Sliding modes and fast periodic oscillations of singularly perturbed relay control systems

Author

Fridman, L.

Author_Institution

Dept. of Math., Samara State Archit. & Civil Eng. Acad.

Volume

1

fYear

1998

fDate

21-26 Jun 1998

Firstpage

569

Abstract

As a mathematical model of chattering in the small neighbourhood of switching surface in the sliding mode systems, we examine the singularly perturbed relay control systems (SPRCS). The sufficient conditions for existence of fast periodic solutions in such systems are found. Their stability is investigated. It is proved that the slow motions in such SPRCS are approximately described using equations obtained from the equations for the slow variables of SPRCS by averaging along fast periodic motions. It is shown that in the case when the original SPRCS contains the relay control linearly the averaged equations and equations describe the motions of the reduced system in the sliding mode

Keywords

reduced order systems; relay control; singularly perturbed systems; stability; variable structure systems; chattering; fast periodic oscillations; reduced system; relay control; singularly perturbed systems; sliding mode systems; stability; sufficient conditions; Actuators; Civil engineering; Control system synthesis; Control systems; Electronic mail; Equations; Mathematics; Relays; Sliding mode control; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1998. Proceedings of the 1998

Conference_Location

Philadelphia, PA

ISSN

0743-1619

Print_ISBN

0-7803-4530-4

Type

conf

DOI

10.1109/ACC.1998.694734

Filename

694734