2 Multi-domain unified modeling method based on graphs
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1. Block Diagram
The block diagram is based on classical control theory. The model is defined by connecting the input and output of basic links such as the integral link, addition link, and multiplication link. It can be considered as modeling based on the system signal flow. In the block diagram, each link has a certain input and output, which belongs to causal modeling. Block diagrams can represent mathematical models of various conventional continuous systems or discrete systems, but they cannot directly reflect the topology of physical systems other than control systems. Block diagram modeling requires users to be familiar with the details of the mathematical model of the physical system. Block diagram-based simulation cannot directly handle algebraic loops, requiring users to handle them manually during modeling.
The Modelica language supports both text modeling and block diagram modeling.
2. Bonding diagram
The bond graph was first proposed by Paynter H. M. of the Massachusetts Institute of Technology in the United States in 196141. Later, Karnopp D.C. and Rosenberg R. C. developed it into a general modeling theory and method [42]. A bond graph is a directed graph in which components are nodes and connections are power bonds, with associated effort and flow variables. The keys represent the power flow between model elements, and the power flow is the product of the potential variable and the flow variable. The components are connected through junction 0 and junction 1. Junction 0 represents Kirchhoff's current law, and junction 1 represents Kirchhoff's voltage law. The bond diagram uses four forms of generalized variables: potential, flow, generalized momentum and generalized displacement. By characterizing the basic physical properties, describing the nine components of the basic connection of power transformation and conservation, the system bond can be drawn according to the direction of the power flow in the system. Combine the graphical model and list the system state equations.
3. Line diagram
The relationship between physical systems and linear graphs was first revealed by Trent and Branin5 in the 1950s and 1960s. Similar to bond diagrams, linear diagrams represent the flow of energy through a system through through and across variables (also called terminal variables). The edges of a linear graph represent the presence of energy flows in system components, and the nodes of the graph represent the terminals of the components. For each edge, there is a terminal equation that represents the relationship between terminal variables. One or more edges and associated terminal equations completely define the dynamic behavior of the component. Terminal diagrams of individual components can be combined into a system diagram by merging nodes with physical connections.