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(ELEC271)[2007](s)final~1833^_29795.pdf
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ELEC271 Automatic Control Systems
Final Exam, Spring 2007
1. Find the transfer function from r to y of the system shown in Figure 1.

Figure 1: A complicated feedback system.
2. In Figure 2, let P (s)= .
s +
Design C(s) such that

J =(.y1(t).22 + .y2(t).22).
w1(t)=(t) +(.y1(t).22 + .y2(t).22).
w1(t)=0 . w2(t)=0 w2(t)=(t)
is minimized and .nd the optimal value of J for the special case when = 0.
w1
-

u1-P (s)
6.

y1 y2

?
C(s)
u2 w2
Figure 2: Feedback system for stabilization.
1
3. Consider a plant P (s) = . Design a unity feedback controller C(s), as in Figure 3 so
1 . s2 that position error constant of the loop transfer function L(s)= P (s)C(s) is in.nity and the closed-loop poles are .1, .2, .1 j. What is the velocity error constant of the loop transfer function?
r
-

Figure 3: A unity feedback system.
.s . 1 s . 2.

4. Compute , .
s +1s +1 1
5. In Figure 2, given P (s)= , design C(s) so that bP,C is maximized. What is the
s(s + 2)
maximum bP,C ?
1