GATE EE 2006 | State Variable Analysis Question 22 | Control Systems

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

GATE EE 2001

MCQ (Single Correct Answer)

-0.3

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\, = \mathop {Lim}\limits_{t \to \infty } x\left( t \right),$$ given the initial state value of $$x\left( 0 \right) = {\left[ {10 - 10} \right]^T},\,\,is$$

$${x_{ss}} = \left[ {\matrix{ 0 \cr 0 \cr } } \right]$$

$${x_{ss}} = \left[ {\matrix{ { - 3} \cr { - 2} \cr } } \right]$$

$${x_{ss}} = \left[ {\matrix{ { - 10} \cr {10} \cr } } \right]$$

$${x_{ss}} = \left[ {\matrix{ \infty \cr \infty \cr } } \right]$$

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