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 synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.

Sliding order and sliding accuracy in sliding mode control

Presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.

A control engineer's guide to sliding mode control

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 methodology is presented of feedback control to achieve accurate tracking for a class of nonlinear time-varying systems in the presence of disturbances and parameter variations. The methodology uses in its idealized form piecewise continuous feedback control laws, resulting in the state trajectory `sliding' along a discontinuity surface in the state space. The idealized form of the methodology results in perfect tracking of the required signals; however certain non-idealities associated with its implementation cause the trajectory to 'chatter' along the sliding surface resulting in the generation of an undesirable high-frequency component which may excite high-frequency unmodelled dynamics of the control systems. To rectify this situation, it is shown how continuous control laws which approximate the discontinuous control law may be used to obtain disturbance and parameter variation insensitive tracking. At the same time, the continuous control laws decrease the extent of unwanted high-frequency signals.

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Tracking control of non-linear systems using sliding surfaces with application to robot manipulators

In this paper a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems. A new pole placement method and a decomposition of near optimal high-gain regulator problems are presented.

A singular perturbation analysis of high-gain feedback systems

A new design concept for adaptive model-following control systems capable of shaping the error transient responses is developed using the theory of variable structure systems and sliding mode. It is shown that the resulting model-following control system exhibits adaptive properties inherent in adaptive model-following systems designed by existing methods. An aircraft control problem which has been approached using various model-following techniques is considered and a performance comparison with the present design is made.

Design of variable structure model-following control systems

This paper presents a guide to sliding mode control for practising control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogues implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.

Sliding sector for variable structure system- On discrete variable structure control with switching sector- Variable structure control of nonlinear sampled data systems by second order sliding modes- On sampled data variable structure control systems- Sliding mode control of systems with delayed states and controls- On global stabilization of nonlinear dynamical systems- A general canonical form for sliding mode control of nonlinear systems- Handling stiction with variable structure control- Equivalent value filters in disturbance estimation and state observation- Sliding mode control of a car-like mobile robot using single-track dynamic model- Park vector based sliding mode control of UPS with unbalanced and nonlinear load- Dynamical adaptive sliding mode control of observable minimum-phase uncertain nonlinear systems- Symbolic computing tools for nonsmooth dynamics and control- Sliding mode control with gain scheduled hyperplane for LPV plant- A study on parameterized output feedback sliding mode controller- Sliding mode tracking control of systems with unstable zero dynamics- On second order sliding mode controllers- A tale of two discontinuities- The problem of chattering: an averaging approach

K.D. Young

Papers

A control engineer's guide to sliding mode control

A singular perturbation analysis of high-gain feedback systems

Design of variable structure model-following control systems

A control engineer's guide to sliding mode control

Variable Structure Systems, Sliding Mode and Nonlinear Control