Input shaping is an effective method for reducing oscillatory motion in linear systems. Many physical systems, however, exhibit discontinuous dynamics, such as saturation, rate limiting, backlash, and dead-zone. These hard nonlinearities can degrade the vibration reducing properties of shaped signals. This paper investigates the detrimental effects of dead-zone on a class of input-shaped commands. A mitigation strategy is proposed for reducing these detrimental effects when the value of the deadzone can be estimated. The robustness of this mitigation approach to uncertainties in the dead-zone width is also determined. Theoretical developments are experimentally verified using an industrial 10-ton bridge crane.

Input shaping is an effective method for reducing oscillatory motion in linear systems. Many physical systems, however, exhibit discontinuous dynamics, such as saturation, rate limiting, backlash, and dead-zone. These hard nonlinearities can degrade the vibration reducing properties of shaped signals. This paper investigates the detrimental effects of dead-zone on a class of input-shaped commands. A mitigation strategy is proposed for reducing these detrimental effects when the value of the dead-zone can be estimated. The robustness of this mitigation approach to uncertainties in the dead-zone width is also determined. Theoretical developments are experimentally verified using an industrial 10 ton bridge crane.

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