Laguerre model time scaling factor

We can compute the coefficients of the Laguerre model using Equations (2.14) for a positive time scaling factor p... 

This is a high order process with severe nonminimum phase behaviour. Its noise-free unit step response is shown in Figure 2.5. This process step response is sampled with an interval At = 1.5 sec. The key to success with the Laguerre model for such a complicated process is to find the optimal time scaling factor p for a given model order N, particularly when the model order is small. Figure 2.6 shows a 3-dimensional plot of the loss function V — for iV = 1,2,..., 10 and 0 < p < 0.1, where the coefficients... 

The first step in estimating a Laguerre model for this process from this step response data is to determine the time scaling factor p and choose a model order N. It is seen from Figure 2.10 that the process has an approximate settling time of 100 sec, which gives us an estimate of the lower bound... 

Since both step responses have approximately the same settling time, the optimal pole location should lie in the same interval. For Step Response 2, the plot of C3C4 is shown in Figure 2.26 and indicates that the optimal time scaling factor is located at p = 0.05. The resulting 3rd order Laguerre model is given by... 

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