Distributed control design for parabolic evolution equations: application to compressor stall control

We present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection. By taking advantage of the spatial invariance of the equations, a linear controller is constructed (following...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control 2004-08, Vol.49 (8), p.1247-1258
Main Authors: Hagen, G., Mezic, I., Bamieh, B.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer science
control theory
systems
Control design
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Controllers
Distributed control
Exact sciences and technology
Laplace equations
Mathematical models
Nonlinear equations
Nonlinear systems
Optimal control
Studies
Sufficient conditions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection. By taking advantage of the spatial invariance of the equations, a linear controller is constructed (following Bamieh et al.) via linear quadratic control of each Fourier mode. We derive sufficient conditions for the linear controller to stabilize the full nonlinear system. Concepts such as controller decentralization, finite-dimensional implementation, inverse-optimality, and beneficial nonlinearities are discussed. In the second part of this paper, these developments are applied to a model of axial compressor control with air injection. The unactuated model is derived following the work of Moore and Greitzer and the model coupled with air injection actuation follows the works of Behnken et al. and Weigl et al. A numerical study of the control designs is pursued and the comparison of controller performance is discussed. The techniques presented here are expected to be useful for distributed control design of a much broader class of nonlinear reaction-diffusion systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2004.832200