Robust LMI position regulation of a bistable Dielectric Electro-Active Polymer membrane

This paper deals with the control of a micrometric positioning system based on an innovative Dielectric Electro-Active Polymer (DEAP) membrane. The membrane generates motion by means of the interaction between a preloading force and the compressive forces between the compliant electrodes surrounding the surface of the polymer. In particular, in this paper the preloading force is generated by a bistable nonlinear spring, which significantly extends the maximum stroke at the cost of a much more nonlinear behavior. To address this challenging problem, in this paper we reformulate the system dynamics in a quasi-LPV framework, and use LMI based optimization to tune a controller ensuring robust performance with respect to such nonlinearities. Since the state variables are not all measurable, we focus on a partial state feedback approach which permits to impose set-point tracking with a desired decay rate specification, overcoming some limitations of standard decay rate design techniques. Several experimental results are performed to validate the proposed approach.