A new Nyquist-based technique for tuning robust decentralized controllers

Alena Kozáková; Vojtech Veselý; Jakub Osuský

Kybernetika (2009)

  • Volume: 45, Issue: 1, page 63-83
  • ISSN: 0023-5954

Abstract

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An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are termed “equivalent subsystems". Local controllers of equivalent subsystems independently tuned for stability and specified feasible performance constitute the decentralized controller guaranteeing specified performance of the full system. To guarantee robust stability, the M - Δ stability conditions are derived. Unlike standard robust approaches, the proposed technique considers full nominal model, thus reducing conservativeness of resulting robust stability conditions. The developed frequency domain design procedure is graphical, interactive and insightful. A case study providing a step-by-step robust DC design for the Quadruple Tank Process [K.H. Johansson: Interaction bounds in multivariable control systems. Automatica 38 (2002), 1045–1051] is included.

How to cite

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Kozáková, Alena, Veselý, Vojtech, and Osuský, Jakub. "A new Nyquist-based technique for tuning robust decentralized controllers." Kybernetika 45.1 (2009): 63-83. <http://eudml.org/doc/37662>.

@article{Kozáková2009,
abstract = {An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are termed “equivalent subsystems". Local controllers of equivalent subsystems independently tuned for stability and specified feasible performance constitute the decentralized controller guaranteeing specified performance of the full system. To guarantee robust stability, the $M-\Delta $ stability conditions are derived. Unlike standard robust approaches, the proposed technique considers full nominal model, thus reducing conservativeness of resulting robust stability conditions. The developed frequency domain design procedure is graphical, interactive and insightful. A case study providing a step-by-step robust DC design for the Quadruple Tank Process [K.H. Johansson: Interaction bounds in multivariable control systems. Automatica 38 (2002), 1045–1051] is included.},
author = {Kozáková, Alena, Veselý, Vojtech, Osuský, Jakub},
journal = {Kybernetika},
keywords = {multivariable system; decentralized controller; frequency domain; independent design; robust stability; unstructured uncertainty; multivariable system; decentralized controller; frequency domain; independent design; robust stability; unstructured uncertainty},
language = {eng},
number = {1},
pages = {63-83},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A new Nyquist-based technique for tuning robust decentralized controllers},
url = {http://eudml.org/doc/37662},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Kozáková, Alena
AU - Veselý, Vojtech
AU - Osuský, Jakub
TI - A new Nyquist-based technique for tuning robust decentralized controllers
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 1
SP - 63
EP - 83
AB - An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are termed “equivalent subsystems". Local controllers of equivalent subsystems independently tuned for stability and specified feasible performance constitute the decentralized controller guaranteeing specified performance of the full system. To guarantee robust stability, the $M-\Delta $ stability conditions are derived. Unlike standard robust approaches, the proposed technique considers full nominal model, thus reducing conservativeness of resulting robust stability conditions. The developed frequency domain design procedure is graphical, interactive and insightful. A case study providing a step-by-step robust DC design for the Quadruple Tank Process [K.H. Johansson: Interaction bounds in multivariable control systems. Automatica 38 (2002), 1045–1051] is included.
LA - eng
KW - multivariable system; decentralized controller; frequency domain; independent design; robust stability; unstructured uncertainty; multivariable system; decentralized controller; frequency domain; independent design; robust stability; unstructured uncertainty
UR - http://eudml.org/doc/37662
ER -

References

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  1. A methodology for sequential design of robust decentralized control systems, Automatica 28 (1992), 997–1001. MR1179702
  2. Improved independent design of robust decentralized controllers, In: 12th IFAC World Congress, Vol. 5, Sydney 1993, pp. 271–274. 
  3. Sequential design of decentralized controllers, Automatica 30, (1994), 1601–1607. MR1299384
  4. Decentralized robust control nased on overlapping decompositions, In: 10th IFAC Symposium om Large Scale Systems, Osaka 2004, pp. 605–609. 
  5. Decentralized robust control of large-scale time-delay systems, In: 17th IFAC World Congress, Seoul 2008, CD-ROM. 
  6. Decentralized LQG/LTR controller design for interconnected systems, In: Proc. American Control Conference, Minneapolis 1987, pp. 1682–1687. 
  7. Local LQG/LTR controller design for decentralized systems, IEEE Trans. Automat. Control AC-32 (1987), 926–930. 
  8. Interaction bounds in multivariable control systems, Automatica 38 (2002), 1045–1051. Zbl1018.93013MR2135100
  9. Robust decentralized control of complex systems in the frequency domain, In: 2nd IFAC Workshop New Trends in Design of Control Systems, Elsevier Kidlington UK, 1998. 
  10. A frequency domain design technique for robust decentralized controllers, In: 16th IFAC World Congress, Prague 2005, Mo-E21-TO/6, CD-ROM. 
  11. Improved tuning technique for robust decentralized PID controllers, In: 11th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems Theory and Applications, Gdansk 2007, CD-ROM. 
  12. Robust decentralized controller design with additive affine-type uncertainty, Internat. J. Innovative Computing, Information and Control (IJICIC), 3 (2007), 5, 1109–1120. 
  13. Simple method for tuning SISO controllers in multivariable system, Indust. Eng. Chem. Process Development 25 (1986), 654–660. 
  14. The generalized Nyquist stability criterion and multivariable root loci, Internat. J. Control 25 (1977), 81–127. MR0439341
  15. The design of linear multivariable systems, Automatica 9 (1973), 201–207. Zbl0249.93022MR0453045
  16. Dynamical Systems and Controlled Processes, Nauka, Moscow 1978 (in Russian). 
  17. A practical decentralized auto-tuning method for TITO systems under closed-loop control, Internat. J. Innovative Computing, Information and Control (IJICIC) 2 (2006), 305–322. 
  18. Selecting control configurations for performance with independent design, Comput. Chem. Engrg. 27 (2003), 101–109. 
  19. Robust performance of decentralized control systems by independent designs, Automatica 25 (1989), 119–125. MR0986579
  20. Multivariable Feedback Control: Analysis and Design, Third edition. Wiley, Chichester – New York – Brisbane – Toronto – Singapore 1996. 
  21. Large scale dynamic system stabilization using the principle of dominant subsystem approach, Kybernetika 29 (1993), 1, 48–61. MR1227741

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