PID is a mathamatical approach to controlling something in the most perfect way all day everyday. The P represents proportionality. The bigger the difference (error) between what some parameter is and what it is suppose to be (setpoint), the larger the correction to cancel the error.
I represents Integration, or the area under the curve of the error, think of it as the product of time and error. The longer the error persists, the greater the I term in the correction.
D represents the Derivative, or rate of change of the process toward or away from the setpoint. This term works in opposition to the P and the I. If they they are both saying to go up and the process starts to go up too fast, then the D will say OK slow down a bit so as not to overshoot.
I prefer to write my own controllers which incorporate these features but which are accompanied with other rules to limit the tendancy to be tuned wrong as often as right, when something that influences the process changes like surrounding temperature, product density, or a million other things. Therefore, I recommend that you take my opening statement (aimed at the purists) with a grain of salt!
The traditional PID approach has been around for a very long time, is over used and by and large they are difficult to impliment correctly unless you use a very skilled approach. Most are wrong as often as they are right and I'll never use another one as long as I live. By that's just me, unconventional!
Best Regards,
Bob A.