To understand PIDcompute you need to know some basic P.I.D. control theory. This is actually a mathematical function only. It will compute the output quantities that is supposed to be applied to the system under control based on the P.I. and D terms defined by the PIDDef function. PID Control apply its output based not just on the current error (= feedback minus setvalue) but also historical error accumulated in the integrator and predicted future error based on the rate of change of the output computed as "differential" term. By varying the P, I and D term the output dynamic can behave differently. Some will cause the system to reach the set point quickly but may have a lot of "overshoots" and oscillate until it settles down. Some may prevent overshoot but take a long time to reach the set point value. Some may even cause the system to oscillate wildly and become unstable. By varying the P, I and D term and conduct experiment to measure the time domain response of the system when subject to a step input (meaning give it a set point value from 0 to a certain set point instantly) you can "tune" the system until it meets the overshoot and rise time specifications.
