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I am learning Control Theory and i have a confusion about whether the following PID controllers are interchangeable or similar.

  1. Are they equivalent? Why?
  2. Is there any difference in how i would implement both of them in code? I have to program this in Arduino.

Here is the first control loop which is the normal definition of a PID controller:

pid1

And here is the changed one with the negative feedback changed to positive and the setpoint changed from positive to negative.

pid2

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  • $\begingroup$ I wouldn't necessarily call this positive feedback. Most definitions of positive feedback generally assume that the setpoint and measurement/feedback are added in phase (typically both with a plus sign). $\endgroup$ – user883521 Jul 2 '19 at 17:02
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No, you can't change that willy-nilly.

The second diagram is perfectly valid, however, if the plant tends to operate in reverse from normal. If you have a plant whose output gets more negative when its input goes positive then you'd use the second one.

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  • $\begingroup$ They can of course be made equivalent if you are allowed to specify negative gains. I have not (yet) seen that implemented in practice... $\endgroup$ – user883521 Jul 2 '19 at 16:53

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