Fuzzy Adaptive Back-Stepping Sliding Mode Controller for High-Precision Deflection Control of the Magnetically Suspended Momentum Wheel

In the magnetically suspended momentum wheel, the orientation of the rotor shaft can be actively changed to generate 2-D torques. An adaptive back-stepping sliding mode control (SMC) method is proposed to precisely control the deflection angles. First, the magnetic torques generated by the magnetic bearings are analyzed. According to the magnetic torques, coupled torques exist and influence the tracking control of the deflection angles. It is difficult to model the coupled torque disturbances because their relationship with translations, deflection angles, currents, and other parameters is complex. By analyzing the dynamics and the magnetic torques, the tracking error dynamic is modeled as a system with unmodeled disturbances and parameter uncertainties. A back-stepping integral sliding mode controller whose sliding surface considers the integrals of the angle error and the tracking error is designed for this system. The switching gain should be relatively large to ensure system stability. This will induce severe chattering, which hinders the precision of the deflection angle. A fuzzy algorithm whose inputs include the sliding value and deflection angle is designed to adaptively tune the switching gain of the sliding mode method. According to the simulation and experimental results, the proposed method improves tracking performances and reduces chattering.