engineering recuitment GATE EE 2023-24 Test Series Control Systems State Space Analysis Transfer Function From State Space Representation
The signal flow graph of a system is shown below.
Then the state variable representation of the system can be
1
\(\bar x = \left[ {\begin{array}{*{20}{c}} 1&1\\ { - 1}&0 \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 2 \end{array}} \right]u\& y = \left[ {0\ 0.5} \right]x\)
2
\(\bar x = \left[ {\begin{array}{*{20}{c}} { - 1}&1\\ { - 1}&0 \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 2 \end{array}} \right]u\& y = \left[ {0\ 0.5} \right]x\)
3
\(\bar x = \left[ {\begin{array}{*{20}{c}} 1&1\\ { - 1}&0 \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 2 \end{array}} \right]u\& y = \left[ {0.5\ 0.5} \right]x\)
4
\(\bar x = \left[ {\begin{array}{*{20}{c}} { - 1}&1\\ { - 1}&0 \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 2 \end{array}} \right]u\& y = \left[ {0.5\ 0.5} \right]x\)