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.