engineering recuitment GATE ECE 2023-24 Test Series Control Systems State Space Analysis State Space Representation
For the signal flow graph shown below, the observable canonical form of the system is
1
\(\begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{r}} 0&1\\ { - 2}&{ - 3} \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 1 \end{array}} \right]r}\\ {y = \left[ {\begin{array}{*{20}{c}} 3&1 \end{array}} \right]x} \end{array}\)
2
\(\begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{r}} 0&1\\ { - 3}&{ - 2} \end{array}} \right]x + \left[ {\begin{array}{*{20}{c}} 0\\ 1 \end{array}} \right]r}\\ {y = \left[ {\begin{array}{*{20}{c}} 3&1 \end{array}} \right]x} \end{array}\)
3
\(\begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{r}} 0&{ - 2}\\ 1&{ - 3} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 3\\ 1 \end{array}} \right]u}\\ {y = \left[ {\begin{array}{*{20}{c}} 0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right]} \end{array}\)
4
\(\begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{r}} 0&{ - 3}\\ 1&{ - 2} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 3\\ 1 \end{array}} \right]u}\\ {y = \left[ {\begin{array}{*{20}{c}} 0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right]} \end{array}\)