This model is an electromechanical system, called the ball-and-wheel system. This system consists of a wheel and a motor. Over the periphery of the wheel, a ball is balanced by controlling the angle of the wheel through the motor. This system is nonlinear and underactuated. Moreover, the equilibrium of this system is open-loop unstable. The system is linearized about the equilibrium position and an LQR controller is designed to stabilize the system. The control law is implemented on an experimental apparatus. The video of both the animation and the experiment show that the system performs well even with disturbance. A good agreement between the simulation and the experimental results is also obtained.

This model was developed and the experiment was conducted by Tzu-Chin Lin and Ming-Tzu Ho at the Department of Engineering Science of National Cheng Kung University, Taiwan.