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

This article presents the design of a robust controller for uncertain systems whose parameters are bounded by intervals. For that, we propose to combine the standard H-infinity approach with interval tools in order to ensure robust performances. The main advantages of the proposed approach are: (1) the natural and ease of modelling of the uncertain parameters, thanks to intervals, and (2) the derivation of a low-order controller since its structure can be fixed a priori and 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 then applied to design a robust controller for a piezoelectric actuator and the experimental results effectively show its efficiency.