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Eliminating unwanted residual vibration is crucial in engineering systems, and this removal should be as effective and swift as possible. Input shaping control emerges as a powerful open-loop control technique to effectively eliminate residual vibrations, and it can be readily implemented in real-world engineering applications. This paper delves into the historical developments of input shaping control over the past seven decades. A key issue in input shaping control has been achieving robustness against modeling errors in both natural frequency and damping ratio. Input shaping control originated in the late 1950s under the name of posicast control. Subsequently, in the late 1980s, its robustness was significantly enhanced by incorporating derivative constraints and allowing nonzero residual vibration at no modeling error. These advancements have paved the way for the widespread application of input shaping control in various engineering problems. In 2019, impulse vectors were introduced as a mathematical tool for designing and analyzing input shapers, leading to the development of new input shapers using impulse vectors. This paper presents a comprehensive overview of the development of input shaping control, including zero-vibration and derivative (ZVD), extra-insensitive (EI), multi-mode, equal time and magnitude (ETM), unity-magnitude (UM), and negative equal-magnitude (NEM ) shapers.
Kang et al. (Tue,) studied this question.