Stabilization of Plate and Ball Nonlinear System With Limited Field-of-View Sensors Using Constrained Adaptive Sliding-Mode Controller

Abstract

This research outlines the design and implementation of a constrained adaptive sliding-mode controller specifically developed for a nonlinear system involving a plate and a ball. A particular platform with rotary actuators has been chosen, and the comprehensive construction methodology is detailed to support the positioning of the ball on the plate. To attain high sampling rates for positional data, a resistive touchscreen panel is employed as a sensor, considering the field of view. The accuracy of the model was validated using real system data, confirming that it accurately represents the actual dynamics. The adaptive sliding-mode controller features error integration, which improves robustness against uncertainties in parameters, such as changes in the weight of the ball. A constrained control framework that utilizes the Barrier Lyapunov function is applied to keep the system state variables within allowable limits, addressing the limitations of the sensors' field of view. Both simulation and experimental findings indicate that the tracking controller, which is integrated with a constrained adaptive sliding-mode structure, successfully stabilizes the nonlinear plate and ball system.