Advertisement

Synthesis of LTI Controllers for MIMO LTI Plants

  • Oded Yaniv
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 509)

Abstract

The objective of this chapter is to present quantitative design techniques for synthesizing a controller and a prefilter for a MIMO plant (either known or highly uncertain), in order to achieve desired closed loop specifications. The basic idea is to break the design process down into a series of stages. Each stage of this sequential process is a simplified SISO or MISO feedback problem which is supported by the QFT MatlabTM Toolbox. A solution to the original problem is then simply a combination of the solutions obtained at each stage.

Keywords

MIMO System Disturbance Rejection Nominal Case Closed Loop Response Quantitative Feedback Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes and References

  1. Horowitz, I., Quantitative Synthesis of Uncertain Multiple Input-Output Feedback Systems, International Journal of Control, Vol. 30, no. 1, 1979b, pp. 81–106.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Horowitz, I., and Loecher, C., Design of a 3 x 3 Multivariable Feedback System with Large Plant Uncertainty, International Journal of Control, Vol. 33, no. 4, 1979, pp. 677–699.MathSciNetCrossRefGoogle Scholar
  3. Golubev, B., and Horowitz, I., Plant Rational Transfer Function Approximation from Input Output Data, International Journal of Control, Vol. 36, no. 4, 1982, pp. 711–723.zbMATHCrossRefGoogle Scholar
  4. Sidi, M., and P. Rosenbaum, P., A New Approach for the Design of Multivariable Feedback Systems, International Journal of Control, Vol. 37, no. 6, 1983, pp. 1355–1370.zbMATHCrossRefGoogle Scholar
  5. Yaniv, O., and Chait, Y., A simplified Multi-Input Multi-Output Formulation for the Quantitative Feedback Theory, Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, Vol. 114, no. 2 1992, pp. 179–185.zbMATHCrossRefGoogle Scholar
  6. Yaniv, O., Synthesis of Uncertain MIMO Feedback Systems for Gain and Phase Margin at Different Channel Breaking Points, Automatica, Vol. 28, no. 5, 1992, pp. 1017–1020.zbMATHCrossRefGoogle Scholar
  7. Yaniv, O., Robust Feedback Synthesis for Margins at the Plant Input, Automatica, Vol. 31, no. 2, 1995a, pp. 333–336.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Yaniv, O., Quantitative Design Method for MIMO Uncertain Plants to Achieve Prescribed Diagonal Dominant closed-loop Minimum Phase Tolerances, International Journal of Control, Vol. 27, no. 2, 1988, pp. 519–528.MathSciNetCrossRefGoogle Scholar
  9. Yaniv, O., Arbitrarily Small Sensitivity in Multiple-Input-Output Uncertain Feedback Systems, Automatica, Vol. 27, no. 3, 1991, pp. 565–568.MathSciNetCrossRefGoogle Scholar
  10. Houpis, C.H., Sating, R.R., Rasmussen, S. and Sheldon, S., Quantitative Theory Technique and Applications, International Journal of Control, Vol. 59, no. 1, 1994, pp. 39–70.zbMATHCrossRefGoogle Scholar
  11. Horowitz, I., Oldak, S., and Yaniv, O., An Important Property of Non Minimum Phase Multiple Input Multiple Output Feedback Systems, International Journal of Control, Vol. 44, no. 3, 1986, pp. 677–688.zbMATHCrossRefGoogle Scholar
  12. Horowitz, I., Feedback Systems with Nonlinear Uncertain Plants, International Journal of Control, Vol. 36, no. 1, 1982, pp. 155–171.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Horowitz, I., and Loecher, C., Design of a 3 x 3 Multivariable Feedback System with Large Plant Uncertainty, International Journal of Control, Vol. 33, no. 4, 1979, pp. 677–699.MathSciNetCrossRefGoogle Scholar
  14. Vidyasagar, M., Control System Synthesis: A Factorization Approach, The MIT Press, Cambridge, Mass., 1985.zbMATHGoogle Scholar
  15. Vidyasagar, M., Bertschmann, R.K., and Sallaberger, C.S., Some Simplifications of the Graphical Nyquist Criterion, IEEE Transactions on Automatic Control, Vol. 33, no. 3, 1988, pp. 301–303.zbMATHCrossRefGoogle Scholar
  16. Walk, J.G., Horowitz, I., and Houpis, H.C., Quantitative Synthesis of Highly Uncertain, Multiple Input Output, Flight Control System for the Forward Swept Wing X-29 Aircraft, Proceedings of the IEEE 1984 National Aerospace and Electronics Conference, Dayton, 21–25 May 1984, Vol. 1, pp. 576–583.Google Scholar
  17. Yaniv, O., and Horowitz, I., A Quantitative Design Method for MIMO Linear Feedback Systems Having Uncertain Plants, International Journal of Control, Vol. 43, no. 2, 1986, pp. 401–421.zbMATHCrossRefGoogle Scholar
  18. Horowitz, I., and Yaniv, O., Quantitative Cascaded Multiple-Input Multiple-Output Synthesis by an Improved Method, International Journal of Control, Vol. 42, no. 2, 1985, pp. 305–331.zbMATHCrossRefGoogle Scholar
  19. Boje, E., Quantitative Design of Scheduled Controllers for Plants with Measurable Transport Rates, Proceedings of the 111th Triennial World Congress of the International Federation of Automatic Control, Tallin, USSR, 13–17 Aug. 1990, Vol. 1, pp. 173–176.Google Scholar
  20. Sidi, M., Feedback Synthesis with Plant Ignorance, Non-Minimum Phase, and Time-Domain Tolerances, Automatica, Vol. 12, 1976, pp. 265–271.CrossRefGoogle Scholar
  21. Horowitz, I., and Sidi, M., Optimum Synthesis of Non-Minimum Phase Feedback Systems with Plant Uncertainty, International Journal of Control, Vol. 27, no. 3, 1978, pp. 361–386.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Sidi, M., On Maximization of Gain-Bandwidth in Sampled Systems, International Journal of Control Vol. 32, 1980, pp. 1099–1109.zbMATHCrossRefGoogle Scholar
  23. Horowitz, I., and Y. Liau, Y., Limitations of Non-Minimum Phase Feedback Systems, International Journal of Control,Vol. 40, no. 5, 1984, pp. 10031015.Google Scholar
  24. Francis, A.F., and Zames, G., On Hoc-Optimal Sensitivity Theory for SISO Feedback Systems, IEEE Transactions on Automatic Control, Vol. 29, no. 1, 1984, pp. 9–16.MathSciNetzbMATHCrossRefGoogle Scholar
  25. Freudenberg, J.S., and Looze, D.P., Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems, IEEE Transactions on Automatic Control, Vol. 30, no. 6, 1985, pp. 555–565.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Freudenberg, J.S., and Looze, D.P., A Sensitivity Tradeoff for Plants with Time Delay, IEEE Transactions on Automatic Control, Vol 32, no. 2, 1987, pp. 99–104.MathSciNetzbMATHCrossRefGoogle Scholar
  27. Middleton, R.H., Trade-offs in Linear Control System Design, Automatica, Vol. 27, no. 2, 1991, pp. 281–292.MathSciNetzbMATHCrossRefGoogle Scholar
  28. Cheng, V.H.L., and Desoer, C.A., Limitations On the Closed-Loop Transfer Function Due to Right-Half Plane Transmission Zeros of the Plant, IEEE Transactions on Automatic Control, Vol. 25, no. 6, 1980, pp. 1218–1220.zbMATHCrossRefGoogle Scholar
  29. Gomez, G.I., and Goodwin, G.C., Integral Constraints on Sensitivity Vectors for Multivariable Linear Systems, Automatica, Vol. 32, no. 4, 1996, pp. 499–518.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Oded Yaniv
    • 1
  1. 1.Faculty of EngineeringTel Aviv UniversityIsrael

Personalised recommendations