Asymptotic properties of root locus for distributed parameter systems

Author

Byrnes, C.I. ; Gilliam, D.S.

Author_Institution

Dept. of Math., Arizona State Univ., Tempe, AZ, USA

fYear

1988

fDate

7-9 Dec 1988

Firstpage

45

Abstract

The authors examine various examples of boundary feedback control in the context of a root locus theory for distributed parameter systems. Using root locus principles they design proportional-error and proportional-rate feedback laws for some explicit examples which are shown to achieve closed-loop stability. They note that while it is possible to develop in abstract a geometric state space interpretation of root locus methods, in the context of singular perturbations, it turns out that even for some very simple examples the corresponding root-locus plots have somewhat disturbing discontinuities, which do not exist in the lumped case and seem not to be explained in an abstract state-space setting. This phenomenon is illustrated in a classical example due to F. Rellich (1969)

Keywords

distributed parameter systems; feedback; root loci; stability; boundary feedback control; closed-loop stability; distributed parameter systems; geometric state space interpretation; proportional-error; proportional-rate; root locus; singular perturbations; Boundary conditions; Control systems; Design methodology; Distributed parameter systems; Eigenvalues and eigenfunctions; Feedback loop; Hilbert space; Mathematics; Stability; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Conference_Location

Austin, TX

Type

conf

DOI

10.1109/CDC.1988.194267

Filename

194267