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Quiz: LCS-Frequency Domain Analysis

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Number of Questions: 20

Question: 16 -

For a stable closed loop system, the gain at phase crossover frequency should always be:

Options:

  1. < 20 dB

  2. > 6 dB

  3. < 6 dB

  4. > 0 dB

    5. Answer:

    > 0 dB
    Solution:

    Phase crossover frequency is the frequency at which the gain of the system must be 1 and for a stable system the gain is decibels must be 0 db

Question: 17 -

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE

Options:

  1. The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.

  2. The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum phase
    systems.

  3. Both the criteria provide information relative to the stable gain range of the system.

  4. The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

    5. Answer:

    The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.
    Solution:

    Let us consider O.L.T.F. of a unity feedback system as

    G(s) = K/s(s+a)

    Which represents a type-1 and order-2 system for which Nyquist plot will be as shown below:

    Closed loop transfer function for the system is given as,

    T(s) = G(s)/1+G(s).1

    after putting value of G(s) and solving:

    T(s) = K/s2+as+K

    We can draw its Nyquist plot by simply substituting s = jωa nd obtain polar co-ordinates of T( jω) for different values of ω as,

    T(jω) = K/(jω)2+a(jω)+K

    T(0) = K/0+0+K = 1

    T(∞) = 0

    Hence statement given in option (The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.) is FALSE.

Question: 18 -

Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0 ?

Options:

  1. -60°

  2. -90°

  3. -45°

  4. -180°

    5. Answer:

    -90°
    Solution:

     Addition of pole causes instability to the system.

Question: 19 -

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

Options:

  1. 90°

  2. -90°

  3. 0°

  4. -180°

    5. Answer:

    -90°
    Solution:

    Pole at 0.01 Hz gives -180° phase. Zero at 5Hz gives 90° phase therefore at 20Hz -90° phase shift is provided.

Question: 20 -

If the gain of the open loop system is doubled, the gain of the system is :

Options:

  1. Doubled

  2. One fourth of the original value

  3. Not affected

  4. Halved

    5. Answer:

    Not affected
    Solution:

    Gain of the open loop system is doubled then the gain of the system is not affected as the gain of the system is not dependent on the overall gain of the system.