Modeling and control of a nonlinear micro-electro-mechanical beam

This thesis develops a new detailed model and new control properties for the control of a nonlinear MicroElectroMechanical Systems (MEMS) and investigates the performance of various controllers. The system is composed of a MEMS cantilever beam, an electrostatic controller, squeeze film damping, and stabilizing velocity and position feedback. The MEMS cantilever beam dynamics are represented by coupled parallel second order modes. The electrostatic controller is a nonlinear subsystem with singularities in beam position. The squeeze film damping is nonlinear with singularities in beam position. Feedback control through the electrostatic controller is nonlinear. The combination of these subsystems, called the Beam System, form a highly nonlinear system with control difficulties including controllability problems, stability problems and computational difficulties due to the singularities. New design modifications are made to the electrostatic controller to increase the available force and to assure controllability through the operating range of the MEMS cantilever beam. Position and velocity performance limits are defined. A new simulation of the system model is developed. System properties are analytically explored and verified by simulation. Control performance of the Beam System is explored using three control schemes, Direct Control (no feedback), Proportional-Integral Control, and Direct Model Reference Adaptive Control. Performances of these three control schemes are compared. These developments are of interest for applications that require precision path control of MEMS structures including accelerometers and the general positioning of microstructures.