PID

 PID controller

A PID controller or regulator is a device that allows a closed-loop system to be controlled to achieve the desired output state. The PID controller is composed of three elements that provide a Proportional, Integral and Derivative action. These three actions are what give the PID controller its name.

Reference signal and error signal

The signal r (t) is called the reference and indicates the state to be achieved at the output of the system y (t). In a temperature control system, the reference r (t) will be the desired temperature and the output y (t) will be the actual temperature of the controlled system.

As can be seen from the above diagram, the input to the PID controller is the error signal e (t). This signal indicates to the controller the difference that exists between the state to be achieved or reference r (t) and the real state of the system measured by the sensor, signal h (t).

If the error signal is large, it means that the system state is far from the desired reference state. If, on the other hand, the error is small, it means that the system has reached the desired state.