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

建议的研究项目的目标是发展的自适应跟踪控制技术的耦合多体系统的刚性和柔性组件。刚性元件由非线性微分代数方程描述。首先，在一个空间维度上用线性偏微分方程描述柔性部件。在项目过程中，还将考虑多维柔性子系统，这些子系统通过适当的方法离散化。在每种情况下，模型都表现出端口汉密尔顿结构，因此可以以数学上严格的方式捕获物理属性（特别是功率平衡）。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，因为任意子系统都可以通过它们的端口耦合。尽管有这些优点，端口哈密顿方法建模得到很少的承认，在力学。因此，这种耦合多体系统的跟踪控制系统的方法仍然缺乏。在这个项目中，首先，重要的系统理论特性，如输入输出配置，可能的延迟和内部动态的稳定性，将进行结构表征的基础上的物理考虑。在此基础上，将开发控制技术，保证跟踪误差在规定的范围内变化。为此，将漏斗控制和基于反演的前馈控制方法相结合，从而在项目的第一阶段为微分代数方程描述的刚性多体系统带来了深远的结果。现在，在该项目的第二阶段，前馈控制器将通过粗离散化设计用于柔性部件的近似，并与用于精确模型的漏斗控制器相结合。后者旨在补偿近似误差。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位于输入的替代输出之间建立函数关系的方法。所开发的方法的性能和可实施性将通过选定的实验不断验证。实验支持技术上合适的控制器设计参数的选择，从而导致理论和实践之间的反馈。

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.