LMI-region pole placement control scheme for an electrostatically actuated micro Cantilever Beam

In the present article the modeling and control design aspects of a narrow micro Cantilever Beam (μCB) with fringing and squeezed thin film damping effects are presented. The suspended clamped-free μCB can move via the application of an external electrically induced force. The nonlinear model of the μCB is linearized at multiple operating points with respect to the beam´s displacement. An LMI-region based pole placement controller is designed for the set of the resulting multiple operating models. Particular attention has been paid in order to examine the effects of the system´s pressure variations. In addition, variations of the LMI-region where the closed loop poles lie, are investigated in order to check changes in critical characteristics of the closed loop system such like velocity, transient effects etc. Numerous test cases have been applied on the μCB´s model and simulation results prove the efficacy of the suggested modeling and control techniques.