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1

### GATE EE 2000

Subjective
Open-loop transfer function of a unity - feedback system is $$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau _D}}} = {{{e^{ - s{\tau _D}}}} \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$\$
Given : $$\,\left| {{G_1}\left( {j\omega } \right)} \right| \approx 1$$ when $$\omega = 0.446$$

(a) Determine the phase margin when $${\tau _D} = 0$$
(b) Comment in one sentence on the effect of dead time on the stability of the system.
(c) Determine the maximum value of dead time $${\tau _D}$$ for the closed-loop system to be stable.

(a) $${52^ \circ }$$
(b) When dead time increases the stability of the system decreases
(c) $${\tau _D}$$ $$=1.947$$
2

### GATE EE 1998

Subjective
The asymptotic magnitude Body plot of a system is given in Figure. Find the transfer function of the system analytically. It is known that the system is minimal phase system. Transfer function $$= {{8\sqrt 2 \left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {s + 8\sqrt 2 } \right)}}$$
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#### Questions Asked from Polar Nyquist and Bode Plot

On those following papers in Marks 5
Number in Brackets after Paper Indicates No. of Questions
GATE EE 2001 (1)
GATE EE 2000 (1)
GATE EE 1998 (1)

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