Polynomial profiles can be used as reference commands to limit induced vibration in flexible systems. Due to their ease of design and low-pass filtering effects, polynomial profiles are often found in cam-follower systems. Polynomial profiles have also been used as smooth reference commands for automated machines. However, despite extensive work to develop and improve such profiles, inherent tradeoffs still exist between induced vibration, rise time, and ease of design. Input shaping is an alternative method for generating motion commands that reduce residual vibration. This paper compares polynomial profiles to input-shaped commands for the application of reducing vibration in flexible systems. Analyses using Laplace transforms reveal that input shapers suppress vibration at regularly spaced frequencies. However, polynomial profiles do not share this property. Simulations and experimental results show that input shaping improves rise time and reduces residual vibration in comparison to polynomial profiles.
