Passivity analysis and control of nonlinear systems modelled by bond graphs

Recent results on the passivity analysis and control of physical systems, based on the balance of dissipated and internally generated energy, are generalised to nonlinear systems represented by bond graphs. For linear systems, the internally generated energy associated with modulated sources can be coupled with the dissipative field, so that if external energy sources are excluded, then the system is passive (or dissipative) if the resulting composite multiport field is passive. Such a result for linear systems was previously conveniently expressed in terms of a characteristic matrix being positive semi-definite. Parasitic elements of previous works are no longer required, which allows working on the original bond graph of lower dimension than the augmented bond graph and for no-linear systems avoid inverting the dissipative nonlinear constitutive relations. For nonlinear systems, passivity is now considered through the explicit difference between the dissipated and the internally generated energy. If this energy difference is positive, the system is passive. For control systems, the current work proposes that the controller is designed to have a structure similar to the plant (linear or nonlinear), and its parameters are chosen to assure that in closed-loop the difference between the dissipated and the internally generated energy is positive. In particular, the control parameters can be chosen to assign a desired dissipated energy or to cancel by feedback the internally generated energy and to add damping, therefore achieving sufficient conditions for the passivity of the closed-loop system.