轨迹基元匹配的柔性迭代学习控制

For precision machining tasks fast conversion in flexible manufacturing, we consider the iterative learning control(ILC) problem when the operating interval and operating tasks are changed. The theory and methods of tracking quickly and accurately the reference trajectory and achieving monotonic convergence in the learning process are studied through trajectory primitive matching to extract the initial iteration control signal. The reference trajectory model with NURBS is established based on the analysis of the characteristics of time and space of reference trajectory. By using the statistical shape analysis method, the trajectory similar mathematical description, parameters and indexes are introduced. The optimization trajectory primitive matching method is studied. The similar trajectory primitives are extracted in turn based on the current reference trajectory. The trajectory primitives are linked to compose a similar reference trajectory. The control signal of the similar reference trajectory is also composed. Time-frequency characteristics of the similar control signal are analyzed by Empirical Mode Decomposition (EMD) algorithm. The initial iteration control signal is extracted. Considered the stage jump of the control signal, H∞ performance analysis and synthesis method for the first iteration ILC system is taken into consideration. Instantaneous frequency of the reference trajectory and the track error are analyzed by EMD algorithm, and the cut-off frequency is tuned. The analysis and synthesis method depended on the cut-off frequency of iterative learning feedforward and H∞ feedback control system is studied. In conclusion, the flexible ILC theory is proposed by trajectory primitive matching, and it is verified by manipulator trajectory tracking control experiments, and it will provide theoretical guidance for ILC in flexible manufacturing.

针对柔性制造中精密加工任务快速转换要求，解决适应作业区间和作业任务变化的ILC问题。研究经轨迹基元匹配挖掘初次迭代控制信号，实现学习过程单调收敛、快速精确跟踪的理论方法。分析参考轨迹时空特性，建立基于NURBS 的时空模型；采用统计形状分析方法，探讨轨迹相似性数学描述方法，归纳轨迹相似性参数和指标；研究轨迹基元优化匹配方法，获取相似轨迹基元序列，合成相似参考轨迹及其控制信号；采用经验模式分解算法，分析相似控制信号时频特性，提取初次迭代控制信号；针对存在阶段性跳变偏差的初次迭代控制信号，研究初次迭代控制系统H∞性能分析与综合方法；采用经验模式分解算法，分析参考轨迹和误差信号瞬时频率，整定截断频率；研究依赖截断频率的迭代学习前馈控制和H∞反馈控制系统分析与综合方法。最终，提出轨迹基元匹配的柔性ILC理论方法；通过机械臂轨迹跟踪控制实验进行验证和分析，为ILC 控制在柔性制造中应用提供理论指导。

迭代学习控制适合于具有重复运行特性的被控对象，主要目标是寻找控制信号，使得迭代学习控制系统的实际输出在有限时间区间上快速无误差地跟踪上期望轨迹。但在实际工程中应用ILC仍存在一些问题，其中一个主要的限制是迭代学习控制要求的期望轨迹在整个迭代过程中必须严格重复，一旦期望轨迹发生了变化，前期学习过程中累积的控制信号将无效，必须重新学习。因此，本项目提出了一种基于期望轨迹基元匹配的迭代学习控制理论与方法，通过轨迹基元匹配从轨迹基元数据库中提取出当前期望轨迹的初次迭代控制信号，实现适应作业区间和作业任务变化的迭代学习控制系统。设计了基于轨迹基元匹配迭代学习控制系统的整体架构。基于NURBS建立了期望轨迹的时空模型；基于Kabsch算法给出了轨迹基元叠合方法，并将轨迹相似度定义为轨迹基元叠合后的误差协方差；进而提出了一种基于非均匀有理B 样条曲线（NURBS）分割与拼接的轨迹基元优化匹配算法；依据线性叠加原理、轨迹叠合的平移向量、旋转矩阵及其时间尺度变换关系，提出了一种初次迭代控制信号提取方法；采用经验模式分解（EMD）算法分析参考轨迹和跟踪误差信号瞬时频率，提出了一种分段滤波的迭代学习控制算法；将初次迭代控制信号在拼接处由边界条件差异对系统影响表示为一种干扰，提出了一种H∞反馈辅助的迭代学习控制方法。针对三轴数控实验平台研发了一种工业以太网EtherCAT通讯的多轴运动控制器，编写了期望轨迹基元优化匹配、初次控制信号提取和ILC算法程序，通过实验验证了本项目研究方法的有效性；形成一种具有实际应用价值的迭代学习控制技术。