Realizability of precompensators in linear multivariable systems: A structural approach

Javier Ruiz; Eduardo Castañeda

Kybernetika (2014)

  • Volume: 50, Issue: 4, page 512-529
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Ruiz, Javier, and Castañeda, Eduardo. "Realizability of precompensators in linear multivariable systems: A structural approach." Kybernetika 50.4 (2014): 512-529. <http://eudml.org/doc/262028>.

@article{Ruiz2014,
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.},
author = {Ruiz, Javier, Castañeda, Eduardo},
journal = {Kybernetika},
keywords = {linear systems; feedback control; compensator realizability; linear systems; feedback control; compensator realizability},
language = {eng},
number = {4},
pages = {512-529},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Realizability of precompensators in linear multivariable systems: A structural approach},
url = {http://eudml.org/doc/262028},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Ruiz, Javier
AU - Castañeda, Eduardo
TI - Realizability of precompensators in linear multivariable systems: A structural approach
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 4
SP - 512
EP - 529
AB - 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.
LA - eng
KW - linear systems; feedback control; compensator realizability; linear systems; feedback control; compensator realizability
UR - http://eudml.org/doc/262028
ER -

References

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  1. Castañeda, E., Ruiz-León, J., 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. 
  2. Gantmacher, F. R., Matrix Theory., Chelsea Publishing Co. 1959. MR0107649
  3. Hautus, M. L. J., Heymann, M., 10.1137/0316007, SIAM J. Control Optim. 16, (1978), 83-105. Zbl0385.93015MR0476024DOI10.1137/0316007
  4. Herrera, A. N., 10.1109/9.159579, IEEE Trans. on Automatic Control. 37 (1992), 1391-1394. Zbl0755.93042MR1183101DOI10.1109/9.159579
  5. Herrera, A. N., On the static realization of dynamic precompensators and some related problems., In: Proc. European Control Conference ECC-91, Grenoble 1991. MR1183101
  6. Isidori, A., Morse, A. S., 10.1016/0167-6911(86)90031-9, Syst. Control Lett. 8 (1986), 63-68. MR0863276DOI10.1016/0167-6911(86)90031-9
  7. Kailath, T., Linear Systems., Prentice Hall, 1980. Zbl0870.93013MR0569473
  8. Kučera, V., 10.1080/00207728108963832, Int. J. Syst. Sci. 12 (1981), 1477-1484. Zbl0476.93025MR0652175DOI10.1080/00207728108963832
  9. Kučera, V., Transfer function equivalence of feedback/feedforward compensators., Kybernetika 12 (1998), 610-624. Zbl1274.93104MR1695366
  10. Kučera, V., Realizing the action of a cascade compensator by state feedback., In: Proc. 11th IFAC World Congress. Tallin 1990, vol. 2, pp. 207-211. 
  11. Kučera, V., Herrera, A. N., 10.1016/0167-6911(91)90015-7, System & Control Letters. 16 (1991), 273-276. Zbl0728.93037MR1102213DOI10.1016/0167-6911(91)90015-7
  12. Ruiz-León, J., Orozco, J. L., Begovich, O., Closed-loop structure of decouplable linear multivariable systems., Kybernetika 41 (2005), 33-45. Zbl1249.93079MR2130483

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