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Conclusions

The expected residual vibration performance measure easily incorporates the probability distribution of modeling errors in both natural frequencies and damping coeffi cients. Using this new measure to analyze several traditional input shaping designs shows that the EI and multihump shapers yield lower expected residual vibration than the equivalent length ZVD and derivative-type shapers for large uncertainties in the natural frequency or large uncertainties in both natural frequency and damping constant. However, the ZVD and derivative shapers lead to smaller residual vibration levels when there is uncertainty in the damping. The results presented also clearly indicate at what uncertainty levels the performance of the EI and multihump shapers become superior to the ZVD and derivativetype shapers, and these results are useful in guiding the choice of the most appropriate type of shaper given the …