Worst-case optimal noncausal motion planning for residual vibration reduction

In this paper we present a novel methodology for the reduction of the residual vibration in point-to-point motions of mechanical systems endowed with elastic transmissions. The technique is based on the system inversion, where a polynomial output function, which describes the motion of the load, is suitably chosen in order to assure the continuity of the input function until a predefined order. The system inversion point can be determined by a simple iterative procedure in order to minimize the worst-case amplitude of the residual vibration in presence of significant uncertainties on the values of the stiffness constant and damping ratio of the system. Results show the effectiveness of the approach and how the optimization of the system inversion point significantly increases its robustness.