中文摘要：

针对非线性、强耦合、直驱型的永磁球形电机动力学系统,设计了一种自适应反演滑模控制器.首先,通过拉格朗日第二方程以及卡尔丹角坐标变换建立永磁球形电机的转子动力学方程.然后,将反演设计方法和滑模控制有机结合抑制外界扰动和参数摄动的影响.其中,基于类李雅普诺夫方法获得外界扰动上界的自适应律,并采用一种新颖的趋近律消除抖振问题.最后,仿真结果对比证实：该控制器不仅能保证永磁球形电机动力学系统高精度的轨迹跟踪、快速的动态响应,而且对外界扰动具有较强的鲁棒性.

英文摘要：

Due to the nonlinear and strong coupling dynamic model of a direct-drive permanent magnet spherical motor （PMSM） dynamics system, an adaptive backstepping sliding mode controller is devel- oped. Firstly, by using the second Lagrange equation and the Carden angle coordinate transformation, the PMSM rotor dynamic model is achieved. Secondly, the proposed approach effectively combines the design techniques of backstepping and the sliding mode control in order to restrain the effects of the ex- ternal disturbance and parameter variations. Adaptive law of the external disturbance upper bound can be derived based on the Lyapunov-like design. Moreover, a novel reaching law is used to overcome the chattering phenomenon. Finally, simulation studies prove that the control scheme has high accuracy, rapid response and strong robustness.