The application of input shaping to a system with varying parameters

The original input shaping technique, that was developed in earlier work, is summarized, and a different definition for residual vibration is proposed. The new definition gives better insight into the ability of the input shaping method to reduce vibration. The extension of input shaping to a system with varying parameters, e.g., natural frequency, is discussed, and the effect of these variations is shown to induce vibration. A modified command shaping technique is developed to eliminate this unwanted motion.