While improving the dynamical performance of a flexible motion control system, additional stresses are generated which induce undesirable vibrations. The design of adequate control algorithms makes it possible to enhance the overall behaviour of the machine while limiting its deformation modes vibrations. This paper presents a comparative study of the influence of different control algorithms on the trade-off between the cycle time and the amplitude of the residual vibrations, which have been applied to a Cartesian robot. While this selection of control algorithms is not exhaustive, these can all easily be implemented in current industrial systems. Each selected control algorithm is analysed along with experimental validations.