Dynamic Sliding Mode Backstepping Control for Vertical Magnetic Bearing System

Abstract

Electromagnets are commonly used as support for machine components and parts in magnetic bearing systems (MBSs). Compared with conventional mechanical bearings, the magnetic bearings have less noise, friction, and vibration, but the magnetic force has a highly nonlinear relationship with the control current and the air gap. This research presents a dynamic sliding mode backstepping control (DSMBC) designed to track the height position of modeless vertical MBS. Because MBS is nonlinear with model uncertainty, the design of estimator should be able to solve the lumped uncertainty. The proposed DSMBC controller can not only stabilize the nonlinear system under mismatched uncertainties, but also provide smooth control effort. The Lyapunov stability criterion and adaptive laws are derived to guarantee the convergence. The adaptive scheme that may be used to adjust the parameter vector is obtained, so the asymptotic stability of the developed system can be guaranteed. The backstepping algorithm is used to design the control system, and the stability and robustness of the MBS system are evaluated. Two position trajectories are considered to evaluate the proposed method. The experimental results show that the DSMBC method can improve the root mean square error (RMSE) by 29.94% compared with the traditional adaptive backstepping controller method under different position tracking conditions.