Design and performance investigation of block-backstepping algorithms for ball and arc system

This paper develops Block-Backstepping algorithms for balancing and tracking control of ball and arc system. Three design procedures are presented and, as such, three proposed controllers would arise. The design of Block-Backstepping controllers has been developed for a linearized model of the system and comprises two main control objectives; firstly to stabilize the ball on the top position of the arc-shaped and, secondly, to place the cart at the desired position. The block-backstepping control law is further enhanced by including an integral action to improve both the steady state characteristics and the robustness of the overall system. Moreover, the internal stability of the system has been analyzed using zero dynamic criteria to guarantee the global asymptotic stable at desired equilibrium point. The results based on simulation are used to assess the performance of the proposed controllers for the suggested underactuated mechanical system.