New results on disturbance rejection for energy-shaping controlled port-Hamiltonian systems

TL;DR

This paper introduces a robust energy-shaping control method for port-Hamiltonian systems that incorporates integral action to reject disturbances while maintaining the system's structure, applicable to a broad class of mechanical systems.

Contribution

It extends previous energy-shaping controllers by relaxing convexity and separability requirements, enabling application to underactuated systems with non-constant mass matrices.

Findings

The proposed controller effectively rejects unknown disturbances.

It preserves port-Hamiltonian structure without unnatural coordinate transformations.

The method is robust against unknown damping in fully-actuated systems.

Abstract

In this paper we present a method to robustify energy-shaping controllers for port-Hamiltonian (pH) systems by adding an integral action that rejects unknown additive disturbances. The proposed controller preserves the pH structure and, by adding to the new energy function a suitable cross term between the plant and the controller coordinates, it avoids the unnatural coordinate transformation used in the past. This paper extends our previous work by relaxing the requirement that the systems Hamiltonian is strictly convex and separable, which allows the controller to be applied to a large class of mechanical systems, including underactuated systems with non-constant mass matrix. Furthermore, it is shown that the proposed integral action control is robust against unknown damping in the case of fully-actuated systems.