Modern control design for MEMS tunable capacitors in voltage reference applications: a comparative study

The open-loop drive of the MEMS tunable capacitor does not guarantee accurate output voltage in an AC voltage reference source (VRS). For a precise regulation, the capacitor movable plate should track the pull-in point trajectory harmlessly and should be kept at a certain distance from the fixed plate. Achievement of this objective is a highly challenging issue, particularly when measurement noise, unmodeled dynamics, and external disturbance are deemed. In addition, the control effort consumed energy requires minimization in MEMS applications. This paper contemplates different modern control strategies for the capacitance regulation, in a step-by-step manner. The addressed and designed controllers include the simple pole placement state feedback controller (PPSFC), PPSFC equipped with the Luenberger observer (LO), linear quadratic regulator (LQR), LQR equipped with an LO, linear quadratic integrator (LQI), and the Kalman filter-based PPSFC. The design process is considered in an evolutionary way. The simulation yields demonstrate accurate tracking of the pull-in trajectory. Among them, the Kalman filter design shows relatively satisfactory robustness against measurement and modeling errors. Ultimately, the article proposes a linear quadratic Gaussian (LQG) controller to cancel measurement noise, nonlinear dynamics, reject constant external disturbance, and minimize the control effort consumed energy in a sub-optimal manner.