Output regulation for linear distributed parameter systems

Author

Bymes, C.I. ; Laukó, István G. ; Gilliam, David S. ; Shubov, Victor I.

Author_Institution

Dept. of Syst. Sci. & Math., Washington Univ., St. Louis, MO, USA

Volume

45

Issue

12

fYear

2000

fDate

12/1/2000 12:00:00 AM

Firstpage

2236

Lastpage

2252

Abstract

This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system

Keywords

distributed parameter systems; eigenvalues and eigenfunctions; linear systems; multidimensional systems; stability; state feedback; tracking; damped hyperbolic system; detectability; disturbance attenuation; error feedback; finite dimensional exogenous system; full state feedback; geometric theory; linear distributed parameter systems; output regulation; parabolic systems; periodic tracking; regulator equations; set point control; stabilizability; Control systems; Distributed parameter systems; Eigenvalues and eigenfunctions; Linear feedback control systems; Nonlinear equations; Output feedback; Regulators; Signal generators; State feedback; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.895561

Filename

895561