Read the following statements in the context of negative feedback system.
Statement 1: Negative feedback always makes the overall system response stable.
Statement 2: Negative feedback system may improve the system’s robustness towards parametric uncertainties.
Choose the correct option from the following:
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Answer & Explanation
Correct AnswerC. Statement 2 is correct and statement 1 is incorrect.
Quick Explanation
Statement 1 is false because negative feedback does not always guarantee stable closed-loop poles. Statement 2 is true because negative feedback can reduce parameter sensitivity; for a standard loop, S = 1/[1 + G(s)H(s)]. Therefore option C is correct.
Formula / Key Relation
T(s) = G(s)/[1 + G(s)H(s)]
Characteristic equation: 1 + G(s)H(s) = 0
Sensitivity: S = 1/[1 + G(s)H(s)]
Detailed Explanation
Correct Answer
C — Statement 2 is correct and Statement 1 is incorrect.
Negative feedback often improves robustness, but stability still depends on the complete loop dynamics; the word “always” makes Statement 1 false.
What This Question Is Really Testing
Two different ideas are being tested: closed-loop stability and robustness to parameter variation. Negative feedback can improve both in many practical designs, but it guarantees neither simply because the feedback sign is negative.
Concept Foundation
For a standard negative-feedback loop:
T(s) = G(s)/[1 + G(s)H(s)]
Characteristic equation: 1 + G(s)H(s) = 0
The roots of the characteristic equation are the closed-loop poles. Their locations decide stability.
Step 1 — Evaluate Statement 1
Statement 1 is false. Negative feedback does not automatically force all closed-loop poles into the left half-plane. If the loop gain and phase cause the characteristic equation to have unstable roots, the closed-loop system is unstable even though the feedback connection is negative.
Step 2 — Evaluate Statement 2
Statement 2 is true. One important benefit of negative feedback is reduced sensitivity to changes in forward-path parameters.
S = 1/[1 + G(s)H(s)]
When the loop gain is appropriately large and the loop remains stable, the sensitivity magnitude can become much smaller than one.
Step 3 — Select the Statement Combination
Statement 1 is false and Statement 2 is true. Hence the correct option is C.
Why This Method Works
The denominator 1 + G(s)H(s) simultaneously explains both ideas: its roots govern stability, while the same loop-gain term appears in the sensitivity reduction factor.
Independent Verification / Cross-Check
The logic is internally consistent: a system can be robust to moderate parameter changes yet still require an independent stability check from poles, Routh, Nyquist or Bode margins.
Concept Extension
Negative feedback commonly reduces sensitivity and steady-state error.
It may increase bandwidth.
Improper loop phase or excessive gain can still create instability.
Exam Strategy
In statement questions, watch absolute words such as always. Separate “feedback benefit” from “guaranteed stability,” then judge each statement independently.
Quick Trick
“Always stable” is too strong; “may improve robustness” is valid.
Why Other Options Are Wrong
A and B incorrectly accept Statement 1. D incorrectly rejects the valid robustness statement. Only C matches “Statement 1 false, Statement 2 true.”
Common Mistake
Equating “negative feedback usually improves stability” with “negative feedback always guarantees stability.”
Exam Tip
Check feedback statements separately: poles decide stability; sensitivity function explains robustness.
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