永磁同步电机调速系统的自抗扰控制

Active disturbance rejection control of speed governing system for PMSM

提出了一种利用反双曲正弦函数的一阶自抗扰控制器,以提高永磁同步电机正弦波脉宽调制(SPWM)调速系统的跟踪精度。研究了永磁同步电机转速环的数学模型;分别设计了一阶跟踪微分器和二阶扩张状态观测器,利用李雅普诺夫函数分析了它们的收敛性;构造了转速环的一阶自抗扰控制器,同时证明了一阶自抗扰控制误差系统的渐近稳定性。最后,将该新型一阶自抗扰控制器作为永磁同步电机的转速调节器,分析了自抗扰控制永磁同步电机的SPWM调速系统。仿真实验表明:自抗扰控制调速系统速度阶跃跟踪的调整时间约为0.15 s,稳态误差小于0.28 r/min;同一调速系统正弦响应的最大跟踪误差约为17 r/min。与PI控制调速系统相比,自抗扰控制永磁同步电机调速系统阶跃响应快速而平稳,无超调,稳态误差小;另外,系统正弦响应的跟踪性能好,跟踪误差小。

A first-order Active Disturbance Rejection Controller（ADRC） with an arc-hyperbolic sine function was presented to increase the tracking precision of the Sinusoidal Pulse Width Modulation（SPWM） speed governing system of a Permanent Magnet Synchronous Motor（PMSM）. A mathematical model for the velocity loop of the PMSM was studied. Then a first-order tracking differentiator and a second-order extended state observer were designed respectively and their convergences were analyzed by using the Lyapunov function. The first-order ADRC of the velocity loop was constructed, and the asymptotic stability of the first-order ADRC error system was verified. Finally, the designed first-order ADRC was used as the rotating speed adjuster of the SPWM, and the SPWM speed governing system with the ADRC was analyzed. Simulation experiments demonstrate that the speed step response adjustment time of the SPWM speed governing system with the ADRC is 0.15s, the steady error is less than 0.28 r/rain, and the maximum sine tracking error is 17 r/min. As compared with a PI controller, the governing system with the ADRC is characterized by fast and stable step response, smaller stable error and no overshoot. Moreover, it shows better sine tracking performance and smaller tracking errors.