Stabilization of an electrostatic MEMS including uncontrollable linearization

Electrostatic micro-actuators are not linearly controllable in a set containing the origin due to a quadratic term of electrical variable appearing as the input to the mechanical subsystem. Consequently, such systems are not feedback linearizable and thus not differentially flat on this set and the application of techniques based on feedback linearization leads usually to an unbounded control. This work aims at developing control schemes which should be bounded everywhere in the whole operational range. As there are no existing general frameworks for tackling the control design for the system under consideration, the approach of Lyapunov design combined with backstepping is used. The obtained control scheme is proved to stabilize the system at the above mentioned uncontrollable set. Furthermore, we address the output feedback control using a reduced order observer and certainty-equivalence implementation. The closed-loop stability is demonstrated by both stability analysis and numerical simulation.