Need for Different Model Types

In the previous chapters deterministic models were derived. They were designed based on the chemical and physical balances and mechanisms of the process and consequently the model described the internal functional behavior. Black-box models, on the other hand, are designed based on the input-output behavior of the process and consequently the model describes the overall behavior. A black-box model consists of a certain stmcture of which the parameters are determined by means of experimental results. Therefore, they often are called experimental models. The main properties of black-box models are the stmcture characteristics, which are level of detail, degree of non-linearity and the stmctural way in which dynamics are composed. 

As already discussed in the previous chapters, process behavior is usually non-Unear. Whether or not the empirical model to be developed should also be non-linear depends on the operating range in which the model will be used. If the process is controlled and the operating range is small, a linear process model may be an adequate approximation of reality. The application of the model will determine whether the model needs to be dynamic or static. For control and prediction type applications, models are usually dynamic. 

If the process conditions vary over a wide range, there may be a need for a non-linear empirical model. In case of a dynamic non-linear model there are a few possibilities for developing such a model, for example a dynamic neural network or a dynamic fuzzy model. One could also develop a Wiener model, in which the process dynamics are represented by a hnear model, such as a state space model. The static characteristics of the process are then modeled by a polynomial, able to represent the non-linearity. 

If the empirical dynamic model is hnear, one could use for example a time series model. Different model types are available and will be discussed in a subsequent chapter. 

If the model is linear and static one coirld for example use partial least squares modeling. State space modeling can be used in its linear or non-linear form, depending on the situation. 

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