Can an input shaper with two impulses suppress nonlinear residual vibrations?

This paper proves that an input shaper with two impulses can eliminate the residual vibrations in nonlinear systems completely when amplitude and application time of the impulses are chosen properly. In order to prove this, we analyzed phase portraits of nonlinear systems subjected to step and S-curve command inputs and verified that vibration free motion can be obtained by an input shaper with two impulses. To support this theoretical proof, simulations are shown for a selected nonlinear system. This paper also presents experimental results using a one link robotic arm with flexible joint to demonstrate that our argument holds true in a real system.