NOTE: Please,include all the calculations, m$-$files and Simulink models, plots and graphics that you produced on your own. In addition, provide detailed analyses for each plot t in your report.Thanks

Problem$-4.$ A unity feedback system has the following forward$-$path transfer function. Do the

following.

$G(s)=\frac{256(s+1)}{(s+4)(s^2+4s+64)}$

$($a$)$ Write analytical expressions for the magnitude, $M(),$ and phase, $(),$ responses of $G(s).$

$($b$)$ Sketch by hand the asymptotic magnitude $M()$ in $dB$ and phase $()$ in degrees responses of

$G(s)$ on the empty logarithmic plane presented in the next page.

$($c$)$ Draw the actual magnitude plot on the asymptotic magnitude sketch you provided in $($b$).$

remember the correction due to the underdamped factor of $G(s).$

$($d$)$Provide a simple table exhibiting the magnitude and phase values at low and high frequencies,

i$.$e$.$ at $0\mathrm{.}01ra\frac{d}{s}$ and $1000ra\frac{d}{s},$ respectively.

$($e$)$By means of the asymptotic sketches, determine the value of the appropriate static error constant

and the steady$-$state error per unit step.

$($f$)$ Obtain the actual $M()$ in dB and phase $()$ in degrees responses of $G(s)$ using MATLAB.