This paper gives new contributions to the development of iterative learning control for distributed parameter systems, based on using finite difference schemes to construct a finite-dimensional approximate model of the dynamics for control law design. To form a basis for the new results, systems whose dynamics are described by a fourth-order partial differential equation are considered together with the associated accuracy and numerical stability checks. Some previous control law designs use only a spatial variable as the control input, which can be a serious obstacle to practical implementation since many actuators and sensors must be deployed. This paper’s new design is based on spatially homogeneous sensing and excitation over a selected sub-area of the domain considered. Supporting numerical case studies are given to support the analysis.

本文基于使用有限差分格式构建控制律设计的动力学的有限维近似模型，为分布式参数系统的迭代学习控制的发展做出了新的贡献。为了形成新结果的基础，将动力学由四阶偏微分方程描述的系统与相关的精度和数值稳定性检查一起考虑。一些先前的控制律设计仅使用空间变量作为控制输入，这可能是实际实施的严重障碍，因为必须部署许多执行器和传感器。本文的新设计基于对所考虑域的选定子区域的空间均匀感测和激发。给出了支持数值案例研究以支持分析。