Spring 2006Final ExamReference speed command ,L = 120 pulses/secKp =0.1 V/pulse, KA= K, Ke=1, N =1.a) write the loop transfer function 6.2 l+l 'UTsb) Sketch the root locus for this system for the amplifier gain K -'. t t{B:l#l|:lf ,n" "","" of K when the roots break awav from the real axis and become - T:o.old) For r( = 5, compute the velocity constant rKve) Sketch the Nyquist D-contour and Nyquist locus for this system. l4:g 1K. A. Wise/--\Open Book, Two 8.5x11 Sheets of NotesI j9 / con"io"r the following notch filter: I\-,/ ---+a) Draw a signal flow graph representing the dynamics shown in the block diagram.b) How many states are required to implement this filter?c) Assign state variables and list the state space matrices ( A, B,C, D\d) Using the matrices inc), re-derive the transfer function. Show all algebraic calcutations andsteps. (You can not just write down the transfer function as the answer).Consider the following phaselockloop dc-motor speed control systemM.oh^ -'_.--.----tL-e^lo-_....'- \S (l+olss 'r3.a) Consider the unitya.1) Sketch thea.2) Sketch thefeedback system with G(s)= /2.root locus for this systemNyquist D-contour and Nyquist locus for this system.\tvW,"-r/t2 *26rnt + af,Page 1 of 43-S-,'f,* + z s,rt s+ urrVt X-r^rtftxY' xt z( rrrs'x+'tc (sr-de 'IeAslbl s1*1E5 lD odlrrjT oF (^rt-6rsvt!x,= xri."' --'d, - ?3 gJ"x.L + Y5b)()= -2r,.l1.(r - Z3d'f! +Yc. [zri -us,,.,]l0;?. -,p'x, - u-r'x.r -rsu:t(.' tvf o r-l .- [-o.ln'l-,r-rs", I ''-L'l-tr- IIslc) el-A: ls -'-lL^" .tn, I{sr-,ri{: t f sr rsurg\+ tStxr url IL -."-!-. c tsr-rs\a +o (st-aiiYI*[:::,1[:l-[:l-rgd s -ZrrrB:[-rrr -2r.',,][ rl ,- \',]d -29 [JS - zLdr4ED \I/ELLS]N]TIATIV!ttr..grrr c *r,fSPEEA-BOEINGPARTNERSHIPFrd[| E-xaM soLoltoJ! -(,!s:l| + 2 glr)E-r+ txrs-L ia\wY'X(st-*\': Is (sr$u\+ira[":"o= [,1e tst-A-i( + D :T€chnic.l Exc€ll€n.6B.oeUjt^z_Ot"129:0,1 v /pJtj€k*, KKc:l N=lloL. \'TIlfo,or4Ea)(r0tfE LT tru. o.r (VgblVs ArbTD{t K?- Nrz- / ro \ c,) c,).L s(,t+ooss),/oZgK(s+-ll)s ( s+ zo\ (9+roo )s (1+o,oss )\+ l,q TS f: o,olt +TsK ( tto,orqs)j ( l+o.or)( si o,os))I FO.olsb\L: .(o.otq)K (5+1r)5 (o,or) (o,os) (srzo) Lsr-ror )l{-KL:O L: 23 (3+1r\5( stro) (gro")As\r,totoftss A- ae;-16i. -?o-too - (-1t)h-r,r L(s) , 2E (s+]r)b(s) s( q+"o)(sfr"!)c)a1 B(@eaur.{ s, - lo,35b Lzs) - q I js'+2.{0s r2b)- s(rs'- q3r(+€'- -{'?'ltto s - ?q'rbooo(s +ro,za) ( s + -ts 129.r)- 1o.16-l- - ( -to,r.)( -ro,r t t) (- to, r tro ) ---lu)Il+KL. O v 2L 2g ( -ro.L r1r )d) 3r 'rge H: I , 0J€ HAua uN,N F5€o6A{!c. K: 5V,r. 0,^ s6. Q^-;1 l- zt(s)(s+rrt-lE>b sso f ,zJ( s+i") Cstlo) Jr {o [- ) : qr4J(14)(la)): a) Ca ' '/ca(()\2pll-rI-"'---bItbr- V:'t:-\It?if:JaTttV',**+t<OSCTL(A{(\^6fi.4rtt^. ( !0fiUp1-gB o,F KISpring 2006,@rtLl ustrate on the tigufe the cM, -GM, anO pfvf .-?ie re,O curve b a unit circte.t?-5LQY = ?o\o 7o* -6y - eDPM = trP{u,0 dGFinal ExamK. A. Wise(s+.\6ta)'Tl.(F tggeaar0g c'u1 15 1,.r trrr.. r1q:.ffifi:i"i:iy"" telow the transfer tunc{ion for this system as sEen from rhe above-qoo fr.lf{,€ }'r taro => rrrrGeruoLX1-t-7.-?b &T !^,> (D [atTU AXis C^ISUA AenlS' $^,! AO\g fh tRS\ru€ opcy OuEgVsNM rs dptrr\-lco' Cnasso,ra,(AP Eraag-iI---.-.,-. i .-.i-- --.-i---:'la" "' Ii -.-''-'..0.1-x l.-' ,, "11(=.8= 630Page 2 ol 4Spring 2006l*Final ExamK. A. \MseOo.5\. lJjsI' gar6ALLyAYS g'T61F;t.51lllustratE on the figurg the GM, -GM, and PM. The red curve is a unit circle.t4--GM = -CO,'LcM= 0)ELprur = ton'tll)' -?8'D$cribe/estimate below the tranefer function for thi8 system as seen from thE aboveNyquist locus.t 1. 6r-o I - 10' =) tN TEt'/wrDn-w-.r, l. *tbf =) o^/? ,,l$t\E Pu€N0 F'XIS CtuEsl^ro(E (,s{a)O0BrJ tof sfB\€ I P@fi\o€ 6aFr Ml^bln----.)-------Pege 3 of4rs tJq"rfu"w*GM=Final Exam{ 1.tu**r r''o-r-GM= 0D PM=K. A. Wise?; -130I-2268L.l0 dsh546v."=9bE *s t\DEscrib6/e3timate below the transfer function for this syst6m as seen from the aboveBode Dlot6 V v-"o4 b)----!Page 4 of