伺服电机具有关于转子位置的空间周期特征，表现为转子的周期旋转或往复摆动，但现有的非线性控制技术却鲜有利用这一显著特征。重复学习控制适用于周期运行的系统，能够实现高精度跟踪周期轨迹和完全补偿周期不确定动态。因此，利用电机的空间周期特征，探索和研究空间域上的重复学习控制理论，是实现电机高精度轨迹跟踪控制的一条新途径。本项目研究内容主要包括：1) 建立空间重复学习控制理论，研究空间域上的重复学习律和控制器设计方法，补偿参数化和非参数化不确定的影响，提高电机稳态跟踪精度；2) 构建时间区间到空间区间的等价转换机制，将电机齿槽转矩脉动的时域非周期特性转化为空间周期函数，以便设计空间重复学习律估计齿槽转矩脉动等空间不确定动态；3) 提出基于空间重复学习控制理论的一体化控制器设计方案，并研究空间自适应鲁棒重复学习控制以及空间状态约束重复学习控制等控制策略，改善电机稳态跟踪性能和瞬态响应速度。

The servo motor has the spatial periodic characteristics of the rotor position, which is represented by the periodic rotation or reciprocating oscillation of the rotor. However, the existing nonlinear control technologies can seldom take advantage of this remarkable feature. Repetitive learning control is applicable for the systems performing periodic operations, and it is capable to achieve the high trajectory tracking accuracy and complete compensation of periodic uncertainties. Consequently, the exploration and research on the repetitive learning control theory in spatial domain becomes a new way to achieve the high accuracy trajectory tracking control of the motor by utilizing its spatial periodic characteristics. The prospective work in this project mainly includes: 1) The spatial repetitive learning control theory is established, and the repetitive learning law and the corresponding controller design in spatial domain are developed to compensate for the effects of parametric and non-parametric uncertainties and improve the motor steady-state tracking accuracy; 2) The transform mechanism from time domain into spatial domain is constructed, and the non-periodic characteristics of the cogging torque ripples in time domain could be transformed into the periodic function in spatial domain, such that the spatial repetitive learning law is applied to estimate the spatial uncertain dynamics including the cogging torque ripples; 3) The integrative motor controller design scheme is proposed based on the repetitive learning control theory, and the repetitive learning control strategies, including spatial adaptive robust repetitive learning control and spatial state-constraint repetitive learning control, are developed to improve the motor steady-state tracking performance and transient response speed.