Visual Servoing Sliding Mode Control with Vibration Model Compensation for Trajectory Tracking in a 2-DOF Ball Balancer System

Ball balancers are nonlinear, electromechanical, multivariable, open-loop unstable systems widely used in research laboratories, aerospace, military, and automotive industries to evaluate control mechanism effectiveness. The inherent difficulty in precisely managing ball position, combined with actuator saturation and system sensitivity to disturbances, makes trajectory tracking a persistent challenge. Conventional controllers often exhibit oscillatory responses with steady-state errors exceeding acceptable limits. Sliding mode control (SMC) offers robustness against model uncertainties; however, chattering finite-frequency, finite-amplitude oscillations near the sliding surface caused by switching imperfections, time delays, and actuator dynamics remain a significant limitation. This study addresses chattering through explicit vibration model compensation integrated into the SMC design for a 2-DOF ball balancer system using a visual servoing approach. A double-loop control architecture is implemented, where the inner loop handles servo angular position control and the outer loop manages ball position tracking through visual servoing feedback. The sliding mode controller is designed with a power rate reaching law, synthesizing two control laws: one with explicit vibration model compensation incorporating damping and stiffness terms, and one without. Experimental validation confirmed that SMC with compensation achieved significantly reduced steady-state error (0.034 mm vs. 0.386 mm) and lower overshoot (3.95% vs. 13.81%) compared to the uncompensated variant, with chattering amplitude reduced by approximately 72%.