Exam 3 solution

# Exam 3 solution - EML4312 Spring 2011 Test 3 Nam...

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Unformatted text preview: EML4312: Spring 2011 Test 3 Nam Instructions. This is a closed— book, closed notes exam No graphical calculators are allowed. You MUST SHOW ALL YOUR WORK TO RECIEVE ANY CREDIT. 1. (25 points) Draw the asymptotic bode plot for the followingopen—loop transfer function. (s+lO)(s+1)l HG?) : S4 (Z/ML 310/02: ~wﬂA= ——}0(4~2) = ~44) ole/Gaza w Y n. .1 m n .1 a G m n .1 m. e S a h P m 1|. t m .u m T. e t e d JD... 0 1 p e .d O B g n m H. pm m t m F \qﬂ m .m p 5 ml.“ ( 2. these values on the plot to receive ANY cre' 't. mine MUST draw HOW you will deter Bode Diagram l"'1"v_!'TT["' ,___'. m" =-‘~'J~ - —J—- —1— 1-..J— L=1 1H. flllli l 11] Frequency (rad/sec) lle! llllll LH“L-_LJewq__%_Jdg4 1§ 53 33:3: K .v 7 IO ~ 180 -270 ' 3%. 39E Bode Plot = «+30 PM. «.1 , 3. (10 points) Determine a State Space Representation for the following transfer function 4, (5 points) Given the'general state space system below _ rt 2 Ax—i—Bu I ‘f , V i the transfer function is H (s) 2' ___§_£§_I_—_':‘_)__é _________________ (ﬁll in the blank). ' 5. (5 points) Given a state feedback controller u 2, r—k , the closed—loop transfer function for the problem in Question 4 is H (s) = __ﬁ_Q4_S_I_‘_C_A_~_B_K_> jﬁ ______________ (ﬁll in the blank). 6. (5 points) Consider the State Space Representation below l3 H l O: [10]. 1. 0 Are the states Controllable? Are they Observable? You MUST SHOW YOUR WORK. 70* [B A8] = Y0Kk[é 0‘] i 2 5:5 unMﬂMﬁ VW [Gil I .5 If?“ [ [I g] {g l ‘2 woken/Aug. E1 _ 7. (25 points) For the following State Space System: [i él Ed 0: [10], .3] determine a feedback gain K (IF POSSIBLE) to place the desired closed 100p poles at ADCL = j 52 + 23 + l. ...
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