Robust control design for an uncertain electrostatic micro-mechanical system via loop shaping

This paper presents the design of a robust model-based controller coupled to a feed-forward compensator set-point regulation maneuvers of an electrostatic micro-mechanical actuator system (eμm-A) with uncertainty on its supporting springs. Linearised models of the nonlinear system are considered at multiple operating points for short-range maneuvers in distances smaller than the systems bifurcation point, while the feedforward compensator provides the nominal voltage. The robust controller, designed via ℋ_∞ loop-shaping, handles any perturbations around these points while guarantees robustness against the switching nature of the linearized system dynamics. Moreover, the controller successfully tolerates any variation of the system´s uncertain parameter. The performance of the designed controller is assessed via a number of appropriate simulation studies to prove its efficacy.