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Question: Consider the PID algorithm in For each of the individual modes-proportional, integral, and derivative-describe with a sketch the result of its calculation when the error is each of the following idealized functions:

(a) a constant,

(b) an impulse, and

(c) a sine (consider one cycle).

(This question provides a thought exercise to help understand the three PID modes; this type of analysis is not performed when monitoring a control system.)

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