Question

\text { A control system as shown in Figure } 5 \text { has a transfer function of } G(s)=\frac{1}{s(s-\gamma)}, \text { where } \gamma \text { is } 6

Let G (s) = K . By sketching the root-locus, show that the closed-loop system is always unstable. (s)=K((v+1) s+\alpha) \text { where } v: 6 \text { and } \alpha: 36 number. Draw the root-locus (Note: you need to show all the necessary steps in drawing theroot-locus) and determine whether that the closed-loop system can be stabilized, if so,determine the range of K for the closed-loop system to remain stable.

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Fig: 5