Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T17:51:23.577Z Has data issue: false hasContentIssue false
  • English
  • Français

Correcteurs proportionnels-intégrauxgénéralisés

Published online by Cambridge University Press:  15 September 2002

Michel Fliess ,
Richard Marquez ,
Emmanuel Delaleau  and
Hebertt Sira–Ramírez
Michel Fliess
Affiliation:
Centre de Mathématiques et leurs Applications, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan, France ; fliess@cmla.ens-cachan.fr.
Richard Marquez
Affiliation:
Laboratoire des Signaux et Systèmes, CNRS–Supélec–Université Paris-Sud, Plateau du Moulon, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France ; marquez@lss.supelec.fr.delaleau@lss.supelec.fr.
Emmanuel Delaleau
Affiliation:
Laboratoire des Signaux et Systèmes, CNRS–Supélec–Université Paris-Sud, Plateau du Moulon, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France ; marquez@lss.supelec.fr.delaleau@lss.supelec.fr.
Hebertt Sira–Ramírez
Affiliation:
Departamento Ingeniería Electrica, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México DF, Mexique ; hsira@mail.cinvestav.mx.
Get access

Abstract

For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.

Keywords

PID controllersgeneralized proportional-integral controllersintegral reconstructorsmodulescalculuslocalization.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 23 - 41
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

B. d'Andréa-Novel et M. Cohen de Lara, Commande linéaire de systèmes dynamiques. Masson (1993).
K.J. Aström et T. Hägglund, PID Controllers: Theory, Design, and Tuning. Instrument Society of America (1995).
Bourlès, H. et Fliess, M., Finite poles and zeros of linear systems: An intrinsic approach. Internat. J. Control 68 (1997) 897-922. CrossRef
A. Erdélyi, Operational Calculus and Generalized Functions. Holt Rinehard Winston (1962).
Fliess, M., Some Basic Structural Properties of Generalized Linear Systems. Systems Control Lett. 15 (1990) 391-396. CrossRef
Fliess, M., Remark, A on Willems' Trajectory Characterization of Linear Controllability. Systems Control Lett. 19 (1992) 43-45. CrossRef
Fliess, M., Une interprétation algébrique de la transformation de Laplace et des matrices de transfert. Linear Alg. Appl. 203-204 (1994) 429-442. CrossRef
M. Fliess, Sur des pensers nouveaux faisons des vers anciens, dans Actes Conférence Internationale Francophone d'Automatique (CIFA'2000), édité par P. Borne, J.-P. Richard et Ph. Vanheeghe. Lille (2000) 26-36.
Fliess, M., Lévine, J., Martin, P. et Rouchon, P., Flatness and defect of non-linear systems: Introductory theory and examples. Internat. J. Control 61 (1995) 1327-1361. CrossRef
Fliess, M., Lévine, J., Martin, P. et Rouchon, P., Lie-Bäcklund, A approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Control. 44 (1999) 922-937. CrossRef
Fliess, M. et Marquez, R., Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Internat. J. Control 73 (2000) 606-623. CrossRef
Fliess, M., Marquez, R. et Delaleau, E., State feedbacks without asymptotic observers and generalized PID regulators, dans Nonlinear Control in the Year 2000, édité par A. Isidori, F. Lamnabhi-Lagarrigue et W. Respondek. Springer, Lecture Notes in Control Inform. Sci. 258 (2000) 367-384. CrossRef
M. Fliess, R. Marquez et H. Mounier, PID-like regulators for a class of linear delay systems, dans Proc. $6^{\rm th}$ Europ. Control Conf. Porto (2001).
M. Fliess, R. Marquez et H. Mounier, An extension of predictive control, PID regulators and Smith predictors to some linear delay systems. Internat. J. Control (à paraître).
Fliess, M. et Mounier, H., Controllability and observability of linear delay systems: An algebraic approach. ESAIM: COCV 3 (1998) 301-314. CrossRef
G.F. Franklin, J.D. Powell et A. Emami, Feedback Control of Dynamic Systems, $3^{\rm rd}$ Ed. Addison Wesley (1994).
N. Jacobson, Basic Algebra I & II. Freeman (1974 & 1980).
T. Kailath, Linear Systems. Prentice-Hall (1980).
P. de Larminat, Contrôle d'état standard. Hermès (2000).
R. Marquez, À propos de quelques méthodes classiques de commande linéaire : commande prédictive, correcteurs proportionnels-intégraux généralisés, prédicteurs de Smith. Thèse, Université Paris-Sud, Orsay (2001).
R. Marquez, E. Delaleau et M. Fliess, Commande par PID généralisé d'un moteur électrique sans capteur mécanique, dans Actes Conférence Internationale Francophone d'Automatique (CIFA'2000), édité par P. Borne, J.-P. Richard et Ph. Vanheeghe. Lille (2000) 453-458.
Martin, P., Devasia, S. et Paden, B., A different look at output tracking: Control of a VTOL aircraft. Automatica 32 (1996) 101-107. CrossRef
J. Mikusinski, Operational Calculus, $2^{\rm nd}$ Ed., Vol. 1. PWN & Oxford University Press (1983).
J. Mikusinski et T.K. Boehme, Operational Calculus, $2^{\rm nd}$ Ed., Vol. 2. PWN & Oxford University Press (1987).
Pernebo, L., An algebraic theory for the design of controllers for linear multivariable systems-Part I: Structure matrices and feedforward design. IEEE Trans. Automat. Control 26 (1981) 171-181. CrossRef
Pernebo, L., An algebraic theory for the design of controllers for linear multivariable systems-Part II: Feedback realizations and feedback design. IEEE Trans. Automat. Control 26 (1981) 182-194.
B. van der Pol et H. Bremmer, Operational Calculus Based on the Two-Sided Laplace Integral, $2^{\rm nd}$ Ed. Cambridge University Press (1955).
Singer, N., Singhose, W. et Seering, W., Comparison of filtering methods for reducing residual vibrations. Eur. J. Control 5 (1999) 208-218. CrossRef
H. Sira-Ramírez, R. Marquez et M. Fliess, On the generalized PID control of linear dynamic systems, dans Proc. $6^{\rm th}$ Europ. Control Conf. Porto (2001).
H. Sira-Ramírez, R. Marquez et M. Fliess, Generalized PID sliding mode control of DC-to-DC power converters, dans Proc. IFAC Conf. Syst. Struct. Control. Prague (2001).
H. Sira-Ramírez, R. Marquez et V.M. Hernández, Sliding mode control without state measurements, dans Proc. $6^{\rm th}$ Europ. Control Conf. Porto (2001).
H. Sira-Ramírez et G. Silva-Navarro, Generalized PID control of the average boost converter circuit model, dans Proc. Nonlinear Control Network Workshop. Sheffield (2001).
J.J.E. Slotine et W. Li, Applied Nonlinear Control. Prentice Hall (1991).
S. Spurgeon et C. Edwards, Sliding Mode Control: Theory and Practice. Taylor and Francis (1998).
K.E. Tan, Q.-G. Wang, T.H. Lee et T.J. Hägglund, Advances in PID Control. Springer (1999).
W.A. Wolovich, Automatic Control Systems: Basic Analysis and Design. Holt Rinehart and Winston (1994).
K. Yosida, Operational Calculus. Springer (1984).