You can read an entire engineering process control book and not get an intuitive feel for what it means. An introductory book basically covers how to use feedback from the output to adjust an input to control processes to achieve a desired setpoint using a "PID" controller. For example, a house thermostat is a controller than uses only the "P" element directly by measuring temperature and acting accordingly. Cruise control and elevators stopping smoothly are other examples. There is a "hysteresis" (aka "gap") in the on and off actions of a thermostat so that the unit is not cutting on and off all the time too rapidly. For example if you set it at "70 F" to heat it might turn on at 69 F and turn off at 71 F. This gap is an approximate method of the "I" in the "PID". PID means proportional, integrative, and differential based on the equations that represent the controller. They can be summed ("wired in parallel") or multiplied but the difference turns out to be semantics in the sense that the multiplier for each (P, I, and D) just changes because the integral of the derivative and the derivative of the integral doesn't really do anything. The "P" is basically a multiplier that matches the output measurement "voltage" with the input control signal "voltage" (it can be anything besides "voltage" like "force" of an output being matched with "rotation speed" of an input in some pure-mechanical design such as a water-powered mill). The "I" is a summation of the past outputs (integration) over some time period so it a "memory of the past". The "D" is the difference over a very brief period of time, the rate at which the output is increasing or decreasing (differential). So it is a "prediction of the future". So here's the simplified summary of a PID controller which shows why it's so useful:
P = present
I = past
D = future
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