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E CMPES NAMszameﬁﬂmS Fall 2009 Quiz 4
Test Time: 8:05—8:45 AM. Be sure to write CLEARLY! 1. (5 points) Write the Matlab command to generate a vector t that starts with 0, ends
with 5, and has a sample period of 0.1. ‘ > é.” i;.xﬁl~!”
it,” Law/mle 2. (6 points) For the time vector 1: deﬁned above, What are; a) t(5 : 10), b) length(t) 
t(end), and c) t(end1)—1? Write the numeric answers. ‘{ 7 r. t: {Cm/J‘s. > 3 m N. W i 35/" A v a .
b) t“)\ '1 Eu : «14/ c.) i “’ TM 4 3. (5 points) Write down the dynamic model for a robot’s translational position a: and
rotational position 6. Included in the model are the constant sample period A, trans lational speed uk and rotational speed 12k. f"\
, 5 > g“ x m a g 2
““=\irt Zﬂia§%>ﬁﬂa m
%L
' \j t; “f’émvk: ‘ 4. (5 points) The wall—following control is given by ac —m'_
UR: = unom) Me = kp ($19 _ dsep) + (Cdw) A Where kp, led, dsep and unom are constants. Substitution of (2) into (1) gives the closed
loop dynamic model of the robot. ' Write down the closed—loop dynamic model of the robot. rm.
x “ (i . ;' \ ‘5 a" '<
><mv\<.>. pizza Evens,4 * 5‘ a i 5:0“; 11.5 5; \cEE‘V'KL/E k” l! if: \M / 35:,
l (6“ ‘ . y
if. \ a ,s\ r: .~
i"? N w \ l K E 3 is i r i f ‘2  ff“. \ l X 3“. \‘ 0 Ci; \ii‘
Ml. \ M‘ .\ JV .5 \\ i I ‘3" (I ; kw ‘3 5‘\ a n.» { 32ml
\u’f §1~TE\ N f " L 5““ E) \E in 1
4...; 5. (5 points) Recall that the control objective is for (m, 6*) = (dsep, 7r/2) to be a stable
and attractive equilibrium point of the closed—loop dynamic model, While the robot moves at a constant speed unom in the y direction.‘ Show that (17*, 6*) = (dsep, i7r / 2) are the two distinct equilibrium points for the closed
loop dynamic model of the robot When 19,, > 0, kg; > 0. Exam—mm “A,”
& my“) .,.._‘.., r l , r ?“ f\ “TW‘M‘T‘MWT
\{K mfg” I\ F “wwwnmmwg g 6. (5 points) Set kp = 0 and determine the ﬁxed point(s) of the closedloop model of the robot. ‘ m ‘ WTmmlm‘mmmwwf? .t H 1/“ . f T";
\ I r a—w \ K
A F“: l
E
a \i «aw ., V» a "A a + Er ' .
l/\\¥{%( isﬁ WC. 5;) {KER/L» l k2 " "‘” X
t \ (M E» % umﬂ j:
\i r
t / ’ f , ‘ _ g "’ RM“ i {7/ x it i
V %  mi” Al” [Al “a i “v w: W a
1 v]; I, a", gag”; /\ an“.. I 3‘ I} h
v 1:: ’ H ’ V ”
M\,\§ﬁ"”~\ i s
a i g l A r i
w~ , \ .3 b ‘ :' M“ y» > 7 xi 1 r‘: P: A '5 ' $ I z :1)
w“ x ,/ mg. mil/ii viii éw V kin/{LN
; “ ‘ '
7. Evaluate each of your team members performah’ce by ﬁlling out the following table.
Use the following ranking: ' 1=excellent, 2zvery good, 3=good, 4=less than satisfactory, 5==totally lame Team Member Name I Ranking ...
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 Fall '09
 Trigraph, Equilibrium point, dynamic model, $19, closed—loop dynamic model

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