QUESTION $3$

Given the transfer function below, write it in standard first order form and determine

the time constant and the steady state gain:

$\frac{Y(s)}{x(s)}=\frac{2}{s+\frac{1}{3}}$

The transfer function that corresponds to the inlet volumetric flowrate $F_{in}(t)$ and the

outlet volumetric flowrate $F_{\text{o}\text{u}\text{s}}(t)$ of two mixing tanks in parallel is given below:

$G(s)=\frac{[(1-a)A_1{R}_1+a{A}_2{R}_2]s+1}{(A_1{R}_{1}s)(A_2{R}_{2}s+1)}$

What are the poles and zeros of the system? Are there any common factors? And under what

conditions?

$[16$ Marks$]$