Adaptive backstepping sliding mode control for 3-DOF permanent magnet spherical actuator

In this paper, a robust adaptive control system combining backstepping and sliding mode control method has been implemented for the 3-DOF permanent magnet (PM) spherical actuator in order to improve its trajectory tracking performance. Due to the complexity of both mechanical structure and electromagnetic field, the dynamic model of a PM spherical actuator inevitably contains uncertainties, such as disturbances and model errors, which will gravely influence the performance of conventional control system. Therefore, a backstepping sliding mode approach is firstly applied, where the backstepping design is to synthesize the controller and the sliding mode term is to compensate disturbances. Then, an adaptive law is presented to estimate the model errors during the control process, where the parameters of the model are initially assumed to be accuracy. Correspondingly, the stability can be guaranteed by choosing the appropriate Lyapunov function. Both simulations and experiments are designed to demonstrate the effectiveness of the proposed control scheme.