Modeling of a six-degree-of-freedom magnetic levitation platform actuated by noncontact Lorentz forces

Abstract

In this study, the modeling of a six-degree-of-freedom (DOF) magnetic levitation platform actuated by noncontact Lorentz forces was analyzed. First, an analytic model of the actuator forces was studied, and the magnetic flux density in the working gap of the actuators was established using the Image Method, Ampere molecular hypothesis, and Biot–Savart law. The dynamics model of the floater actuated by the actuators was then built using the Newton–Euler method. Moreover, the double-pendulum chaotic nonlinear system of the hoisted floater was simplified as a single-DOF system, in which the interaction effects between two DOFs were considered. Furthermore, modeling of the platform control system was performed, which included an acceleration measuring unit with six uniaxial accelerometers, a position measuring unit with three two-dimensional PSDs, and a control unit that decouples the six-DOF control. Finally, an experimental setup was built to perform ground tests on the platform. The results verified the platform modeling; translational and rotational positioning accuracies were approximately 5 μm and 40 μrad at the six DOFs, respectively, and the vibrational suppression efficiencies were greater than 90% for low frequency disturbances. Moreover, Kalman estimators and disturbance observers were introduced into the controller to estimate the movement of the floater and observe the direct disturbance. Simulation testing demonstrated a significant improvement in the vibration-suppression performance of the platform.