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.)