Robust nonlinear control of the electromagnetically controlled oscillator

Most microelectromechanical systems are based on electromagnetic or electrostatic actuation forces. It is well known that linear controllers based on linearized models have a stable actuation range of one third of the nominal gap, while at larger displacements the electrostatic force dominates resulting in the electrodes pulling together. For Hammerstein systems with quadratic input nonlinearity we propose a nonlinear controller that guarantees stability and bounded disturbance rejection. For a single-sided electromagnetic oscillator we use this controller to achieve tracking. For a double-sided electromagnetic oscillator, we propose a control algorithm that achieves the desired performance while guaranteeing that the electromagnetic plates never pull together. These nonlinear controllers are robust since their stabilization and disturbance rejection properties do not require knowledge of the inertia, damping and stiffness of the plant.