Constrained finite time optimal control of a micro-capacitor

In this article the control problem of a non-linear micro-capacitor (μ - C) is considered. Utilization of FEM can approximate the μ - A dynamics nonlinear-PDE to a finite nonlinear-ODE. The nonlinearity stems from the plate's rigid-body motion, while all flexibility effects are considered as additive linear-terms. The control methodology we employ is a combination of two ideas. First we use standard linearization techniques to compute PWA approximations of the original nonlinear system around multiple operating points. Next we employ the theory of Constrained Fine Time Optimal Controllers (CFTOC) in order to design (off-line) explicit switching controllers for the set of PWA systems obtained in the first step. The ensuing switched PWA controller is applied to the the original-nonlinear system. We investigate, via extensive simulations, the efficacy of using this control approach for output set-point tracking objectives.