OK this is good! There are a few differences between your test and the instructables test. First, you are using a LEM Hass 300-s, and are commanding 20 amps. I was commanding 5 amps I think, so the response instructables response would be a lot faster, since the current wouldn't take as long to get to 5 and it would to get to 20. Also, if you are running it at 36v, maybe the resistance of the phases are high enough so that 20 amps is barely achieveable using the 36v battery pack? What is the HP rating of your motor? I did a test on a 6.6kW (I think) motor. My guess is a higher power motor would have lower resistances, and faster convergence times.
Also, you haven't tried increasing ki-id yet. kp-id just gets you close to converging, and ki-id really drives it to zero fast. Here's what I would do next: Start at kp-id = 2000, and gradually increase ki-id (not kp-id). Start at maybe 2, and go up by 2 at a time.
Also, the oscillations you are seeing aren't really oscillations, but just noise (your noise level is perfectly acceptable). Oscillations will be clearly defined damped sine waves with a much lower frequency than the jaggedy spikes you are seeing.
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