Title: Polynomial chaos for the design of robust controller with time specifications: a comparison of two approaches

Authors: Amani Added; Maher Ben Hariz; Faouzi Bouani

Addresses: Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES20 Laboratoire d'Analyse, de Conception et de Commande des Systèmes, 1002, Tunis, Tunisia ' Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES20 Laboratoire d'Analyse, de Conception et de Commande des Systèmes, 1002, Tunis, Tunisia ' Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR11ES20 Laboratoire d'Analyse, de Conception et de Commande des Systèmes, 1002, Tunis, Tunisia

Abstract: This paper deals with the design of a robust controller for stochastic dynamic systems. A new method is proposed to compute the controller parameters to achieve the desired time requirements. It is based on the polynomial chaos expansion which is used to provide a high order deterministic state space model. Then, the controller parameters are obtained by minimising a cost function which depends on the closed loop and the desired characteristic polynomials. The proposed method is compared to a classical method founded on an uncertainty parametric model. The control law problem is formulated as a min-max optimisation. Developed controllers ensure desired closed loop performances such as settling time and overshoot. Simulation results are presented and compared to highlight the efficiency and the performances of the proposed controllers.

Keywords: robust controller; low order controller; stochastic uncertainties; polynomial chaos; min-max optimisation; GGP; generalised geometric programming; closed-loop performances.

DOI: 10.1504/IJMIC.2021.123380

International Journal of Modelling, Identification and Control, 2021 Vol.38 No.3/4, pp.248 - 258

Received: 30 Jun 2020
Accepted: 02 Mar 2021
Published online: 13 Jun 2022 *

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