DocumentCode :
2267702
Title :
Controller design for linear time-periodic delay systems via a symbolic approach
Author :
Ma, Haitao ; Deshmukh, Venkatesh ; Butcher, Eric ; Averina, Victoria
Author_Institution :
Dept. of Mech. Eng., Alaska Univ., Fairbanks, AK, USA
Volume :
3
fYear :
2003
fDate :
4-6 June 2003
Firstpage :
2126
Abstract :
This paper presents a symbolic method for the delayed state feedback controller (DSFC) design for the linear time-periodic delay (LTPD) systems that are open loop unstable. By using shifted Chebyshev polynomials, the closed loop "monodromy matrix" of the LTPD system is obtained symbolically in terms of controller parameters. The stability criterion is given in terms of the eigenvalues of such a symbolic monodromy matrix. This enables one to design a delayed state feedback controller (DSFC) to asymptotically stabilize the original unstable dynamic system. Two controllers designs are presented. The first design is a constant gain DSFC and the second one is a periodic gain DSFC. The periodic gain DSFC has a larger region of stability in the parameter space than the constant gain DSFC. The asymptotic stability of the LTPD system obtained by the proposed method is illustrated in numerical examples by stabilizing an open loop unstable delayed Mathieu equation.
Keywords :
Chebyshev approximation; asymptotic stability; closed loop systems; control system synthesis; delay systems; linear systems; matrix algebra; open loop systems; periodic control; polynomials; stability criteria; state feedback; Chebyshev polynomials; Mathieu equation; asymptotic stability; closed loop system; controller design; delayed state feedback controller; linear time periodic delay systems; monodromy matrix; open loop unstable system; stability criterion; symbolic approach; Chebyshev approximation; Control systems; Delay lines; Delay systems; Eigenvalues and eigenfunctions; Linear feedback control systems; Open loop systems; Polynomials; Stability criteria; State feedback;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference, 2003. Proceedings of the 2003
ISSN :
0743-1619
Print_ISBN :
0-7803-7896-2
Type :
conf
DOI :
10.1109/ACC.2003.1243388
Filename :
1243388
Link To Document :
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