P10.27 An engineering design team is attempting to control a process shown in Figure P10.27. It is agreed that a system with a phase margin of P M. . = 50° is acceptable. Determine G s c( ).

First, let G s c( ) = K and find

(a) a value of K 

that yields a phase margin of P M. . = 50° and the sys

tem step response for this value of K.

(b) Determine the settling time, percent overshoot, and the peak time.

(c) Obtain the system closed-loop frequency response, and determine Mpω 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 P M. . = 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 control

lers for G s c( ) by comparing settling time (with a 2%

criterion), percent overshoot, peak time, Mpω, and bandwidth. 

G(s)= = K(s+12) (s+20)