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Quizzes_3and4

# Quizzes_3and4 - CMPE 8 NAME Fall 2008 Quiz 3 Test Time...

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Unformatted text preview: CMPE 8 NAME: Fall 2008 Quiz 3 Test Time: 12:00e12:40 PM l. (10 points) The pendulum has the rotational angle variable 6, and the model for the pendulums motion has the form gk-l-l =f(6k,'9k_1), k = 27 3: Write the discrete—time dynamic model of the pendulum, including the affects of gravity and of friction in the joint. Your answer should include parameters (1, b, I, A) = (length of pendulum, friction coefﬁcient, moment of inertia, sample period). (W 2e,;o,_,~— Am met“) New» 2. (10 points) For the dynamic model of the pendulum above, compute the equilibrium anige(s) 6*. Show all steps to get full credit. 3.“ (10 points) Write a function in Matlab whose output is a plot of the pendulum angle orbit (61, 62,63," .E versus time (t1,t2,t3,.. .,E with the pendulum model starting from W with (l b, I E as function input parameters, and with start time t1 = 0 end time W = 20, and sample period A— ~ 0.01. 9. 10M Mggﬁﬁm 1. (Mia reg/fa: (if {Zilw'iletéajE w (t 4- Bonus (5(p01ntsE The lndulum model With torque control input me has the form 9k+1— — f(6k16k-1) + A2111” it ~..-.- 2,3, . (1) where f(0k,9kn1E is the pendulum model as before. With 6 x 7r as the upright (in- verted) angle show that the inverted angle' is a ﬁxed point for the model (1), when the ' 1 feedback torque 11k“ — 01(7r — 6k.) is used. Show all work. W gu+\i?%“giM-A ﬂﬁEQ/‘l (3'1) Al% ”4V %1l‘+Aay([email protected]~:E lath ' Kali o) 5 Bonus: (2 points) Elf c1 > 0 makes the inverted angle stable and attractive: what would likely be the stability of the inverted angle ﬁxed Wﬁtwﬁh cl < 0? - CMPE 8 NAME: Fall 2008 Quiz 4 Test Time: 12:05—12:45 PM. Be sure to write CLEARLY! 1, (5 points) Write the Matlab commands to generate a time vector t that starts with 10, ends with 20, and has a sample period of 0.5. >> if: [\G :. 0% 3/201.) 2. (6 points) For the time vector t deﬁned above, what are: a) t(3), b) 13(8) and c) the length of the vector? a) {K b) [’65 c) M a—-—.. l 3. (3 points) Evaluate each of your team members performance by ﬁlling out the following table Use the following ranking: lmexcellent, 2=very good, 3zgood, 4=less than satisfactory, 5=totally lame Team Member Name | Ranking Team Name: 4. (5 points) Write down the dynamic model for a robot’s translational position x and rotational position 6. Included in the model are the constant sample period A, trans— lational speed uk and rotational speed '03:. \$k+1= XlQJV— AULJQCUCED(®LAB (1) E 19+]- (":5 I I 1 r i R r b EV} . ‘7‘». 5. (5 points) The wall—following control is given by 33k — RSk—i T= ' <2) Where kp, id, dsep and umm are positive constants. Substitution of (2) into (1) gives .the closed—loop dynamic model of the robot. ”k = ”110111: vi: = l(31::(33ls: _ deep) "l" kd Write down the closed—loop dynamic model of the robot. ARM: Kiel? Awhom Cdg< \$14) MELHT Qt JVZEPQWW 5951553 1L J%\Kpjl(§er[\, 6. (5 pOints) Recall that the control objective is for (33*, 9*) = (dsep, 7T / 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 (32*, 6*) = (dsep, fir/2) are the two distinct equilibrium points for the closed— loop dynamic model of the robot. ...
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