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# GATE 2023 Control Systems Quiz 12

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Question 1

For a control system given by characteristic equation, s3 + Ks2 + (2K + aK – 1)s + 2aK = 0. The condition for stability is

Question 2

If the plot shown represents the pole-zero plot of open loop transfer function H(s). The value of H(s) at s = 1 is 10. The unity negative feedback closed loop transfer function is Question 3Multiple Correct Options

DC gain of a transfer function of a system is:

Question 4

A polynomial, s3 + 2s2 – 2s + 4. The number of roots of the polynomial on the open left half of complex s-plane is-

Question 5

The Routh – Hurwitz array is given for a third order characteristic equation as follows The values of a, b, c, d are respectively, for which the system should be marginally stable

Question 6Multiple Correct Options

The characteristic equation of a system is given as s3 + 9s2 + 4s + k = 0

If the system is marginally stable then

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