PID-Structured controller design for interval systems : Application to Piezoelectric Microactuator.

International audienceThis paper addresses the modeling and robust PID controller design for piezoelectric mi- crosystems. Piezoelectric cantilevers, used as microac- tuators 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 uncer- tainties, then classical H1 and -synthesis approaches were applied. These techniques were e ciency but they were of high order which is not suitable for em- bedded microsystems. Furthermore, when the num- ber of uncertain parameters increases, the modeling of microsystems became delicate and di cult. 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 speci ed performances. In addition to thesimplicity 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 microactu- ators proves the e ciency of the proposed method