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摘要: 针对现有迭代学习控制方法中迭代次数依赖初始跟踪误差及系统不确定性影响控制精度等问题, 提出一种数据驱动鲁棒固定次迭代学习控制方法. 首先, 通过构造沿迭代轴的双曲正切型趋近律, 设计固定次迭代学习控制器, 推导出跟踪误差的稳态误差带并移除迭代次数上界依赖初始误差这一限制, 保证系统跟踪误差在固定迭代次数内收敛. 在此基础上, 基于系统输入输出数据设计沿迭代轴更新的参数自适应律与扩张状态观测器, 估计未知参数并补偿系统中未知干扰, 进而提高系统的鲁棒性与跟踪精度. 理论分析和仿真结果验证了所提方法的有效性.Abstract: A data-driven robust fixed-iteration learning control method is proposed to overcome limitations in existing iterative learning control methods, such as the dependence of iteration number on initial tracking errors and reduced control accuracy due to system uncertainties. First, a fixed-iteration learning controller is designed using a hyperbolic tangent reaching law constructed along the iteration axis. The steady-state error band of the tracking error is derived and the restriction of the upper bound for the iteration count, dependent of the initial error, is removed to ensure the system tracking error converges within a fixed number of iterations. Furthermore, parameter adaptive laws and an extended state observer, updated iteratively using system input-output data, are developed to estimate unknown parameters and compensate for unknown disturbances in the system. This ensures the robustness and tracking accuracy of the system. Theoretical analysis and simulation results validate the effectiveness of the proposed method.
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图 6 不同初始状态下$\max |e_k(t)|$的变化曲线
Fig. 6 Variation curve of $\max |e_k(t)|$ in different initial states
图 4 最大跟踪误差$\max |e_k(t)|$变化曲线
Fig. 4 Variation curve of the maximum tracking error $\max |e_k(t)|$
图 8 最大跟踪误差$\max |e_k(t)|$的变化曲线
Fig. 8 Variation curve of the maximum tracking error $\max |e_k(t)|$
表 1 不同初始条件下DDRFxILC方法的性能对比
Table 1 The performance comparison of the DDRFxILC method under different initial conditions
初始状态 进入稳态所需
迭代次数稳态误差均值 稳态误差
标准差第30次迭代
误差$ {\boldsymbol{x}}_0=5{\boldsymbol{f}}_k $ 9 $ 3.00\times 10^{-3} $ $ 5.80\times 10^{-3} $ $ 5.07\times 10^{-4} $ $ {\boldsymbol{x}}_0=10{\boldsymbol{f}}_k $ 10 $ 2.70\times 10^{-3} $ $ 4.90\times 10^{-3} $ $ 3.75\times 10^{-4} $ $ {\boldsymbol{x}}_0=20{\boldsymbol{f}}_k $ 11 $ 2.70\times 10^{-3} $ $ 5.50\times 10^{-3} $ $ 3.08\times 10^{-4} $ 
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