Optimal multivariable PID regulator

Jiří Mošna; Pavel Pešek

Kybernetika (2000)

  • Volume: 36, Issue: 2, page [243]-253
  • ISSN: 0023-5954

Abstract

top
A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted as an optimal multivariable matrix PID regulator.

How to cite

top

Mošna, Jiří, and Pešek, Pavel. "Optimal multivariable PID regulator." Kybernetika 36.2 (2000): [243]-253. <http://eudml.org/doc/33480>.

@article{Mošna2000,
abstract = {A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted as an optimal multivariable matrix PID regulator.},
author = {Mošna, Jiří, Pešek, Pavel},
journal = {Kybernetika},
keywords = {PID regulator; MIMO controlled plant; PID regulator; MIMO controlled plant},
language = {eng},
number = {2},
pages = {[243]-253},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal multivariable PID regulator},
url = {http://eudml.org/doc/33480},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Mošna, Jiří
AU - Pešek, Pavel
TI - Optimal multivariable PID regulator
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 2
SP - [243]
EP - 253
AB - A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted as an optimal multivariable matrix PID regulator.
LA - eng
KW - PID regulator; MIMO controlled plant; PID regulator; MIMO controlled plant
UR - http://eudml.org/doc/33480
ER -

References

top
  1. Ackermann J., Sampled–Data Control Systems, Analysis and Synthesis, Robust System Design, Springer–Verlag, Berlin 1985 Zbl0639.93001MR0699111
  2. Åström K. J., Wittenmark B., Computer–Controlled Systems, Theory and Design, Prentice–Hall, Englewood Cliffs, N. J. 1984 
  3. Bryson A. E., Ho, Yu–Chi, Applied Optimal Control, Gin and Company, Waltham, MA 1969 
  4. Dai L., Lin W., 10.1016/S0005-1098(96)80008-2, Automatica 32 (1996), 1713–1718 (1996) Zbl0873.93047MR1427141DOI10.1016/S0005-1098(96)80008-2
  5. Francis B. A., Wohman W. M., 10.1016/0005-1098(76)90006-6, Automatica 12 (1976), 457–465 (1976) MR0429257DOI10.1016/0005-1098(76)90006-6
  6. Kalman R. E., Canonical structure of linear dynamical systems, SIAM J. Control 1 (1962), 596–600 (1962) Zbl0249.34005MR0138865
  7. Kwanty G. H., Young D. K., 10.1016/0005-1098(82)90068-1, Automatica 18 (1982), 385–400 (1982) MR0667558DOI10.1016/0005-1098(82)90068-1
  8. Mošna J., Melichar J., Pešek P., Optimality versus complexity: Optimal matrix PID regulator, In: Preprints of the 3rd European IEEE Workshop CMP’98, Prague 1998, pp. 139–143 (1998) 
  9. Mošna J., Pešek, Sampled–data control: Optimal matrix PID regulator, In: The Eighteenth IASTED International Conference on Modeling, Identification and Control, Innsbruck 1999, pp. 305–308 (1999) 
  10. Vidyasagar M., Control System Synthesis, A Factorization Approach, The MIT Press, Cambridge, MA 1987 Zbl0655.93001MR0787045
  11. Štecha J., Robustness versus control quality in asymptotic reference tracking, In: Proceedings of the Fifteenth IASTED International Conference Modeling, Identification and Control, Innsbruck 1996, pp. 292–294 (1996) 
  12. Štecha J., Robust and nonrobust tracking, Kybernetika 34 (1998), 203–216 (1998) 
  13. Young K. D., 10.1109/TAC.1984.1103585, IEEE Trans. Automat. Control AC-29 (1984), 567–569 (1984) Zbl0532.93034DOI10.1109/TAC.1984.1103585
  14. Žampa P., On a new system theory and its new paradigms, In: Cybernetics and Systems’96, Austria Society for Cybernetic Studies, Vienna 1996, Volume 1, pp. 3–7 (1996) 
  15. Žampa P., Mošna J., Prautsch P., New approach to optimal control theory, In: The 2nd IFAC Workshop on New Trends in Design of Control Systems, Smolenice 1997 

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.