Shaping Inputs to Reduce Vibration: A Vector Diagram Approach

This paper describes a method for limiting vibration in flexible systems by shaping the system inputs. Unlike most previous attempts at input shaping, this method does not require an extensive system model or lengthy numerical computation; only knowledge of the system natural frequency and damping ratio are required. The effectiveness of this method when there are errors in the system model is explored and quantified. An algorithm is presented which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimated natural frequency. A procedure for shaping inputs to systems with input constraints is outlined. The shaping method is evaluated by dynamic simulations and hardware experiments.