A modified adaptive backstepping method for shaft deflection tracking control of magnetically suspended momentum wheel with nonlinear magnetic torque

A modified adaptive backstepping tracking method is proposed to improve the tracking performance of the magnetic bearing system with nonlinear magnetic toque. For a magnetically suspended momentum wheel, two dimensional gyroscopic torque can be produced when the rotor shaft is actively deflected by the active magnetic bearing. High precision rapid tracking control of shaft deflection is desiderated to provide high precision and wide bandwidth outputting torque. The nonlinearity of magnetic bearing is analyzed initially, and the stiffness coefficients of magnetic bearing can be treated as bounded continuous functions with respect to deflection angles. A fuzzy function based adaptive law is proposed to estimate the stiffness coefficients. Combining with a modified backstepping method, the proposed control strategy can deal with the nonlinearity efficiently when the shaft deflects rapidly, and its stability is proved by Lyapunov stability theory. To validate the effectiveness of this method, numerous simulations are performed and the results indicate that this method improves the tracking precision when tracking high frequency reference deflection angles.