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Quiz: LCS-Frequency Domain Analysis

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Number of Questions: 20

Question: 1 -

The open loop transfer function of a unity feedback system is given by

G(s) = 3e-2s/s(s+2)

The gain and phase crossover frequencies in rad/sec are, respectively

Options:

  1. 0.632 and 1.26

  2. 1.26 and 0.632

  3. 0.485 and 0.632

  4. 0.632 and 0.485

    5. Answer:

    1.26 and 0.632
    Solution:

    |G(s)| = 1

    ωg = 1.26

    ∠ GH = 180°

    ωφ = 0.632

     

Question: 2 -

The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in the figure, if G(s) has no pole in the right-half of s-plane, the number of roots of the system characteristic equation in the right-half of s-plane is

Options:

  1. 1

  2. 0

  3. 2

  4. 3

    5. Answer:

    0
    Solution:

    N = 0 (1encircle mention CW direction and other in CCW)
    P=0 (no pole in right half)
    So, N = P − Z
    Z = P − N = 0
    ∴ No roots on RH of s-plane.

Question: 3 -

The system with the open loop transfer function

G(s)H(s) = 1/s(s2+s+1)

has a gain margin of

Options:

  1. 3.5dB

  2. 6dB

  3. 0dB

  4. -6dB

    5. Answer:

    0dB
    Solution:

    use ωφ when ∠of G(s)H(s) = −180°

    after solving: ωφ = 1 rad/sec

    and

    G.M. = −20log1 = 0

Question: 4 -

The gain margin and the phase margin of a feedback system with

G(s)H(s) = s/(s+100)3 are

Options:

  1. ∞,0°

  2. 88.5 dB,∞

  3. ∞,∞

  4. 0 dB,0°

    5. Answer:

    ∞,∞
    Solution:

    G.M. and P.M. of the system cannot be determined.

Question: 5 -

A system has poles at 0.01 Hz, 1 Hz and 80Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

Options:

  1. 0°

  2. −90°

  3. −180°

  4. 90°

    5. Answer:

    −90°
    Solution:

    Pole at 0.01 and 1 Hz gives −180° phase. Zero at 5 Hz gives +90° phase
    ∴ at 20Hz −90° phase shift is provided.