Week 5 Modeling -- Approximate Linear SOPDT Model   

Objectives   

To learn how to model second-order-plus-dead-time (SOPDT) with Excel. To observe the dynamic response of the approximate linear SOPDT model for a system. To observe the impact of parameter values on the dynamic response. To adjust the linear SOPDT model parameters to get the model results to agree with the experimental results.

Modeling Assignments   

Preliminary   

There are two things to add to the Excel model you developed last week. Last week's model started at zero (0) for input and output. We want our model to be somewhere else in the operating range of the system. Last week's model did not take into account that the operating point at which we want to model our system is not at a value of zero (0) on the input signal. So, we need to add the baselines for our system to the Excel model.

Open last week's Excel model and add two items in the parameter list. Here is a suggestion as to what to add (the numerical values are just examples).

inbl=

30

outbl=

3

Use the menu Insert/Name>/Define... to make both of these added parameter usable names in your formulas. Then in cell B2 add the "Input Baseline" as shown here:

=IF(A2>td,A,0)+inbl

 

And in cell C2 add the "Output Baseline" as shown here:

=IF(A2>td+to,A*K*(1-EXP(-(A2-td-to)/tau)),0)+outbl

Copy both of these formulas down to the bottom of your spreadsheet.

Save this file.

Approximate SOPDT Method   

Reference: Smith & Corripio, pp 308-315

Open the file developed as described above. Open the file with the experimental data in it. What you're going to do is to put these two files together.

Select the "model" file. Select columns B and C by clicking on the B at the top of the column and dragging across to the C at the top of the next column. Insert 2 columns by pulling down the Insert menu and choosing Columns.

Now select the "experimental data" file. Select the experimental data (time, input and output columns) by clicking at the top of the columns as above. Copy that data by pulling down the Edit menu and choosing Copy. Then go back to the "model" file, select columns A, B and C and paste this data. Paste the data by pulling down the Edit menu and choosing Paste.

Suggestion: Now save this file with a new name.

Adjust the length of the model columns (D and E) to the same as data columns (A, B and C). Do this by either dragging down or by using Edit/Clear. Now draw a graph of the data and the model by highlighting the first five columns and using ChartWizard as last week.

Now adjust the parameters so that the model curves fit the data curves as nearly as possible. Here is a suggested order of doing this:

• Set input baseline and output baseline so the baseline parts of the model curves agree with the experimental data.

• Set td and A so that the model input curve agrees entirely with the experimental input curve.

• Set K, to and t so that the model output curve agrees with the experimental output curve as close as possible. Suggested values of these come from your previous analysis.

• Now, adjust K, to and t so that the model output curve agrees with the experimental output curve as best as possible.

• Do this modeling for each of the step response experiments that you analyzed in Week 3.

FAQ: How do I use the "Defined Names" on separate worksheets?

By the way, there is a file like the one you've developed available on the Internet at http://chem.engr.utc.edu/engr329/xls/W5SOPDT-2.XLS .

 

After modeling every step function you completed, upload the Excel file on you team's file exchange area that shows these results and clearly identifies which experiments you analyzed.