Pre-shaping techniques for reducing residual vibrations

In this work a pre-shaping technique is used in order to reduce the residual vibrations of a vibrating system in a point-to-point motion. In this method the acceleration profile is made-up of a summation of sinusoidal terms with given motion time. By considering the residual mechanical energy of the system as a cause of its steady state residual vibrations, this method finds the relations among the harmonic amplitudes, in order to avoid the residual vibrations at a given natural frequency by minimizing the amount of system residual mechanical energy. In order to have a system robust with respect to the uncertainties in the evaluation of the natural frequency, a method is presented that makes the residual vibrations null at two different reference frequencies around the estimated one. In this way, there is a large around of the estimated frequency, where the residual vibration is maintained low. Moreover, the thesis analyzes the influence of different choice of the reference frequencies and the motion time on the amount of residual vibrations. This method is also used in order to design a filter that decreases the residual vibrations of the system with respect to a given motion profile for the support. So this filter is robust with respect to system parameter uncertainties and also it’s not sensitive to motion command profile.