1
GATE ECE 2018
+2
-0.67
The state equation and the output equation of a control system are given below:

$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$

$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$

The transfer function representation of the system is
A
$${{3s + 5} \over {{s^2} + 4s + 6}}$$
B
$${{3s - 1.875} \over {{s^2} + 4s + 6}}$$
C
$${{4s + 1.5} \over {{s^2} + 4s + 6}}$$
D
$${{6s + 5} \over {{s^2} + 4s + 6}}$$
2
GATE ECE 2017 Set 2
+2
-0.6
A second order LTI system is described by the following state equation. \eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr & {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr}When x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t)=X1(t). The systyem is A undamped (oscillatory) B under damped C critically damped D over damped 3 GATE ECE 2016 Set 3 MCQ (Single Correct Answer) +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
4
GATE ECE 2015 Set 3
+2
-0.6
A network is described by the state model as \eqalign{ & {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \cr & \mathop {{x_2}}\limits^ \bullet = - 4{x_2} - u, \cr & y = 3{x_1} - 2{x_2} \cr}\$

the transfer function H(s)$$\left[ { = {{Y\left( s \right)} \over {U\left( s \right)}}} \right]is$$

A
$${{11s + 35} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
B
$${{11s - 35} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
C
$${{11s + 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
D
$${{11s - 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
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