This paper addresses the periodic position tracking and load force disturbance rejection in linear permanent magnet synchronous motors (LPMSM). Periodic position tracking is a challenge for LPMSMs, as there are electromagnetic forces that are not uniform along the actuator stroke due to end effects, which can lead to position variations. The proposed control structure combines a proportional–integral (PI) controller in the direct-axis control loop and a modified PI plus a multiple resonant controller (PI-RES) in the quadrature-axis control loop to ensure periodic reference tracking and disturbance rejection. The controller design is carried out by solving a convex optimization problem under linear matrix inequality (LMI) constraints, which guarantee closed-loop stability and transient performance. Simulations and experimental results are performed using a dual quasi-Halbach permanent magnet array linear tubular actuator with a coreless moving armature. The effectiveness of the proposed method is evaluated by applying position reference signals with different frequencies and harmonic compositions in conjunction with two types of load force disturbances. Experiments show the proposed controller results in precise reference tracking with negligible steady-state error.

中文翻译：

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多环谐振控制应用于线性永磁同步电机的周期性位置跟踪

本文讨论了线性永磁同步电机 (LPMSM) 中的周期性位置跟踪和负载力扰动抑制。周期性位置跟踪对于 LPMSM 来说是一个挑战，因为由于末端效应，沿致动器行程的电磁力不均匀，这可能导致位置变化。所提出的控制结构结合了直轴控制环路中的比例积分（PI）控制器和正交轴控制环路中的修正PI加多谐振控制器（PI-RES），以确保周期性参考跟踪和干扰抑制。控制器设计通过求解线性矩阵不等式（LMI）约束下的凸优化问题来进行，保证了闭环稳定性和瞬态性能。仿真和实验结果是使用带有无芯移动电枢的双准 Halbach 永磁体阵列线性管状执行器进行的。通过应用具有不同频率和谐波成分的位置参考信号并结合两种类型的负载力扰动来评估所提出方法的有效性。实验表明，所提出的控制器可以实现精确的参考跟踪，并且稳态误差可以忽略不计。