Abstract: Because the current responses of the permanent magnet synchronous motors (PMSMs) are much faster than the mechanical dynamic, a tracking differentiator (TD)-based dual-time-scale sliding mode control (SMC) method is proposed in this paper. Firstly, the mathematical model is established in the two-phase synchronous rotating orthogonal reference coordinate system, while the fast and slow subsystems are subsequently obtained based on the quasi-steady-state theory. Secondly, in order to address the contradiction problem between the reaching velocity and the chattering phenomenon existing in the traditional exponential reaching law, a novel reaching law is introduced, thus the reaching-time and switching-band are compared and analyzed. Then, the SMC laws are separately designed the within dual-time-scale, thus resulting the eventual TD-based composite non-cascade sliding mode controller. Finally, the advantages and effectiveness of the proposed methods are demonstrated by the simulation comparisons and experimental results. The research results illustrate that the proposed control strategy can realize the tracking without any overshoot, and the dynamic response procedure of the servo system is very fast. The control system has the perfect dynamic performance when the PMSM operates in the reverse direction, and possesses the strong robustness against the external load disturbances.

Key words: Permanent Magnet Synchronous Motors (PMSMs), Dual-Time-Scale, Tracking Differentiator(TD), Sliding Mode Control (SMC), Reaching Law, Non-Cascade