【目的】为了提高基于非线性磁链观测器(NFO)的永磁同步直线电机(PMSLM)无位置传感器控制系统的控制精度，本文考虑了PMSLM固有的端部效应对电机模型参数的影响，并对NFO进行了重构。此外，为了提高传统扩张状态观测器(ESO)在PMSLM无位置传感器控制系统中的抗扰动能力，提出了一种变增益扩张状态观测器锁相环(VGESO-PLL)位置解算方法。【方法】首先，考虑到PMSLM固有的端部效应在电机运行过程中所造成的电压偏差，对现有数学模型进行了修正，并对NFO进行重构。然后，通过分析ESO带宽对位置估计性能的影响，提出了一种改进的VGESO控制方法。该方法在传统ESO中引入了受估计速度导数驱动的带宽变化律，以动态改变ESO带宽，从而提高了瞬态条件下的速度观测精度。最后，通过欧拉离散方法，对VGESO的特征方程进行求解，并结合Jury判据给出了VGESO带宽选择范围。【结果】试验结果表明，在速度从0.1 m/s突增至0.3 m/s的工况下，VGESO-PLL的最大速度估计误差相较于传统PLL减小了8.05%，虽然最大速度估计误差和ESO-PLL一致，但速度估计误差波动范围较ESO-PLL更小；在速度从0.3 m/s突减至0.1 m/s的工况下，VGESO-PLL的最大速度估计误差相较于传统PLL减小了73.1%，较ESO-PLL减小了37.7%。【结论】本文重构的NFO能够反映PMSLM端部效应的影响，所提VGESO-PLL位置解算方法可以有效改善PMSLM在速度突变工况下的速度观测精度，有效提高了VGESO的抗扰动能力。

[Objective] To enhance the control accuracy of the nonlinear flux observer (NFO)-based sensorless control system for permanent magnet synchronous linear motor (PMSLM), the influence of the inherent end effects in the PMSLM on the motor model parameters is considered and the NFO is redesigned accordingly in this paper. Furthermore, to improve the disturbance rejection capability of the traditional extended state observer (ESO) in PMSLM sensorless control system, a position calculation method employing a variable gain ESO with phase-locked loop (VGESO-PLL) is proposed. [Methods] Firstly, considering the voltage deviation caused by the inherent end effects of the PMSLM during motor operation, a modification to the existing mathematical model was implemented and then the NFO was redesigned. Then, by investigating the impact of ESO bandwidth on position estimation performance, an improved VGESO control method was proposed. This method incorporated a bandwidth variation law driven by the derivative of the estimated speed into the traditional ESO, enabling dynamic adjustment of ESO bandwidth and to enhance the speed observation accuracy under transient conditions. Finally, the characteristic equation of the VGESO was solved by adopting Euler discretization method, and the allowable bandwidth range of the VGESO was determined using the Jury criterion. [Results] Experimental results showed that under operating condition at sudden acceleration from 0.1 m/s to 0.3 m/s, the maximum speed estimation error of the VGESO-PLL was reduced by 8.05% compared to the traditional PLL. Although the maximum speed estimation error was identical to that of ESO-PLL, its speed estimation error exhibited a smaller fluctuation range than ESO-PLL. And under operating condition at sudden deceleration from 0.3 m/s to 0.1 m/s, the maximum speed estimation error of the VGESO-PLL was reduced by 73.1% compared to the traditional PLL and by 37.7% compared to the ESO-PLL. [Conclusion] The restructured NFO in this paper can reflect the influence of the PMSLM end effects. And the proposed VGESO-PLL position calculation method can effectively enhance the speed observation accuracy of the PMSLM under sudden speed change conditions, thereby enhancing the disturbance rejection capability of the VGESO.

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