On Port-Hamiltonian Formulation of HystereticEnergy Storage Elements: The Backlash Case
This work addresses a domain-specific modeling challenge in control systems and circuit theory, representing an incremental advancement in the formulation of hysteretic elements.
The paper tackles the problem of modeling hysteretic energy storage elements by developing a port-Hamiltonian formulation, specifically for backlash-driven elements, and demonstrates its applicability in RLC circuits with hysteretic inductors.
This paper presents a port-Hamiltonian formulation of hysteretic energy storage elements. First, we revisit the passivity property of backlash-driven storage elements by presenting a family of storage functions associated to the dissipativity property of such elements. We explicitly derive the corresponding available storage and required supply functions `a la Willems [1], and show the interlacing property of the aforementioned family of storage functions sandwiched between the available storage and required supply functions. Second, using the proposed family of storage functions, we present a port-Hamiltonian formulation of hysteretic inductors as prototypical storage elements in port-Hamiltonian systems. In particular, we show how a Hamiltonian function can be chosen from the family of storage functions and how the hysteretic elements can be expressed as port-Hamiltonian system with feedthrough term, where the feedthrough term represents energy dissipation. Correspondingly, we illustrate its applicability in describing an RLC circuit (in parallel and in series) containing a hysteretic inductor element.