Interpretation of smooth reference commands as input-shaped functions

The paper offers a new approach for analyzing smooth reference commands. This approach treats smooth command profiles as input-shaped functions. Input shaping is a method of reducing residual vibration by convolving a sequence of impulses with a baseline system command. The sequence of impulses, known as the input shaper, is the key to predicting a system´s vibratory response. By interpreting smooth commands as input-shaped functions, fundamental frequency analysis results are derived. This leads to common criteria for comparing smooth reference commands to input-shaped commands.