Magneto-mechanical modelling and quantitative feedback theory control of a magnetic levitation test bed: theory and experiments

Abstract This paper presents the modelling and robust control of a one-degree-of-freedom ferromagnetic beam actuated by a pair of electromagnetic actuators in differential configuration. A grey-box model is constructed by combining analytical formulations, actuator characterization and experimental frequency-domain identification, enabling accurate capture of unmodelled dynamics. The baseline controller stabilizes the open-loop unstable magnetic levitation system (MLS) in real time, but exhibits limited robustness to disturbances and parameter variations. To address this, a quantitative feedback theory design with Nichols-plane loop shaping is implemented using both analytically and experimentally derived loop transfer functions. Experimental tuning of the loop transfer function leads to the required performance metrics of gain and phase margin, as well as a sensitivity reduction compared to the baseline controller. This study establishes an effective framework for high-fidelity modelling and robust control of MLSs.