针对存在有界的、周期变化的非线性不确定动态的二阶系统，提出一种使系统渐近地跟踪目标轨迹的控制律。考虑仅能施加单向控制量的系统，所提出的控制律利用饱和函数和基于在线学习的估计器相结合来学习和估计未知非线性动态特性，并对未知动态进行补偿以保证系统跟踪误差渐近收敛于零。同时引入自适应陷波滤波器（Adaptive notch filter，ANF）来在线估计未知非线性动态特性的频率。不同于以前的方法，提出的基于ANF的饱和改进型重复控制律只需要未知动态特性是有界的（未知动态特性的结构、参数、频率是不需要预先知道的）。最后将此控制律应用到只能提供竖直向上电磁力的EMS型磁悬浮系统中，设计出适合磁悬浮系统的控制策略。仿真结果证明了所提出的控制策略的有效性。
An improved saturated learning-based control law is proposed to deal with a class of unidirectional control input systems to make the systems track the target trajectory asymptotically. Considering the systems with unidirectional control input only, the presented control law utilizes a saturated function and repetitive learning estimator to online learn and estimate the unknown periodic nonlinear dynamics, and compensate for the unknown dynamics to ensure the convergence of the tracking error asymptotically. At the same time, an adaptive notch filter(ANF) is utilized to online estimate frequency of the periodic dynamics in conjunction with the improved saturated learning-based control law. Differing from the previous methods, the presented control law only needs the uncertain dynamics is bounded (the structure, parameters and frequency of the uncertain dynamics is not need to be given beforehand). At last, the presented control law is applied to the electromagnetic suspension system(EMS), which can only provide a vertical upward electromagnetic force. The simulation results are given to demonstrate the effectiveness of the proposed control strategy.
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