The following diagram shows a contml system with conditional feedback. The transfer function G( s) denotes the controlled process, and D ( s) and H ( s) are the controller transfer functions.

R(s) +0 l •01--

Y(s)

~~ L:cb--

Conditional Feedback

--

Control System

(a) Derive the transfer functions Y(s)/R(s)!N=O and Y(s)/N(s)lu=o·

(b) Find Y(s)/ R(s)IN=O when D(s) = G(s).

(c) Let G(s) - D (s) - --,--~1 0-;-0--,- - - (s+l)(s+5)'

and find the output response y(t) when N(s) = 0 T(t) = l(t)' (u. 1mit step funclion).

(d) With G(s) and D(s) as given in part (c), select among the following choices of H(s) such that when n(t) = l(t) and r(t) = 0, the steady state value of y(t) is equal to zero. (There may be multiple answers.)
H(s)- 10 - s(s + 1)
10 H ( s) = -:--( s-+-:-1-;-;) (-s +----::72)
H(s) = ~(s + ~) H(s) = K (n =positive integer, select n} s + 2 sn It is important to note that the poles of the closed-loop system must all be in the left half s-plane for the final value theorem to be valid.
Problem