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Unformatted text preview: [4’10 :1‘9/ :3 was
275: cf“ 16.060 Quiz
November 20, 2001
._. __., 1. Develop a state space model and determine the A, B, C and D matrices for each of the 8
following systems ' I Q
. " 1 
a G s = m
) ( ) (s2 + s + 4) 
("t l ‘1' ”it I H L ;. a 5.
'9) 6(3) :"EEL E I U
(s + 3 +4) '
. (52 +1) I
C) 0(5) = “2—“
(s + s + 4)
2. Given the fountains, state space system / ﬂ
ﬂ '5’
A— "'3 _1 31 C—2 3 0"[0] I
. — _2 __ 4 —' 1 _ [ ] _ 3) Determine its stability b). Determine its inputfoutput transfer function~  3. Determine the state transition matrix for a state space system with the folloWing A //
matrix _‘__H Mm... F a: a] 4. For the following state space system . \R‘  _
A=[g _12] B=[?] C=[l 1] D=[0] " //{)
detennine the ontp'ut response to a unit step input and the following initial conditions .310) = [3] _. . A secondorder openloop system is subjected to a unity step input. The response is shown 3:
below. The percentage overshoot is 16.3% and the time to peak is 0.9083. (0
a) Calculate _
_ i. The damping ratio, C (hint: use the data on the following page)
ii. The damped natural ﬁequency, (0d
— b) What are the openloop poles of the system?
3
n
a
a
0) Design a PD compensator which, when used in a unity feedback closed100p system
will yield closed100p poles at
s=——3.46:t has ,1. #0 ,q 0é
/ ' "'
6. What value(s) of the constant c 1will make following state space system (1
uncontrollable? . _ 3a. C citll his] i ' // . '7. Determine a full state feedback matrix K for the following system l3 lei—lg 1 ll Blgl c—rhl 3] 0131
. _l:1 3 Ol _l1l lo 0 ll l0l so that the closed loop system has poles at +3j.3j, and 4 ...
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 Fall '03
 willcox
 Aeronautics

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