(Solution) - Consider a plant whose open loop transfer function is G s H s -(2025 Original AI-Free Solution)

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Consider a plant whose open-loop transfer function is
G(s) H (s) = 1 / s [(s + 2)2 + 9]
The complex poles near the origin give only slightly damped oscillations that are considered undesirable. Insert a gain Kc and a compensator Gc (s)in series to speed up the closed-loop response of the system. Consider the following for Gc(s):
a. The lead compensator
b. The lag compensator
c. The so-called reverse-action compensator
Gc (s) = 1 - T1s / T2s + 1
Obtain the root locus plots for the compensated system using each compensator. Use the compensator parameters. Determine which compensator gives the best response.