Application of Lagrange Method to Analyze Forces of Gyroscope Inverted Pendulum

This study is to design an inverted pendulum as a simple model of a two-wheeled vehicle. The inverted pendulum is a mechanical balance system where the center of mass is at the top. Control of the inverted pendulum mechanism is obtained from the spinning flywheel and then changes one axis to produce force. Considering the problem of free motion in the design and flexibility of actuators in a traditional inverted pendulum, this system is designed with a structure that has a compact control actuator. Lagrange method is used to design a dynamic model of a gyroscope inverted pendulum to obtain an equilibrium condition. To find out the system response that has been made, modeling has been applied to Matlab Simulink. PID control has been designed to obtain a system that has better capabilities. Finally, this paper will evaluate some of the strengths and weaknesses of this control approach, compared to other balancing techniques.