WUSTL ESE 543 - ESE 543 Homework 1 solution.pdf (8 pages)

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ESE 543 Homework 1 solution.pdf



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ESE 543 Homework 1 solution.pdf

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Pages:
8
School:
Washington University in St. Louis
Course:
Ese 543 - Control Systems Design by State Space Methods
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Spring 2006 K A Wise FinalExam Open I j9 Book Two8 5x11Sheetsof Notes con io rthefollowing notchfilter I t2 26rnt af a Drawa signalflowgraphrepresenting thedynamics shownin theblockdiagram b Howmanystatesarerequired to implement thisfilter c Assignstatevariables andlistthestatespacematrices A B C D d Usingthematrices inc re derive thetransfer function Showall algebraic calcutations and steps Youcannotjustwritedownthetransfer function astheanswer phaselockloop Consider thefollowing dc motor speedcontrolsystem M oh Referencespeedcommand L 120pulses sec Kp 0 1V pul se KA K Ke 1 N 1 tL e lo S l olss r l l UTs a writethelooptransfer function 6 2 b Sketch therootlocusforthissystem gainK fortheamplifier t t B n of K whentherootsbreakawavfromtherealaxisandbecome T o ol l l lf d For r 5 computethe velocityconstantrKv e Sketchthe NyquistD contourand Nyquistlocusfor this system l4 g 1 3 a Consider theunityfeedback system withG s 2 a 1 Sketch therootlocusforthissystem a 2 SketchtheNyquistD contour andNyquistlocusforthissystem t vW r Page1 of 4 soLoltoJ Frd E xaM 3 S s l 2 glr E r txrs L i f zs rts urr Vt X r rtftx a wY X Y x t z rrrs x 5 b t Aslbl s1 1E5lD odlrrjToF rt 6rsvt x xr 3gJ x L Y i d l0 p x u r x r rsu t tv 2r l1 r Z3d f f o r l o l n l r rs I L l c el A ls L l tn I t sr ri c zri o 1 tr f srrsur I st aii B 2r rl rgd s Zrrr e rrr I etst A i D d 29 JS zLdr 4 ED I ELLS E xc ll n 6 c r f ttr grrr SPEEA BOEING N T IA T IV T ch n i c l sl I I 1 l L c sr de us st I s sr u ira g tStxr url I c tsr rs a o Y Y P A RT NERSHI P B oeUjt z 1 2 9 0 1 v p Jt j Ot k K Kc l o N l lo s 1 o os s l q T S t Ts a r0tfE LTtr L ArbTD t K N VgblVs TI u o r l fo o r4E r z r o c c j I F O o l s L s t ooss L o o t q K 5 1 r 5 o or o os srzo Lsr ror l K L O b L b s ZgK s ll s s zo 9 roo u l I o too 1t h r r 2E s r K tt o orq s l o or si o os 2 3 3 1 r 5 s t r o g r o As r totoftss A ae 16i s f o ol L b Lzs q I js 2 0sr2b s q o sfr s rs q3r lttos q rbooo s r o za s t s 1 2 9 r 1o 1 6 c a1 B eaur s lo 3 l K L O v 2 l L 5 to r ro rt t to r tro 2 g r o L r 1r d 3r rge H I 0J HAua uN N F5 o6A c K 5 V r 0 s6 Q 1l zt s s rrt l E b sso f zJ s i Cstlo J r o qr4J 1 4 la a Ca ca ll 2 p r I t It if a T J r V b I tb tt V t OSCTL A 6 0fi fi 4rtt Up1 gBo FK I Spring2006 K A Wise FinalExam r i i iI I i la 0 1 xl 11 i l ustrateonthetigufethecM GM anOpfvf ie re O curveb a unitcircte tL QY o o 7o u 0d G ffifi i i iy X 1t t 6y 5L eD PM trP 8 630 telowthetransfer tunc ion forthissystem assEen fromrheabove qoo fr lf r taro rrrrGeruoL 7 b T D atTU AXisC ISUA AenlS AO g fh tR s 6ta S ru opcyOuE lco Cnasso ra Tl F tggeaar0g c u1 15 trrr r1q gVsNM rs dptrr AP 1 r Eraag Page2 ol 4 Spring2006 K A Mse FinalExam l t 5 1 lllustratE onthefigurgtheGM GM andPM Theredcurveis a unitcircle L cM t4 0 GM EL prur ton tll 8 CO D cribe estimate belowthetranefer functionforthi8systemas seenfromthEabove Nyquistlocus t 1 6r o I 10 tNTEt wrDn w r l tbf o l t EPu E s a O0BrJtof sfB I P fi o 6aFr Ml bln rs Pege3 of4 N0 F XIS CtuEsl ro Oo 5 lJjsI gar6 ALLyAYSg T61F tJq rfu w K A Wise FinalExam I 130 226 G M 8L l0 ds GM r o r 1 tu r 0D PM 6v 4 h5 9bE s t DEscrib6 e3timate belowthetransferfunction forthissyst6mas seenfromtheabove BodeDlot 6 V v o4 b Page4 of 4


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