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Closed Loops and Root Locus

Consider the root locus for ... (*see attachments for function and diagram)
i) Graphically, find the gain required to give dominant closed loop poles with ... (*see attachment for function)
ii) For the above value of gain, find natural frequency and hence sketch the expected reference to output step response, assuming that the underdamped poles are dominant
iii) Add a sketch of the negative gain root locus to the diagram


Solution Summary

The solution provides detailed explanations and graphs for finding gain in closed loop, values of gain and natural frequency, and negative root locus.