Assume that you have a system in a feedback loop:

The transfer function, G(s), is given by:

It is required that the closed loop system have poles at s = -1 + 2j and s = -1 - 2j.

• Is it possible to get poles at that position using a proportional gain?  Why not?  (Reasoning based on the root locus probably gets this answer fastest.)
• If a compensator is used with a zero at s = -1 (an arbitray choice), can a pole be placed to give the required closed loop poles?
• What is the gain, Kc, for the compensator, assuming the compensator is of the form Gc(s) = Kc(s-z)/(s-p)?  (And, we have chosen z = -1, right?)
• Sketch the root locus for the system + compensator.