PID Controller

P (proportional), I (integral), D (derivative) controller is a feedback control mechanism used in control systems.

Plant model

Before we start designing our PID Controller, let us first define our plant model. For simplicity, let us assume that our plant model is,

Feedback Controller

The feedback term of this controller comprises of,

1. Proportinal Term

   where is proportional gain.

2. Integral Term

   where is integral gain.

3. Derivative Term

   where is differential gain.

   is the error → the difference between the set point and the actual measurement.

The ouput of the PID Controller is the sum of all the above terms,

Control

Now try adjusting the , and values such that the actual value matches the desired value. You will notice that some configuration of values provides better control with minimal oscillations and overshoots.