Controls Lab OnLine

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Assignment 6

Here is what the graph of that looks like:

where K is the gain, to is the dead-time and tau is the first-order time constant, or characteristic time, of the FOPDT system. The variables m(t) and c(t) in these equations are deviation variables.

We want to have Excel draw a graph of these equations so we can see the effect of the various parameters and see what parameters best match our experimental results.

We're going to build our model in a file that has some experimental sine-response data in it. Open an Excel by double clicking on the Excel icon. Open the data file from Week 6 by using the File/Open... menu item.

Part of the spreadsheet will look like this:

The first 22 lines are not useful for plotting, so delete them.

We're going to enter in two columns of numbers to have Excel plot for us. The columns are "Input" and "Output." Type each of these names in the top row of the spreadsheet in columns D and E, respectively. Move to the right in the spreadsheet by touching the "tab" key or using the -> key or by clicking where you want to move to.

We're going to put formulas in cells D2 and E2 for the functions m(t) and c(t). In columns F and G, we're going to put names and values for A, f, K, to, tau, input baseline and output baseline. Let's use 2, 3, 0.2, 0.3, 0.4, 40 and 11, respsectively. So those columns will look like this:

Click on E2 and put in this formula:

Save the file.

Now you should have 5 columns with the values in them that we want. Save the file.

Scroll back to the top of the spreadsheet. Highlight the five columns we want to plot by clicking on the A at the top of column A and dragging over to the E above column E.

Now click on the graphing button (ChartWizard).

Move the cursor over the spreeadsheet and click-and-drag a rectangle as large as you want your graph. Then answer questions posed by the Chart-Wizard. ALWAYS CHOOSE SCATTER PLOT!

When the graph is drawn, double click on it to make it a separate window, then click on the upper right "grow"-box to enlarge the graph. Save the file.

Now go back to the parameter cells and change one of them and watch the graph change. Find the values of the parameters that make the model agree well with the experimental results. Save the file.

Do the above comparison for three experimental results comparisons. Do it for the data at the lowest frequency, do it for the data at the frequency closest to the "corner" frequency and do it for the data at the highest frequency.

From last week, you got some values of the Amplitude Ratio (AR) and Phase Angle (PA) for the sine inputs to your system at some different frequencies. Enter these into a new Excel spreadsheet, like this:

You are leaving columns C and F blank for now; later you'll put the model equations in there. It will be useful if you enter column D by using a formula and setting it to column A. The formula for cell D2 is =A2.

In the cell in column F BELOW the last experimental point, let's say, F10, enter this formula for the phase angle

Now plot the amplitude ratio part of the Bode plot by highlighting columns A, B and C; choosing the ChartWizard, selecting Scatter and selecting log-log plot.

Bode Diagram Excel SpreadSheet