Modelado y simulación del péndulo de base móvil

Abstract

This article describes the simulation and control of a mobile base pendulum (PBM), which consists of a mechanism with two wheels and a vertical cylindrical rod, which can rotate freely on its own axis, then the mobile must move to compensate for the angular displacement of the pendulum. The objective is to develop a mathematical model to simulate the dynamic behavior of the mechanism and thereby develop a Proportional, Integral and Derivative (PID) controller, optimal that manages to maintain this pendulum at a vertical degree in a time ts ≤ 1 second, with an entry angle of ± 10 degrees. The Newton-Euler (NE) methodology was used to determine the dynamic equations of motion, by analyzing the free body diagram and using the physical laws that allow defining the forces acting on the system to achieve the state of equilibrium. These simulations were carried out with the SolidWorks (SimMechanics Link) and Matlab (Simulink) tools, in addition a closed loop system was used to analyze the output signal Y (s) with respect to the input signal U (s). The contributions of this development consist of designing high-precision controllers with the purpose of improving industrial automation processes from the implementation of a control system, in areas such as robotics, marine vehicles, aerospace, to name a few examples.