Sliding Mode Control of Ball-on-Wheel System

To study non-linear systems, Ball-on-Wheel (BOW) is an ideal set-up. It is also underactuated as the ball can not be held at any arbitrary position on the wheel. This system poses a control challenge to balance the ball on top of the wheel by rotating the wheel in either direction. Such a system is mathematically simulated and a sliding mode control law is developed to overcome the disturbance in the wheel velocity. The control law shows almost zero overshoot and quickly brings the ball to its equilibrium position. Robustness of this controller is also checked by calculating the integral of absolute error for parametric uncertainty in wheel's moment of inertia. The results are found to be satisfactory.