1
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 2 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
3
GATE ECE 2015 Set 2
+2
-0.6
The state variable representation of a system is given as \eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \left[ {\matrix{ 1 \cr 0 \cr } } \right] \cr & y = \left[ {\matrix{ 0 & 1 \cr } } \right]x \cr}The response y(t) is A sin(t) B 1-et C 1-cos(t) D 0 4 GATE ECE 2015 Set 3 MCQ (Single Correct Answer) +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
$${{11s - 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
EXAM MAP
Medical
NEET