Perhaps one additional remark:
As mentioned by MisterT it is the GOAL to make the output error zero. Of course, this cannot be achieved by 100%.
As an example take the response to an input step. It is the goal of the PID controller to keep the system reaction (step response) within certain limits (small overshoot and small ringing) and to ensure at the same time a quick reaction of the input step. These requirements make it necessary to find a good trade-off for the three PID constants.
In this context, the classical method as described by Ziegler and Nichols can be recommended.