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IMA Journal of Mathematical Control and Information Advance Access originally published online on October 9, 2008
IMA Journal of Mathematical Control and Information 2008 25(4):447-459; doi:10.1093/imamci/dnn008
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Generalized internal model architecture for gain-scheduled control

Wei Xie{dagger}

School of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China

Toshio Eisaka{ddagger}

Department of Computer Sciences, Kitami Institute of Technology, 165 Koencho, Kitami, Hokkaido 0908507, Japan

{dagger} Email: weixie{at}scut.edu.cn

{ddagger} Corresponding author. Email: eisaka{at}cs.kitami-it.ac.jp

Received on June 13, 2007; Revision received March 23, 2008. Accepted on March 28, 2008

A two-degree-of-freedom controller architecture and its design strategy for linear parameter-varying (LPV) systems, where the dependent parameters are assumed to be measurable, are proposed in the generalized internal model control (GIMC) framework. First, coprime factorization and Youla parameterization for LPV systems are introduced based on a parameter-dependent Lyapunov function. Then, the GIMC architecture for linear time-invariant systems is extended to LPV systems with these descriptions. Based on this architecture, good tracking performance and good robustness (disturbance rejection) are compatibly achieved by a nominal controller and a conditional controller, respectively. Furthermore, each controller design problem is formulated in terms of linear matrix inequalities related to each L2-gain performance. Finally, a simple design example is illustrated.

Keywords: internal model control; gain-scheduled control; two-degree-of-freedom; linear parameter-varying systems; Youla parameterization.


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