Previous Year Question
An LTI system having transfer function G(s) = 10/(s + 5) is controlled by a proportional controller with a gain of Kp = 2. Consider the unity feedback system. Find the steady state error of the closed loop system, if the reference signal is a step input with a magnitude of 5.
Correct answer: A
Explanation
With proportional gain Kp=2, the forward path is 20/(s+5). The position error constant is Kp0=lim GOL(s)=4. For a step of magnitude 5, ess=5/(1+4)=1.
Formula
Kp0=limₛ→0 20/(s+5)=4; ess=A/(1+Kp0)=5/5=1
Step-by-step solution
Correct Answer
A — 1
Concept and Reasoning
With proportional gain Kp=2, the forward path is 20/(s+5). The position error constant is Kp0=lim GOL(s)=4. For a step of magnitude 5, ess=5/(1+4)=1.
Calculation / Key Relation
Kp0=limₛ→0 20/(s+5)=4
ess=A/(1+Kp0)=5/5=1
Exam Takeaway
For a type-0 unity-feedback system, step error is A/(1+Kp0).
Common Mistake
Do not use the controller gain alone as the position error constant.
Common mistake
Do not use the controller gain alone as the position error constant.
Exam tip
For a type-0 unity-feedback system, step error is A/(1+Kp0).
Quick method
For a type-0 unity-feedback system, step error is A/(1+Kp0).