Control of Flow in a Pump Loop

This homework is a direct result of the class exercise with a pump loop. The first step is just good practice for checking input models.  The input deck  provided for this exercise has at least one geometric error.  The system uses 1" ID piping loop everywhere,  and you can assume that the original choice of DX's accurately reflects the loop geometry. Provide a written description of direct geometry calculations to cross-check the input. For each component specify the:

  1. Component length (main and side leg for the tee);
  2. Component hydraulic diameter ;
  3. Cross-sectional area calculated from 2) assuming a circular pipe;
  4. Number of cells and cell lengths;
  5. Calculated cell volumes based on 3) and 4);
  6. Calculated total component volumes. Compare with component volume values in the file trcout and identify and correct likely errors in the input.

While you've got pump.inp open take a look at the control system with the model editor.  Describe what the control system is doing.

Once the deck has been corrected, run it  using the command line "trace -p pump" and copy the trcdmp (pump.dmp) file to a file named TorqStep.rst in your "hw8" directory. Copy the file TorqStep.inp into your "hw8" directory and execute it using  the command line "trace -p TorqStep".  This deck makes a small increase in the pump motor torque.  Plot the pump mass flow vs, time, and adjust the scale on the time and mass flow axes so that you can extract the information that you need for a Cohen and Koon estimate of the gain and integration timescale for use in a PI controller.  Provide me with the plot that you use, and a writeup of all steps used to determine the controller parameters.  The easiest way to extract the plot is to print it from ACGrace in PNG or JPEG format and embed it into an MS Word document with your writeup.

Now convert TorqStep.inp to use its PI controller from the corrected pump.inp restart, and run it with your parameters.  When you next plot mass flow vs. time, you will probably see one of two general forms for the plot of mass flow rate vs. time.  One possibility is that  the flow rate overshoots the set point and relaxes back towards the set point of 6 kg/s.  This means that either your gain is too low or your integration timescale is too high or some of both. The other possible pattern is that the flow rate immediately goes into oscillations, due to a gain that is too high, or (less likely) an integration time scale that is too low. Try changing the gain in the approriate direction by factors of two until results quit getting better. By better, I mean time to converge on 6 kg/s is decreasing.    Give me  two plots of mass flow vs. time with curves for all gains that you have tried.  The first should have the scaling that AcGrace selected, and the second should have a scaling that you have selected to clearly show which is converging quickest.  This second plot will have a minimum time greater than 10 and a maximum time less than 20, and will have some results off-scale.

Return to the original gain from the Cohen and Koon analysis.  Change the the integration timescale by a factors of 2 in the appropriate direction until answers quit improving.  Give me plots similar to those for gain.  Finally, based on what you've seen, pick four more combinations of gain and integration timescale to see if you can do better than your previous best.  Give me plots of this study, and your final choice for gain and integration timescale.

By now you've collected a bunch of material.  Submit it to the ANGEL dropbox in one of two ways:
  1. Embed all plots and analysis in an MS Word file with your writeup; or
  2. Collect all files including a writeup referencing other files by name into a zip file.

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