Nonlinear control of an electrostatically actuated MEMS

Of the wide variety of actuation methods that have been developed for microelectromechanical systems (MEMS), electrostatic devices are the most common. The operation of these devices may be primarily categorized as digital and analog. Although the technology in digital operations is quite well developed the analog operations are not as developed due to an inherent nonlinear phenomenon in electrostatic actuation commonly known as "snap-through" "or pull-in." The concern of this thesis is analog control of electrostatically actuated MEMS devices. A simple 1-D model of electrostatic actuation is sufficient to capture the salient nonlinearities of the general problem. Several analog control schemes for such a model are proposed in the literature based on physical intuition. In the first part of the dissertation we show how these control schemes can be derived from the application of standard nonlinear control theory. Then we employ notions of feedback linearization, passivity and nonlinear state estimation to derive much improved control schemes that eliminates snap-through, improve performance with respect to low overshoot and faster settling times. The second part of the dissertation is concerned with generalizing the analog control notions developed for the 1-D model to a 3-D model where the device is assumed to freely rotate as well as translate. We first note that the system can be perceived as a coupled electromechanical system where the configuration space of the mechanical subsystem is the special Euclidian motion group SE{S). Thus we approach the problem from the setting of finding intrinsic control strategies for mechanical systems on general Lie groups. Furthermore, we do it in such a way that no coordinates need to be introduced on the Lie group. Thus, apart from the simplicity it provides, the tools developed in here may be of great importance to long term trajectory planning and optimal control problem on Lie groups and stabilization and active vibration absorption of rigid 3-D structures.