An engineering design team is attempting to control a process shown in Figure PI0.27. The system has a controller Gc(s), but the design team is unable to select Gc(s) appropriately. It is agreed that a system with a phase margin of 50° is acceptable, but Gc (s) is unknown. Determine Gc(s).
First, let Gc(s) = K and find (a) a value of K that yields a phase margin of 50° and the system's step response for this value of K. (b) Determine the settling time, percent overshoot, and the peak time, (c) Obtain the system's closed-loop frequency response, and determine Mpa > and the bandwidth. The team has decided to let

and to repeat parts (a), (b), and (c). Determine the gain K that results in a phase margin of 50° and then proceed to evaluate the time response and the closed loop frequency response. Prepare a table contrasting the results of the two selected controllers for Gc(s) by comparing settling time (with a 2% criterion), percent overshoot, peak time, Mpo), and bandwidth

K (s 12) G,(s) = (s+20) Process Controller Gs)s10) Ris)