1
GATE ECE 2022
+1
-0.33

The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to $$\infty$$.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

A
$$G(s) = {1 \over {{{(s + 1)}^5}}}$$
B
$$G(s) = {1 \over {{s^5} + 1}}$$
C
$$G(s) = {{s - 1} \over {{{(s + 1)}^6}}}$$
D
$$G(s) = {{s + 1} \over {{s^6} + 1}}$$
2
GATE ECE 2011
+1
-0.3
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by
A
$$G\left(s\right)H\left(s\right)=k\frac{s\left(s+1\right)}{\left(s+2\right)\left(s+3\right)}$$
B
$$G\left(s\right)H\left(s\right)=k\frac{\left(s+1\right)}{s\left(s+2\right)\left(s+3\right)^2}$$
C
$$G\left(s\right)H\left(s\right)=k\frac1{s\left(s-1\right)\left(s+2\right)\left(s+3\right)}$$
D
$$G\left(s\right)H\left(s\right)=k\frac{\left(s+1\right)}{s\left(s+2\right)\left(s+3\right)}$$
3
GATE ECE 2002
+1
-0.3
Which of the following points is NOT on the root locus of a system with the open loop transfer function $$G\left(s\right)H\left(s\right)=\frac K{s(s+1)(s+3)}$$\$
A
$$s=-j\sqrt{3}$$
B
$$s=-1.5$$
C
$$s=-3$$
D
$$s=-\infty$$
4
GATE ECE 2001
+1
-0.3
The root-locus diagram for a closed loop feedback system is shown in Figure. The system is overdamped.
A
$$only\;if\;0\;\leq\;K\;\leq\;1$$
B
$$only\;if\;1\;<\;K\;<\;5$$
C
$$only\;if\;\;K\;>\;5$$
D
$$if\;0\;\leq\;K\;<\;1\;or\;K\;>\;5$$
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