Fractional Order Approach for Conical Active Magnetic Bearings Under Time Delay and Supply Faults

A conical magnetic bearing system (CAMBs) has emerged as a promising solution for various applications relying on magnetic force, thanks to its unique geometry, which reduces the need for multiple active magnets and reduces energy consumption for supporting maximum loads and lower copper losses. Due to the inherent nonlinearity and coupling characteristics of the 5-DOF CAMBs, a detailed mathematical model as well as the design of a highly accurate control scheme are essential, especially under the influence of external disturbances, unbalance disturbances, and supply faults. The proposed mathematical model integrates both the electrical and mechanical systems, making it subject to mismatched and matched disturbances. Furthermore, the system also accounts for issues such as supply faults, supply saturation, and time delays in both power supplies and sensors. To address these challenges, a cascade control structure for CAMBs is proposed, comprising an outer loop and an inner loop. The outer loop employs fractional order sliding mode control (FOSMC) to regulate the rotor’s displacement and rotational angle. Meanwhile, the inner loop utilizes a fractional-order PID (FOPID) controller to control coil currents, effectively mitigating the influence of eddy currents and the time delay issues associated with power supplies and sensors. Furthermore, disturbances are addressed through a hybrid extended state observer (ESO) structure, where a fast ESO is implemented in the inner loop, while a slow ESO is applied to the outer loop to observe mismatched and matched disturbances. Overall stability of the closed-loop system control is mathematically proven. Finally, the simulation evaluation using particle swarm optimization for CAMBs under disturbances, faults, and time delays demonstrates that the proposed control system achieves effectiveness, feasibility, and robustness.