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Stability analysis using Routh-Hurwitz Criterion

  • 2. 7 -r- sJ rS AT COMPK in
  • 3. "tD;t r;tclio o * Lern i I dlte?r NC : /€ he:l. Qn ir) rrlr.b O o Tqh h in th Tf ejJ rrern&vs t suj4;r ;e n t g^r ;s ti fa the the Ch Crite'rriQO Ch d.ho cte ?f t Fts) €- gn ,trfherfe Coe eca :n Alt o'r-.[-d h rnatio n l+ io h ha,l od +h nomf
  • 5. ? H c 6iterrioo al I in r-be .l+ / r ha-l fl - Lab u latio n "o ,] oJl- Lh Ftn hr z the s[St 1(s+-z) +-r = rr 1[st t) (stz) _ S{ *+r-s+ q+ z) f 3 = o - a .l- :- ,4.s +ae-ru a'k no Sf 3
  • 6. T- ---- cornnne nL olStAbj4il f 'uite'uict, if +he Jb 'Z-F1oS L t>;bt- 5 -1)(ro) -[t(7 =- < 2, J '----+- t__ _J t 3 ,L 71.-ls 017 I St r r ,-o -=----
  • 7. I TT Ca rl T c '-l he 1>r -!- {7 --<- ouUh tctb ioo p)aff1€ 0 Lh "J coe oon- Z CLfO ne9 rtb f{it De e.'T m il! + 5 q-r 2_ -5 =- )- 2: t = Jr ir f -=L T( €s k 7 l-! O -> ; L>L e)enent rc .-'Ae Qon-zeTc- f f", . t otD -ffri: f o s eci -u de,: (i t-{t- -g-c e e rl r'lu" e-;v-il9
  • 8. -t __ o _:- -L 9e+ 3 t t t .D ax lf: h{ e )<- .--e.-< Qn F-- t -< -Thr ,:,rJ iS u'th bu
  • 9. on th -joe _2 7 'I- L L L Z __ 25 S 5C'= -2! -5 = DiVi' -25 L .-z L ul ion the intJ U" O a t,/Dit_
  • 11. L-6 = -3t 3'| I L'12 :Q 61^ s S s2 rtil +h< ala-lrrL ?al cat he Q.u Pa's = aC4s zsJ=O 2 5 3 j6-j:/ -g- 7 ,'u lsitit{- n (
  • 12. dar =L L .t >- b a-ile or eo tLs o bz b=z - 2J ,tcl Yite rpotS : ----- ./- 7 -------- ? ---- -_-_ + = -2 T L 2
  • 13. t L -- ^ + o tr rroobs 2 t3TT iS aDeflL o n t r q srd-b rA of) i_s; 7 2 6-71 = -7 tl s iri I t 6-S L 'g T?aht
  • 14. not e r. ' -v]^ o 1gb uth' d;soo I paharneK?r c-o -ld;;
  • 15. 0r) I q Dh.L)_5K b* +IY ri ?r-io o *o i'0 D'. "2)*5 K>o '17<z,z6 - a< Sfo q CT itt?r ro n
  • 16. ;+ inrli ate s th C.to" 1t 0,25s =C
  • 17. L+ o"qt)(t +o'L53, o"z5s t- e j5 B 0,65 .65 3 Z L =6,5 T ---*J ,, ( I --06 o ?'-D o "65- 'is aq o TDuc__4 =O 0,65 n- I
  • 18. o,€5 -5-o "' O"6 L= -68 = -F i3-x62= iVEN J 9tc ,'6-l o"Las S K S'
  • 19. 2-rK -f rt9; o ztn=-U -_ a tK ztK T =O 1 ,r cD= L ra/lct c t ) KtT T p.
  • 20. K Er__ Lirnitqff ;d on -f- rr ,'r) )e ! L--Da-T', L -o.t Lonna
  • 22. - jtD io tb-< 'ha-hactqJU 5* 331 ZS - 1 )' -1 3 a. 1- 3_ 1) + 3 '+ -J-2 Z)L '-) -r1)_ L e + -_37 3 a , 1-- 1 U
  • 23. >oab e+o S) = qt -L =-F o-Ya hc| icl z - 7 -.r"n" D+ Ti Zs-Q = 21= i 55 J:-- -@ 2 "L I F,rp"rr q1 ?rccd L4 t,/ Fronn o -Tlr 3" 36 a)) 16.9
  • 24. Locu s ; c.-I) sSi b& cne o -L-he -!,". De (, -4 t,'l P" tr tni _f Ih ide h e 70 o_t5 h art(K Roc oLTF =. ts) Ht i> c(s) cLT F = (s) rD rt (5) K J Q= S s(sr
  • 25. ,1 ,/ gtr Lf ct cL> 9 :n _(, = 2rJ -K =-2 --vLl-6 DC"te J.c uJes ,1 o,.t, -*2l-j+-Y, ': -2 t O tc c^r - L<- Rcal I -J I jl 6 -2 - Jtu.2-- 'rla{ Z Si = C.' 26+ lf@ ' f---- : 2 T-l icP
  • 26. rh oJes -r, cJeq t't,, rlhen K--1-1 Josed ho t he P oJ es a-e TeaJ | ^l tejh e O dh( o S K<ce, th ni o-les- a>re TtaJ I J es a-he Ca 'rl : t :! LrcLt S te JJs Lts h u llas rr)c,,/( i h 1* C slH(s) '= US{
  • 27. ft(.:-.li-l (s) G,Is n oir- c,r-r ri ifr c'n : ri cr t l-L ruS tC ( _,( .i- A -Lf <-/ - * l'tr /c / 't/, Lf' I- zti tt 2t
  • 28. OLT F v cah; o o '=5 {= 1-e SI SI he j;, o th TO 0t g i'o *L =7 K :7 -i-5 -L5 t 1 + in *t + i TL Y V<n steJGr
  • 29. /)ro 't./ | Iil-r -R urle r : lbg -:{c,r' t l*_'c uS -1--gto R tr-X- +_a: i+:---L: iE ZZ Ncte ]riil lcci te rrn;na? ?r ?enJ c cn tdcl nrt 1R L Rt- --T- Lt-[ j
  • 30. ints' *l A ToDb }CIcU QNC] =& Fq - Zevo ^d =C -I € nd T DO 0k (4 | .t- Real c c LTi= CT AL CA, -[oc i s -[oc nt-l mbe -z bra -r hr .l -rb Le-t r-n ort< to q2 c tcs ,"ve S b-r I Z -7- 7 SS" tE "o) 7t( h 6 vc= ->P=Tz 0l es Z<T CL
  • 31. T I '6{r)ir-le b{QaFc+4 clr i[3 6ry1:4ur bve 'F, nd -the --sdj?='- c hatr q c+ *'r ;st-ic E g n " -'-- 1 r q(sjHrs)= 1,)rsf 3) f K(Sr6):O );.: 6(st 6 ni i- Lr l p(1J--. ,--!-'A /J =_t3)
  • 32. LrS f3 T2 IL|j $= -2.L '{S be ttr-, = :1a, bz bet-r-o ee n Z(YC, 7'-LE: -: JeS lo ffi (n1< )<sve 4 ?rDot *cci cn v c I CLI Qn CLN I9c' ,-S +h e nu o f rrJt Lhe bt e cuL) oi"Q cio
  • 33. r{ - __ -Lc--r he ?iqht - h, fhp q- cl} i'n is ,.,)t 'l t rt( Ag-hcl t scun th Cc a>t'oqCt tht in < th r-k E rrtoile tocrh C{ar-) cL ) i'Ot ! ;c nS , Ar, hei 'L9 ? A-o'ra ;n tt D Sr'Cf; Je- s )t's -' t.r > l-hgl '-Ln qU t ht I ar)
  • 34. 74' = (,3clri bLrh'Co S 1r-,o?,ff D'b -5ol RooL, k! --t ;nd ID he Lhe otbe t b'tartChr S !.nci : nd, 'd r_f' c ; cil +il nb zeus cn S r'troo 6,7 Ir € n, h ! t :C) lbt ju-/ ?'D S --1 I *'-{ I Ia -i t I i e red (i. TT t^V brJr't an
  • 35. J'.c tancht S(S+3 (sf 6 t AE S=Ar-3,-6 -Ln o 1!o -[oc i = =3 <z RL *> ; :_*{ K=o -b K: o oJe 0n the_ recF <> --- AS ghoorQ iQ he b cve . -t-- l A a_ / r a ?-r.(Tl = -b LU
  • 36. ) 19D : 6C)o e= 1_)+I) tW g' 7( D+t ir-L .'ji/ n.-' f ..^,j 'S t htze 1 9oo ri It Is K {s.r3)(s+e J t€) c
  • 37. sf 7 g L +:gs' ,) - + Jgs r j g I i + +- r> <> <t b t-c t fS th noU ev i5 tic =O s(s tg(ste K .- LJ $- -I"27 .pbt-ucrs-co + G, Sf (2 1g 8s i xloLL) >T rn A Rc,Ufh
  • 38. ind TOGJ O. rq[l)-K = o -., d; t( -K: O .-- | F'qT LCL= C =-16L nsL ?r2Q) t) 'l- I- 7 he' =aGZ R> L6L fuc,r'