Extension of a Linear Controller Scheme to Non-Linear Systems and its Application on Inverted Pendulum

TL;DR

This paper extends a linear control scheme to stabilize a non-linear inverted pendulum, demonstrating its effectiveness through experimental validation and emphasizing the role of an integrator in disturbance rejection.

Contribution

It introduces a control scheme based on classical control theory for non-linear systems, specifically applied to the inverted pendulum, with experimental validation.

Findings

Successful stabilization of the non-linear inverted pendulum.

Validation of boundedness and convergence of the system.

Effective disturbance rejection due to the integrator.

Abstract

This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance rejection is emphasized. The system's dynamics are obtained by the Euler Lagrange method and are approximated for small-angle as balancing the pendulum is the objective. Experimental results demonstrate that the proposed control scheme can achieve the stabilization of a non-linear system. Also, the boundedness and convergence of the non-linear system with the controller subjected to the initial condition are validated.