PID
A Proportional Integral Derivative controller (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly and rapidly, to keep the error minimal.
Proportional term
The proportional term (sometimes called gain) makes a change to the output that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant, called the proportional gain.
Integral term
The contribution from the integral term (sometimes called reset) is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain.
The integral term is given by:
Derivative term
The rate of change of the process error is calculated by determining the slope of the error over time (i.e., its first derivative with respect to time) and multiplying this rate of change by the derivative gain. The magnitude of the contribution of the derivative term (sometimes called rate) to the overall control action is termed the derivative gain.
So what is PID in simple terms?
The easiest way to think of PID is to compare it with a small boat trying to row across a fast flowing river.
In the above example if you leave point A and head for point B you would have to compensate for the flow of the river and aim for a point North of point B. As you start to cross the river you would find that the currents effect on the boat varies and corrections will need to be made. This is automatically carried out with PID control. You aim for point B and go straight to it without wasting time and energy.
With Out PID using ON / OFF control.
Using on off control you have a dead band to allow a switching Hysterias between the on and off levels. You would apply FULL power followed by none.
With PID.
This offers an efficient control varying the Output proportionally to the requirement and hence offers a smooth control and very little if any oscillation.