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Quiz: LCS-Frequency Domain Analysis

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Number of Questions: 20

Question: 6 -

The gain margin of the system under closed loop unity negative feedback is

G(s)H(s) = 100/s(s+10)2

Options:

  1. 0 dB

  2. 46 dB

  3. 26 dB

  4. 20 dB

    5. Answer:

    26 dB
    Solution:

    Φ = −90° − 2 tan−1 (ω /10)

    For phase cross–over frequency,

    Φ = −180°
    ∴−180 = −90°

    −2 tan−1 (ω /10)
    ⇒ ω = 10rad / sec

    Put, s = jω

    G(jω)H(jω) = 100/jω(jω+100)2

    G.M.in dB = 20log 20 = 26dB

Question: 7 -

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

G(s) = K/(s+1)(s+2)

The
gain margin of the system in dB is given by

Options:

  1. ∞

  2. 1

  3. 20

  4. 0

    5. Answer:

    ∞
    Solution:

    For 2nd order system GM=∞

Question: 8 -

The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5/√2 rad/sec . The transfer function of the system is

Options:

  1. 720/s2+12s+144

  2. 1125/s2+25s+225

  3. 375/s2+5s+75

  4. 500/s2+10s+100

    5. Answer:

    500/s2+10s+100
    Solution not available.

Question: 9 -

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

Options:

  1. +40 dB/decade

  2. -80 dB/decade

  3. -40 dB/decade

  4. +80 dB/decade

    5. Answer:

    -80 dB/decade
    Solution:

    →In a BODE diagram, in plotting the magnitude with respect to frequency, a pole introduce a line 4 slope-20dB/dc
    →If 4th order all-pole system means gives a slope of (-20) * 4 dB/dec i.e. -80dB/dec

Question: 10 -

The Nyquist plot of G( jω)H( jω) for a closed loop control system, passed through (−1, j0) point in the GH plane. The gain margin of the system in dB is equal to

Options:

  1. greater that zero

  2. zero

  3. infinite

  4. less than zero

    5. Answer:

    zero
    Solution:

    G.M = 20log 1/a dB

    a=1

    ∴G.M. = 0