Robust PID Control for a Micro-Actuator with Structural Uncertainty

In this article the effects of unaccounted structural dynamics within the control scheme of a micro-Actuator (mu-A) are presented. The mu-A is composed of a micro-capacitor, whose one plate is clamped while its other flexible's plate motion is constrained by hinges acting as a combination of springs and dashpots. The dynamic model of the mu-A allows both linear and angular movements of the plate. Rather than designing a controller for the augmented system, a simplified robust PID control law for the reduced model is employed. The reduced non linear model (RnM) assumes only linear motion for the mu-capacitor's plate. The RnM is linearized at multiple operating points, and the designed PID-controller, tuned via LMI-theory, stabilizes all linear modes. The overall scheme comprises: a) a feedforward controller which stabilizes the micro-actuator around its nominal operating points, and b) a robust PID controller which handles deviations from the operating points. The resulting overall control scheme is applied to the non linear (bimodal structure) of a mu-A, where simulation results are used to investigate the efficacy of the suggested control architecture