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Introduction to modeling:
For a complex production process, it is usually very complicated, difficult and sometimes even impossible to carry out theoretical analysis and experimental research on physical objects. At this time, we need a physical model as the research object, and through the study of the model, we can draw conclusions or speculations that are also applicable to the physical object.
A model usually refers to a representation of the characteristics of an actual system or process, or a structure mapped into it. It can reflect the behavior characteristics of a system or process in a form that meets the needs of research work. Usually, the model should not only basically reflect the actual situation, but also be simplified appropriately to facilitate application.
The physical model is a physical model. The theoretical basis of establishing physical model is "similarity principle". The physical model can be a small copy of the original (geometric similarity); It can also be an analog device (with similar characteristics). General geometric similarity can not completely guarantee the similarity of features, so it is rarely used in the study of dynamic features.
However, analog devices based on similar characteristics have been widely used. The physical properties of the simulated device may be fundamentally different from those of the original device. For example, computer simulation is a general electrical model based on similar characteristics.
Mathematical model is an abstract model and a mathematical structure reflected by the relationship between variables related to a system or process. Such as algebraic equations (groups), differential equations (groups), or graphs, numerical tables, etc. The mathematical model describing dynamic system is usually a set of differential equations and algebraic equations, also known as dynamic mathematical model.
At this time, the steady-state characteristics of the system are also included in its dynamic mathematical model. The static system is only described by algebraic equations (groups), and there is a general functional relationship between variables, which is called static mathematical model. If the dynamic nature of a system can be ignored and treated as a static system, it can be approximately described by a static mathematical model.
Although the mathematical model is abstract, it can fully and accurately reflect the essence of the system or process. By establishing the mathematical model of the process, we can grasp the characteristics of the process and provide basis and conditions for various research purposes. The task of process modeling and identification is to establish a suitable process mathematical model, that is, to model the process.
Generally, establishing mathematical models requires less investment. The method of theoretical and experimental research using mathematical models has been paid more and more attention and widely used.
Especially with the development and popularization of computer technology, the mathematical modeling of a practical problem is often the premise of computer application. On the other hand, electronic computers also provide many conveniences and create very favorable conditions for theoretical and experimental research using mathematical models.