The state-space representation of a system model is given as

with $$x=\left\{\begin{array}{c}{x}_1\\ x_2\end{array}\right\},A=\left[\begin{array}{cc}0& 1\\ -2& -\frac{2}{3}\end{array}\right],B=\left[\begin{array}{c}0\\ 3\end{array}\right],C=\left[\begin{array}{cc}1& \frac{1}{2}\end{array}\right],D=0,u=u$$

a. Construct the block diagram.

b. Find the transfer function $Y\left(s\right)/U\left(s\right)$ directly from the block diagram.

c. Find the transfer function $Y\left(s\right)/U\left(s\right)$ from the state-space form and compare with (b).

Transcribed Image Text:

(x = Ax+ Bu y=Cx+Du