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A closed loop system has the characteristic equation given by s3 + Ks2 + (K + ) s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?
  • a)
    0 < K < 0.5
  • b)
    0.5 < K < 1
  • c)
    0 < K < 1
  • d)
    K > 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A closed loop system has the characteristic equation given by s3 + Ks2...
Given CE = s3 + ks2 + (k + 2) s + 3 = 0
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A closed loop system has the characteristic equation given by s3 + Ks2...
To ensure stability of the closed-loop system, all the roots of the characteristic equation must have negative real parts. Therefore, the condition that should be satisfied is:

K > 0

This is because if K is negative, then one of the roots will have a positive real part, leading to instability. If K is equal to zero, then one of the roots will be zero, which may lead to marginal stability or instability depending on the system's dynamics. Therefore, the only condition that guarantees stability is K>0.
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A closed loop system has the characteristic equation given by s3 + Ks2 + (K + ) s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?a)0 < K < 0.5b)0.5 < K < 1c)0 < K < 1d)K > 1Correct answer is option 'D'. Can you explain this answer?
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A closed loop system has the characteristic equation given by s3 + Ks2 + (K + ) s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?a)0 < K < 0.5b)0.5 < K < 1c)0 < K < 1d)K > 1Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A closed loop system has the characteristic equation given by s3 + Ks2 + (K + ) s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?a)0 < K < 0.5b)0.5 < K < 1c)0 < K < 1d)K > 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed loop system has the characteristic equation given by s3 + Ks2 + (K + ) s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?a)0 < K < 0.5b)0.5 < K < 1c)0 < K < 1d)K > 1Correct answer is option 'D'. Can you explain this answer?.
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