Model validation for control and controller validation in a prediction error identification framework-Part I: theory

  • Authors:

  • Michel Gevers;Xavier Bombois;BenoıT Codrons;GéRard Scorletti;Brian D. O. Anderson

  • Affiliations:

  • Centre for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium;Department of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands;Laborelec S.C., product line 'Process Control', B-1630 Linkebeek, Belgium;LAP ISMRA, 6 boulevard du Maréchal Juin, F-14050 Caen Cedex, France;Department of Systems Engineering, Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

We propose a model validation procedure that consists of a prediction error identification experiment with a full order model. It delivers a parametric uncertainty ellipsoid and a corresponding set of parameterized transfer functions, which we call prediction error (PE) uncertainty set. Such uncertainty set differs from the classical uncertainty descriptions used in robust control analysis and design. We develop a robust control analysis theory for such uncertainty sets, which covers two distinct aspects: (1) Controller validation. We present necessary and sufficient conditions for a specific controller to stabilize-or to achieve a given level of performance with-all systems in such PE uncertainty set. (2) Model validation for robust control. We present a measure for the size of such PE uncertainty set that is directly connected to the size of a set controllers that stabilize all systems in the model uncertainty set. This allows us to establish that one uncertainty set is better tuned for robust control design than another, leading to control-oriented validation objectives.