PD Controller (Proportional-Derivative) Controller in Control System

How does a PD controller work?

Prediction of the behavior of error will always result in better stability. In order to avoid effects of the sudden change in load, the derivative of the error signal taken in this mode to predict the trend of a controlled variable. So let us see in detail, how does PD Controller work.

Almost all physical processes have transportation lag (Dead Time) in their system (usually due to improper allocation of the sensor) since only proportional controller’s output will react after some time to sudden change in load and which may result in a huge transient error.  But, with the addition of a derivative controller, this mode becomes capable of predicting error with consideration of dead time. So that, sudden jerks or spike signals are not given to actuator, hence improves the life span of actuators.

Mathematically this is represented as,

PD Controller


  • P = PD controller’s output

  • KP = Proportional Gain

  • ­KD= Derivative Gain

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

  • P­(0) = Controller’s output when error is zero

From the equation, we can say that this mode cannot eliminate the steady state error of proportional controller. However, It can handle fast process load changes as long as the load change steady state error is acceptable.

Applications of PD Controller

Maintaining a level of liquid inside the tank is a sluggish and integrating process and many cases due to improper allocation of level sensor (in this case which is measured as a function of flow) result into the significant addition of transportation lag. PD controller mode has the capability to predict future of error, hence the effect of additional dead time is reduced. A sudden change in desired value of level will result in high overshoot in the case of PI control mode, but in the case of PD control mode, this integrating effect will be reduced by addition derivative term with the proportional term.

PD Controller


  1. Overall stability of system improves

  2. Capable of handling processes with time lag

  3. Reduces settling time by improving damping and reducing overshoot


  1. Not suited for fast responding systems which are usually lightly damped or initially unstable.

  2. Amplifies noise at higher frequencies which result in improper handling of actuators.

  3. Does not eliminate steady state error


Please watch below video for more understanding on PD Controller:


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