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

A robust proportional integral derivative (PID) controller coupled to a feedforward compensator is designed for set-point regulation manoeuvres of an electrostatic micromechanical system. The system is linearised 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 utilisation of a linear matrix inequality (LMI) approach, which guarantees robustness against the switching nature of the linearised 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.