| Summary: | This paper develops a proposed block-backstepping algorithm for balancing and tracking control of ball and arc system. Two block-backstepping designs have been presented; one from the linearized model and other from a nonlinear model of the considered underactuated system. Also, two main control objectives have been achieved; firstly to bring the ball to rest on the top of the arc and secondly to make the cart track a defined reference trajectory. Moreover, integral action is included in the developed block-backstepping control law to improve the steadystate characteristics and to enhance the robustness of the overall system. Additionally, the internal stability of the nonlinear system has been analyzed using zero dynamic criteria to guarantee the global asymptotic stability at the desired equilibrium point. The performance of the designed control algorithm is assessed via simulated results. The results show that the block-backstepping controller designed for nonlinear system gives better transient performance than that designed for the linear system. Also, the nonlinear controller can cope with larger initial angular ball position without loss of stability.
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