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