Most positioning systems experience residual vibration during operation. Such residual vibration can be eliminated or reduced to an acceptable level by using the input shaping method. However, adopting the input shaping methods typically introduces a certain amount of time-delay into a system. This study focused on the development of a delay-time adjustable input shaping method to eliminate vibration caused by repetitive motion in positioning systems. The proposed input shaping method, called the virtual mode (VM) input shaper, uses a virtual frequency parameter that adjusts delay-time and cancels residual vibration. Unlike most previous input shaping studies, this study investigated VM input shaping performance to eliminate the steady-state vibration induced by repetitive motion in positioning systems. To this end, an analytical formulation was derived and used for simulating the input shaping performance with varying dominant parameters involved in a system. Experiments were also performed to validate the proposed method.

This study proposed the proper detonation delay time of a main warhead after a precursor warhead detonation in an arbitrary tandem shaped charge missile as 407 μsec. In addition, the available detonation delay time range of the main warhead was proposed to be between 396 μsec and 418 μsec. The proposed figures were based on the analysis of the target protection capability and the scattering reactor behaviors of the explosive reactive armor with dual reactive panels. By virtue of this work, the determination of main warhead detonation delay time is more effective and convenient. Finally, the tandem shaped charge missile with more effective penetration performance also could be developed in the future.