Robust, Digital, Nonlinear Control of Magnetic-Levitation Systems

Abstract

This paper presents a robust, adaptive, nonlinear controller for a class of magnetic-levitation systems, which includes active-magnetic bearings. The controller is analytically and experimentally shown to be superior to a classical linear control system in stability, control effort, step-response performance, robustness to parameter variations, and force-disturbance rejection performance. Using an adaptive backstepping approach, a Lyapunov function is generated along with an adaptive control law such that the nonlinear, closed-loop, continuous system is shown to guarantee stability of the equilibrium and convergence of the parameter estimates to constant values. The control system error coordinates are proven to be bounded in the presence of a bounded force disturbance input. The novelty of this controller is that it is digitally implemented using Euler integrators with anti-windup limits, it is single-input-single-output requiring only a measurement of the position of the levitating object, and it is designed to adaptively estimate not only the uncertain model parameters, but also the constant forces applied to the levitating object in order to ensure robustness to force disturbances. The experimental study was conducted on a single-axis magnetic-levitation device. The controller is shown to be applicable to active-magnetic bearings, under specific conditions, as well as any magnetic-levitation system that can be represented in output-feedback form.