Continuous-time input-output decoupling for sampled-data systems

Osvaldo Maria Grasselli; Laura Menini

Kybernetika (1999)

  • Volume: 35, Issue: 6, page [721]-735
  • ISSN: 0023-5954

Abstract

top
The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned hybrid control problem to an equivalent purely continuous-time decoupling problem. A simple necessary and sufficient condition for the existence of a solution of such a continuous-time decoupling problem is given for square plants (with and without the additional requirement of the asymptotic stability of the over-all control system), together with a parameterisation of all the decoupling controllers. Moreover, for square plants, it is shown that, whenever the hybrid control problem admits a solution, any solution of the corresponding decoupling problem for the discrete-time model of the given continuous-time system is also a solution of the hybrid control problem.

How to cite

top

Grasselli, Osvaldo Maria, and Menini, Laura. "Continuous-time input-output decoupling for sampled-data systems." Kybernetika 35.6 (1999): [721]-735. <http://eudml.org/doc/33458>.

@article{Grasselli1999,
abstract = {The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned hybrid control problem to an equivalent purely continuous-time decoupling problem. A simple necessary and sufficient condition for the existence of a solution of such a continuous-time decoupling problem is given for square plants (with and without the additional requirement of the asymptotic stability of the over-all control system), together with a parameterisation of all the decoupling controllers. Moreover, for square plants, it is shown that, whenever the hybrid control problem admits a solution, any solution of the corresponding decoupling problem for the discrete-time model of the given continuous-time system is also a solution of the hybrid control problem.},
author = {Grasselli, Osvaldo Maria, Menini, Laura},
journal = {Kybernetika},
keywords = {continuous-time control; input-output decoupling; sampled-data systems; unity feedback control; continuous-time control; input-output decoupling; sampled-data systems; unity feedback control},
language = {eng},
number = {6},
pages = {[721]-735},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Continuous-time input-output decoupling for sampled-data systems},
url = {http://eudml.org/doc/33458},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Grasselli, Osvaldo Maria
AU - Menini, Laura
TI - Continuous-time input-output decoupling for sampled-data systems
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 6
SP - [721]
EP - 735
AB - The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned hybrid control problem to an equivalent purely continuous-time decoupling problem. A simple necessary and sufficient condition for the existence of a solution of such a continuous-time decoupling problem is given for square plants (with and without the additional requirement of the asymptotic stability of the over-all control system), together with a parameterisation of all the decoupling controllers. Moreover, for square plants, it is shown that, whenever the hybrid control problem admits a solution, any solution of the corresponding decoupling problem for the discrete-time model of the given continuous-time system is also a solution of the hybrid control problem.
LA - eng
KW - continuous-time control; input-output decoupling; sampled-data systems; unity feedback control; continuous-time control; input-output decoupling; sampled-data systems; unity feedback control
UR - http://eudml.org/doc/33458
ER -

References

top
  1. Argoun M. B., Vegte J. van de, 10.1080/00207178008961074, Internat. J. Control 31 (1980), 4, 665–675 (1980) MR0572135DOI10.1080/00207178008961074
  2. Chen. C. T., Linear System Theory and Design, Holt, Rinehart and Winston, New York 1984 
  3. Descusse J., Lafay J. F., Malabre M., Solution to Morgan’s problem, IEEE Trans. Automomat. Control AC-33 (1988), 8, 732–739 (1988) Zbl0656.93018MR0950794
  4. Desoer C. A., Gündes A. N., Decoupling linear multiinput multioutput plants by dynamic output feedback: an algebraic theory, IEEE Trans. Automat. Control AC-31 (1986), 8, 744–750 (1986) Zbl0603.93029MR0848673
  5. Dickman A., Sivan R., 10.1109/TAC.1985.1103964, IEEE Trans. Automat. Control AC-30 (1985), 4, 401–404 (1985) Zbl0581.93019MR0786718DOI10.1109/TAC.1985.1103964
  6. Falb P. L., Wolovich W. A., 10.1109/TAC.1967.1098737, IEEE Trans. Automat. Control AC-12 (1967), 6, 651–659 (1967) DOI10.1109/TAC.1967.1098737
  7. Francis B. A., Georgiou T. T., 10.1109/9.1310, IEEE Trans. Automat. Control AC-33 (1988), 9, 820–832 (1988) Zbl0651.93053MR0953876DOI10.1109/9.1310
  8. Franklin G. F., Emami–Naeini A., 10.1109/TAC.1986.1104361, IEEE Trans. Automat. Control AC-31 (1986), 7, 661–664 (1986) DOI10.1109/TAC.1986.1104361
  9. Grasselli O. M., Longhi S., Tornambè A., Valigi P., 10.1109/9.508911, IEEE Trans. Automat. Control AC-41 (1996), 7, 1031–1037 (1996) Zbl0875.93264MR1398790DOI10.1109/9.508911
  10. Gündes A. N., 10.1109/9.256385, IEEE Trans. Automat. Control AC-37 (1992), 10, 1572–1575 (1992) Zbl0770.93063MR1188761DOI10.1109/9.256385
  11. Hautus M. L. J., Heymann M., Linear feedback decoupling – transfer function analysis, IEEE Trans. Automat. Control AC-28 (1983), 8, 823–832 (1983) Zbl0523.93035MR0717840
  12. Lin C. A., Necessary and sufficient conditions for existence of decoupling controllers, IEEE Trans. Automat. Control AC-42 (1997), 8, 1157–1161 (1997) Zbl0890.93039MR1469078
  13. Urikura S., Nagata A., 10.1109/TAC.1987.1104641, IEEE Trans. Automat. Control AC-32 (1987), 474–482 (1987) Zbl0622.93046MR0887584DOI10.1109/TAC.1987.1104641
  14. Wang Q. G., 10.1016/0005-1098(92)90128-3, Automatica 28 (1992), 411–415 (1992) Zbl0766.93044MR1157011DOI10.1016/0005-1098(92)90128-3
  15. Wonham W. M., Morse A. S., 10.1137/0308001, SIAM J. Control 8 (1970), 1–18 (1970) Zbl0206.16404MR0270771DOI10.1137/0308001
  16. Yamamoto Y., 10.1109/9.286247, IEEE Trans. Automat. Control AC-39 (1994), 4, 703–713 (1994) Zbl0807.93038MR1276768DOI10.1109/9.286247

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.