Dynamic Modeling and Simulation of a Rotational Inverted Pendulum

TL;DR

This paper develops a dynamic model of a rotational inverted pendulum using Euler-Lagrange mechanics, designs a physical prototype in SolidWorks, and verifies the model through simulation and phase space analysis.

Contribution

It introduces an alternative dynamic modeling approach for the inverted pendulum and compares theoretical results with simulations for validation.

Findings

Model accurately predicts pendulum motion

Simulation results match theoretical equations

Phase space analysis identifies stability regions

Abstract

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic model of the system in SolidWorks software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the theoretical results, It was made a contrast between the solutions obtained by simulation SimMechanics-Matlab and the system of equations Euler-Lagrange, solved through ODE23tb method included in Matlab bookstores for solving equations systems of the type and order obtained. This article comprises a pendulum trajectory analysis by a phase space diagram that allows the identification of stable and unstable regions of the system.