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

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 H∞ 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 fixed 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.