Q301
The state model \[ arrayl x ( k + 1 ) = [ array*20c 0&1\\ - & - array ]x ( k ) + [ arrayl 0\\ 1 array ]u ( k )\\ y ( k ) = [ 0\,\,\,1 ] [ array*20c x_1& ( k )\\ x_2& ( k ) array ] array\] is represented in the difference equation as
The state model
\begin{array}{l} x\left( {k + 1} \right) = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - \beta }&{ - \alpha } \end{array}} \right]x\left( k \right) + \left[ \begin{array}{l} 0\\ 1 \end{array} \right]u\left( k \right)\\ y\left( k \right) = \left[ {0\,\,\,1} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}&{\left( k \right)}\\ {{x_2}}&{\left( k \right)} \end{array}} \right] \end{array}
is represented in the difference equation as
\begin{array}{l} x\left( {k + 1} \right) = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - \beta }&{ - \alpha } \end{array}} \right]x\left( k \right) + \left[ \begin{array}{l} 0\\ 1 \end{array} \right]u\left( k \right)\\ y\left( k \right) = \left[ {0\,\,\,1} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}&{\left( k \right)}\\ {{x_2}}&{\left( k \right)} \end{array}} \right] \end{array}
is represented in the difference equation as
A.
y(k + 2) + αy(k + 1) + βy(k) = u(k)
B.
y(k + 1) + αy(k) + βy(k - 1) = u(k)
AnswerC.
y(k - 2) + αy(k - 1) +βy(k) = u(k)
D.
y(k - 1) + αy(k) + βy(k + 1) = u(k + 1)
Answer: Option B
Solution
Answer: Option B
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