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(20 pts) This problem should be completed without the aid of MATLAB. Design a compensator for the system below to place closed-loop poles at s12 = -15 + j15. Clearly

detail your design procedure and specify the compensator transfer function, including gain. Provide a qualitative sketch of the root locus for the compensated system (i.e., no calculations are necessary for the root locus sketch).

Fig: 1

Fig: 2