Dynamic, modeling and simulation of an underactuated system

TL;DR

This paper models and simulates an underactuated rotary inverted pendulum using Lagrangian mechanics, compares CAD-based physical modeling with mathematical equations, and analyzes system stability through phase space trajectories.

Contribution

It introduces a combined approach of CAD modeling and Lagrangian dynamics for simulating an underactuated system, including stability analysis.

Findings

CAD and mathematical models show consistent dynamics

Identification of stable and unstable regions in phase space

Validation of simulation methods for underactuated systems

Abstract

In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler Lagrange's equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system.