Linearization of a class of non-linear systems modelled by multibond graphs

Based on non-linear systems described by multibond graphs, a procedure designed to present symbolic linearization of these multibond graphs, is presented in this paper. Firstly, a junction structure of a multibond graph with multiport gyrators that represent Eulerian junction structures is proposed. In addition, non-linear multiport resistors are considered. By knowing the non-linear causal paths and loops of the non-linear multibond graph, the linearization is obtained by two steps: (1) The original multibond graph on the nominal operating point is evaluated; (2) New and additional paths based on the non-linear causal paths and loops are included. The state space representation of the linearized multibond graph using the corresponding junction structure is presented. An advantage of this methodology is its ability to allow the user to define a nominal operating point in which the linearization will be carried out. In order to apply the proposed methodology, two physical systems are modelled and linearized by multibond graphs: a synchronous generator and a two degrees of freedom PUMA. Simulation results of these non-linear and linearized systems are shown.