Robust proportional-integral-derivative controller design for an electrostatic micro-actuator with measurement uncertainties

In this study the effects of unaccounted modal dynamics within the control scheme of an electrostatic micro-actuator (μ-A) are presented. The μ-A is composed of a-capacitor, whose one plate is clamped on the ground whereas its other plate is floating on the air. The dynamic model of the μ-A allows both lateral and angular movements of the upper plate. The feedback controller is designed based on the single-mode (lateral) linearised model. The reduced non-linear model (RnM) is linearised at multiple operating points, and the designed proportional-integral-derivative (PID)-controller, tuned via linear matrix inequalities (LMIs)-theory, stabilises all linear modes within the polytopic defined by the vertices of the linearised systems. The overall scheme comprises: (a) a feedforward controller that stabilises the μ-A around its nominal operating points and (b) a robust PID controller that handles deviations from the operating points. The resulting overall control scheme is applied to the non-linear (bimodal structure) of a μ-A, and the simulation results derived are used to investigate the efficacy of the suggested control architecture.