Stabilization of a mass and spring system with electromagnetic actuation

In order to examine the problem of deforming a membrane into a paraboloid shape by means of electrostatic forces, we consider a system involving a mass, a spring, and an electromagnet. We show that if the equilibrium gap is less than two-thirds of the relaxed gap, then the equilibrium is unstable. We then demonstrate controllers that stabilize these unstable equilibria and consider the actuator requirements needed to effect stabilization. Finally, we describe a control experiment designed to test control laws for stabilization of the membrane.