Input Shaping Vibration Control for Nonminimum Phase Systems

Many systems exist that contain coupled rigid body and flexible body dynamics. Rigid body repositioning of these systems can be problematic due to unwanted residual vibration of the flexible body degrees of freedom. Input shaping is a method for generating system commands creating desired rigid body motion where the flexible body motion being quiescent at the end of the maneuver. Either operator-in-the-loop or batch commands are convolved with a carefully designed input shaping filter to produce the eventual system input. Systems with minimum phase zeros are easily accommodated using input shaping filters designed for the system without zeros, and then using a secondary pole-zero cancellation filter. This approach cannot be practically applied to nonminimum phase systems since the resulting system input may become unbounded. This paper considers input shaping methods for generating residual vibration-free input time histories for non-minimum phase, oscillatory systems using bounded inputs. An example is presented where the system is an undamped oscillator with a single right plant zero.