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Nonlinear control in the Year 2000 pp 367–384Cite as

State feedbacks without asymptotic observers and generalized PID regulators

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 258))

Abstract

For constant linear systems we introduce the class of exact integral observers which yield generalized PID regulators with good robustness properties. When utilized in conjunction with static state feedbacks they permit to bypass classical asymptotic observers. Three illustrative examples are examined:

  1. 1.

    a classical PID controller where we replace the derivative term by appropriate integral ones;

  2. 2.

    a generalized PID for a second order system with a non-trivial zero dynamics;

  3. 3.

    a real DC motor without mechanical sensors.

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. We conclude by discussing possible extensions, especially nonlinear ones.

Work partially supported by the European Commission’s Training and Mobility of Researchers (TMR) under contract ERBFMRXT-CT970137. One author (RM) was also partially supported by the Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICIT), Venezuela.

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Author information

Author notes

  1. Richard Marquez

    Present address: Departmento de Sistemas de Control, Facultad de Ingeniería, Universidad de Los Andes, 5101, Mérida, Venezuela

Authors and Affiliations

  1. Centre de Mathématiques et Leurs Applications, École Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235, Cachan, France

    Michel Fliess

  2. Laboratoire des Signaux et Systèmes, CNRS-Supélec-Université Paris-Sud Plateau de Moulon, 3, rue Joliot-Curie, 91192, Gif-sur-Yvette, France

    Richard Marquez & Emmanuel Delaleau

Authors
  1. Michel Fliess
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  2. Richard Marquez
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  3. Emmanuel Delaleau
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Corresponding author

Correspondence to Richard Marquez .

Editor information

Alberto Isidori (Professor)Françoise Lamnabhi-Lagarrigue (Docteur D’état)Witold Respondek (Professor)

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© 2001 Springer-Verlag London Limited

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Fliess, M., Marquez, R., Delaleau, E. (2001). State feedbacks without asymptotic observers and generalized PID regulators. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110227

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  • DOI: https://doi.org/10.1007/BFb0110227

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-363-8

  • Online ISBN: 978-1-84628-568-4

  • eBook Packages: Springer Book Archive

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