Bi-state control of a duffing microresonator on the falling edge of the instability

This work is the first investigation of a bi-state control technique capable of servoing on the falling edge of the microelectromechanical Duffing resonant bifurcation setpoint. The Duffing microresonator, fabricated in an SOI-MEMS process, features a sharp jump in oscillation amplitude at the bifurcation and is, therefore, ideal for ultrasensitive detection of mass or stress shifts that modify the resonance frequency and hence the jump frequency. The resonator “instability tongue” is characterized to identify the bifurcation points as a function of drive gain. The control system states are set through the AC drive gain while operating at a fixed drive frequency such that one of the system states is within this instability tongue whereas the second state resides outside of this tongue. The amplitude servo point is chosen at the maximum “on” amplitude prior to the jump event. The states are driven by 300 kHz pulse width modulation that is set much faster than the amplitude response dynamics and inhibits the system from latching off as would happen in static operation.