Suppression of motion-induced residual longitudinal vibration of an elastic rod by input shaping

Various input-shaping schemes such as the "zero-vibration" (ZV), "zero-vibration-and-derivative" (ZVD), "negative ZV" (NZV), and "negative ZVD" (NZVD) schemes have previously been proposed to suppress motion-induced residual vibration of lightly damped structures. In such schemes, the input command of the dynamical system in question is properly administered (i.e., shaped), so that the dominant induced vibration modes are annihilated through destructive interference. Here we are concerned with the effects of system payload on the vibration reduction capabilities of the aforementioned input-shaping schemes, especially when they are applied to continuous systems. By use of the simple structure of a linearly elastic rod as a specific example, it is demonstrated that both the minimum achievable residual vibration amplitude and the tolerance of detuning parameter errors of the input-shaping schemes are sensitive to the amount of payload on the system. It is therefore imperative to take the factor of system payload into account in the design of practical input shapers.