What is the exact role of the integrals in a PID Controller? I am trying to understand the function of a PID Controller.
It returns a value, which is the sum of three components. The proportional, derivative and integral components. I am having issues grasping the usage of the integral component.
I know what an integral is. Integration is, in this case, the accumulation of the errors captured by the controller. In other words, in every iteration the current error is added to some variable, which is then multiplied by some constant and added to the result.
However, I fail to see how is such accumulation practically helpful. I mean, its actual role in the formula.
I have seen several pages. All of them mention the same thing: it eliminates some "offset". I'm afraid I don't know what this "offset" means and, more importantly, how does it eliminate it exactly. For example, I understand very well the role of the derivative, as you can get the previous instant rate of change which allows you to attempt to predict the future error.
I was hoping this was the right place to ask this.
 A: Each of the coefficients of PID controller has a zone of responsibility. The differential coefficient reacts to attempts to shake the controller, a proportional - defines a linear step response of the input parameter. "Integral" eliminates accumulation of errors.
Tuning the PID is conducted in the above order. Ie, tuning the "integral" is conducted after the other factors.
A: An easy way to see what happens is to use only $K_p$ (proportional gain).
The Error will get multiplied by a constant and sent as an output of the controller to the actuator:
$PID_{output}=K_p*Error$
As the Feedback matches the Setpoint, the actuator will reduce its output, ironically this creates the "steady state error", error cannot reach zero.  An easy way to visualize this is that if the Error approaches zero, the actuator output will also approach zero.
To eliminate the steady state error, you activate the integral part of the PID and this helps maintaining the actuator output level when error approaches zero.
A: I had worked with PID controllers in the application of gas chromotography.  the integral function of PID control feedback mechanism is akin to your "tare" function in a weighing machine.  When you go to a counter in a store, you measure your purchases (eg, food items), that guy at the counter presses tare button to bring the meter read "0" offsetting the error of not only the previous measurement but also all the positive and negative errors it had accumulated over the past measurements.  If the dust keeps accumulating on the weighing pan, the measurements gets adjusted strongly to subtract the weight of the dust.  Similarly, in a PID controller, the offset is nothing but to get the process shoot to the baseline by reacting strongly ( by a stronger feedback to in-control process by adjusting to the errors of all the past measurements summed up (both negative and positive errors). This was my understanding of the integral component of the PID controller.  I hope this answers your question.
