Resonance, bifurcation and chaos control in electrostatic transducers with two external periodic forces

This paper studies the dynamics of the electrostatic transducers described by two nonlinearly coupled differential equations of motion submitted to two external periodic forces. The method of multiple scales is used to find solutions in the resonant and nonresonant cases. Chaotic behavior is found in terms of the amplitude of the second external force. A feedback controller is applied to drive the chaotic states of the system to an appropriately defined reference signal in spite of modelling errors, parametric variations and perturbing external forces. Computer simulations are provided to illustrate the operation of the designed control scheme.