Question: A control system for an automobile suspension tester has negative unity feedback and a process [12] L(s) = Gc(s)G(s) = K(s2 + 4s + 8)

A control system for an automobile suspension tester has negative unity feedback and a process [12]
L(s) = Gc(s)G(s) = K(s2 + 4s + 8) / s2(s + 4)
We desire the dominant roots to have a ζ equal to 0.5. Using the root locus, show that K = 7.35 is required and the dominant roots are s = -1.3 ± j2.2.

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