Problem $1.$

$1.$ Write down a Matlab code to construct each given transfer function and plot the poles and zeros of the overall feedback system $($you may use pzmap function in Matlab$).$

$2.$ In order to track the roll angle command $\backslash (\backslash$phi$\_\{\backslash$text $\{$com $\}\}\backslash ),$ decide on the type of controller $(\backslash (\backslash$mathrm$\{$P$\},\backslash$mathrm$\{$PD$\}\backslash ),$ PID etc.$)$ and design the controller using Matlab rlocus function. In the control design achieve the following objectives.

$-$ Settling time should be less than $\backslash (0\mathrm{.}5[$s$]\backslash ),$

$-$ Maximum percent overshoot should be less than $\backslash (5\backslash \%\backslash ).$

Remember that in order to achieve objectives you may also add a pre$-$filter after you design your controller $($if necessary$).$ Plot the step response with given $\backslash (\backslash$phi$\_\{\backslash$text $\{$corm $\}\}=10\backslash$left$[^\{\backslash$circ$\}\backslash$right$]\backslash )$ command using Matlab step function, and present all the controller $($and pre$-$filter$)$ parameters you have found.