永磁同步电动机的电流响应远快于机械动态,因此提出一种基于跟踪微分器的双时间尺度滑模控制方法.首先,在两相同步旋转正交坐标系上建立数学模型,并基于准稳态理论得到快慢子系统.其次,为了解决传统指数趋近律中趋近速度与抖振现象相互矛盾的问题,引入一种新型趋近律,并对其能达时间和切换带进行对比分析.然后,在双时间尺度内分别设计控制律,构建基于跟踪微分器的复合非级联滑模控制器.最后,通过仿真对比和实验结果验证方法的优势和有效性.研究结果表明,该控制策略能实现无超调跟踪,且伺服系统的动态响应迅速;在永磁同步电动机发生反转和受到外部负载扰动时,控制系统仍具有良好的动态性能和较强的鲁棒性.

Due to the much faster response time of permanent magnet synchronous motor (PMSM) compared to mechanical dynamics, a tracking differentiator (TD)-based dual-time-scale sliding mode control (SMC) method is proposed. First, the mathematical model is established in a two-phase synchronous rotating orthogonal reference coordinate system, and the fast and slow subsystems are then derived based on the quasi-steady-state theory. To address the conflict between reaching velocity and chattering phenomenon existing in the traditional exponential reaching law, a novel reaching law is introduced, allowing for a comparison and analysis of the reaching-time and switching-band. Next, the SMC laws are separately designed within a dual-time scale, thus resulting in the eventual TD-based composite non-cascade sliding mode controller. Finally, the advantages and effectiveness of the proposed methods are demonstrated through the simulation comparisons and experimental results. The results illustrate that the proposed control strategy can realize tracking without any overshoot, ensuring a fast dynamic response procedure in the servo system. The control system has the perfect dynamic performance when the PMSM operates in the reverse direction, and possesses strong robustness against the external load disturbances.