Decentralized PID Controller Design

  • Zhizheng WuEmail author
  • Azhar Iqbal
  • Foued Ben Amara


In this chapter, a decentralized PID control structure is proposed for a magnetic fluid deformable mirror (MFDM)-based AO system. Two decentralized PID control algorithms that can be used to control the surface shape of continuous surface mirrors, including MFDMs, are presented. First, the development of a decoupled plant model, to be used in the controller design, is presented in Sect. 7.1. In Sect. 7.2, a decentralized proportional-plus-integral (PI) controller is presented, which is designed based on the assumption that the plant model is fully decoupled and the wavefront corrector (WFC) dynamics are omitted. To overcome stability robustness issues and improve the control performance, a decentralized robust proportional-integral-derivative (PID) controller is presented in Sect. 7.3, where the uncertainties in the decoupled nominal dynamic model of the plant are considered. The robust PID controller design problem is transformed into a mixed \( {H_2}/{H_\infty } \) multi-objective optimization problem. The control performance of the two control algorithms is verified in the AO setup in Sect. 7.4, followed by the summary in Sect. 7.5.


Root Mean Square Error Root Mean Square Linear Matrix Inequality Static Output Feedback Adaptive Optic System 
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  1. Albertos P, Prez PA, Sala A (2004) Multivariable control systems: an engineering approach. Springer, LondonzbMATHGoogle Scholar
  2. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiazbMATHCrossRefGoogle Scholar
  3. Brousseau D, Borra EF, Thibault S (2007) Wavefront correction with a 37–actuator ferrofluid deformable mirror. Opt Express 15:18190–18199CrossRefGoogle Scholar
  4. Cao YY, Lam J, Sun YX (1998) Static output feedback stabilization: an LMI approach. Automatica 34(12):1641–1645zbMATHCrossRefGoogle Scholar
  5. Chen T, Francis B (1996) Optimal sampled data control systems. Springer, LondonzbMATHGoogle Scholar
  6. Laird P, Caron N, Rioux M, Borra EF, Ritcey AM (2006) Ferrofluid adaptive mirrors. Appl Opt 45(15):3495–3500CrossRefGoogle Scholar
  7. Phillips CL (2000) Feedback control system. Prentice-Hall, Englewood CliffsGoogle Scholar
  8. Zhou K, Doyle J, Golver K (1995) Robust and optimal control. Prentice Hall, Upper Saddle RiverGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Shanghai UniversityShanghaiChina, People’s Republic
  2. 2.University of TorontoTorontoCanada

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