Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking

This study addresses an output-error-constrained tracking problem for the one degree of freedom parallel-plate electrostatic actuator. The authors first formulate the control problem as a robust output regulation problem for an output feedback system. Then they show that it can be further converted into a robust regulation problem with output constraint by internal model design. Finally, a regulation controller for this regulation problem by using a barrier Lyapunov function technique is designed. By an appropriate selection of some controller parameter and an appropriate initial displacement of the movable plate, the final designed output-error-constrained tracking control law ensures that, in the presence of large parameter variations, the harmonic displacement of the parallel-plate electrostatic actuator can be beyond the pull-in position and up to the full gap without contacts between the movable and fixed plates during the transient period.