A frequency independent approximation and a sliding mode control scheme for a system of a micro-cantilever beam

In the present article, a sliding mode controller is proposed for a micro-cantilever beam (μCB) with fringing and squeezed film damping effects. The narrow micro-cantilever beam can move via the application of an external electrically induced force. The introduction of the squeezed film parameters results in a frequency-dependent nonlinear system. Particular attention, has been paid, in order to approximate the frequency dependent μCB model, with a valid, frequency independent one, that would be incorporated in the design of a robust sliding mode controller. The suggested control technique enables compact realization of a robust controller tolerant in device characteristics' variations, nonlinearities and types of inherent instabilities. Robustness of the proposed control scheme against disturbances is proved by Lyapunov's second method. In addition, bifurcation analysis is carried on the beam's nonlinear model, and numerous simulation test cases are presented in order to test the suggested modeling and control techniques.