Robust Energy Shaping Control of an Underactuated Inverted Pendulum

TL;DR

This paper presents a robust energy shaping control method for an underactuated inverted pendulum, using analytical solutions to PDEs and a novel disturbance compensation term, validated via simulations.

Contribution

It introduces a new IDA-PBC scheme with concise PDE solutions and a robust term for disturbance rejection in inverted pendulum control.

Findings

Effective stabilization demonstrated through numerical simulations.

The control law effectively compensates for specific disturbances.

Concise analytical solutions simplify practical implementation.

Abstract

Although the stabilization of underactuated systems remains a challenging problem, the total energy shaping approach provides a general framework for addressing this objective. However, the practical implementation of this method is hindered by the need to analytically solve a set of partial differential equations (PDEs), which constitutes a major obstacle. In this paper, a rotary inverted pendulum system is considered, and an interconnection and damping assignment passivity-based control (IDA-PBC) scheme is developed by deriving concise analytical solutions to the kinetic and potential energy PDEs. Furthermore, a novel robust term is incorporated into the control law to compensate for a specific class of disturbances that has not been addressed within the existing IDA-PBC literature. The effectiveness of the proposed method is validated through numerical simulations, demonstrating satisfactory control performance.