Comparison between P, PI, PD and PID controllers

control-system

#1

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 ) : Screenshot%20(38)
Proportional - Integrated ( PI ) : Screenshot%20(40)
Proportional - Differential ( PD ) : Screenshot%20(39)
Proportional - Integrated - Differential ( PID ) : Screenshot%20(44)

Gain in Frequency Domain

Proportional ( P ) : Screenshot%20(38)
Proportional - Integrated ( PI ) : Screenshot%20(41)
Proportional - Differential ( PD ) : Screenshot%20(42)
Proportional - Integrated - Differential ( PID ) : Screenshot%20(43)

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