From fractal robustness to the CRONE approach

Équipe CRONE - LAP - ENSERB, Université Bordeaux I, 351, cours de la Libération - 33405 Talence cedex, France

Abstract

This article deals with the transposition of ''fractal robustness'' to automatic control. The considered dynamic model which governs this phenomenon is a non integer order linear differential equation where the natural frequency and the damping ratio of the oscillatory mode of the solution are determined. A remarkable result is that the damping ratio is exclusively linked to the non integer order of the differential equation. This is the corner stone of the CRONE control. The dynamic behaviour of this control is described in tracking and in regulation. The robustness of the damping ratio and of the resonance ratio is demonstrated. An open loop is defined using closed loop performance specifications. A CRONE regulator is approximated by an integer order transmittance. Finally, the principle of the CRONE suspension, the synthesis method and the performance are developed.