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An Algebraic Method for Pole Placement in Multivariable Systems

  • M. de la Sen
Article
  • 82 Downloads

Abstract

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.

Keywords

Sampling Period Algebraic Equation Weak Condition Kronecker Product Controller Parameterization 
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References

  1. [1]
    Araki, M. and Hagiwara, T., Pole-Assignment by Multirate Sampled-Data Output Feedback, Int. J. of Control, 1096, 46(6):1661-1673.Google Scholar
  2. [2]
    Berg, M. C. Amit, N. and Powelll, J. D., Multirate Digital Control System Design, IEEE Trans. Automat. Control, 1988, 33(12):1139-1150.Google Scholar
  3. [3]
    Berg, M. C. Mason, G. S. and Yang, M. S., New Multirate Sampled-Data Control Structure and Synthesis Algorithm, 1992, 15(5):1183-1191.Google Scholar
  4. [4]
    Chalam, V. V., Adaptive Control Systems (New York: Marcel Dekker).Google Scholar
  5. [5]
    De La Sen, M., Aplication of the Nonperiodic Sampling to the Identifiability and Model Matching Problems in Dynamic Systems, Int. J. of System Sci.1983,14(4):367-383.Google Scholar
  6. [6]
    De La Sen, M., A Method for Improving the Adaptation transient using adaptive sampling, Int. J. of Control, 1984, 15(3):315-328.Google Scholar
  7. [7]
    De La Sen, M., A Method for Improving the Adaptation Transient Using Adaptive Sampling, Int. J. of Control, 1984,40(4):639-665.Google Scholar
  8. [8]
    De La Sen, M. and Etxebarria, V., Discretized Models and the Use of Multirate Sampling for Finite Spectrum Assignment in Linear System with Commensurate Time DelaysGoogle Scholar
  9. [9]
    Etxebarria, V., Adaptive Control with a forgetting factor with Multple Samples Between Parameter Adjustments, Int. J. of Control, 1992, 55(5):1189-1200.Google Scholar
  10. [10]
    Fuster, A., and Guilien, J. M., New Modelling Technique for Aperiodic Sampling of Linear Systems, Int. J. of Control, 1987,45(3):951-968.Google Scholar
  11. [11]
    Fuster, A., and Guilien, J. M., Questions of Controllability and observability for nonuniformly Sampled Sata Systems, Int. J. of Control, 1088,47(4):248-252.Google Scholar
  12. [12]
    Fuster, A., External Descriptions for Multivariable Systems Sampled in an Aperiodic Way, IEEE Trans. Automat. Control, 1988, 33(4):381-384.Google Scholar
  13. [13]
    Fuster, A., A Joint Criterion for Reachability and Observability of Nonuniformly Sampled Discrete Systems, IEEE Trans. Automat. Control, 1991,36(11):1281-1284.Google Scholar
  14. [14]
    Karslyan, E. V., Frequency Domain Synthesis of a Class of Multivariable Control Systems. Automation and Remote Control, 1991, 52,324-334.Google Scholar
  15. [15]
    Luo, N. and Feng, C., A New Method for Suppressing High-Frequency Chattering in Variable Structure Control Systems, Proc. of IFAC Symp. on Nonlinear Control Systems Design, 1989, 1: 117-122.Google Scholar
  16. [16]
    Regalia, P. A. and Mitra, S. K., Kronecker Products, Unitary Matrices and Signal Processsing Application, SIAM Review, 1989,31(4):586-613.Google Scholar
  17. [17]
    O'Reilly, J., Observers for Linear Systems (London: Academic Press).Google Scholar
  18. [18]
    O'Reilly, J. and Leithead, W. E., Multivariable Control by Individual Channel Design, Int. J. of Control, 1991,54(1):1-46.Google Scholar
  19. [19]
    Porter, B. and Crossley, R., Modal Control. Theory and Applications (London: Taylor and francis).Google Scholar
  20. [20]
    Tao, G. and Ioannou, P. A., Robust Stability and Performance Improvement of Discrete-time Adaptive Control System, Int. J. of Control, 1989,50(5):1835-1855.Google Scholar
  21. [21]
    Tao, G., Model-Reference Adaptive-Control of Multivariable Plants with delays, Int. J. of Control, 1992, 55(2):393-414.Google Scholar
  22. [22]
    Tao, G., On Robust Adaptive-Control of Robot Manipulators, Automatica, 1992,28(4):803-807.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • M. de la Sen
    • 1
  1. 1.Department de Electricidad y Electrónica Facultad de CienciasUniversidad del Pais VascoSpain

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