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、分析与控制提供了一种框架，其中复杂性可能源于多物理场耦合、非平凡域及多种非线性特性。PH表示的一个主要优势在于其显式构造了功率接口（即端口），这些接口允许子系统之间以功率守恒的方式互连，从而模块化地构成柔性多体系统。本文针对具有非线性材料特性的几何精确弦杆，提出了其PH表示形式。此外，利用保结构离散技术，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结构与端口（速度与力的配对）。同时，采用离散导数方法以实现能量一致的时间步进方案。通过代表性算例验证了新模型数值特性。所建立的PH状态空间模型可用于保结构仿真、模型降阶以及前馈与反馈控制设计。