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Also, reading the PID tutorial here: http://www.societyofrobots.com/programming_PID.shtml it says that the "integral" term is acceleration or the next derivative. How is that so? From wikipedia, "the contribution from the integral term is proportional to both the magnitude of the error and the duration of the error".

surely that would be a net error/overall error/gross error

As for the PID explanation, I thought the "I" term was supposed to increase the response if the error persisted over time.