Amity University 2007 B.E Electrical and Electronics Engineering CONTROL SYSTEMS 2 KS WITH ANSWERS - Question Paper

13. Define phase margin?
The phase margin, ? is that amount of additional phase lag at the gain cross over frequency, ?gc needed to bring the system to the verge of instability. It is provided by, 180° + ?gc, where ?gc is the phase of G(j?) at the gain cross over frequency.
Phase margin, ? = 180° + ?gc
Where, ?gc = Arg [G(j?)] ?=?pc
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14. What is phase and Gain cross-over frequency ?
The gain cross-over frequency is the frequency at which the magnitude of the open loop transfer function is unity.
The phase cross-over frequency is the frequency at which the phase of the open loop transfer function is 180°.
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15. Write the expression for resonant peak and resonant frequency,

Resonant frequency, Mr = ____1_____
2tv(1- t )
Resonant Peak, ?r = ?n v(1 - two t2 )
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16. Write a short note on the correlation ranging from the time and frequency response ?
There exist a correlation ranging from time and frequency response of 1st or 2nd order systems. The frequency domain specification can be expressed in terms of the time domain parameters t, and ? . For a peak overshoot in time domain there is a corresponding resonant peak in frequency domain.
For higher order systems there is no explicit correlation ranging from time and frequency response. But if there is a pair of dominant complex conjugate poles, then the system can be approximated to 2nd order system and the correlation ranging from time and frequency response can be estimated.
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17. What is Bode plot ?
The bode plot is a frequency response plot of the transfer function of a system. It consists of 2 plots-magnitude plot and phase plot.
The magnitude plot is a graph ranging from magnitude of a system transfer function in db and the frequency ?. The phase plot is a graph ranging from the phase or argument of a system transfer function in degrees and the frequency ?. Usually, both the plots are plotted on a common x-axis in which the frequencies are expressed in logarithmic scale.
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18. What is approximate bode plot ?
In approximate bode plot, the magnitude plot of 1st and 2nd order factors are approximated by 2 straight lines, which are asymptotes to exact plot. 1 straight line is at 0db, for the frequency range 0 to ?c and the other straight line is drawn with a slope of ± 20n db/dec for the frequency range ?c to 8. Here ?c is the corner frequency.

Earning:   Approval pending.