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Originally Posted by Ether
I think you are confusing the integral term with the derivative term.
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How I was taught PID was that the integral takes the current accumulation of the error, which could be translated into the state of the system. Thus, if you tune the I term properly, it could be properly used to correct the loop. I even heard the word "predict" when I was learning PID. Now I realize that my mentor probably meant that it was for correction rather than prediction.
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The error should be decreasing, not growing, if the controller is working properly.
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My bad, I meant that the number of iterations is growing, not the error. My fault.