Specified-duration shapers for suppressing residual vibrations

Input-shaping control has received considerable research attention for suppressing residual vibrations. Although numerous studies have been conducted on designing input shapers with arbitrary robustness to modeling errors, no studies have focused on the design of input shapers with arbitrarily specified shaping times. In this study, a specified-duration (SD) shaper, which is an input shaper with an arbitrarily specified shaping time, and a systematic method to design an SD shaper using impulse vectors are proposed. As the specified shaping time increases, the SD shaper increases the number of impulses one by one according to the number of added derivative constraints, thereby improving robustness to modeling errors. The performance of the SD shaper was evaluated for a second-order system through computer simulations. The simulation results revealed that the SD shaper suppresses residual vibrations of the vibratory system at the specified shaping time. The validity of the SD shaper was experimentally verified using a horizontal beam vibration apparatus. The results of this study provide insight into the development of vibration suppression strategies with input shaping control.