# Root Locus for a Closed Loop System

Sketch the root locus for the following closed loop system {see attachment} as {SYMBOL1} varies from -{SYMBOL2} to +{SYMBOL2}. You should calculate all steps and show the positive and negative gain loci. It is recommended that you first find the positive locus and then sketch the negative {SYMBOL2} locus.

(Real axis solutions of {see attachment} are s = + 1.061 and s = +3.605. Do not attempt to solve for other solutions)

*Please see attachment for proper citation of symbols and closed loop system diagram.

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#### Solution Preview

It can be seen that this close loop system with unity feedback is equivalent to the following block diagram (see attachment) where K is a proportional gain and H(s) is an open-loop transfer function.

It can be seen that the variable alpha in the transfer function of the original ...

#### Solution Summary

This solution sketched an equivalent block diagram sketch for the closed loop system with unity feedback where K is a proportional gain and H(s) is an open-loop transfer function. 16 equations and 4 graphs are used in determining and explaining this solution. 625 words.