A Comparison of Adaptive Control Methods for the Ball Balancing Table System

The purpose of this paper is to present and compare adaptive control algorithms: Model Identification Adaptive Control (MIAC) and Model Reference Adaptive Control (MRAC), with their modifications that allow to improve quality of control in specific cases. The ball balancing (BBT) table physical stand, which is an example of a ball on plate system, was used, and the balancing problem that occurs could potentially lead to work on stabilizing a boat or a drone. This paper presents a non-linear model of the object and its linear approximation in the vicinity of the operating point, additionally demonstrating the process of parameters identification with the Recursive Least Square (RLS) method. The quality of the adaptive control algorithms was compared during transients and in steady state. The research showed the possibilities of both indirect and direct adaptation of the controller parameters, depending on the selected method. Quality indices, such as the cost of control and the integral of absolute error, were utilized for the comparative analysis. The advantages of the compared algorithms and their modifications, that can enhance the system performance in special cases, were also demonstrated. The tested adaptive control algorithms made the system robust to modeling errors (lack of knowledge of parameters) or other internal disturbances.