1
GATE EE 1991
Fill in the Blanks
+2
-0
A first order system and its response to a unit step input are shown in Fig. below. The system parameters are
$$a=$$ ____________
$$K=$$ ___________
2
GATE EE 1991
+1
-0.3
A unity feedback system has an open-loop transfer function of the form $$KG\left( s \right) = {{K\left( {s + a} \right)} \over {{s^2}\left( {s + b} \right)}};\,\,\,\,b > a$$ Which of the loci shown in Fig. can be valid root-loci for the system?
A
B
C
D
3
GATE EE 1991
Subjective
+5
-0
A unity feedback system has the forward loop transfer function $$G\left( s \right) = {{K{{\left( {s + 2} \right)}^2}} \over {{s^2}\left( {s - 1} \right)}}$$

(a) Determine the range of $$K$$ for stable operation

(b) Determine the imaginary axis crossover points

(c) Without calculating the real axis break - away points, sketch the form of root loci for the system.

4
GATE EE 1991
MCQ (More than One Correct Answer)
+1
-0.3
The system having the Bode magnitude plot shown in Fig. below has the transfer function
A
$${{60\left( {s + 0.01} \right)\left( {s + 0.1} \right)} \over {{s^2}{{\left( {s + 0.05} \right)}^2}}}$$
B
$${{10\left( {1 + 10s} \right)} \over {s\left( {1 + 20s} \right)}}$$
C
$${{3\left( {s + 0.05} \right)} \over {s\left( {s + 0.1} \right)\left( {s + 1} \right)}}$$
D
$${{5\left( {s + 0.1} \right)} \over {s\left( {s + 0.05} \right)}}$$
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