Define transfer function using matlab command and plotting time response of the system which

subjected to unit step function for open loop transfer function of $2$ systems in series and plotting the

time response of the system for closed loop transfer function by combining both systems in series

together.

$\%$ Defining Transfer Functions

$Gn=\left[\begin{array}{cc}3& 2\mathrm{.}4\end{array}\right]$;

$Gd=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$;

Gsys $=tf(Gn,Gd)$;$\%G(s)$

$C=[5]$;

Csys $=tf(C,1)$;$\%C(s)$

$Hn=0\mathrm{.}25$;

$Hd=\left[\begin{array}{cc}1& 25\end{array}\right]$;

Hsys $=tf(Hn,Hd)$;$\%H(s)$

sysCGtf $=$ series$($Csys$,$ Gsys$)$;

sysCLTF $=$ feedback$($sysCGtf$,$ Hsys$)$;

$\%$ Closed Loop Transfer Function $($CLTF$)$ Should Look like this:

$\%C(s)**G(S)+G(S)$

$\%$

$\%1+[C(s{)}^{**}G(S)+G(s){]}^{**}H(s)$

$B=$ isstable$($sysCLTF$)$; $\%$ Stability Check

$\%$ Plotting CLTF as a whole:

figure$(1)$

hold on

plot$($step$($sysCLTF$))$

grid on

ylabel$(\text{'}$Amplitude$\text{'})$

xlabel$(\text{'}$Time$\text{'})$

hold off

$\%$ Plotting $G(s)$

figure$(2)$

subplot$(2,1,1)$

step$($Gsys$)$

grid on

subplot$(2,1,2)$

step$($Hsys$)$

grid on

$\%$ Plotting $H(s)$

figure$(3)$

$a=$sim${(}^{\text{'}}$model.$sl{x}^{\text{'}})$;

b $=$ a$.$y$.$data;

$c=$ a$.$t$.$data;

plot$($c$,$ b$)$;