Negative input shapers for explicit fractional derivative systems

Input shaping is a technique that reduces residual vibration by generating a self-canceling command signal. This technique is developed by N.C. Singer and W.P. Seering for flexible structures, and applied especially in aerospace field and robotics. Traditionally, input shaper has contained only positive impulses. However, negative valued impulses allow to decrease the shaper length. In previous works, positive ZV and ZVD shapers are synthesized to fit fractional order systems. In this paper, negative input shapers are extended to explicit fractional derivative systems, then, a comparative study is presented.