Consider the second$-$order system

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

We would like to add a transfer function of the form $D(s)=K\frac{s+a}{s+b}$ in series with $G(s)$ in a unity$-$feedback structure.

$($a$)$ Ignoring stability for the moment, what are the constraints on $K,a,b$ so that the system is type $1?$

$16-$Mec$-$A$3/$May $2017$

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$($b$)$ What are the constraints placed on $K,a,b$ so that trie system is stable and type $1?$

$($c$)$ What are the constraints on a and $b$ so that the system is type $1$ and remains stable for every positive value for $K?$