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Root Locus and Root Locus Design (Gain, Controller, Location of Contoller, Required Controller Gains)

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Please help me with the attached root locus design question (see attachment).

(Involves: plotting the root locus, determining gain, designing a proportional and integral controller, determining the location of the controller zero, and finding the required controller gain).

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Solution Summary

The solution, attached, is provided step-by-step equationally with explanation and in-document diagrams.

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