Consider the following generic feedback control system.

w(t)!

_r_(t_) _+@--jD(s)j :-@---jG(s)l y(t).

r 1 13 1 I A GeneTal Control System

(a) Find the transfer function from the Teference r(t) to the output y(t)

i.e. Tr(s).

(b) Find the tmnsfeT function from the disturbance w(t) to the output y(t) i.e. Tw(s).

tk

(c) FaT a generic reference, r ( t) = k! , show that the steady state error with respect to the refeTence is given by r _ 1. (1 - Tr) eBB- lffi k . B->0 S tk

(d) For a generic disturbance, w(t) = k!, show that the steady state eTror with Tespect to the disturbance is given by w l" -Tw eBB= lffi -k-. B->0 S

(e) Explain the meaning of system type in terms of the steady state errors e~ , and e~ •

Problem