Robust control of parametric uncertain systems : application to the control of piezoelectric cantilevers.

Abstract : The design of control laws requires accurate system models and knowledge of the effects of the environment. Such models are often difficult to obtain because of the incomplete knowledge on the system due to the nonlinearities and time-varying parameters. Furthermore, many simplifications are often introduced during the modelling in order to obtain usable models. As a result, the used models are subjected to uncertainties. To reach high performances in presence of models uncertainties, robust control laws are used. H∞ and μ-synthesis are the most appreciated. However one of their disadvantages is the derivation of high-order controllers. In this work, interval arithmetic is introduced to characterize parametric uncertainties and to design robust controller, ensuring the performances for the uncertain systems. The proposed approach is based on a given interval model which represents a family of models and a wanted interval closedloop (a family of models describing desired performances). The controller synthesis is formulated as a set-inclusion problem. The interval techniques are introduced to solve this problem and to compute the set solution of the controller parameters. The main advantage of the proposed method is that a lower order robust controller can be easily derived. An application to the control of piezocantilevers (used for Microsystems) is performed using the proposed robust control method. The experimental results with piezocantilevers prove the efficiency of the proposed method.
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Contributor : Martine Azema <>
Submitted on : Thursday, December 16, 2010 - 4:55:03 PM
Last modification on : Friday, July 6, 2018 - 3:06:07 PM


  • HAL Id : hal-00547586, version 1


Sofiane Khadraoui, Micky Rakotondrabe, Philippe Lutz. Robust control of parametric uncertain systems : application to the control of piezoelectric cantilevers.. 3rd Edition of the Small Workshop on Interval Methods, SMIM'10., Jun 2010, Nantes, France. ⟨hal-00547586⟩



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