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Quiz: LCS-Root Locus

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Number of Questions: 17

Question: 6 -

The value of “a” so that the system has a phase–margin equal to π/4 is approximately equal to

Options:

  1. 0.74

  2. 1.40

  3. 2.40

  4. 0.84

    5. Answer:

    0.84
    Solution:

    180 + tan-1 aω -180° = PM

Question: 7 -

The open-loop transfer function of a unity feedback system is

G(s) = K/s(s2+s+2)(s+3)

The range of K for which the system is stable is

Options:

  1. 21/4 > K > 0

  2. −6 < K < ∞

  3. 13 > K > 0

  4. 21/4 < K < ∞

    5. Answer:

    21/4 > K > 0
    Solution not available.

Question: 8 -

If the closed-loop transfer function of a control system given as

T(s) = (s-5)/((s+2)(s+3))

the it is

Options:

  1. unstable system

  2. uncontrollable system

  3. non-minimum phase system

  4. minimum phase system

    5. Answer:

    non-minimum phase system
    Solution:

    As there is a right half zero, the system is a non-minimum phase system.

Question: 9 -

For the polynomial

P(s) = s5+s4+2s3+2s2+3s+15

the number of roots which lie in the right half of the s-plane is

Options:

  1. 1

  2. 3

  3. 2

  4. 4

    5. Answer:

    4
    Solution not available.

Question: 10 -

The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/ sec respectively are

Options:

  1. 1, 1

  2. 1, 0.75

  3. 2, 2

  4. 2, 0.75

    5. Answer:

    2, 0.75
    Solution:

    1+ G(s)H(s) = 0

    s3 + as2 + (2 + K)s + K +1 = 0

    Use Routh's Array

    [a (2 + K) - (K + 1)]/a = 0 and a = K+1/K+2