Integral, Derivative and Proportional Controls – Different Type of Controllers

Automatic Control Systems

Understanding the functions of different controllers is necessary for control engineer to find the problem in the automatic controls. An automatic controller is a device which measures the value of a variable quantity or condition and operates to correct or limit the deviation of this measured value from a selected reference. It includes both the measuring means and the controlling means.

As a control engineer we should know about different controllers used and the function of different controllers and the action taken by them. We have already studied about control systems and focussed our attention on Pneumatic and Electronic Control Mechanisms. Now we will be discussing about Integral, Derivative and Proportional Controls in this article as follows:

On-Off Controller

This is the simplest, cheapest and most reliable of controls. It is found to be most competent in handling variables associated with a batch process.


  • Space temperature control in dryers and in air conditioning
  • Level limits in tanks and reservoir etc

Such processes respond gradually and smoothly to the full on-off action of the controller and are defined as a "bath-tub " processes, because of large demand in contrast to supply.

Proportional Control

This type of control mechanism is useful for controlling most variables which lack the stabilising effects of favourable storage capacity. Such "shower-bath" processes as they are more commonly known, require that the transfer of material (fluid flow rate, gas pressure, liquid level) or energy , temperature and pressure must be kept constinuously in step with the demand.

PID controllers

Proportional controllers are used in case of " How much error exists?". In this type of controller, it judges the error and acts accordingly.

Output = Gain x Error

Proportional controller output is directly proportional to the error signal so that it aims is to correct the error and attain the set point. Hence it is also defined as a control which is proportional to the deviation from set-point of the measured value.

It is represented by:

proportional controller – proportional to "Θ"

Typical examples of these are self acting temperature controllers and conventional pressure reducing valves .

Integral Controller

Integral controllers are used in the case "How far is the error from the set value?". This types of controller judges the position of the set value and acts accordingly.

It is defined as the control action which changes at a rate proportional to the deviation, the rate of change being proportional to the deviation.

In practice this means that with measured value and set point coincident, the final control element may be in any position within the range.

It is represented by:

Integral controller – proportional to – ∫ ∂Θ ⁄ ∂t.

Derivative Control

A derivative controller is used in case of "How much time it takes to bring the system to the set-point"?. This is used wherever transfer lag problems are involved.

It is represented by:

DERIVATIVE CONTROLLER – proportional to – ∂Θ ⁄ ∂t

The derivative controller cannot be used independently. Either it should be used along with proportional controller or with integral controller. The set valve is quickly attained by using the derivative controller.

Derivative action over-correction is good as an experienced operator will give manual over-correction before seeking a final average setting.

References & Image Credits


Automatic Control System,

The PID Controller,

Image Credits

By mightyohm,