Feedback Control of a Nonlinear Electrostatic Force Transducer

We document a feedback controller design for a nonlinear electrostatic transducer that exhibits a strong unloaded resonance. Challenging features of this type of transducer include the presence of multiple fixed points (some of which are unstable), nonlinear force-to-deflection transfer, effective spring-constant softening due to electrostatic loading and associated resonance frequency shift. Furthermore, due to the utilization of lowpass filters in the electronic readout circuitry, a significant amount of transport delay is introduced in the feedback loop. To stabilize this electro-mechanical system, we employ an active disturbance-rejecting controller with nonlinear force mapping and delay synchronization. As demonstrated by numerical simulations, the combination of these three control techniques stabilizes the system over a wide range of electrode deflections. The proposed controller shows good setpoint tracking and disturbance rejection, and improved settling time, compared to the sensor alone.