This model is a control laboratory experiment, called the ball-on-sphere system. This system consists of a sphere, two motors, and two friction wheels. On the top of the sphere, a small ball is balanced by rolling the sphere along each of two horizontal axes through friction wheels driven by motors. Control of this system is a challenging task because of inherent nonlinearity, instability, and underactuation. A LQR stabilizing control law is obtained based on linearized system model. To examine the performance of the control strategy in the presence of disturbance, in the simulation two impulsive disturbances are added to the position of the ball (impulsive disturbance is indicated by “disturbance”). As shown, the control system recovers from the impulsive disturbances. 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 Chien-Chen Huang, Yen-Hsiang Huang, and Ming-Tzu Ho at the Department of Engineering Science of National Cheng Kung University, Taiwan.