Robust PID-control design for an electrostatic micromechanical? actuator with structured uncertainty

In this article, a robust PID controller coupled to a feedforward compensator is designed for set-point regulation maneuvers of an electrostatic micromechanical system. The system is linearized at multiple operating points, and the feedforward compensator provides the nominal voltage. Perturbations around these points, are handled from the PID-controller, whose gains are tuned via the utilization of an LMI-approach which guarantees robustness against the switching nature of the linearized system dynamics. The maximum microspring-stiffness parametric uncertainty that can be tolerated within this scheme, is computed through the use of the small-gain theorem. Simulation studies are presented that proves the efficacy of the suggested scheme.