随机噪声干扰下的迭代学习控制器设计

为解决迭代学习控制系统中随机噪声扰动问题，提出基于无限脉冲响应（ⅡR）数字滤波器的优化迭代学习控制器设计方法。该方法在首次迭代时对系统输出误差进行基于小波变换的两轮实验法滤波；其次根据小波滤波获得的输出误差确定部分及原误差信号作为输入输出辨识出等效ⅡR线性滤波器，并重构优化误差目标函数，进一步利用优化方法对迭代学习控制器优化设计；最后利用获得的线性滤波器及新学习律对系统进行后续批次迭代，直到满足收敛条件为止。仿真显示：在针对输出误差二范数这个性能指标，该方法与小波滤波相比，降低了近15%，并消除了由于小波滤波阈值选取过小产生的振铃现象；在批次间噪声累积上，降低了9%左右。仿真结果表明，提出的等效滤波器综合设计方法，有效抑制了随机噪声的影响，并提高了系统跟踪的准确性。

Design of iterative learning controller for systems with random noise

To reduce the negative impact of stochastic noise in iterative learning control system, an iterative learning controller design method based on the Infinite Impulse Response (ⅡR) digital filter was proposed. For the first batch, the output errors from two repeated experiments were filtered by wavelet transform. Then the input/output data during the wavelet filtering process were used to obtain an equivalent ⅡR filter, which would be used to reconstruct the error objective function and optimize the iterative learning controller. Finally, the obtained ⅡR filter was applied to filter out the stochastic noise from subsequent batches until the convergence condition was met. Through simulation, compared with wavelet filtering, it could be demonstrated that by applying the proposed method, the 2-norm of output error could be reduced by nearly 15% and the ringing caused by setting the wavelet filter threshold too small was also avoided. The cumulative noise between the batches could be reduced by about 9%. The simulation results show that the proposed algorithm not only significantly reduces the negative effect of stochastic noise, but also effectively improves the accuracy of the tracking system.