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Real-World Applicationshard
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A plant is governed by the transfer function G(s)=frac1(s+1)(s+2)G(s) = \\frac{1}{(s+1)(s+2)}G(s)=frac1(s+1)(s+2). Under proportional feedback control with gain KpK_pKp​, the closed-loop system has the transfer function T(s)=fracKps2+3s+(2+Kp)T(s) = \\frac{K_p}{s^2 + 3s + (2 + K_p)}T(s)=fracKp​s2+3s+(2+Kp​). For what range of KpK_pKp​ is the closed-loop system stable?