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Theses

Synthèse de régulateurs numériques robustes multivariables par optimisation convexe

Abstract : The dissertation is essentially concerned with methods of robust digital multivariable and monovariable controller design. For controller desing, a linear discrete-time model of plant to be controlled is used. The controller robustness is treated by sensitivity frequency analysis
(sensitivity is transfer function/matrix of closed loop). Correspondingly to H∞ design, the singular values of frequency responses are used for the analysis.

The work is divided into five parts. The first part concerns monovariable systems and the rest is focussed on multivariable domain. The five parts deal with the following issues:

• The first part (Chapter 2) is related to robust digital monovariable controller design by pole placement, sensitivity shaping and convex optimisation [LK98, LL99]. It presents a new approach by pole placement using 2nd order digital notch filters and an associated software package developed in this framework. The software reflects the improvements which drastically simplify the design procedure. The section concerning convex optimisation recalls some basic principals and introduces a notation used later for multivariable systems.
• The second part (Chapter 3 and 4) reminds basic theory of multivariable control and it develops the idea of robust multivariable controller design by pole placement and sensitivity shaping. The controller has a form of an observer with an estimated state feedback and it is used later as a central controller for convex optimisation controller design.
• The third part (Chapter 5) is the main part of the work and it develops a multivariable controller design method by sensitivity shaping and convex optimisation. The method is based on a similar principles as a monovariable design technique [Lan98, LL99] and it is implemented as an interactive toolbox for Matlab. The multivariable pole placement is implemented in this application as well. The toolbox is a part of the dissertation and it is briefly described in this chapter.
• The fourth part (Chapter 6) treats multivariable pre-compensator tracking part design using convex optimisation. The pre-compensator allows to separate robustness specifications disturbance rejection, uncertainty treating...) and tracking specifications (rising time, maximal overshoot...).
• The fifth part (Chapter 7) concerns multivariable controller reduction technique by identification in closed loop. The developed method is an extension of an approach developed for monovariable controllers [LKC01].
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Hynek Prochazka. Synthèse de régulateurs numériques robustes multivariables par optimisation convexe. Automatique / Robotique. Institut National Polytechnique de Grenoble - INPG, 2004. Français. ⟨tel-00169982⟩

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