Abstract: For the speed tracking control problem of permanent magnet synchronous motor (PMSM), an reduced-order observer-based back-stepping speed tracking control method is presented. Firstly, the output value of the rotational speed of the PMSM is used to construct a full dimensional Luenberger observer. By using Lyapunov stability theory, the linear matrix inequality (LMI) based design method of observer is obtained. Then, based on the full order observer, a reduced order observer is designed by using matrix decomposition techniques. To realize the high precision tracking for the motor speed, a back-stepping control strategy of the closed-loop system is also proposed. Finally, the effectiveness of the proposed method is verified by numerical simulation. The simulation results show that the designed controller can make the output of the system quickly track the reference speed and has high tracking accuracy.

Key words:  PMSM, observer, speed sensorless, back-stepping control

摘要： 针对永磁同步电机(PMSM)的速度跟踪问题，提出一种基于降维观测器的反推控制器设计方法。首先，利用永磁同步电机的转速输出值构造全维Luenberger观测器，并利用Lyapunov稳定性理论，获得基于线性矩阵不等式(LMI)的观测器设计方法。然后，基于获得的全维观测器，利用矩阵分解技巧设计降维观测器，并运用反推控制策略来设计闭环系统控制器，实现电机转速输出对期望输出信号的高精度跟踪。最后，通过数值仿真，验证所提出方法的有效性。仿真结果表明，设计的控制器能使系统的输出快速跟踪参考转速，具有较高的跟踪精度。

关键词: 永磁同步电机, 观测器, 无速度传感 , 反推控制