Minimizing structural vibrations with Input Shaping (TM)

A new method for commanding machines to move with increased dynamic performance was developed. This method is an enhanced version of input shaping, a patented vibration suppression algorithm. This technique intercepts a command input to a system command that moves the mechanical system with increased performance and reduced residual vibration. This document describes many advanced methods for generating highly optimized shaping sequences which are tuned to particular systems. The shaping sequence is important because it determines the trade off between move/settle time of the system and the insensitivity of the input shaping algorithm to variations or uncertainties in the machine which can be controlled. For example, a system with a 5 Hz resonance that takes 1 second to settle can be improved to settle instantaneously using a 0.2 shaping sequence (thus improving settle time by a factor of 5). This system could vary by plus or minus 15% in its natural frequency and still have no apparent vibration. However, the same system shaped with a 0.3 second shaping sequence could tolerate plus or minus 40% or more variation in natural frequency. This document describes how to generate sequences that maximize performance, sequences that maximize insensitivity, and sequences that trade off between the two. Several software tools are documented and included.