The most promising method seems to be the approaches that first excite ringing and secondly cancels it 11,12,13,14,15 . For a single oscillation mode, as assumed in this context, the approach simply subdivides a step into two. The first step excites the vibration and the second one cancels it. This can be seen in Figure 10 that is based upon an input shape as shown in Figure 11. In practice the method is somewhat more complex since ringing may occur at more than one frequency.
Step responses fro a system with position feedback from the motor.
The curves above show the movement of the load. The input curve is shown in Figure 11. Ringing is completely avoided. Shaped input curve applied to the position loop for the step responses in Figure 10. Shaped inputs may be applied in a feedforward mode, i.e. matching input curves may be applied simultaneously for both torque, velocity and position.