From fractal robustness to non-integer approach in vibration insulation: the CRONE suspension

We deal with the transposition of fractal robustness in automation and mechanics through the CRONE control and suspension. Fractal robustness expresses the robustness of damping in nature, and that fractality ensures through non-integer derivation. This concept is illustrated by the relaxation of water on a porous dyke, its damping being independent of the motion water mass. This robust phenomenon is paradoxical in the integer approach of mechanics, where any relaxation presents a damping linked to the carried mass. The dynamic model which governs this phenomenon is established. It consists in a differential equation of non-integer order between 1 and 2, whose solution depends on the carried water mass, but whose damping is independent of it. The transposition of this template in automation and mechanics defines the non-integer approach used by the CRONE control and suspension