Dual-loop PID controller design and simulation for zero-power single-degree-of-freedom permanent electromagnetic suspension system

In mass transportation and active magnetic bearings, magnetic levitation technologies show great commercial potential. However, instability and nonlinearity pose challenges to electromagnetic suspension (EMS) systems. This paper focuses on the dual-loop PID controller design for a zero-power single-degree-of-freedom (DoF) permanent electromagnetic suspension (PEMS) system. The single-DoF PEMS system model is established, highlighting the linear relationship between magnetic force and excitation current, achieved via a floating rare-earth permanent magnet. A symmetric hall-effect-based distance sensor is used, making magnetic force proportional to the square of transformed distance, represented by compensated magnetic flux density. The dual-loop PID controller, with a PD controller for the distance loop and an I controller for the power loop, is designed to stabilize the system and achieve zero-power suspension. Numerical simulations demonstrate the effectiveness and robustness of the proposed controller under mass step changes. Results indicate that the controller maintains stability if the proportional gain exceeds the critical value during transients, especially for positive currents. However, excessive transient currents can cause integral windup in the power loop, affecting stability. The study shows that a suitable nominal natural frequency of the distance PD controller at a given equilibrium point can ensure sufficient stability margins against moderate mass step changes over a large range. This work provides a robust dual-loop PID framework that achieves zero-power suspension with fixed control parameters. The approach enhances both efficiency and scalability, offering a foundational PEMS module for extension to multi-DoF maglev systems.