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LMI-Based Decentralized PID Controller Design With Application to the Shape Control of Magnetic Fluid Deformable Mirrors

[+] Author Affiliations
Zhizheng Wu

Shanghai University, Shanghai, China

Azhar Iqbal, Foued Ben Amara

University of Toronto, Toronto, ON, Canada

Paper No. IMECE2010-40215, pp. 185-194; 10 pages
doi:10.1115/IMECE2010-40215
From:
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME

abstract

In this paper, a decentralized robust PID controller design method is proposed for multi-input multi-output systems. The system model is first decoupled in the low frequency range, and only the diagonal entries in the DC-decoupled plant model are retained. To deal with the resulting unmodeled high frequency dynamics, a decentralized robust PID controller design method is proposed, where the robust stability and transient response performance of the resulting closed loop system are formulated as a multi-objective H∞ /H2 static output feedback problem. The desired parameters of the PID controller are determined by solving a static output feedback problem using linear matrix inequalities (LMIs). Finally, the performance of the proposed control algorithm is experimentally evaluated on the adaptive optics system involving a prototype magnetic fluid deformable mirror (MFDM). The experimental results illustrate the effectiveness of the proposed control algorithm for the MFDM surface shape tracking in the closed loop adaptive optics system.

Copyright © 2010 by ASME

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