迭代学习控制的最优学习律和简化学习律的频域研究

Study of Optimal Learning Law and Simplified Learning Law of Iterative Learning Control in Frequency Domain

为了在线性时不变MIMO系统中得到迭代学习控制的最优学习律和便于工程实现的简化学习律,在频域上对其进行了相关研究。以系统的传递函数矩阵为基础,依据Parseval定理,将时域误差关联为频域误差,再利用Jordan标准形矩阵等矩阵性质,得到了学习律的通适收敛条件。通过分析该条件,得出了收敛速度最快的一次迭代就能完成的最优学习律。由于高阶导数不利于消除噪音,因此文中还讨论了导数的降阶,给出了简化学习律算法。仿真结果表明,最优学习律和简化学习律是有效的。

To obtain the optimal learning law and simplified learning law which is convenient for engineering implementation of iterative learning control in LTI MIMO system,this paper carried out some studies in frequency domain.Based on the transfer function matrix of system,the time-domain error is converted to frequency-domain error according to Parseval theorem,and the general convergent condition of learning law can be obtained by using matrix properties of Jordan canonical form.The optimal learning law which needs only one time iterative computation with fastest convergence rate can be got by analyzing the aforementioned conditions.Since the higher derivative is not conducive to eliminating noise,the reduced order of derivative was discussed to get a simplified learning law.Simulation results show that the optimal and simplified learning law is effective.