Port-hamiltonian formulation of an electrical circuit using different kinds of states

Abstract

This work focuses on a dynamic electrical circuit whose dynamics are affine in the control input. Such dynamics are considered to be re-expressed in a canonical form, namely the port-Hamiltonian (pH) representation with dissipation, where the Hamiltonian is a quadratic function and has the unit of energy or power. On this basis, it allows revealing the transformation of energy (or power) inside the system, including the energy supply, storage and dissipation, thereby facilitating Lyapunov-based or energy-related control approaches for stabilization and optimization purposes. Two pH representations are proposed and compared; the first one is established with difficult-to-measure states while the second one is obtained with easier-to-measure states.