Optimal Lyapunov-Based Sliding Mode Control for Slotless-Self Bearing Motor System

A slotless self-bearing motor (SSBM) is a new type of electric motor, with its levitating and rotating capability as a drive system. In the design of motor, the iron core of stator was removed, it could have many advantages such as small size, light, no friction loss, low losses, high speed. Besides, disturbance and uncertainty factors are the unexpected values, which impacting strongly to the output of the control system. In this paper, to reject the effects of these factors, an optimal Lyapunov-based (OLB) sliding mode control (SMC) was proposed to control the movements and rotation of SSBM system. First, the mathematical model with uncertainty and disturbance factors of the SSBM system was rewritten to show the detail configuration of the proposed motor. Second, the OLB-SMC controllers were designed for the control of displacements on x-, y-axes, rotor speed on omega-axes, respectively. Third, the stability analysis of control algorithm was demonstrated via the Lyapunov stability theory. Finally, the experimental test was implemented to prove the high performance of the OLB-SMC for SSBM system. The practical results show that the effectiveness of OLB-SMC controller for SSBM system. The novelty of the proposed method is that the stability condition was newly proposed based on the transformation from scalar equation to state-space equation, where the gains of controller were found based on the linear matrix inequality.