H∞ and interval techniques to design robust low order controllers: application to piezoelectric actuators

This paper addresses the design of robust controllers for interval systems. For that, the H∞-standard approach is combined with interval techniques in order to derive controllers that ensure robust performances. The main advantages of the proposed approach are: 1) the natural and ease of modeling of the uncertain parameters thanks to intervals, 2) the low order of the controller since it can be lower than the order of the system, 3) and the fact that the structure of the controller can be fixed a priori. The paper is particularly focused, but not limited, on the design of a robust PID controller structure thanks to the proposed approach which is the combination of H∞-tools and interval tools. The systems to be controlled are with order n which makes the proposed approach more general. Experiments on a piezoelectric actuator (piezocantilever) are carried out and show the efficiency of the proposed method.