This is a system you have seen before. (Click
here for the original problem which also describes Dr. Abner Mallity's
problems with his Russian chauffeur, Picup Andropov.)
The Bode' plot is shown below - excluding the Ki term. Note the left scale is the angle in degrees and the right scale is db gain.
Determine the gain which will produce a phase margin of 50o. Determine the gain which will produce a phase margin of 30o.