Dynamical analysis and chaos control of MEMS resonators by using the analog circuit

This paper investigates the chaos control problem of microelectromechanical system (MEMS) resonators by using the analog circuits. The dynamical analysis, based on bifurcation diagrams, phase diagrams and Lyapunov exponents (LEs), illustrates that transient chaotic behaviors and chaotic behaviors strongly depend on system parameters and the initial conditions of the MEMS resonator. Then, based on the energy flow theory, the circuit differential equation is consistent with its differential equation governing the dynamics, which could mimic the micro-resonator dynamic properties. Accordingly, an analog circuit is designed, and abundant experimental data reveal chaotic behaviors of the MEMS resonator at around 58.791 Hz (1.71 V) and 58.704 Hz (1.68 V). After that, to suppress harmful chaotic oscillation, an adaptive control scheme is proposed and verified by an analog circuit consisting of an error module, a parameter update module and a control input module. Finally, the experimental results of the circuit control system prove the effectiveness of the proposed control scheme.