Question

Directions: The question consists of two statements, one labeled as ‘Statement (I)’ and the other labeled as ‘Statement (II)’. You are to examine these two statements carefully and select the answers to these items using the codes given below:

Statement (I): A PI controller increases the order of a system by units but reduces the steady-state error.

Statement (II): A PI controller introduces a pole at either the origin or at the desired point on the negative real axis.
1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true

Answer 1

Correct Answer - Option 1 : Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)

PI controller:

• PI controller is a combination of the proportional controller(P) and integral controller (I).
• So, it adds features of both proportional and integral controller.
• Thus integral controller adds a pole either at the origin or at the desired point on the negative real axis, so the order of the system gets increased but it reduces the steady-state error or the offset error.

 

Effects of Proportional Integral (PI) controllers:

• Increases the type of system by one.
• Rise time and settling time increases and Bandwidth decreases.
• The speed of response decreased i.e. transient response becomes slower.
• Decreases the steady-state error and steady-state response is improved.
• Decreases stability.
• It improves the steady-state part and affecting the transient part

 

​Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)

Controller	Transfer function	Application
Proportional (P)	Kp	To change the transient behavior
Integral (I)	KI/s	To decrease the steady-state error
Derivative (D)	KDs	To improve system stability
Proportional Integral (PI)	\(\frac{{s{K_p} + {K_I}}}{s}\)	To decrease the steady-state error without affecting stability
Proportional Derivative (PD)	Kp + KDs	To improve stability without affecting the steady-state error
Proportional Integral Derivative (PID)	\({K_p} + {K_D}s + \frac{{{K_I}}}{s}\)	To improve stability and decrease steady-state error