Even this simple model type has a relatively complex modular structure (see Figure 6), because for each measurement point a separate FOPTD model has to be set up and the initial temperature of the measurements has to be subtracted.
Since there are seven measurement points and each FOPTD model contains three parameters, the overall model has totally 21 parameters.
Due to the five parameters, there is more freedom in the equivalent circuit model for adjusting the signal behavior at a given point as with the three parameters of the FOPTD model.
(ii) The time for optimization is much higher (60 minutes for the Monte Carlo algorithm with the numerous Python script calls versus less than 1 second for the least squares method with the FOPTD models) since iterative optimization methods have to be used instead of the least squares method.
As soon as parameter identification is used, the identified parameters have no better physical meaning than the parameters of the phenomenological FOPTD model.
Notations Abbreviations FOPTD: First order plus time delay CAD: Computer-aided design PC: Personal computer RMSE: Root-mean-square error SSE: Sum of squared errors.
In the adaptive control system, the updated transfer function model (9) is further reduced to a FOPTD model
The model parameters [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are updated by fitting the FOPTD model (14) at each sampling time to a simulated step response of the model (9) using the Smith's approximation technique .
The updated FOPTD model is directly applied for controller parameters on-line adaptation using controller tuning rules developed for simple dynamic models.