A Study Of Mathematical Modelling Of Control Systems: (A Case Study Of The Inverted Pendulum)
DOI:
https://doi.org/10.60787/tnamp.v21.480Keywords:
Inverted Pendulum, Euler-Lagrange, Ordinary differential equation, Partial differential equation and transfer functionAbstract
This paper aims to study the mathematical modeling of control systems by examining the dynamics of an inverted pendulum and analyzing the system of nonlinear differential equations associated with it. The objective is to formulate a mathematical model of the inverted pendulum system. The Euler-Lagrange equations were utilized to derive the equations of motion. Additionally, the paper seeks to compute the controllability of the linearized system, obtain the transfer functions, and analyze the state-space representation of the model. Finally, graphical profiles illustrating the system's behavior are provided. This work stabilized the pendulum, enabling precise and rapid control of the carriage's position on the track
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