3. A unity-feedback system has the following open-loop transfer function: G(s) = frac{10}{s(s + 2)^2} A gain K is cascaded with G(s), such that the open-loop transfer function is now K G(s). The gain is varied until the system becomes oscillatory (unstable). Use analytical methods to determine the value of K and the frequency of oscillation. Verify your results by using MATLAB. Additionally, plot the root locus of this system and verify the value for K.
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Step 1: Given the open-loop transfer function: \[ G(s) = \frac{10}{s(s+2)^2} \] When a gain \( K \) is cascaded with \( G(s) \), the new open-loop transfer function becomes: \[ K G(s) = \frac{10K}{s(s+2)^2} \] Show more…
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