# Integral control of port-Hamiltonian systems: non-passive outputs without coordinate transformation

## TL;DR

This paper introduces a novel integral control method for port-Hamiltonian systems that maintains the system's physical structure without coordinate changes, effectively rejecting disturbances while preserving non-passive output regulation.

## Contribution

It presents a dynamic extension integral controller that preserves port-Hamiltonian form directly in original coordinates, unlike previous coordinate-dependent solutions.

## Key findings

- Controller effectively rejects matched and unmatched disturbances.
- Maintains port-Hamiltonian structure and physical interpretability.
- Closed-loop dynamics align with Control by Interconnection scheme.

## Abstract

In this paper we present a method for the addition of integral action to non-passive outputs of a class of port-Hamiltonian systems. The proposed integral controller is a dynamic extension, constructed from the open loop system, such that the closed loop preserves the port-Hamiltonian form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the non-passive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed loop dynamics have a natural interpretation as a Control by Interconnection scheme.