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Robust stabilization using time-scaling and Lyapunov redesign: The ball-beam system

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2 Author(s)
Maruthi, T.R. ; Dept. of Electr. Eng., Indian Inst. of Technol. Madras, Chennai, India ; Mahindrakar, A.D.

This paper proposes a nonlinear stabilizing controller for a ball on an end-actuated beam system, which is robust to an uncertainty in the mass of the ball. To this end, the dynamics is time-scaled into two subsystems termed as the `Outer-Loop' and the `Inner-Loop' dynamics. An Outer-Loop controller generates a reference trajectory for the beam's pitch angle, which if faithfully followed, would result in the stabilization of all states of the system. A robust Inner-Loop controller is synthesized using the Lyapunov redesign technique, which forces the actual pitch angle to stabilize to the trajectory of the Outer-Loop controller. It is shown that the effects of the uncertainty in the mass of the ball are eliminated by the Inner-Loop controller. The uncertainty tolerance limit of this robust controller is also characterized through a necessary condition. Experiments validate the effectiveness of this strategy in stabilizing the system.

Published in:

Control Automation Robotics & Vision (ICARCV), 2010 11th International Conference on

Date of Conference:

7-10 Dec. 2010