基于扩张状态观测器的鲁棒迭代学习控制

Robust iterative learning control based on extended state observer

针对一类包含模型不确定和外界干扰等非重复扰动的线性离散系统,本文通过将迭代学习控制与自抗扰技术相结合,提出一种新的基于扩张观测器的鲁棒迭代学习控制方法.本文以时间轴和迭代轴两个方向同时出发考虑系统的非重复扰动估计和稳定收敛问题.将与时间和迭代轴同时相关的模型不确定及外界干扰等因素归纳为系统总扰动,针对其非重复变化特性给出了扩张观测器的设计,保证在批次内快速、准确地估计系统总扰动;基于上述扰动估计,设计新型的迭代学习控制律,利用线性矩阵不等式方法证明了整个鲁棒迭代学习系统的稳定性和收敛性,并给出合理的控制器参数估计条件.此外,讨论了迭代学习控制中第一批次的控制律设计问题,给出合理的自抗扰控制器设计.最后通过仿真对比实验验证了本文方法的可行性和有效性.

In this paper, a new robust iterative learning control (ILC) method based on extended state observer is proposed, which combines ILC and active disturbance rejection control (ADRC) for a class of linear discrete systems with uncertainties and disturbances. The estimation of non-repetitive disturbances and system’s stability are considered on two directions, time and iterative. The uncertainties and disturbances are treated as total disturbance, which is time and iterative related function. Extended state observer is proposed to ensure the total disturbance can be estimated quickly and accurately in a batch. A new ILC law is designed based on the above disturbance estimation. The stability and convergence of the robust iterative learning system are proved by linear matrix inequality (LMI). At the same time, a reasonable parameters estimation condition for the controller is given. In addition, the design of the first batch of the robust ILC is discussed, and a suitable ADRC is designed. Finally, the feasibility and effectiveness of the proposed method are verified by simulation experiments.