MIMO PID Controller Synthesis with Closed-Loop Pole Assignment

  • Tsu-Shuan Chang
  • A. Nazli Gündeş
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 14)

For certain classes of linear, time-invariant, multi-input multi-output plants, a systematic synthesis is developed for stabilization using Proportional + Integral + Derivative (PID) controllers, where the closed-loop poles can be assigned to the left of an axis shifted away from the origin. The real-parts of the closed-loop poles can be smaller than any given negative value for some of these classes. The classes that admit PID-controllers with this property of small negative real-part assignability of closed-loop poles include stable and some unstable plants.


Simultaneous stabilization and tracking PID control Integral action Stability margin 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aström, K. J. and Hagglund, T. (1995). PID Controllers: Theory, Design, and Tuning, Second Edition. Instrument Society of America, Research Triangle Park, NCGoogle Scholar
  2. 2.
    Ho, M.-T., Datta, A., and Bhattacharyya, S. P. (1998). An extension of the generalized Hermite-Biehler theorem: relaxation of earlier assumptions. Proceedings of 1998 American Control Conference, 3206–3209Google Scholar
  3. 3.
    Silva, G. J., Datta, A., and Bhattacharyya, S. P. (2005). PID Controllers for Time-Delay Systems. Birkhäuser, Boston, MAGoogle Scholar
  4. 4.
    Gündeş, A. N. and Ozguler, A. B. (2007). PID stabilization of MIMO plants. IEEE Trans. Automatic Control, 52:1502–1508CrossRefGoogle Scholar
  5. 5.
    Goodwin, G. C., Graebe, S. F., and Salgado, M. E. (2001). Control System Design. Prentice-Hall, Upper Saddle River, NJGoogle Scholar
  6. 6.
    Gündeş, A. N. and Desoer, C. A. (1990). Algebraic Theory of Linear Feedback Systems with Full and Decentralized Compensators. Lecture Notes in Control and Information Sciences, 142, Springer, GermanyCrossRefGoogle Scholar
  7. 7.
    Vidyasagar, M. (1985). Control System Synthesis: A Factorization Approach. MIT Press, Cambridge, MAGoogle Scholar
  8. 8.
    Chang, T. S. and Gündeş, A. N. (2007). PID controller design with guaranteede stability margin for MIMO systems. Proc. World Congress Eng. Comput. Sci., San Francisco, USA, 52: 747–752Google Scholar
  9. 9.
    Johansson, K. H. (2000). The quadruple-tank process: A multivariable laboratory process with an adjustable zero. IEEE Trans. Contr. Sys. Technol., 8:456–465CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V 2009

Authors and Affiliations

  • Tsu-Shuan Chang
    • 1
  • A. Nazli Gündeş
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of CaliforniaDavis

Personalised recommendations