the condition of invariance requires use of infinitely high gains, discontinuous systems require use of finite control gains. From a technological point of view also, the increasing use of electric inertia-less actuators built around power electronics which operate in a switching mode only naturally favors use of discontinuous control algorithms over employing continuous control algorithms where the control is shaped as a high frequency discontinuous signal whose mean value is equal to the desired continuous control.

However there are many problems faced in the attempt to employ the properties of sliding modes for the design of automatic control systems. Various publications on the matter show diverse viewpoints leading to diverse sliding mode equations. This paper is an attempt to survey the current developments vis-à-vis remedies to the problems in SMC.