PID controls are used to bring things to a desired level.  Maybe it’s the temperature of a liquid or the speed of a motor.  Using the PID’s 3 components (Proportional, Integral & Derivative), users can adjust how quickly and cleanly a desired level are achieved.
Example: Lets say we’ve got a pot of water on a burner and want to bring it up to 90°C quickly, without overshooting the temperature by more than 1°.  How would you do this?  You’d probably turn the burner on high until the temperature gets within a few degrees of 90°, then scale back the burner so the temperature rises slower to prevent overheating.  This scaling back the burner would likely happen in several stages until you reach a steady 90°.  A PLC could do this process for you using PID.  First a couple terms:
- Set Point: 90°C.  The value were trying to reach and hold
- Input (also called Process Variable): the water temperature.  What were trying to get to the Set Point.
- Output (also called Control Variable):Â the Burner. Â What we adjust to reach our Set Point.
- Error: the difference between the Output and the Set Point.
Proportional: Looks at the present. Â It uses the current error to determine Input. Â Typically it is in charge of most of the error reduction.
Integral: Looks at the past.  It uses a sum of past errors to eliminate long term error.
Derivative: Looks at the future. Â Trying to predict where the signal is going, it can be used to prevent both overshooting Set Points and output ringing.
Instead of going into detail on this subject, we point you to a great article written by Tim Wescott on the subject: PID without a PHD.
                                    
Perhaps the definition of a PID should include the – implied – fact that the control is being done by watching the input/feedback, a measurement of the thing being controlled, and that changes in the output are made based on that.
I think your definitions on ‘Input’ and ‘Output’ are swapped if you mean ‘input to the PID control’. You should also inclde the industry terms SP (setpoint), PV (process Variable) and CV (Control variable)
Your example of a pot of water at least as far as the mental image should include “which has a thermometer on it”
Hey Bernie,
I just added your suggestion to the PID definition.
Yep it looks like Input and Output were switched. I’ve corrected it now.
I’ll add an image to clear the pot, water & thermometer example.