Simulation of Mode Switching Systems Using Switched Bond Graphs

Abstract: In this thesis one approach to model and simulate mode switching systems is studied. This approach, switched bond graphs, is an extension of the bond graph language in the sense that it allows modeling of mode switching phenomena. The classical bond graph language as well as the switched bond graph language are presented. Different aspects of these tools are discussed, and one aspect specially considered is causality. Computational causality shows in what order the variables in a model should be calculated to get efficient simulation code. Causality can also be used to make analysis of the model. For classical bond graphs, causality is a fixed property. For switched bond graphs causality becomes mode varying. With the mode varying causality, it follows that there will be a different continuous model for each mode. Many other and similar approaches do not allow one model for each mode. They express the description of all modes in one single model. The reason for this is the exponential increase of modes for a linear increase in the number of modeled switching phenomena.The main contribution of the thesis is mediated by an actual implementation, where it is shown that the simulation procedure is algorithmic from a switched bond graph model. Two different simulation procedures are presented: MTS simulation and mode-by-mode simulation. Of these procedures, MTS-simulation is implemented. In the MTS-simulation algorithm, the complete mathematical description of all modes will be derived before the simulation starts. In mode-by-mode simulation, the mathematical description will be derived for one mode at a time. The simulation of one mode will take place before equations for the next mode are derived. This algorithm circumvents the combinatorial explosion in the number of modes.The modes can be categorized by their properties in different ways. Two different categorizations are discussed in the thesis. The first categorization is to divide the modes into conflicting and non-conflicting modes. Conflicting modes may reflect errors in the model or undesired behaviors of the system. The other categorization is made by how fast the different modes are left when activated during simulation. These properties are interesting when dealing with the transition conditions. Two mode switching systems, modeled using switched bond graphs, are simulated using the presented algorithms. The models are analyzed, and a discussion about the properties of the different modes in these models is conducted.