GATE EE 2014 Set 2 | State Variable Analysis Question 8 | Control Systems

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-0.3

The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u$$ is

$$\left[ {\matrix{ {{e^t}} & 0 \cr {{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & 0 \cr {{t^2}{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & 0 \cr {t{e^t}} & {{e^t}} \cr } } \right]$$

$$\left[ {\matrix{ {{e^t}} & {t{e^t}} \cr 0 & {{e^t}} \cr } } \right]$$

GATE EE 2006

MCQ (Single Correct Answer)

-0.3

For a system with the transfer function $$H\left( s \right) = {{3\left( {s - 2} \right)} \over {{s^3} + 4{s^2} - 2s + 1}},\,\,$$ the matrix $$A$$ in the state space form $$\mathop X\limits^ \bullet = AX + BU$$ is equal to

$$\left( {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr { - 1} & 2 & { - 4} \cr } } \right)$$

$$\left( {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 1} & 2 & { - 4} \cr } } \right)$$

$$\left( {\matrix{ 0 & 1 & 0 \cr 3 & { - 2} & 1 \cr 1 & { - 2} & 4 \cr } } \right)$$

$$\left( {\matrix{ 1 & 0 & 0 \cr 0 & 0 & 1 \cr { - 1} & 2 & { - 4} \cr } } \right)$$

GATE EE 2003

MCQ (Single Correct Answer)

-0.3

A second order system starts with an initial condition of $$\left( {\matrix{ 2 \cr 3 \cr } } \right)$$ without any external input. The state transition matrix for the system is given by $$\left( {\matrix{ {{e^{ - 2t}}} & 0 \cr 0 & {{e^{ - t}}} \cr } } \right).$$ The state of the system at the end of $$1$$ second is given by.

$$\,\,\left( {\matrix{ {0.271} \cr {1.100} \cr } } \right)$$

$$\left( {\matrix{ {0.135} \cr {0.368} \cr } } \right)$$

$$\left( {\matrix{ {0.271} \cr {0.736} \cr } } \right)$$

$$\left( {\matrix{ {0.135} \cr {1.100} \cr } } \right)$$

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is

$${\left( {s{\rm I} - A} \right)^{ - 1}}$$

$${e^{AT}}\,X\left( 0 \right)$$

Laplace inverse of $$\,\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}} \right]$$

Laplace inverse of $$\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}X\left( 0 \right)} \right]$$