1.

The state equation and the output equation of a control system are given below:\(\begin{array}{l} {\rm{\dot x}} = \left[ {\begin{array}{*{20}{c}} { - 4}&{ - 1.5}\\ 4&0 \end{array}} \right]{\rm{x}} + \left[ {\begin{array}{*{20}{c}} 2\\ 0 \end{array}} \right]{\rm{u}}\\ {\rm{y}} = \left[ {\begin{array}{*{20}{c}} {1.5}&{0.625} \end{array}} \right]{\rm{x}} \end{array}\)The transfer function representation of the system is

A. \(\frac{{3{\rm{s}} + 5}}{{{{\rm{s}}^2} + 4{\rm{s}} + 6}}\)
B. \(\frac{{3{\rm{s}} + 1.875}}{{{{\rm{s}}^2} + 4{\rm{s}} + 6}}\)
C. \(\frac{{4{\rm{s}} + 1.5}}{{{{\rm{s}}^2} + 4{\rm{s}} + 6}}\)
D. \(\frac{{6{\rm{s}} + 5}}{{{{\rm{s}}^2} + 4{\rm{s}} + 6}}\)
Answer» B. \(\frac{{3{\rm{s}} + 1.875}}{{{{\rm{s}}^2} + 4{\rm{s}} + 6}}\)


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