Tracking control of an electrostatic torsional micromirror beyond the pull-in limit with enhanced performance

In this paper, we will study the output-error-constrained tracking control problem of an electrostatic torsional micromirror beyond the pull-in limit. We will first show that this problem can be formulated as a robust output regulation problem and it further boils down to a robust regulation problem with output-constrained by adaptive internal model design, the solution of which would in turn lead to the solution of the original problem. Then we design a regulation controller for such a regulation problem by using the barrier Lyapunov function technique. Our adaptive control law ensures the electrostatic torsional micromirror with a enhanced tracking performance in the sense that the moveable micromirror can achieve the sinusoidal wave scanning of any frequency up to a full gap operation without contacts of the fixed bottom electrode, and furthermore, the estimated sinusoidal wave frequency converges to its real value.