I thought I would try to explain PID control for the guys here who are using PID controllers but do not know exactly how it works. Most probably don’t care as long as it works or will just use autotune but here goes anyway.
(P)roportional control simply gives you a proportion of the output for a particular amount of error in the system. The error is the difference between the process set point and the actual temperature. If your proportional value is set to 5% then your system gain is the inverse or 1/.05 which would be 20. This means that if your set point is 750 degrees then you will have 100% output until your actual temperature gets to 712.5 degrees. After this the output (heat) will start to reduce depending on the amount of error.
There are two types of proportional control. If you can vary your output (heat) then you will get a proportion of the heat depending of the amount of error. The heater in a lead pot is either on or off so you must use the second method which is referred to as Time Proportioning. Time proportioning allows the controller to use a specified amount of time, usually 30 seconds, and divide the on and off time depending of the amount of error. So, if you need 50% output the heat will be on for 15 seconds and off for 15 seconds. The most common controller used by forum members here does not give the option of choosing the amount of time but it does time proportioning using its own internal time setting.
Now here is the problem with proportional only control. As you approach your set point the output will decrease and when you reach set point the proportional output is zero. So you can never actually reach set point. The system will stabilize at some point below set point depending on the load (amount of heat needed). This is where Integral control takes over.
(I)ntegral control adds a small amount of output depending on the time that the error exists. If you set your integral control on 30 seconds then the controller will add a small amount of output to the amount dictated by the proportional control output every 30 seconds. If your integral value is too low then the system will oscillate or go way over temperature then way under temperature. It may stabilize but a much too low value will cause the oscillations to continually increase and go out of control or never stabilize. The higher you set the integral value the longer it will take the system to reach set point but it will not oscillate. Your goal is to find a setting that will get to set point as fast as possible with as little oscillation as possible. The optimal value will give you quarter amplitude dampening which means that each overshoot and undershoot is ¼ of the previous one until the system completely stabilizes. Basically, if the temperature overshoots 10 degrees then it should undershoot 2 ½ degrees then overshoot by less than 1 degree (.625 degrees) and so on until it starts to control at set point. Of course, when you add lead to the pot the temperature will drop, the error will increase and the output will go back up until the system again stabilizes.
(D)erivative control reduces the output depending on how fast the error is increasing or decreasing. This allows the controller to anticipate the needed output depending on how fast the error is diminishing. This is used for very fast responding systems like motor controls where the set point can be reached in a matter of seconds or in some cases even less. When controlling heat the derivative control is normally not necessary or even counterproductive so it is not normally used.
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