Kybernetika 50 no. 4, 512-529, 2014

Realizability of precompensators in linear multivariable systems: A structural approach

Javier Ruiz-León and Eduardo CastañedaDOI: 10.14736/kyb-2014-4-0512

Abstract:

In this work, given a linear multivariable system, the problem of static state feedback realization of dynamic compensators is considered. Necessary and sufficient conditions for the existence of a static state feedback that realizes the dynamic compensator (square or full column rank compensator) are stated in structural terms, i. e., in terms of the zero-pole structure of the compensator, and the eigenvalues and the row image of the controllability matrix of the compensated system. Based on these conditions a formula is presented to find the state feedback matrices realizing a given compensator. It is also shown that the static state feedback realizing the compensator is unique if and only if the closed-loop system is controllable.

Keywords:

linear systems, feedback control, compensator realizability

Classification:

93C05, 93B52

paper.pdf

References:

  1. E. Castañeda and J. Ruiz-León: New results on the state feedback realizability of full column rank precompensators. In: 6th International Conf. on Electrical Engineering, Computing Science and Automatic Control, Toluca 2009.   CrossRef
  2. F. R. Gantmacher: Matrix Theory. Chelsea Publishing Co. 1959.   CrossRef
  3. M. L. J. Hautus and M. Heymann: Linear feedback: An algebraic approach. SIAM J. Control Optim. 16, (1978), 83-105.   CrossRef
  4. A. N. Herrera: Static realization of dynamic precompensators. IEEE Trans. on Automatic Control. 37 (1992), 1391-1394.   CrossRef
  5. A. N. Herrera: On the static realization of dynamic precompensators and some related problems. In: Proc. European Control Conference ECC-91, Grenoble 1991.   CrossRef
  6. A. Isidori and A. S. Morse: State feedback implementation of cascade compens. Syst. Control Lett. 8 (1986), 63-68.   CrossRef
  7. T. Kailath: Linear Systems. Prentice Hall, 1980.   CrossRef
  8. V. Kučera: Exact model matching, polynomial equation approach. Int. J. Syst. Sci. 12 (1981), 1477-1484.   CrossRef
  9. V. Kučera: Transfer function equivalence of feedback/feedforward compensators. Kybernetika 12 (1998), 610-624.   CrossRef
  10. V. Kučera: Realizing the action of a cascade compensator by state feedback. In: Proc. 11th IFAC World Congress. Tallin 1990, vol. 2, pp. 207-211.   CrossRef
  11. V. Kučera and A. N. Herrera: Static realization of dynamic precompensators for descriptor systems. System \& Control Letters. 16 (1991), 273-276.   CrossRef
  12. J. Ruiz-León, J. L. Orozco and O. Begovich: Closed-loop structure of decouplable linear multivariable systems. Kybernetika 41 (2005), 33-45.   CrossRef