为了解决初态偏差对直线电机位置完全跟踪的影响, 针对存在初态偏差的永磁直线同步电机位置伺服系统, 提出了一种迭代学习控制算法. 该算法在控制输入矩阵未知的情况下, 利用初始跟踪误差不断修正上一次的初始状态, 同时利用跟踪误差和跟踪误差导数不断修正上一次控制输入, 并利用λ范数理论严格证明了算法的收敛性, 给出了算法的收敛条件. 理论和仿真结果表明, 所提算法能够使永磁直线同步电机在任意初始状态下, 随迭代次数的增加可实现在有限时间区间上对期望位置的完全跟踪, 且对直线电机的负载扰动, 摩擦力和推力波动等重复性扰动具有很好的抑制作用.

In order to solve the impact of the initial errors on the position full tracking of the linear motor, an iterative learning control algorithm is proposed for the position servo system of permanent magnet synchronous motors with initial state errors. The algorithm can constantly correct the last initial state with the initial tracking error under the condition of the unknown control input matrix, and constantly correct last control input using tracking error and tracking error derivative. And the convergence of the algorithm is proved strictly by the $\lambda$-norm theory, and the convergence condition is given. The results of theory and simulation show that the proposed algorithm can make the motor realize complete tracking of the desired position in a finite time interval with the increase of the number of iterations in any initial state, and can suppress the repeated disturbances such as load disturbance, friction and thrust fluctuation of linear motor.