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An on-off damping radial spring-damper can be attached to a pendulum to suppress its nonlinear sway motion. This paper studies the class of on-off damping controller, which switches the damping level from high to low and back at fixed times every quarter of period. Among this class, this paper shows the solution of the lower bound controller producing the lowest amplitude-frequency curve. The lower bound curve shows some fundamental natures of the system and gives some useful directions for a good on-off damping controller.

Lower bound of performance index of anti-sway control of a pendulum using on-off damping radial spring-damper