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quiz4solutions

# quiz4solutions - .«r a it E CMPES NAMszameﬁﬂmS Fall...

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Unformatted text preview: .«r a it. 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(end-1)—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) + (Cd-w) 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 closed-loop 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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