Control Systems
Frequency Domain Analysis
Practice questions from Frequency Domain Analysis.
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IncorrectThe Nyquist plot of a system is given in the figure below. Let , and be the positive frequencies at the points , and , respectively.
Which one of the following statements is TRUE?
is the gain crossover frequency and is the phase crossover frequency
is the gain crossover frequency and is the phase crossover frequency
is the gain crossover frequency and is the phase crossover frequency
is the gain crossover frequency and is the phase crossover frequency
Gain cross over frequency is one at which or
This is obtained by intersection of Polar or Nyquist Plot with the unit circle in GH Plane.
Clearly in Nyquist plot, at
Phase crossover frequency is one at which ,
i.e., Nyquist plot crosses (-) ve real axis
In the context of Bode magnitude plots. . decade is the same as
20 dB/ decade =6 dB/ octave
40 dB/ decade =12 dB/ octave
The open loop transfer function of a unity negative feedback system is , where and are positive constants. The phase cross-over frequency, in rad/s, is
We know phase crossover frequency is that frequency at which phase of the open loop transfer function is .
Now finding the phase of , we get
Phase of
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is , where and c are positive constants. The value of is __________. (rounded off to the nearest integer).
From the given Bode magnitude plot, it is clear that there is one pole at origin, so we get so
and at frequency
As the slope is decade previously to make it 0 slope we will need a zero at frequency , so system has a zero,
and at frequency ,
As the slope is decade previously to make it decade slope we will need 2 poles at frequency , so
