Bond graph modelling of hard nonlinearities in mechanics: A hybrid approach

This paper addresses the issue of hard nonlinearities encountered in the field of mechanics. It focuses on three typical examples of them, namely dry friction, backlash and irreversible motion transmission. Such phenomena are widespread in mechanical devices, the overall dynamics of which may be deeply affected in some conditions. Since hard nonlinearities differ from smooth ones in that the resulting dynamics generally cannot be linearized around setpoints, it is necessary to explicitly take them into account in the modelling process, especially when a control objective is considered. A hybrid approach mixing bond graph with ideal switches and finite state automata is proposed in order to abstract the previous nonlinear dynamics in elementary models that may be further integrated in whole representations of mechanical systems. After a detailed description of each model, the efficiency of the approach is illustrated on the example of a mechanical system combining all the nonlinear phenomena of interest.