A review on the composite controllers along with the proportional controller

Considering a unit negative feedback system, with
Setpoint - R(S) ,

Output - C(S)
Error signal - E(s) = R(S) - C(S)
Manipulated signal - M(S)
The type of controller used defines the output of the system. Here, specifically we see the following controllers alone.

**Proportional** ( P )
**Proportional - Integrated** ( PI )
**Proportional - Differential** ( PD )
**Proportional - Integrated - Differential** ( PID )

## Gain in time domain

**Proportional** ( P ) :
**Proportional - Integrated** ( PI ) :
**Proportional - Differential** ( PD ) :
**Proportional - Integrated - Differential** ( PID ) :

## Gain in Frequency Domain

**Proportional** ( P ) :
**Proportional - Integrated** ( PI ) :
**Proportional - Differential** ( PD ) :
**Proportional - Integrated - Differential** ( PID ) :

## Advantages:

**Proportional** ( P ) : Speed controlled ( Increase gain)

**Proportional - Integrated** ( PI ) : Good damping, Offset is zero ( because of Integration), No steady state error
**Proportional - Differential** ( PD ) : Maximum overshoot decreases, Rise time, settling time is reduced , Bandwidth is increased.
**Proportional - Integrated - Differential** ( PID ) : Decreases rise time (Kp), Eliminates steady state error (Ki), Decreases overshoot and settling time ( Kd).

## Disadvantages:

**Proportional** ( P ) : Offset issue
**Proportional - Integrated** ( PI ) : Slow Response, Stability
**Proportional - Differential** ( PD ) : Offset, Steady state error

## System Filteration

**Proportional** ( P ) : Linear network ( No filteration)
**Proportional - Integrated** ( PI ) : Low pass filter
**Proportional - Differential** ( PD ) : High pass filter
**Proportional - Integrated - Differential** ( PID ) : Band pass or Band reject depending on gain values