Time-Varying Sliding Modes for Second and Third Order Systems

By: Andrzej Bartoszewicz, Aleksandra Nowacka-Leverton

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Paperback | 3 April 2009

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A principal objective of control engineering is to design control systems which are robust with respect to external disturbances and modelling uncertainty. This objective may be well achieved using the sliding mode technique - which is the main subject of this monograph. More precisely, "Time-Varying Sliding Modes for Second and Third Order Systems" focuses on only one, but very important aspect of the sliding mode system design, i.e. the problem of the sliding plane selection. In this self-contained monograph, the main notions and concepts used in the field of variable structure systems and sliding mode control are presented before in the main part the issue of the switching surface design is discussed. This is done by considering two standard plants, which are very often encountered in the control engineering practice: the second and the third order nonlinear and possibly time-varying systems.

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"This monograph discusses the design of switching lines (or surfaces) for sliding-mode control of systems ... . All derivations are carried out explicitly, arriving at analytical formulas and graphs, which may make the book most useful for engineers and students in the control design community who want to see the derivation behind classical control design principles." (Jan Sieber, Zentralblatt MATH, Vol. 1192, 2010)

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Introduction	p. 1
Preliminaries	p. 1
Variable Structure Systems	p. 1
Sliding Mode Control	p. 4
Previous Work on Sliding Mode Control with Time-Varying Switching Surfaces	p. 10
Time-Varying Sliding Modes for the Second Order Systems	p. 17
Control Strategy	p. 18
Switching Line Design Minimising IAE	p. 23
Switching Line Design Subject to Input Signal Constraint	p. 24
Switching Line Design Subject to Velocity Constraint	p. 33
Switching Line Design Subject to Input Signal and Velocity Constraints	p. 42
Switching Line Design Minimising ITAE	p. 46
Switching Line Design Subject to Input Signal Constraint	p. 47
Switching Line Design Subject to Velocity Constraint	p. 56
Switching Line Design Subject to Input Signal and Velocity Constraints	p. 62
Time-Varying Sliding Modes for the Third Order Systems	p. 67
Control Strategy	p. 68
Switching Plane Design Minimising IAE	p. 72
Switching Plane Design Subject to Input Signal Constraint	p. 73
Switching Plane Design Subject to Acceleration Constraint	p. 86
Switching Plane Design Subject to Velocity Constraint	p. 99
Switching Plane Design Subject to Acceleration and Velocity Constraints	p. 107
Switching Plane Design Subject to Acceleration and Input Signal Constraints	p. 114
Switching Plane Design Subject to Input Signal and Velocity Constraints	p. 117
Switching Plane Design with Acceleration, Velocity and Input Signal Constraints	p. 122
Switching Plane Design Minimising ITAE	p. 139
Switching Plane Design Subject to Input Signal Constraint	p. 140
Switching Plane Design Subject to Acceleration Constraint	p. 149
Switching Plane Design Subject to Velocity Constraint	p. 156
Switching Plane Design Subject to Acceleration and Velocity Constraints	p. 161
Switching Plane Design Subject to Acceleration and Input Signal Constraints	p. 166
Switching Plane Design Subject to Input Signal and Velocity Constraints	p. 169
Switching Plane Design with Acceleration, Velocity and Input Signal Constraints	p. 173
Conclusions	p. 181
References	p. 183
Index	p. 191
Table of Contents provided by Ingram. All Rights Reserved.

Time-Varying Sliding Modes for Second and Third Order Systems

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