CRONE Control Research Articles

A New Control Strategy Based on the Concept of Non Integer Derivation: Application in Robot Control

This paper deals with the robustness as far as damping is concerned, and more particularly the robustness as for control damping versus the parameters of the plant.After defining robustness in time domain, it presents the non integer approach of the CRONE control, a french abbreviation of “Commande Robuste d’Ordre Non Entier”, namely “Non Integer Order Robust Control”. This approach uses the mathematical principle which insures the robustness of stability degree in nature, namely non integer derivation.An open loop frequency template is deduced from the non integer order differential equation which describes the relaxation of the ebb and flow on a DOrous dyke, this phenomenon being robust as for stability degree since the damping factor is independent of the motion water mass. This template illustrates robustness in frequency domain.The general expressions of the damping factor and the resonance factor are proved. These one indeed translate the robustness of the control.The last part of the paper deals with the synthesis of a CRONE regulator insuring a precorrection of the plant, in the general case of an indifferent frequency placement of the template. The study plant is achieved by an inclining polar table which constitutes an elementary manipulator with three degrees of freedom. This one is chosen because of its structure which insures large inertia variations, strong dynamic couplings and a great number of nonlinearities.