Figure P12.2 shows a pneumatic positioning system, where the displacement x is controlled by controlling the applied

Question:

Figure P12.2 shows a pneumatic positioning system, where the displacement x is controlled by controlling the applied pneumatic pressure p1. Assume that the pressure p2 is constant, and consider the specific plant
Gp (s) = X (s) / P1 (s) = 1 / s2 + s
Design a compensator for the plant so that Cu = 20/sec, the gain margin will be no less than 10 dB, and the phase margin no less than 50o.