The bond graph is a modeling method that has many advantages. First, we can rather easily construct a model of a system through the bond graph because it depicts physical structures of a system rather than physical laws. Moreover, this feature gives us good insights, which can hardly be obtained through modeling methods based on physical laws only. These insights make analysis and design of a system easier in some cases. Second, since the bond graph describes complex systems in a unified fashion, models in various domains can be easily combined and experiences in one domain can be applied to other domains. Third, a mathematical model can be systematically derived from a bond graph model. In addition to these, there are many advantages in the bond graph modeling method.
Even though the bond graph has many advantages, it has much trouble modeling large complex systems: a bond graph model of a system becomes complicated as its complexity increases. The hierarchical bond graph can solve this problem since a hierarchical structure can effectively represent large complex systems. Top-down method and/or Bottom-up method are employed for representing a bond graph hierarchically. Top-down is a method to construct a hierarchical model from the top to the bottom and Bottom-up from the bottom to the top. Yet, there is no guideline informing us when and how we should apply Top-down or Bottom-up. In some cases, especially for large systems, a modeling process cannot be systematically performed, thereby taking much time to get a whole model. Even though we know which of these two methods we should use, it is difficult to proceed with modeling if we do not know how to use them. This thesis proposes a guideline for Top-down/Bottom-up method. On top of the guideline, many examples are presented, which help us to understand how to use them. Using the guideline and the examples, we can model large complex systems systematically
It is necessary to obtain a mathematical model for predicting behavior of a model constructed through the proposed modeling method or for designing a controlled system for the model. It takes much time and effort to manually derive the mathematical model for large complex systems. So, to automatically derive a mathematical model from a hierarchical bond graph model, modeling software has been developed. This software has the following functions. First, a hierarchical bond graph model can be constructed through the proposed modeling method in this software. Second, the software can automatically derive a mathematical model from the hierarchical bond graph model. Third, the software can treat nonlinear systems as well as linear systems. Finally, a mathematical model can be expressed as a symbolic form as well as a numerical form. The symbolic form enables us to perform various analyses such as qualitative analysis and sensitivity analysis of parameters for the model.
To verify the modeling strategy combining the proposed modeling method and software, a hydraulic excavator system has been modeled. The system is large complex system composed of a manipulator, hydraulic actuators and engine/pump. Through the modeling strategy, this large complex system has been modeled systematically and effectively and a complicated mathematical model has been derived automatically. This mathematical model has been used profitably for the analysis and the solution of the vibration problem of an excavator system and control design for tracking control of an excavator manipulator. This example proved that the proposed modeling strategy is effective and solves the problems related to excavator modeling.
