Static model means that the relationship between variables of the system to be described does not change with time, and is generally expressed by algebraic equations. Dynamic model refers to a mathematical expression that describes the laws of system variables changing with time, and is generally expressed by differential equations or difference equations. In classical control theory, the common system transfer function is a dynamic model, which is transformed from the differential equation describing the system.
2. Distributed parameter and lumped parameter model
Distributed parameter model uses various partial differential equations to describe the dynamic characteristics of the system, while lumped parameter model uses linear or nonlinear ordinary differential equations to describe the dynamic characteristics of the system. In many cases, the distributed parameter model can be simplified to a lumped parameter model with low complexity through spatial discretization.
3. Continuous-time and discrete-time models
The model in which the time variable changes in a certain interval is called continuous-time model, and the models described by differential equations above are all continuous-time models. When dealing with lumped parameter model, time variables can also be discretized, and the obtained model is called discrete time model. The discrete-time model is described by the difference equation.
4. Parametric and nonparametric models
The models described by algebraic equation, differential equation, differential equation and transfer function are all parametric models. The establishment of parametric model is to determine the parameters in the known model structure. Parametric models are always obtained through theoretical analysis. The nonparametric model directly or indirectly gets the response from the experimental analysis of the actual system, and the impulse response or step response of the system recorded through the experiment is the nonparametric model.
Extended data:
Mathematical model modeling process
1, model preparation
Understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. The essence of the problem is contained in mathematical thought and runs through the whole process of the problem, and then the problem is described in mathematical language. Requirements in line with mathematical theory, in line with mathematical habits, clear and accurate.
2. Model assumptions
According to the characteristics of the actual object and the purpose of modeling, the problem is simplified with accurate language and some appropriate assumptions are put forward.
3. Model structure
On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and constants, and establish the corresponding mathematical structure (try to use simple mathematical tools).
4, model solving
Using the obtained data, all parameters of the model are calculated (or approximately calculated).
5. Model analysis
The idea of establishing the model is expounded, and the results are analyzed mathematically.
6. Model test
The model analysis results are compared with the actual situation to verify the accuracy, rationality and applicability of the model. If the model is in good agreement with the actual situation, the practical significance of the calculation results should be given and explained. If the model is not consistent with the actual situation, it is necessary to modify the assumptions and repeat the modeling process.
Baidu Encyclopedia-Mathematical Model