GATE ECE 2006 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

A linear system is described by the following state equation $$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),A = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right].$$$
The state-transition matrix of the system is

$$\left[ {\matrix{ {\cos t} & {\sin t} \cr { - \sin t} & {\cos t} \cr } } \right]$$

$$\left[ {\matrix{ { - \cos t} & {\sin t} \cr { - \sin t} & { - \cos t} \cr } } \right]$$

$$\left[ {\matrix{ { - \cos t} & { - \sin t} \cr { - \sin t} & {\cos t} \cr } } \right]$$

$$\left[ {\matrix{ {\cos t} & { - \sin t} \cr {\cos t} & {\sin t} \cr } } \right]$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ The value of 'a', so that the system has a phase-margin equal to $$\pi $$/4 is approximately equal to

2.40

1.40

0.84

0.74

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their frequency responses are, respectively

$$\sqrt {{a^2} - 4b,} $$ $$\sqrt {{a^2} + 4b,} $$

$$\sqrt {{a^2} - 4b,} $$ $$\sqrt {{a^2} - 4b,} $$

$$\sqrt {{a^2} + 4b,} $$ $$\sqrt {{a^2} - 4b,} $$

$$\sqrt {{a^2} + 4b,} $$ $$\sqrt {{a^2} + 4b,} $$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain margin of the system in dB is equal to

infinite

greater than zero

less than zero

zero

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