1
GATE ECE 2016 Set 3
Numerical
+2
-0
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G\left(s\right)=\frac{K\left(s+2\right)}{s^2+2s+2}$$ and H(s) = 1 respectively.If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is_____________.
2
GATE ECE 2016 Set 3
+1
-0.3
The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is
A
$$G=\frac{G_1G_2}{1 + G_1H_1}$$
B
$$G=\frac{G_1G_2}{1\;+\;G_1G_2+\;G_1H_1}$$
C
$$G=\frac{G_1G_2}{1\;+\;G_1G_2H_1}$$
D
$$G=\frac{G_1G_2}{1\;+\;G_1G_2\;+\;G_1G_2H_1}$$
3
GATE ECE 2016 Set 3
+2
-0.6
The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is
A
-2.0 < K < 0.5
B
0 < K < 0.5
C
0 < K < $$\infty$$
D
0.5 < K < $$\infty$$
4
GATE ECE 2016 Set 3
+2
-0.6
A second-order linear time-invariant system is described by the following state equations \eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr & {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr}\$

Where x1(t), then the system is

A
controllable but not observable
B
observable but not controllable
C
both controllable and observable
D
neither controllable nor observable
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