Polynomial controller design based on flatness

Frédéric Rotella; Francisco Javier Carillo; Mounir Ayadi

Kybernetika (2002)

  • Volume: 38, Issue: 5, page [571]-584
  • ISSN: 0023-5954

Abstract

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By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.

How to cite

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Rotella, Frédéric, Carillo, Francisco Javier, and Ayadi, Mounir. "Polynomial controller design based on flatness." Kybernetika 38.5 (2002): [571]-584. <http://eudml.org/doc/33604>.

@article{Rotella2002,
abstract = {By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.},
author = {Rotella, Frédéric, Carillo, Francisco Javier, Ayadi, Mounir},
journal = {Kybernetika},
keywords = {polynomial controller; linear system; parameters design; polynomial controller; linear system; parameters design},
language = {eng},
number = {5},
pages = {[571]-584},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Polynomial controller design based on flatness},
url = {http://eudml.org/doc/33604},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Rotella, Frédéric
AU - Carillo, Francisco Javier
AU - Ayadi, Mounir
TI - Polynomial controller design based on flatness
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 5
SP - [571]
EP - 584
AB - By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.
LA - eng
KW - polynomial controller; linear system; parameters design; polynomial controller; linear system; parameters design
UR - http://eudml.org/doc/33604
ER -

References

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  1. Aström K. J., Bernardson B., Ringdhal A., Solution using robust adaptive pole placement, In: Proc. European Control Conference (ECC’91), Grenoble 1991, pp. 1341–2346 (1991) 
  2. Aström K. J., Wittenmark B., Computer Controlled Systems, Theory and Design, Prentice Hall, Englewood Cliffs, N.J. 1990 
  3. Bitaud L., Fliess, M., Lévine J., A flatness based control synthesis of linear systems and application to windshield wipers, In: Proc. European Control Conference (ECC’97), Bruxelles 1997 
  4. Fliess M., Sur des pensers nouveaux faisons des vers anciens, In: Proc. CIFA2000, Lille 2000, pp. 26–36 
  5. Fliess M., Lévine J., Martin,, Ph., Rouchon P., Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sci. Paris I-315 (1992), 619–624 (1992) Zbl0776.93038MR1181303
  6. Fliess M., Lévine J., Martin, Ph., Rouchon P., Linéarisation par bouclage dyna- mique et transformées de Lie–Backlund, C. R. Acad. Sci. Paris I-317 (1993), 981–986 (1993) MR1249373
  7. Fliess M., Lévine J., Martin, Ph., Rouchon P., 10.1080/00207179508921959, Internat. J. Control 61 (1995), 6, 1327–1361 (1995) MR1613557DOI10.1080/00207179508921959
  8. Fliess M., Lévine J., Martin, Ph., Rouchon P., 10.1109/9.763209, IEEE Trans. Automat. Control 44 (1999), 922–937 (1999) MR1690537DOI10.1109/9.763209
  9. Fliess M., Mounier H., 10.1051/cocv:1998111, ESAIM: Control, Optimization and Calculus of Variations 3 (1998), 301–314 (1998) Zbl0908.93013MR1644427DOI10.1051/cocv:1998111
  10. Fliess M., Sira-Ramirez, H., Marquez R., Regulation of non minimum phase outputs: a flatness approach, In: Perspectives in Control Theory & Applications, Colloquim in Honor of I. D. Landau, Paris, Springer–Verlag, Berlin 1998 
  11. Franklin G. F., Powell J. D., Workman M., Digital Control of Dynamic Systems, Addison–Wesley, Reading 1998 Zbl0697.93002
  12. Isidori A., Nonlinear Control Systems, Springer–Verlag, Berlin 1989 Zbl0931.93005
  13. Horowitz I. M., Synthesis of Feedback Systems, Wiley, New York 1963 Zbl0515.93023
  14. Kailath T., Linear Systems, Prentice–Hall, Englewood Cliffs, N.J. 1980 Zbl0870.93013MR0569473
  15. Kučera V., Analysis and Design of Discrete Linear Control Systems, Prentice Hall, Englewood Cliffs, N.J. 1991 Zbl0762.93060MR1182311
  16. Landau I. D., Identification et Commande des Processus, Hermès, Paris 1993 
  17. Landau I. D., Lozano R., M’Saad M., Adaptive Control, Springer–Verlag, New York 1998 Zbl1234.93002MR1483072
  18. Lévine J., Lottin J., Ponsart J. C., 10.1109/87.531919, IEEE Trans. Control Systems Techn. 4 (1996), 5, 524–44 (1996) DOI10.1109/87.531919
  19. Lévine J., Are there new industrial perspectives in the control of mechanical systems? In: Advances in Control (P, M. Frank, ed.), Springer–Verlag, New York 1999, pp. 197–226 (1999) 
  20. Marquez R., Delaleau E., Fliess M., Commande par PID généralisé d’un moteur électrique sans capteur mécanique, In: Proc. CIFA 2000, Lille 2000, pp. 453–458 
  21. Nijmeijer H., Schaft, Van Der, Nonlinear Dynamical Control Systems, Springer–Verlag, Berlin 1990 Zbl0701.93001MR1047663
  22. Rotella F., Carrillo F. J., Flatness based control of a turning process, In: Proc. CESA’98, Vol. 1, Hammamet 1998, pp. 397–402 (1998) 
  23. Rotella F., Carrillo F. J., Flatness approach for the numerical control of a turning process, In: Proc. European Control Conference (ECC’99), Karlsruhe 1999 
  24. Rotella F., Carrillo F. J., Ayadi M., Digital flatness-based robust controller applied to a thermal process, In: IEEE–CCA, Mexico–City 2001, pp. 936–941 
  25. Rothfuß R., Rudolph, J., Zeitz M., 10.1016/0005-1098(96)00090-8, Automatica 32 (1996), 10, 1433–1439 (1996) Zbl0865.93046MR1420044DOI10.1016/0005-1098(96)00090-8

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