Combining H∞ approach and interval tools to design a low order and robust controller for systems with parametric uncertainties : application to piezoelectric actuators.

Sofiane Khadraoui (1) , Micky Rakotondrabe (1) , Philippe Lutz (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

This paper presents the design of a robust controller for uncertain systems whose the parameters are bounded by intervals. For that, we propose to combine the standard H1 approach with interval tools in order to ensure robust performances. The main advantantages of the proposed approach are: 1) the natural and ease of modeling of the uncertain parameters thanks to intervals, 2) and the derivation of a low order controller since its structure can be xed a priori and since the order is lower than the system order. In particular, we demonstrate that a PID-structure can be used to control a nth order interval system. The approach is afterwards applied to design a robust controller for a piezoelectric actuator and the experimental results effectively show its efficiency.

Mots clés: Interval system; parametric uncertainties; robust control design; robust performances; standard H1; piezoelctric actuators.; piezoelctric actuators

Domaines: Micro et nanotechnologies/Microélectronique

Sofiane Khadraoui, Micky Rakotondrabe, Philippe Lutz. Combining H∞ approach and interval tools to design a low order and robust controller for systems with parametric uncertainties : application to piezoelectric actuators.. International Journal of Control, 2012, 85 (1-3), pp.251-259. ⟨10.1080/00207179.2011.644582⟩. ⟨hal-00799338⟩