Determination of Second order Discrete time Transfer Function

Download the Analysis folder from the sbhs website. It will be available under downloads section. Download the file for SBHS Analysis Code (local & virtual). The name of the file is scilab_codes_analysis. The download will be in zip format. Extrat the downloaded zip file. You will get a folder scilab_codes_analysis.

Open the scilab_codes_analysis folder and then locate and open the folder Step_Analysis.

Inside this folder, locate and open the folder Discrete-order2

Copy the prbs test data file to this folder.

Start scilab and change the working directory to Discrete-order2

Open the file optimize.sce in scilab editor and enter the name of the data file (with extention) in the filename field.

Save and run this code and obtain the plot as shown in figure 7.8. This plot will also show the second order discrete time transfer function's coefficients a1, a2, b1 and b2.

The values are also shown on scilab console as shown in figure 7.9

The results presented are obtained for the data file prbs-data-virtual.txt. This data file is present under the prbs directory for virtual experiments.The plot thus obtained is reasonably good. See the Scilab plot to get the values of

and

. The figure 7.8 shows a screen shot of the same. We obtain

= -1.82,

= 0.833,

= 0.0017,

= -0.00086, . The transfer function obtained here is at the operating point of 50 percentage of heat. If the experiment is repeated at a different operating point, the transfer function obtained will be different. The gain will correspondingly be more at a higher operating point. This means that the plant is faster at higher temperature. Thus the transfer function of the plant varies with the operating point. Let the transfer function we obtain in this experiment be denoted as

. We obtain

$\displaystyle G(z)=\frac{0.0017 -0.00086z^{-1}}{1-1.826z^{-1}+0.833z^{-2}}z^{-5}$ (7.5)

**Figure 7.8:** PRBS second order fit

**Figure 7.9:** PRBS second order model

rokade 2017-04-23