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Someone decided that for your system, you needed accuracy of ~+/- 0.75 degrees. Since you have a resolution of almost the same, you need to be perfect.
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Alright, after another talk with a mentor, it's been clarified that we don't need such exact precision. Our problem was that the motor was overshooting by over 20 pulses at some points, then taking 5-10 seconds to readjust to a reasonable position. So, I will take some previous suggestions about tuning the PID so that we can get the motor returning to a more reasonable pulse count, perhaps +/- 5 pulses, without wildly missing the mark beforehand.