Nonlinear feedback controller of a microbeam resonator

This paper is concerned with the modeling, nonlinear dynamic analysis and control design of an electrostatically actuated clamped-clamped microbeam. The model accounts for the mid-plane stretching and nonlinear form of the electrostatic force actuated along the microbeam span. A reduced-order model is constructed, using the method of multiple scales, to examine the microsystem static and dynamics behaviors. To improve the microbeam behavior, a nonlinear feedback controller is proposed. The main control objective is to make it behave like commonly known one-degree-of-freedom self-excited oscillators, such as the van der Pol and Rayleigh oscillators, which depict attractive filtering features in their dynamic frequency responses. For this, a review of the nonlinear dynamics of one of these oscillators is first provided to gain insight into its appealing filtering characteristics. We then present a novel control design that regulates the pass band of the considered microbeam and derive analytical expressions that approximate the nonlinear resonance frequencies and amplitudes of the periodic solutions when it is subjected to one-point then to fully distributed feedback forces. We apply Floquet theory to ascertain the stability of the limit cycles. We finally suggest an electronic circuitry made of six analog devices AD633JN for the implementation of the proposed feedback controller.