Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major benefit of the PH representation is the explicit formulation of power interfaces, so-called ports, which allow for a power-preserving interconnection of subsystems to compose flexible multibody systems in a modular way. In this work, we present a PH representation of geometrically exact strings with nonlinear material behaviour. Furthermore, using structure-preserving discretization techniques a corresponding finite-dimensional PH state space model is developed. Applying mixed finite elements, the semi-discrete model retains the PH structure and the ports (pairs of velocities and forces) on the discrete level. Moreover, discrete derivatives are used in order to obtain an energy-consistent time-stepping method. The numerical properties of the newly devised model are investigated in a representative example. The developed PH state space model can be used for structure-preserving simulation and model order reduction as well as feedforward and feedback control design.

翻译：Port-Hamiltonian（PH）系统为复杂动力系统的建模、分析与控制提供了框架，此类系统的复杂性可能源于多物理耦合、非平凡域及多种非线性特性。PH表示的主要优势在于其显式定义了功率接口（即端口），这些端口能够以功率守恒方式实现子系统的互联，从而以模块化方式构建柔性多体系统。本文针对具有非线性材料特性的几何精确弦，提出了其PH表示形式。进一步地，利用结构保持离散化技术，建立了相应的有限维PH状态空间模型。通过应用混合有限元方法，半离散模型在离散层面保留了PH结构及端口（速度与力的成对组合）。此外，采用离散导数方法实现能量一致的时间步进算法。通过典型算例考察了新设计模型的数值特性。所发展的PH状态空间模型可用于结构保持仿真、模型降阶以及前馈与反馈控制设计。