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# quiz2sol - 16.06 QUIZ 2 Each question is worth an equal...

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Unformatted text preview: 16.06 QUIZ 2 November 19, 2003 Each question is worth an equal number of points. Problem 1 Given the following system- A=t333l W €101] M01 La) Determine the system state transition matrix Lb) If the initial condition for the system state vector is- _f0l 5—H and the input is a unit step function, determine the output by using convolution integrals. - \$43 ~t (a) SI'A' [o s] _. - r q -! u I _ 9 i 7 : - 573 M543); ‘> ‘5 l 0 543‘}: O 5 L 5 9 _ J. 13.. ’3‘ 5+3. 5 343 E 0 .5 t _:._ :15 (a: More)? -~.zt J-i I 6 3 3 L— o t j Problem 2 You are to design the attitude control system for a boost vehicle with a large and massive rocket motor. The transfer function relating 6(1), the pitch angle of the boost vehicle, to uﬂ), the input command to the rocket motor actuator, is as follows— ®(s)_ 10 (32 +1) a [1(3)—(S+10) (st—1) where 8(3): Laplace Transform of the vehicle pitch angle U(s)= Laplace Transform of the input to the rocket motor actuator 2.3,) Create a state space mode] of this system 2b) Develop a full state feedback control system so that the poles of the closed loop system are at- s=-5 s=-l+j s=—l -j (a) 8m we pairs at; 210m; ; ( DPSI'WJ CLGrﬁﬂLPG‘S'Ir'C €?um{r‘an f5: (5.: {Ms H-gﬂww} :0 :> 53+7524125 Ho:0 5Jch #chﬂgmﬂ', 7’" (’79-!!- ff U - uc ‘ XX; .\ i: r"'A—€6()& 4 8m. *2 w __ . I' 0 ‘7 4-5%:[333{_[37[k,mmf__F U .I o J r 401 yo} 040x, I—lolé 404019 To 945:! (Lax. €f’ﬂ./ UJC JV 540/7104“ an“ q NH“), of J9 (VF, [0 f O] ! Jig Gian efn. r) 5—3 4{IO4{0{(3)\$2 4 ((019.1); 4(/0#,-/0} :0 C2) E?Umlc 6) GM! [ix and full-’9 {1" inﬂate: (JOKJOt/D ( MIL—2 my; —I '2 © «2 H - :. 7 ( So (meld/Fr 35'. fl )U: (1C =2x, 43):? 40.313/ Problem 3 Consider the plant 2 6(3): s2 +1 3.3) To achieve a second-order system that has a damping ratio of 0.707 and a time constant of 0.53, where should the closed-loop poles be located? 3.1)) Design a PD compensator which, when used in a unity feedback closed-loop system will meet the design speciﬁcations in 3.3). Be sure to state the ﬁnal transfer function for your Gc(s). Problem 4 The plant (52 +2s+2) G“) 2 3(52 + s +0.5) has zeroes at s 2 -1i j and poles at s = 0, s = —0.5 i 0.5}. Consider the root locus plot for unity feedback. 4.3) Calculate the angle of departure from the upper complex pole for K>O 4.1)) Calculate the angle of arrival at the upper complex zero for K>0 4.c) Sketch the root locus for K90. 4.d) On a separate plot, sketch the root locus for K<0. (q) We Mfr-W: [9 4 r0 Han-’8‘] ‘ l 2’ 4902135] ~' - W 3/; 4340/ _..1' 3) r___.__... __ ._ . (L; AWL: (whim: [5 Jr \$007 ._ m" M703 715(3) me] _~ J30" H <1 o .xky ) ] (Ct/was o( Cé’fqrrhxe an! (I'm-ml 5%de \$7 070”? ...
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## This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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quiz2sol - 16.06 QUIZ 2 Each question is worth an equal...

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