Adaptive control of coupled rigid and flexible multibody systems with port-Hamiltonian structure

提出的研究项目的目标是开发具有刚性和柔性部件的耦合多体系统的自适应跟踪控制技术。刚性分量用非线性微分代数方程来描述。首先用一维空间的线性偏微分方程来描述柔性分量。在此过程中，还将考虑采用合适的方法对多维柔性子系统进行离散化。在每种情况下，模型都显示出一个端口-哈密顿结构，因此物理特性（特别是功率平衡）可以用数学上严格的方式捕获。端口-哈密顿系统的一个显著特征是它们本质上是模块化的，因为任意子系统可以通过它们的端口耦合。尽管有这些优点，但在力学中，port- hamilton建模方法得到的认可很少。因此，对这类耦合多体系统的跟踪控制还缺乏系统的方法。在这个项目中，首先，重要的系统理论性质的结构表征，如输入输出配置，可能的延迟和内部动力学的稳定性，将在物理考虑的基础上进行。在此基础上，将开发控制技术，保证跟踪误差在规定范围内的演变。为此，将漏斗控制和基于逆的前馈控制方法相结合，在项目的第一阶段对用微分代数方程描述的刚体多体系统进行了深远的研究。现在，在项目的第二阶段，前馈控制器将被设计为通过粗离散化来近似柔性组件，并与精确模型的漏斗控制器相结合。后者用于补偿近似误差。利用端口-哈密顿系统的模块化结构，将研究递归前馈控制设计的可能性。对于漏斗控制的适用性，将考虑在原始输出和与输入共存的替代输出之间建立函数关系的方法。所开发方法的性能和可实施性将通过选定的实验不断得到验证。实验支持了技术上合适的控制器设计参数的选择，从而实现了理论与实践的反馈。

The objective of the proposed research project is the development of adaptive tracking control techniques for coupled multibody systems with rigid and flexible components. The rigid components are described by nonlinear differential-algebraic equations. The flexible components are described by linear partial differential equations in one spatial dimension for a start. In the course of the project also multi-dimensional flexible subsystems will be considered, which are discretized by suitable methods. In each case, the models exhibit a port-Hamiltonian structure, and hence the physical properties (in particular, the power balance) can be captured in a mathematically rigorous way. A distinctive feature of port-Hamiltonian systems is that they are intrinsically modular, because arbitrary subsystems can be coupled via their ports. Despite these advantages, the port-Hamiltonian approach to modeling gets only little recognition in mechanics. Therefore, systematic methods for tracking control of such coupled multibody systems are still missing. In this project, first, a structural characterization of important system theoretic properties, such as input-output configurations, possible delays and the stability of the internal dynamics, will be conducted on the basis of physical considerations. Building on that, control techniques will be developed which guarantee the evolution of the tracking error within a prescribed margin. To this end, methods from funnel control and inversion-based feedforward control are combined, which led to far-reaching results for rigid multibody systems described by differential-algebraic equations in the first phase of the project. Now, in the second phase of the project, the feedforward controller will be designed for an approximation of the flexible components via coarse discretizations and combined with a funnel controller for the exact model. The latter is intended to compensate the approximation errors. Exploiting the modular construction of port-Hamiltonian systems, the possibility of a recursive feedforward control design will be investigated. For the applicability of funnel control, approaches which establish a functional relation between the original output and an alternative output that is co-located to the input will be considered. The performance and implementability of the developed methods will be constantly verified by means of selected experiments. The experiments support the selection of technically suitable controller design parameters and thus lead to a feedback between theory and practice.