Bi-State Bifurcation Control of a Shaped-Comb Parametric Resonator

This work employs behavioral modeling to develop a bi-state control technique capable of servoing at the onset of the microelectromechanical parametric resonant bifurcation setpoint. The parametric resonance features a sharp “turn-on” in oscillation amplitude at the bifurcation, enhancing sensitivity to resonance frequency change. A bi-state controller is constructed to servo at this sharp jump point. It has two states of operation: one state is within the instability tongue where the oscillation amplitude builds up exponentially; another state resides outside of the tongue where the oscillation turns off. The rapid turn on and off of the parametric resonance keeps the resonant amplitude small and circumvents the slow build-up time. Both the simulated and experimental loop transient responses are presented.