Passivity, Port-Hamiltonian Formulation and Solution Estimates for a Coupled Magneto-Quasistatic System

TL;DR

This paper analyzes a coupled magneto-quasistatic system from a systems theory perspective, proving passivity, representing it as a port-Hamiltonian system, and providing estimates for system states and long-term behavior.

Contribution

It establishes passivity and port-Hamiltonian structure for the magneto-quasistatic system, and derives estimates for current and magnetic potential based on initial data and inputs.

Findings

The system is passive with respect to injected voltages and currents.

It admits a port-Hamiltonian representation using Dirac and resistive structures.

Current and magnetic potential can be estimated from initial conditions and voltages.

Abstract

We study a~quasilinear coupled magneto-quasistatic model from a~systems theoretic perspective.} First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover, by defining suitable Dirac and resistive structures, we show that it admits a~representation as a~port-Hamiltonian system. Thereafter, we consider dependence on initial and input data. We show that the current and the magnetic vector potential can be estimated by means of the initial magnetic vector potential and the voltage. We also analyse the free dynamics of the system and study the asymptotic behavior of the solutions for $t\to\infty$.