Assertion (A): A PI controller increases the order of the system by units but decreases the steady state error.Reason (R): A PI controller introduces a pole at either the origin or at a desired points on the negative real axis.
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A PI controller adds an integrator pole at the origin and a finite zero, increasing system type and reducing/eliminating steady-state error for appropriate inputs. The assertion is therefore true. The reason is false because a PI controller's added pole is specifically at the origin; the finite negative-real-axis point is the controller zero, not an arbitrary added pole.
Formula / Key Relation
GPI(s)=Kp + Ki/s
=Kp(s+Ki/Kp)/s
Pole: s=0
Zero: s=−Ki/Kp
Detailed Explanation
Concept & ReasoningThe PI transfer function is K_p + K_i/s = K_p(s+K_i/K_p)/s. It introduces one pole at s=0 and one zero at s=−K_i/K_p. The integrator raises low-frequency gain and can improve steady-state accuracy, but it also changes transient/stability characteristics. Reading pole versus zero correctly is the key to the assertion-reason pair.How to Solve It in the ExamPI = pole at origin + finite zero.Important Exam PointSeparate the roles of the integrator pole and controller zero.Editorial / Answer-Key NoteThe official GPSC final answer key revised the provisional outcome for this question from A to C.Related Revision PathThis question sits in the…
Concept & Reasoning
The PI transfer function is K_p + K_i/s = K_p(s+K_i/K_p)/s. It introduces one pole at s=0 and one zero at s=−K_i/K_p. The integrator raises low-frequency gain and can improve steady-state accuracy, but it also changes transient/stability characteristics. Reading pole versus zero correctly is the key to the assertion-reason pair.
How to Solve It in the Exam
PI = pole at origin + finite zero.
Important Exam Point
Separate the roles of the integrator pole and controller zero.
Editorial / Answer-Key Note
The official GPSC final answer key revised the provisional outcome for this question from A to C.
Related Revision Path
This question sits in the revision path Control Systems → Controllers → PI Controller .
Quick Trick
PI = pole at origin + finite zero.
Common Mistake
Saying PI introduces a pole at a chosen negative real-axis point; that point is the zero.
Exam Tip
Separate the roles of the integrator pole and controller zero.
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