HW2Solution - ARO 322 Aerospace Feedback Control Systems...

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Unformatted text preview: ARO 322 Aerospace Feedback Control Systems Homework #2 Due 10/10/2007 I. Write down the differential} equations of motion for the foliowing mechanical system. modLHQA cu; q dwer [51) 2. For the automobile shown in the figure, (a) Write the equations of motion governing this system. (b) "Find the transfer function between the controi input, u, and the output, y. my}; :5 -— kaéep... gaping) --—~ U) NVYS “a: u... K\'—a-—>c.) - ~5L) ~LZ) "‘Tméfnfi Lcupmce, fiansgprm) Wt 311 m 59-x L5) 4- 1<><L$J- 341%» + bsxw-«bSXlsJ woes) :2 DU) MS'L its) + Kym) -- Kst) +b5‘1\$)-b$><lS) '9. 1n mamx ermrw.J equms 3 ¢ 1.; Can be, mnttenaa “m 51+ 195+ 34 -—- gum) X’LS) D w- @s 449 M$L+b$+l< Y5) U “‘00), .U‘gi'a msZ-tbsuq u :(U) 3;; debt: “Lbsww U] d9; m swung «@5449 .— g-Hg b45244, bsHA m "'15 2'4' b5 3L. Uh: mth IQS'L'Y “+19 LMSL‘FbS-Hg wgs-Hg)” J W») .L U“) ,::: MS +b$+K “7151+ b5+ \K) LM $1+b$+9 ‘_ ll ms‘L-s-bs 5-K MMSQ-Ffi‘n-v M) b$3+LM+mj V391 3. The motor in the figure has an eiectrical constant K3, a torque constant K, an armature inductance La, and a resistance Ra. The rotor has an inertia J1 and a Viscous friction B. The load has an inertia of J2. The two inertias are connected by a shaft with a spring constant k and an equivalent viscous damping b. Write the equations of motion and 21) Find the transfer function 91(s)/ 141(3) b) Find the transfer function 93(s)/ 741(3) 0) Find the transfer function 9;(s)/ Va(s) "'1 “the, circuit. atom: 5,292. ._.,.. ,bkég'“ é.) «Ame-veg mg.) C) Armo’wfl Ci'rw‘b‘ Tm: Kkiq M... ED Mom -\:q 14,38 Lcuflqce, fizz-ans {firm 0:} chuflah‘m,‘ Hg) We, 3% 3‘. Stew) + BS Q 63+ WSQ;=LS) - 1°: 58:. ls) + Katy -- "C 9:- “) :2. "7;, KS) 151- 813.5) + M 92. k5.) -— b5 9‘ is) + K 6w) --I< Qty-m -~ (.6) \qus) -— Kes 9,5):- qu IqL5J+ Re; 11115) 43;) ILLS) == Kl: IQ L5) W1 Tau); “L? [5) M K4..— Subs-h-L-Lu-f'g IqLSJ Tcm L83 ‘h'bu L?) , Va\ 5) “- K-eflseg LS):- Rq) Tm . Kb W, Tm U) =**—— Kb CVQLSJ “' Ke-‘QILfl .._...... CD Eggs 4- 2(1) 751816) «1-? +505 3L9...» 5.5 GLLS) + K8,\.SJ~K 6219;: l Liam-5+ Ra ) W, [133% + LIRH ma figs“; Luke» «1.0.4r Rq+KeKb2$+KRq191w t D - b,Lq'5"-+ %&+ Mags + M. 6543) == Va L5) “'0 ’ % Kt [32.5" + 195 + KJ 9M5) __ Lbs-HA) 3‘sz “-“'=—-D MU U §awm3 +Lo. mun-am Uh) «’4 W W? (“mew Rum ) U) EMS) a: Kt [151+bsa-K) VcJ-‘J M 9&5 + Llamas: Law-xmzqus + [db 4' Kekkji-l— KLle-I'J! Rm,» 4- b, +qux+ 3;“!ng Q! Rafi-1&4“ 121.19 + +KRQJL+ e Ki. {1954-19 [5) _. I ‘9, 2» m i ) V0.5) D\S) 4. Problem 6.44 ofthe textbook \ R Pam) . ML MVQ)Auo*n—\:ma, 44w efiw‘mg I WW3: R§Lo3+ Jaj'taqc)dm .._LL) 0 Va. H) m K IE) W KB "Twang LOLPJQLa magma 6?} (.4) A (‘3’): \I‘UoJ ..-.= Kits) 4— ILS’) ..______.. L3) 5. Problem 6.48 of the textbook \sL-v \‘L‘HJ So 3mm Emmy... .5 . KS), @Lflv \‘S‘A‘SD *- L} N KS”) “+0 L5 ’43 The SW 31538051 )5 C {5) w W m)... (‘7' whom, 5 Q4) LS-m \$"+_IJ NM: (4.9) :2: 11+ “E” + _...___.C + MDS'I—E'j which S 3.4 5-H SL-H ‘ fivms, nos-‘53 pqm'aq .chh‘an QqunJim, A- Li’s/h cw)’, ,. Us): -~ .._........' +Jw+25 (WM’ 2i+ sf: 6. Problem 6.49 of the textbook La) Siam—a, . be. cm W P5124 5: ~9— ‘4 5::in are, cm gig-her 0h “4.. IQ'HT""‘9'nd shag or 071—944. gmoainctva (axis. In 40“; fin“; is maggjnqua: S—tGLM-Lv Pomm 'H‘Q imaafrxwa 0xva (P) Pqu cue.) _-: ~2. «L 55-1.} W— was «a 129% w “6’9 K9) ’PMas an; 5:...1, 5.1.44 4 5’5), - {one Pom on a’iaka— mm sfde) @) POW-5’ Q32.) :2 “.1; 3.; #0.: i0. €665 L Lam m $0304 cw LeH— mug: 3M9 - L8) ...
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This note was uploaded on 09/14/2008 for the course ARO 322 taught by Professor Bhandari during the Spring '08 term at Cal Poly Pomona.

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HW2Solution - ARO 322 Aerospace Feedback Control Systems...

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