1
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
The signal flow graph of a system is shown below. GATE ECE 2010 Control Systems - State Space Analysis Question 24 English

The state variable representation of the system can be

A

$$\mathop x\limits^ \bullet = \left[ {\matrix{ 1 & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u$$
$$y = \left[ {\matrix{ 0 & {0.5} \cr } } \right]x$$
B
$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ { - 1} & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ 0 & {0.5} \cr } } \right]x \cr} $$
C
$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 1 & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ {0.5} & {0.5} \cr } } \right]x \cr} $$
D
$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ { - 1} & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ {0.5} & {0.5} \cr } } \right]x \cr} $$
2
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
The signal flow graph of a system is shown below. GATE ECE 2010 Control Systems - State Space Analysis Question 23 English

The transfer function of the system is

A
$${{s + 1} \over {{s^2} + 1}}$$
B
$${{s - 1} \over {{s^2} + 1}}$$
C
$${{s + 1} \over {{s^2} + s + 1}}$$
D
$${{s - 1} \over {{s^2} + s + 1}}$$
3
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A signal flow graph of a system is given below. GATE ECE 2008 Control Systems - State Space Analysis Question 25 English

The set of equations that correspond to this signal flow graph is

A
$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ \beta & { - \gamma } & 0 \cr \gamma & \alpha & 0 \cr { - \alpha } & { - \beta } & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr 0 & 1 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$
B
$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ 0 & \alpha & \gamma \cr 0 & { - \alpha } & { - \gamma } \cr 0 & \beta & { - \beta } \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 0 & 0 \cr 0 & 1 \cr 1 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$
C
$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ { - \alpha } & \beta & 0 \cr { - \beta } & { - \gamma } & 0 \cr \alpha & \gamma & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr 0 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$
D
$${d \over {dt}}\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = \left[ {\matrix{ { - \gamma } & 0 & \beta \cr \gamma & 0 & \alpha \cr { - \beta } & 0 & { - \alpha } \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] + \left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr 1 & 0 \cr } } \right]\left( {\matrix{ {{u_1}} \cr {{u_2}} \cr } } \right)$$
4
GATE ECE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$
If the initial state vector of the system is $$x\left( 0 \right) = \left[ {\matrix{ 1 \cr { - 2} \cr } } \right],$$
then the system response is $$x\left( t \right) = \left[ {\matrix{ {{e^{ - 2t}}} \cr { - 2{e^{ - 2t}}} \cr } } \right].$$
If the initial state vector of the system changes to $$x\left( 0 \right) = \left[ {\matrix{ 1 \cr { - 1} \cr } } \right],$$
then the system response becomes $$x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} \cr { - {e^{ - t}}} \cr } } \right].$$

The eigen value and eigen vector pairs $$\left( {{\lambda _{i,}}{V_i}} \right)$$ for the system are

A
$$\left[ { - 1,\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]} \right]and\left[ { - 2,\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]} \right]$$
B
$$\left[ { - 2,\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]} \right]and\left[ { - 1,\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]} \right]$$
C
$$\left[ { - 1,\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]} \right]and\left[ {2,\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]} \right]$$
D
$$\left[ {1,\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]} \right]and\left[ { - 2,\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]} \right]$$
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