Conditions on Shifted Passivity of Port-Hamiltonian Systems

TL;DR

This paper investigates shifted passivity in port-Hamiltonian systems, providing conditions for guaranteeing it, extending to feedback control, and demonstrating applications on generator and rigid body models.

Contribution

It derives new conditions for shifted passivity in port-Hamiltonian systems with convex Hamiltonians, including quadratic cases, and explores controller design implications.

Findings

Conditions for shifted passivity are established.

Extended to output feedback control scenarios.

Validated on generator and rigid body models.

Abstract

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.