1
GATE EE 1998
Subjective
+5
-0
The state-space representation of a system is given by $$\left[ {\matrix{
{\mathop {{X_1}}\limits^ \bullet } \cr
{\mathop {{X_2}}\limits^ \bullet } \cr
} } \right] = \left[ {\matrix{
{ - 5} & 1 \cr
{ - 6} & 0 \cr
} } \right]\left[ {\matrix{
{{x_1}} \cr
{{x_2}} \cr
} } \right].$$
Find the Laplace transform of the state transistion matrix. Find also the value of $${x_1}$$ at $$t=1$$ if $${x_1}\left( 0 \right) = 1$$ and $${x_2}\left( 0 \right) = 0.$$
Find the Laplace transform of the state transistion matrix. Find also the value of $${x_1}$$ at $$t=1$$ if $${x_1}\left( 0 \right) = 1$$ and $${x_2}\left( 0 \right) = 0.$$
2
GATE EE 1997
Subjective
+5
-0
Determine the transfer function of the system having the following state variable representation:
$$\eqalign{ & X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 40} & { - 44} & { - 14} \cr } } \right]x + \left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right]u \cr & y = \left[ {\matrix{ 0 & 1 & 0 \cr } } \right]x \cr} $$
$$\eqalign{ & X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 40} & { - 44} & { - 14} \cr } } \right]x + \left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right]u \cr & y = \left[ {\matrix{ 0 & 1 & 0 \cr } } \right]x \cr} $$
Questions Asked from State Variable Analysis (Marks 5)
Number in Brackets after Paper Indicates No. of Questions
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits