PROBLEM #4: The open-loop transfer function of a unity feedback system is given as KG(s) = frac{K(s - 2)(s - 1)}{s(s + 1)}. Sketch the root locus of the system and do the following: (a) Find the asymptotes as well as the breakaway and break-in points. (b) Find the jomega-axis crossings. (c) Find the range of K for stability. (d) Find the value of K that yields a stable system with second-order complex poles with a damping ratio of 0.5.
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The given open-loop transfer function is \(G(s) = s(s+1)\). This is for a unity feedback system, which means the feedback loop has a transfer function of 1. Show more…
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8. Given the unity feedback system where G(s) = K / (s(s + 2)(s + 3)) do the following: (1) Sketch the root locus. (2) Find the value of K to make the system marginally stable and Find the two poles on the imaginary axis. (3) Find the value of K for which the closed-loop transfer function will has a pole on the real axis at -0.5. (4) As changing the G(s) to G1(s), sketch the root locus of G1(s). And discuss the results. G1(s) = K(s+1)/(s(s+2)(s+3))
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