Modeling and control for stability and rotation velocity of a rotary inverted pendulum

The rotary inverted pendulum is a highly nonlinear, multivariable and dynamically unstable model. It is a fundamental and interesting problem in control theory. The objective of this paper is to: (i) derive the mechanical model of a rotary inverted pendulum by using Euler-Lagrange equation, (ii) design control systems for the rotary inverted pendulum with PID controller and pole placement method, and (iii) propose a simple method to accelerate the rotation speed. The effectiveness of these control techniques is shown in simulation results. An experimental prototype is also completed to test the control algorithms. With theory analysis and experiment results, it is verified that both controllers are good at maintaining the system stability while the PID method shows a better transient response. The proposed method also has a great advantage in accelerating the rotation velocity.