PID-structured controller design for interval systems: Application to piezoelectric microactuators

This paper addresses the modeling and robust PID controller design for piezoelectric microsystems. Piezoelectric cantilevers, used as microactuators in micromanipulation and microassembly con texts, are particularly concerned. Due to their small sizes, these systems are very sensitive to environment (temperature, vibration, etc.) and to usury during functioning. Their behaviors often change because of the parameters variation. For that, linear modeling with uncertainty has been used to account the uncertainties, then classical H_∞ and μ-synthesis approaches were applied. These techniques were efficiency but they were of high order which is not suitable for embedded microsystems. Furthermore, when the number of uncertain parameters increases, the modeling of microsystems became delicate and difficult. In this paper, we propose to model the uncertain parameters by bounding them with intervals. After wards, we propose to design a robust PID controller by using interval arithmetic and related tools in order to ensure the specified performances. In addition to the simplicity of the uncertainties modeling, the derived controller is of low order. The controller synthesis is formulated as a set-inversion problem. An application to the control of piezoelectric microactuators proves the efficiency of the proposed method.