Virtual constraints for the orbital stabilization of the Pendubot
Résumé
A method for the generation of attractive and neutrally stable limit cycles for nonlinear systems is presented. It consists in designing an output that, when regulated through a suitable feedback, forces the existence of a limit cycle or neutral oscillations in the zero dynamics. Conditions are then given to ensure that those characteristics of the zero-dynamics translate to the whole system. A particular focus is made on the gen- eration of neutrally stable oscillations through that method, because it is not always easy to build an output that results in the existence of a limit-cycle in the zero-dynamics. A special case where such a difficulty arises is given in the analysis of oscillations generation around the up- per vertical for the pendubot. The regulation of the output results in neutrally stable oscillations, and we present a method for imposing that those oscillations converge towards the desired ones.