基于卡尔曼滤波的迭代学习控制方法研究

针对一类非线性欠驱动机械系统在干扰环境下动态性能变差的问题，提出了一种基于卡尔曼滤波器的遗忘因子型迭代学习控制律，以实现闭环系统的稳定控制和干扰抑制。首先，将卡尔曼滤波器作为系统的状态观测器，在含有随机噪声干扰的情况下，估计系统的最优状态；其次,通过设置自适应遗忘因子来动态适应迭代学习过程中的误差变化，使系统快速收敛并准确跟踪参考轨迹，实现运动过程中重复干扰信号的抑制；最后，以Quanser公司生产的柔性尺为实验平台来研究非线性欠驱动被控对象实际系统的控制方法，并对所提方法分别进行理论数值仿真与实物实验验证。仿真及实物实验结果表明，本文提出的控制方法可以保证被控系统稳定运行，当环境中存在随机非重复性噪声或重复性干扰时，被控系统都可以保持良好的鲁棒性。

An iterative learning control method based on a Kalman filter

A forgetting factor iterative learning control law based on a Kalman filter is proposed to solve the problem whereby the dynamic performance of a class of nonlinear underactuated mechanical systems will deteriorate in a disturbance environment in order to realize the stable control and interference suppression in the closed-loop system. The Kalman filter is used as the state observer to estimate the optimal states of the system with Gaussian noise. The adaptive forgetting factor is then set to dynamically adapt to the error variation in the iterative learning process so that the system can track the reference trajectory accurately and quickly. Finally, the flexible ruler produced by the Quanser Company is used as the experimental platform to study the control method of the actual system of the nonlinear underactuated controlled object. The proposed method has been verified by theoretical numerical simulation and real experiments. Simulation and real experiment results show that the proposed control method can ensure the stable operation of the system, and the system can also maintain good robustness when random noise exists in the environment.