Cons'ider the following control system where the feedback gain {3 is subject to var"iations.

10 r +ff\ ~-~() a--------~~- (s+l)(s+lO)

-1 []]--------'

Control System with Variations in {3 y ~ -u The objective is to design a controller for this system so that the output y(t) accv.mtely tracks the reference input r(t).

(a) Let /3 = 1, and the following three options for the controller Di ( s)

are available:

where K is a constant. Choose the contmller (including a particular value for K) that will Tesult in a type 1 system with a steady state eTmr of less than 1 1 0 •

(b) Next, suppose that, due to haTsh conditions, there is some attenuation in the feedback path that is best modeled by (3 = 0.9. Find lhe steady state error due to a mmp input for Llu choice of Di(s) in part (a).

(c) If ,3 = 0. 9, what is the system type for part

(b) ?
Problem