In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus one is interested in passivity with respect to the shifted signals. We consider port-Hamiltonian systems with strictly convex Hamiltonian, and derive conditions under which shifted passivity is guaranteed. In case the Hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices, our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix. Moreover, we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback, thus paving the path for controller design. Stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions. The utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system.
翻译:在本文中,我们审视了港口-安密尔顿系统的转移被动特性。 转移被动特性说明在许多应用中,投入和产出变量的预期稳定状态值是非零的,因此人们对转移信号的被动性感兴趣。 我们认为,港口-安密尔顿尼安系统是严格保守的汉密尔顿系统,并得出了保证转移被动性的条件。 如果汉密尔顿系统是四面形,国家依赖性在消散和互连矩阵中以近似的方式出现,我们的条件将适当构建的恒定矩阵的负半无限期性降低。 此外,我们阐述了如何将这些条件扩大到通过产出反馈实施转移被动属性,从而为控制者设计铺平道路的情况。 强制平衡性系统的稳定性正在被分析,以拟议的被动性条件加以分析。结果的实用性和相关性通过应用第6顺序同步生成模型和受控制的僵硬体系统加以说明。