Abstract

Plant modeling is one of the most important technical areas for control system developments. To establish a desired plant modeling environment, various technologies are necessary, such as system identification, physical modeling, model simplification, boundary modeling, optimization, function approximation, design of experiments, model execution including DAE (Differential Algebraic Equation) solver, physical law library. Unfortunately, each technology is almost isolated and the integrated modeling environment shared among researchers and engineers has not been well established.

In the automotive industry, static experimental models have been introduced with Design of Experiments (DoE) for nonlinear systems to mitigate the time consuming issue rapidly progressing in the engine control calibration area. According to the success of the remarkable reduction of calibration time, the automotive industry has studied to apply dynamic models to the calibration process. However, it is not easy to identify the adequate equations of dynamical model even for only the calibration of a small control component. The difficulty can result from the facts that multiphysics modeling and the systematic method integrating physical and experimental models have not been well established.

Almost all researchers admit that combining physical and experimental models is a practical way. However, it seems that there is no systematic way to develop such a model. There are two approaches to obtain the target plant model which has the minimum order and the minimum parameters, basically. One is the gray box approach that combines experimental models to a physical model. It should be formalized to guarantee to reduce the dependency of model quality on the model developer. The other is the way to put “physical structure”, which means relationships between model coefficients, to a pure experimental model, such as Taylor series and the linear combination of basis function. “Physical structure” can be preliminary knowledge in other words and applied to model parameters optimization.

Bond-Graph is the popular multiphysics modeling based on the description of the energy conservation law. However, it deals with only two kinds of the variables of which the multiplication forms the energy flow. However, on the compressible fluid domain, three variables such as pressure, density and velocity are necessary to calculate an energy flow. Thus, Bond-Graph should be extended. In this lecture, a novel multiphysics modeling based on the considered conservation laws is introduced.