Singular Perturbations for Implicit port-Hamiltonian systems

In this work, we present the standard Singular Perturbations technique applied to Implicit port-Hamiltonian systems. The investigation produces a structure-preserving reduced-order model if certain additional passivity conditions are satisfied. Moreover, such an investigation provides a different insight into the standard Singular Perturbations approach relating the negligible time constant parameters $\varepsilon$ to energy parameters. We analyze the deviation between the complete system model and the reduced one via a Lyapunov-based approach. We then conclude the paper by applying the proposed reduced order model to a DC-motor example to show the effectiveness of the development.

I. Introduction

The port-Hamiltonian approach to modeling and control-ling complex physical systems constitutes a well-established framework that originated with the seminal work by van der Schaft and Maschke [1], [2]. For a comprehensive overview of this field, including control techniques, one can refer to [3]–[5].