Abstract
The internal model principle is the study of the necessary structure of the compensators designed to make a given system to satisfy a given specification in the presence of exogenous signals whose dynamics are also given. The first result, due to Wonham et al. and other authors, states that to manage the variation of exogenous variables, any compensator must contain a copy of the model of the dynamics of these signals; the known proofs of this vague assertion seem to be highly restrictive. This Note shows that a transparent, and rather elementary exposition of the internal model principle can be derived from the differential algebra language.
Key Words
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. BENGTSSON:[1977]: Output regulation and internal models. A frequency domain approach,Automatica, 13, 333–347,
CI. BYRNES & A. ISIDORI:[1989]: Régulation asymptotique des systèmes non linèraires, C. R. Acad. Sci.Paris, 309 Sér. I, 527–530.
CI. BYRNES & A. ISIDORI [1990]: Output regulation for nonlinear systems, IEEE Trans. Automat. Control,AC-35, 131–140.
E.J. DAVISON:[1976]: The robust control of a servomechanism problem for time-invariant multivariable system, IEEE Trans. Automat. Control, AC-21,25–34.
M.D. Di BENEDETTO:[1987]: Synthesis of an internal model for nonlinear output regualtion, Internat. J.Control 45,1023–1034.
S. DIOP:[1989]: Théorie de l’Elimination et Principe du Modèle Interne en Automatique,Thèse de Doctorat, Universitè Paris-Sud, Orsay.
S. DIOP: [1990a]: Elimination in control theory, to appear in Math. Control Signals Systems.
S. DIOP: [ 1990b]: Finite moronisms of differential algebraic varieties and elimination theory,Preprints of the Conference Analysis of Controlled Dynamical Systems,Lyon, 1990.
A.F. D’SOUZA:[1988]: Design of Control System, Printice-Hall, New Jersey.
M. FLIESS:[1989]: Automatique et corps différentiels, Forum Math., 1,227–238.
B. FRANCIS & W.M. WONHAM:[1976]: The internal model principle of control theory, Automatica, 12,457–465.
J.S.A. HEPBURN & W.M. WONHAM:[1984]: Error feedback and internal model principle of regulator theory on differentiable manifolds, IEEE Trans. Automat. Contr., AC-29, 5, 397–403.
CD. JOHNSON:[1968]: Optimal control of the linear regulator with constant disturbances, IEEE Trans. Automat. Control, AC-13, 416–421.
R.E. KOLCHIN:[1973]: Differential Algebra and Algebraic Groups, Academic Press, New York.
P. NASLIN:[ 1968]: Technologie et Calcul Pratique des Systèmes Asservis, Dunod, Paris.
W.A. WOLOVICH & P FERREIRA:[ 1979]: Output regulation and tracking in linear multivariable systems, IEEE Trans.Automat. Control, AC-24, 460–465.
W.M. WONHAM:[1979]: Linear Multivariable Control: a Geometric Approach, 2nd ed., Springer-Verlag, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Diop, S. (1991). On the internal model principle. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_31
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0439-8_31
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
eBook Packages: Springer Book Archive