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# Control system questions

1. The breakaway point  of the root locus from the real axis of a  closed loop control system G(s)H(s) is (GATE 1995)

G(s)H(s) =$\frac {K (s+10)}{(s+2)(s+5)}$ lies

a) Between -2 and origin

b) Between -2 and -5

c) Between -10 and -infinity

d)  At infinity

2) A unity feedback system has open loop transfer function  G(s)H(s)= $\frac {K}{s(s+4)(s+16)}$ . Its root locus plot intersects the jw axis at

a) $\pm j2$

b) $\pm j4$

c) $\pm j8$

d) Does not intersect the jw axis

3) A unity feedback system has open loop transfer function  G(s)H(s)= $\frac {6K}{(s+1)(s+2)(s+3)}$ . What is the maximum value of K for which the given open loop TF is stable enough?

a) $\sqrt {11}$

b) 6

c) 10

d) 6 $\sqrt {11}$

4) The value of K for which the unity feedback system

$G(s)$ =$\frac {K}{s(s+2)(s+4)}$ crosses the imaginary axis is

a) 8

b) 16

c) 48

d)64

…….

** BODE PLOT QUESTIONS***

5) The Bode plot for the gain magnitude of a minimum phase system G(s) is shown in the figure. The transfer function G(s) is

a) $\frac {100}{(1+S/10)(1+S/250)}$

b) $\frac{40}{S(S+250)}$

c) $\frac {100}{(S+10)(S+250)}$

d)  $\frac {100S}{(S+10)(S+250)}$

6) For a transfer function  $D(s)=\frac {0.5s+1}{0.05s+1}$ . Maximum phase lead of the compensator is   (GATE EE-2000)

a) 52 deg at 4 rad/s

b) 52 deg at 10 rad/s

c) 55 deg at 12 rad/s

d) None of the above.