# CONTROL SYSTEMS STUDY MATERIAL | PID CONTROLLER

CONTROL SYSTEMS STUDY MATERIAL

PID CONTROLLERS

1. PROPORTIONAL CONTROLLER:

GC (S) = KP = Open loop transfer function with controller

It is used to vary the transient response of a system. Proportional controller is usually a amplifier with gain KP.

One cannot  determine the steady state response by changing KP . Steady state response depends on the type of the system.

2. INTEGRAL CONTROLLER:

GC (s)  =  K I / S

It is used to decrease the steady state error by increasing the type of the system.

3. DERIVATIVE CONTROLLER:

GC (S) =  KD . S

It is used to increase the stability of the system. Stability of any system is increased by adding zeros.

Disadvantage: Steady state error increases  , since the type of the system decreases.

4. PROPORTIONAL + INTEGRAL (PI) CONTROLLER:

GC (S) = KP +  KI / S

It is used to decrease the steady state error without effecting stability. Since a pole at origin and zero is added.

5. PROPORTIONAL + DERIVATIVE (PD) CONTROLLER:

GC (S) = KD . S + KP

It is used to increase the stability without effecting steady state error. Since type is not changed and zero is added.

6. PROPORTIONAL + INTEGRAL + DERIVATIVE (PID) CONTROLLER:

GC (S) = KP + KI / S + KD . S

It is used to decrease the steady state error and to increase the stability. Since pole at origin and two zeros are added. One zero compensate the pole and other zero will increase the stabilty.