A compact, structural analysis amenable, port-Hamiltonian circuit analysis
John D. Pryce
TL;DR
This paper introduces a compact port-Hamiltonian formulation for RLC circuits, ensuring successful structural analysis and providing a reliable regularization method for numerical solutions of the resulting differential-algebraic equations.
Contribution
It presents a simple port-Hamiltonian model for RLC circuits and proves structural analysis always succeeds for well-posed circuits, aiding numerical solution stability.
Findings
Structural analysis always succeeds on the proposed formulation.
The DAE system size is at most the number of edges in the circuit.
Provides a correct regularization for numerical solutions.
Abstract
This article presents a simple port-Hamiltonian formulation of the equations for an RLC electric circuit as a differential-algebraic equation system, and a proof that structural analysis always succeeds on it for a well-posed circuit, thus providing a correct regularisation for numerical solution. The DAE is small - its number of variables/equations is at most the number of edges in the circuit graph.
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Taxonomy
TopicsControl and Stability of Dynamical Systems · Modeling and Simulation Systems · Numerical methods for differential equations