$A_{nxn},B_{nx1},C=[1$cdots$0{]}_{1xn},D=0$

$K=\left[\begin{array}{ccccccc}0& 0& 0& \text{c}\text{d}\text{o}\text{t}\text{s}& 0& 0& 1\end{array}\right]{}^{-1}{p}_d(A)$

$S(s)=\frac{1}{1+GF}=1-G_c(s)$

$G_{\text{m}\text{a}\text{x}}=||S(j{w}_{\text{m}\text{a}\text{x}})|{|}_{\text{m}\text{a}\text{x}}$

You are expected to make various calculations by using the A$,$ B$,$ C matrices and the poles vector containing the poles to be assigned, with the help of the equations given above. Calculate Phi and pdA values, K state space controller gain,

S$($s$)$ Sensitivity transfer function and the maximum value of the

frequency response of this transfer function and the frequency that

maximum value occurs.

$[$Phi$,$pdA,K$,$S$,$G$\_$max,w$\_$max$]=$ackerData$($A$,$B$,$poles$)$

Code the Matlab function shown above.Respectively; $G_c$ is the closed loop transfer function, $F$ is the transfer function of the controller, $S(s)$ is the sensitivity transfer function, G$\_$max is the maximum value of the sensitivity transfer function and w$\_$max is the frequency at which this value is reached.

To find S$,$ you will need to reorganize the closed$-$loop state space mode $($you should use A$-$BK instead of matrix A$)$ in terms of the transfer function.

Your code must work for input of any order. Those who attempt to scan all frequencies through loops $($for$-$while etc.$)$ will be deducted $25$ points. The maximum value of the system and the frequency that provides it can be obtained with Matlab's $[$gpeak$,$fpeak$]=$ getPeakGain$($sys$)$ command.