GATE EC 2017 Set 2 — Question 46
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Control Systems → Stability Analysis → Routh-Hurwitz Criterion
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Question
A unity feedback control system is characterized by the open-loop transfer functionThe value of for which the system oscillates at is ________.
Correct answer
0.74 to 0.76
Solution
The characteristic equation of a unity feedback system is given by .Substituting the given open-loop transfer function:For the system to oscillate at a frequency , we substitute into the characteristic equation:Separating the real and imaginary parts to zero for marginal stability:Imaginary part:Since the system oscillates, , so . This matches the frequency given in the problem.Real part:Substituting :Thus, the value of for which the system oscillates at is .
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