基于相位超前2D模型的渐变重复过程鲁棒迭代学习控制

Iterative learning control plays a crucial role when problems of high precision control for complex systems with repetitive trajectories are considered in the area of industrial control. However, classical methods of iterative learning control are based on ideal assumptions that boundary conditions, parameters of system models and operation trajectories are identical during each trial. As a result, the control performance of these methods is not as good as expected in practice. This project is dedicated to the analysis and synthesis of systems with gradually changing pattern, and the attention is focused on the design of models and controllers from a fresh perspective. The essential contents of the study can be briefly summarized as follows. Firstly, by capturing the gradually changing pattern and repetitiveness, such systems can be modeled as phase-lead 2D systems. Then, a generalized version of Kalman-Yakubovich-Popov (KYP) lemma for phase-lead 2D systems will be proposed over any given finite frequency range. In light of the KYP lemma derived, the approaches which integrate robust dynamic output feedback and iterative learning control will be provided. On one hand, robust dynamic output feedback control is introduced to guarantee a prescribed disturbance attenuation level for such systems with parameter uncertainties. On the other hand, by taking the previous trial data into consideration, new iterative learning control algorithms are proposed to obtain high precision control. Moreover, the known information of the systems will be used to speed up the convergence rate. The study will resolve the compromises between the convergence rate of the obtained algorithm and the gradual change and repetitiveness of the systems. Finally, the new practical control strategies will be presented and applied to the upper limb rehabilitation exercise platform, which will be helpful for the enhancement of the results derived. .Overall, the aim of this project is to explore the inherent relationship between the repetitive process with gradually changing pattern and phase-lead 2D systems, which will contribute to improvements of theory and technology for repetitive process with gradually changing pattern.

针对具有重复运动特性的复杂系统进行高精度控制是工业界面临的难题，迭代学习控制是解决该问题的有效途径。然而，传统迭代学习控制要求在每个运行周期中的系统初始状态、对象模型参数和运动轨迹等严格一致，成为制约这一技术发展的瓶颈。本项目以渐变重复过程为研究对象，探索新的建模和控制方法。具体来说，通过分析研究对象的渐变特性和周期重复性，将渐变重复过程建模为相位超前2D系统，并在指定的有限频段上给出此类系统的广义KYP引理；提出基于鲁棒动态输出反馈的迭代学习控制方案，通过输出反馈控制实现系统对模型参数变化及干扰等因素的鲁棒性，利用以往周期的数据信息设计迭代学习控制算法，实现高精度的控制效果；分析算法的收敛速度，解决收敛速度与系统渐变、周期重复变化之间的矛盾；将所得理论成果应用于上肢医疗康复系统，改进、提升研究成果。.本研究旨在揭示渐变重复过程与相位超前2D系统的内在联系，为研究渐变重复过程提供新的思路。

针对具有重复运动特性的复杂系统进行高精度控制是工业界面临的难题，迭代学习控制是解决该问题的有效途径。项目提出系统模型参数辨识的新方法，主要针对输出误差类辨识模型和随机梯度辨识算法开展了研究，通过引入加权、多新息和最新估计的辨识思想对基本的随机梯度辨识算法进行了改进，使得改进的辨识算法针对输出误差类辨识模型拥有更高的辨识精度和更快的收敛速度，同时改进的辨识算法具有更小的计算量，克服了基本的随机梯度辨识算法辨识精度低的缺点。 .Itoˆ型微分方程被广泛用于描述存在结构突变和随机干扰的实际系统，这类系统被称为Itoˆ型Markov跳跃系统。在研究Itoˆ型Markov跳跃系统的线性二次型最优控制时，耦合Riccati矩阵方程有着重要的作用。项目采用迭代技术，对与Itoˆ型Markov跳跃系统相关的一类耦合Riccati矩阵方程的求解问题展开研究。项目分别提出两种改进的Riccati迭代算法与Lyapunov迭代算法。利用最新估计信息与加权因子，分别对Riccati迭代算法与Lyapunov迭代算法进行改进，提出新的算法来求解耦合Riccati矩阵方程；然后在一定初始条件下，结合数学归纳法与Riccati、Lyapunov方程的相关比较定理，证明所提出的算法生成的矩阵序列具有单调性与有界性，即收敛性，并且收敛于Riccati矩阵方程的唯一正定解；通过数值仿真可证实所提出的改进算法收敛速度更快。 .作为理论结果在工程实际中的应用，本文以航天器轨道控制系统为背景，考虑执行机构故障引起的系统结构突变和外部噪声干扰，将运行在圆轨道的航天器建模为一类转移率时变的 Itoˆ 型 Markov 跳跃随机系统。将航天器轨迹跟踪问题转化为 Itoˆ 型 Markov 跳跃随机系统的模型参考跟踪控制问题。考虑系统转移率的时变性，完成了航天器轨道悬停任务的设计。利用前面给出的基于耦合 Riccati 方程的无限时间线性二次型最优控制器设计方法，完成了航天器轨道绕飞任务的设计。这些工作是项目提出的理论方法在工程应用中的初步尝试，为理论成果向实际应用转化提供了技术途径。