 # Integral and Derivative Control

Two other common control techniques are used to eliminate the problems found when using proportional only control. These are known as integral and derivative control. Sometimes they are used individually but more often they are combined with proportional control.

## Integral Action

Integral action gives an output which is proportional to the time integral of the error. It is also called reset control. It is possible to use integral action itself, but this is not a common situation.

## P and I Control

Integral action is generally applied with proportional control, yielding so-called proportional and integral control (P+I). This combination is favorable in that some of the advantages of both types of control action are available.

The main advantage of P+I is that it can eliminate the offset in proportional control.The disadvantages of P+I are that it gives rise to a higher maximum deviation, a longer response time and a longer period of oscillation than with proportional action alone. This type of control action is therefore used where the above can be tolerated and offset is undesirable.

## Derivative Action

This kind of action gives an output which is proportional to the derivative or the rate of change of the error. It is also known as rate control. This kind of action could not be used alone in practice. This is because its output is only related to the rate of change of the error.

The error could be huge, but if it were unchanging, the controller would not give any output. Thus although it is theoretically possible, it is practically impossible.

## P and D Control

Derivative control is usually found in combination with proportional control, to form so-called P+D. By adding the derivative action, lead is added in the controller to compensate for lag around the loop, and so P+D can eliminate excessive oscillations.

A disadvantage is that it can not eliminate the offset although somehow it makes it smaller.

## Proportional, Integral and Derivative Action

In applications, sometimes the above three action are combined together to set up the proportional plus integral plus derivative action, i.e, P+I+D.This combined action is able to:

• eliminate the offset due to the existence of integral action
• reduce the maximum deviation and time of oscillation, which is a compromise between the advantage and disadvantage of P+I and P+D
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