So, I've worked through the entire lab now and I've got some clarification from the professors, so I have a pretty good handle on what is expected in the reports (which I think will be a bit less work than what I initially thought the professors wanted from all of you):

For the first part of the task letter, you are going to have a plot of speed versus voltage and find the slope of the line to get an open-loop gain K. Additionally, you need to look at a plot of tau (at each individual voltage point) versus voltage to figure out the voltage range where the 1st order assumption is appropriate and use those values to get a system average tau (time constant).

Then, you will need a plot for closed-loop tau versus proportional gain which will have a modeled curve and an experimental curve on it. The modeled tau values will be calculated using the formula on slide 28 (tau_cl = tau/(1+KKcl)) and the experimental values will be determined using the method on slide 21. Also, you will need another plot that has steady-state error plotted against proportional gain and again two curves for modeled and experimental. The modeled values will come from the formula on slide 30 whereas the experimental values will just come from their experimentally measured plots.

The last part of the task letter asks you to compare the performance of the PID controller to your two proportional controllers, one of which had zero overshoot and one which minimized steady state error. These you could potentially plot in the same figure to assess settling time, steady state error, error due to oscillation at steady state, and overshoot for each case (obviously the PID will be the best). Also, you will want to compare the loaded motor to the unloaded cases with your 3 controllers, and you can use the same metrics I mentioned above.

Hopefully this will give everyone a good idea of how to get going on the report and if there are questions feel free to post to the forum or ask me some questions in office hours.