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The forward path of your control diagram consists of the following transfer functions connected in series: $$ \begin{align*} G(s) &= \frac{s+8}{s^2-2s-3}\rightarrow \text{Plant}\\ K(s) &= K \rightarrow \text{Controller} \end{align*} $$ The Loop Transfer Function then is (by considering all other components' dynamics equal to $1$): $$ L(s) = K\cdot \...


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