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S.H. Zak

Bio: S.H. Zak is an academic researcher from Purdue University. The author has contributed to research in topics: Multivariable calculus & Variable structure system. The author has an hindex of 1, co-authored 1 publications receiving 1821 citations.

Papers
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Journal ArticleDOI
01 Mar 1988
TL;DR: In this paper, the design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented.
Abstract: 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. >

1,860 citations


Cited by
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Journal ArticleDOI
TL;DR: A tutorial account of variable structure control with sliding mode is presented, introducing in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach.
Abstract: 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. >

2,884 citations

Journal ArticleDOI
TL;DR: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
Abstract: 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.

2,714 citations

Journal ArticleDOI
TL;DR: An accurate assessment of the so-called chattering phenomenon is offered, which catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding Mode control research.
Abstract: 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.

2,082 citations

Journal ArticleDOI
TL;DR: The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters.
Abstract: The basic concepts, mathematics, and design aspects of variable-structure systems as well as those with sliding modes as a principle operation mode are treated. The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters. The control algorithms and data processing used in variable structure systems are analyzed. The potential of sliding mode control methodology is demonstrated for versatility of electric drives and functional goals of control. >

1,890 citations

Journal ArticleDOI
TL;DR: This paper presents a treatment of discrete variable structure control systems, and a recently introduced "reaching law approach" is conveniently used to develop the control law for robust control.
Abstract: This paper presents a treatment of discrete variable structure control systems. The purpose is to lay a foundation upon which design of such type of systems can be made properly. Phenomena of switching, reaching, and quasi-sliding mode are investigated thoroughly. Terms pertaining to discrete variable structure control are defined. A method of quasi-sliding mode design is given. The inherently existing quasi-sliding mode band is analyzed. A recently introduced "reaching law approach" is conveniently used to develop the control law for robust control. Comments are given regarding chattering. The design technique is illustrated by a simulated system. >

1,428 citations