Comparison of robust input shapers

The rapid movement of machines is a challenging control problem because it often results in high levels of vibration. As a result, flexible machines are typically moved relatively slowly. Input shaping is a control method that allows much higher speeds of motion by limiting vibration induced by the reference command. To design an input-shaping controller, estimates of the system natural frequency and damping ratio are required. However, real world systems cannot be modeled exactly, making the robustness to modeling errors an important consideration. Many robust input shapers have been developed, but robust shapers typically have longer durations that slow the system response. This creates a compromise between shaper robustness and rise time. This paper analyzes the compromise between rapidity of motion and shaper robustness for several input-shaping methods. Experimental results from a portable bridge crane verify the theoretical predictions.