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The use of machine tools within the framework of high speed machining puts heavy demands on the material structure, thus generating damaging vibrations during machining phases. Two complementary methods can be planned to improve the dynamic behaviour: a mechanical solution (to rigidify, etc.), and a solution that involves taking the dynamic behaviour into account by a judicious control law. It is this second method that we explore. In this paper, we propose: - Firstly, to explore the classic industrial control methods based on a PI controller and filtering methods applied to translation resonant load. - Secondly to explain how, starting from a strategy of behaviour model control, we can make the whole chain rigid, thus making it possible to obtain significant dynamic performances and a higher degree of accuracy. This behaviour model control, based on the techniques of pole assignment, constrains the flexible process to behave like the model.