Derivative Controller in Control System

How does Derivative Controller work?

With an integral controller, we can calculate accumulated error, but with the derivative control, we can calculate the ratio of error change per unit time, hence act as a predictor. Derivative controller action responds to the rate at which the difference between desired value and the measured value is changing that is derivative of the error.  Mathematically represented as below,


  • KD­ = Derivative gain

  • The derivative controller is also known as Rate action controller or anticipatory controller.

  • ep (t)= Desired Value of controlled variable – Measured Value


The derivative controller is not used alone because it provides no output when the error is constant.


  1. Effect of transportation lag occurred due to the remote allocation of the sensor can be minimized.

  2. Accumulation of error which will go to affect on actuator saturation can be minimized.

  3. Peak errors are minimized.


  1. Cannot be used when an error is constant. (Derivative of constant value is zero).

  2. A small change in error will affect largely on controller’s output. The high derivative gain will result in heavy overshoots and overall system’s stability.