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Acs Module 1

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104 views88 pages

Acs Module 1

acs notes

Uploaded by

josh joshy
Copyright
© © All Rights Reserved
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Tnibroductton. fos the canolylis cand design of Joodback. aystime i ok fecus cod frequency eopense. pmethads , the | ding Ao Peepers oP / | [physical ystems sequined to fo. erodatled i. the jor | unetion . Though. Eke Laannfes Junckion. model provides ws i ‘4 Brenner € Lasts nimple cand pewrful vanabyis cand design tedwiques Ue ()Banoper panction roundel i only Lappplizatic te Hineas fime ‘ineasank Ayetens | [f) Tranofer Junation model in restricted to egle “inpt | band puk rysten, « | (i) peer nok provide. ef the pystern - ~ ot ook docs, cand. ppequeness clometin, methods Raned on transfer furction prod vag. efantially Lsial cand exon, precedes “Buu protec mm no: of inputs oyytern kadebar ony bine Lrstant 6s . oy on tfeutt to Viawalige cand oragange eet Jead be option poyomene ns vard may cok ; he. stole ppace. Variable, ip o- pourerpul cand idestqr © cconbiol pyle + hnlqys Med Gk & applicable bo cang hype of pyster- (ia Jive cand pon-binces pygptems ) time. Yertank cand Bina anviattant fyploms cand reulliple Yopuk cand ullfple, exctpul pagetored) HT. ceon. be py cued writ jritial vconelilerns the Vaitattes ocd to deprisent De aystern ccars & cary Matiadles in the nyplers Wie internol statin of the aysleer cok cous nakant cca be prdictd . he plate ej diane aystin is valptinirais pat teh that the Kreculedlge. ©} theee. VMearrables vat ether Laity ue. Knewledge Of tha inputs ‘ Lcompletaty cclatiarnines the. Gehaution® 9) the Ayptain for Lio: A nok of Mariailes talteh cdeseribes the ayptern cak cealled Ta the tote Variable for 2a, pystern in Lopro.al consists 8} ro inpuls , Peutpat cand 9 —nlale Vasile Joc, Mate. Vasiablen — ser) 700K), Ben (ED input Varraflles = UCD , Salk), = +--+ Umble) eulput Variafles — SD, Salkd y-- --- -. Geld The nlate ppoce Aapreoentalten Of ra pyplere mag Me Ninuoligd 3a Glo cdiagiaro foam var Ahouire felew . (2 — poe, So Cents) fr a ve Gatel y enti pore Tver le v Ayptes ied so 09 en) "5, © nora, Alate. Variables POE ae The. .cliyferent Mariables may Me atpaerertecl fy AB)” \ aha, 1 Neelys Ccolumn male) vas shown holes. | 1 Uw a Anpat Mute S f) & | nt ueey= Just), te}pee : ‘ 4 ° _ Veto Daye + eden Y=) iO ; Alle Vacate x (=) Sait Veal pio) i .§ I. P| t) = . S Site. Equations 2 - one The pictorial Aeprcventation 4 the Atale. medol 4 the dyptem. ip walled plate ecliaquen The ptate. claguam a be ayn coe & nse eC fom ein argnal flew geoph fom She late ecliagrarr Ye Alale. medol is censlud using thee, facie clernents Sealar, Chelde, cand Trlegrator : aiptero Known vas atate ¢ , Aealas is wed fo multiply va. signal 4 wconstank, ~ ae * ¥(O) sa [| sax) Adder ir used de cadd bea on more dignals fa; the eupat of tha adder in dha ures g dncering Aignols a x “® axl) Xa) Xofk) iL Tntoqator is Luved to integral dhe signal Trey vase word be inleguale. tho douche tobe. a Je up tho alate \Yoriadles » The initial cconditions can he Adedoel using van adder vofles integrator . ® (D x Opp OG once 40) ) Che Bleck cliagram vand nignal, plow gaph, Aepcrentation of Abe Ayptera, in dims. vclornain in Ahern \otoxo . I= VED LO ® Op x ¢ oe =) Se © gs lol Lew wap ef ala Consbusetion & Time demain Alate dhiog tare The varies aleps jor conbuuching Jha. state | (FS edad A nore integeatou | fh poeue the input Je the lstegiator as fuse | Date esiables cand wo tho “oul Alot Vaniallles » (i) The plate Mariables cand spel vase rultiplisd fy appropiialt pcalas cand then vaddod se ge He. five udoxivative & Atele Vawatle. . [) Neo, the fink ederitetive 9, alate Variable 4s give | vas unpuk te the. Ucom, ending intignates . Bimillan | tho input of call other inlogtatos Care Haired Ly ennideung the tate equaticns ena by ene... J ) Lock culpek equate. ie ef lunclion fatale auc wand inpubs . “Theufose the Btate Yartatles cerned snpuls ade raultipled ys vapprepatale. acalatrn cand shen added fe ugk the eulpet: vderimadtives {pak gf Me integuation vax {flores - mY _Apoerilee! ay dhe lala. priéelol « ayslere Jo ~ oo Oly 7 Xy o © 1 \erala Uo and yn Xs 0 A 93 m3. Paces the Glock scliagram vane aignal flee quopr g the ' | igre! feo geoph | a o> ~ y v an Xe=¥p B %Q=% bx | ©) Prase the Bleck cliagam cand dignal fine gieph gf Ye luster ucleseriGeel by the slate prteelel - EL EE EMER a= =, ° @) | ea the plate. medal cand pignol ple gaph duster. we 4s tho. Block einen hoon Sap Spe ee Y Toe ["* | | - | “The lol late mada oy Of Ale. given ryptere a; SE: ZTE: 0-9 Sigal flow gteph oye OL te Q ee the signal flees gph a the oe [2 Zab oli [ie tend yf x QD Do Me signal {eu ga 4 ; Ia aleke re f ph the pyptem dercrileel by ao AQ ag olfey l =| ali ° \ ck | uw and Y= 23 acy ° \ © ls 0. a ae 7S ae Grunt — and | > Voltage Jo jhe Ry, C elements “he prygicel Mariadls of mechanical ryploe Laue, > Displacement > Velecity or Accoleration. the vadkvenbages 4 wchesaing Pphgpicol Vaiialls ar stale \erialles vere; he only isodvantage in ccheesing phy Mewalles var the slate Vauatle & that the Asluatlors ¢ a [eore va clifficute claak zsh yp Le. blaine = Boole eae Gen oleclual Aystem ean, a) J 5 oe unclamental elements Awnintors, indtreton yecpoctbns Untng these elements the ‘electrical chant Of the ayplom~ in ediawn- Then the ychfectial tation gevesung tha yslere ean he. joarned Gy Sn \MEulous noclts tn She nfo cand aa 4 “choosing \awour clone pols - iw aK ; VOD=RED 5 LD vce NX 7 / —__ Won . » ie ol | > voids Ld fis) j (= TJ VG de ae 75 SL void=L finde jito-c sy (we) | Sep ' Belect Ihe induefor vceument cane veapacitor Voltage. ry stale Variable . Sep 2 Apply kel wand RL do the cele vane Cbtain creak Yariatles (Voltage cand vewuent) - in terms ef rlate Yariafle « kp 3} Beloet the voll . Lage OF CLONE td energy dispoking element (it; avointod vas dhe eulput - BRellarms @) Olttein the state medel Gf the ayitem shown in Jae 00053 _ +e ae a foe iy 3 en ig = 3a Ve = 23+ SCE) = ULE =U ‘Apply ita to Loep - | =e 20 ry Ry $4 di “Ve =0 6) U —-2aR -Lyce) - Qe =O U- eR) —203 = Ling =q = = RI 4 ' Bee ee tT ¥ —_—7 apply Kut te _fesp- 2 Le 7 [aeq, Meee fe. = -lg om — Raq #28 = © . Ee axa +a fe. ptote equations axe; Gq =a Rk a yu = ay xy Ly feed i? Li yy = — Ra _l os, = Te OR te B= aa -24 = Jak us choose the crunk though & vand Ry vas dhe oP Variables Y= ck through Rady aot a = ck thaugh Ra = is = Sh stale meelel do ; ().[3 = Riflt ° —4, | Pa u | eo i “Ro “ig salal 4 fu Ve “Ye o |} ° BLES JE] Tee QD | Ebay the Ale meelel oy the electuicel relwvork phe \in dtgeae. bay choosing VCE) cand Valb) van Aleta Yariolt & val) wd An __ cl | R | eee | | = Zet\\ Vile) ==41 Va Ce) =2t9 weed =U Apry_bet so Wel sak node VCE - | y pi ok a Wile) =Va.ce + edn _o = a Mi bo c we _ Vat ae dy 4 ° |» 4 TR SB toy =o c= -¥ te = ke 1 + Ire a — > @ Apply Keb wt neoecla Voli oo vwtD ed : OZ PR tn — Rk ° Valid wi Sa 4 einen _ de = v — = + 32 oy | R “Rp tome nzo “xX = Re-G --2_ Fe Re a | She Slate. dio, LCA equal d ce = fre 3 + Yee Sea ° \ | SQ = Yee og - Bre a + Vee U 8) L fot the oulput Pe the comant Hough too OD neriatow My Valtd-VOD seo R —_- Ya = WO fhe ntate mredel is 5 SEIS Lh gic ip tig = c_dus “aE~ ato ce Bey = Yo + Vn a Arp, Hv vat leop- | #1" -ti dit ys 20 —2® U-S4R% —L sy — 203 = 0 — R cy) (Re Yee | ¥ Je = la Vy Ce —tee=| +o oy 2 R - —_* at = bree + YU Apply Kt vot loop a fie —________ Lg die 4, ig a —Ga 4Vg =O | ——7 2a 2 +50 RQ Ug 420g = 0 | | de = Re Yin + jhe = — : The. ptate eqprections sae; = -R a 7 7 TO ee ATU | > = -Ro ! Ta ~ Tyo +G Ua Ye 21 + Ye a 2 = | Ew cheoya the Volloge vactoss Rand Py won the ofp equation » | Sy AR = sae | Yo = jee = ~raRy “The plata mectel is; -f Oo ~My \fey ‘hk, 0 GL Te SEE SE o 0 Q)|Oltain the atate model ef the electrical nelucoue = hao in bigness - eo eT se Ye wo Te Te] | Solution for i74 ip =a Vey = 2, Neg == ec = U(ED=¥ Apply wet cal nexle & : > _-® . L Za j ig = Ca ave 4. Veo. de Re Pa — St = Om Ra oi = Yea a7 igs 4 — Hep law 40 jist leer 20-1 Se —Vey = U - aq — bys - =O a4 = acy = Yaya + YL —® eee ty ¢ ly q Apply KUL bo zecend Loop mani = ty dio Vea +e = © —@,, ye, ° eT % elo Se — Hy + H&B =O —— — 2 = Yg ~ Wey —=® “The Atala eguatlions vane 5 ay = oR cy - glo + Yoo Ly Pa ig 2 - Vba ey = = Ve,ou - Ye, 2a sy = Yea ea ~ Roca Lok the output YC Be the Vollmyge accom Ra. dey Yo Ven = OU: Rif, O° yy S “se ’ I. ° a} Yio “Yo ma 4 + = | : Yer ~Yey ° o WI" | 5 oe 60 wall) Lo Q)\€0 2) taco Lhe — Meelel 2 the following lochidD pypters KM See) val 4, ce i a ‘ 4 c te 4 BPR ‘Ve "| [ a Selution ENA 1 bbe Nog FOO. 7 cote i ay a foe, iy = 0% i /\s io ig => 4 ae Ra Ya Vv SS v na Vea =u Apply el vot node ig tea Mee, Ae ve ey = ty FEATS Oty adea-ag eI Appry FUL to leer ~ © Hyd Neg Ney = 2 “St fey Nev ® e1ysq — SH $5 = | sae Yios - yu —=@ Apply Keul lo feep-3 ew ee -1a cig io hy + =e 2 Sf — be 4 Veg La ag - 2OR242CU = “RZ, ot 4 Ya wy 8 the let. equations vase ; ala My ee — Voy 208 Me = Rah, Xa + Yha Hu m= Her - Vrycp o> bu xy = Year - Yeo Xa fot the eutput Y,(e) Go fhe current flewing fiangh wack Yocer fe Me cunts 018 (ED) = Uae = A - Wl = ig = oa + The. ptatt. modal is ° ° is o) jo -}o Rho ata |a)o ky 0 “ne a Vea ~'leg wes op ®) Ola the plate apace, medel af the escheat nts IO) ‘ Isheon éeleco Rte heron belere L ou - | Aerio es Solution. fl iy=ou | in => | Ne => =| je@a =Un Appts kul, wl dosp =I e-iie -AidiL ve se ——7O ae wR Ve = Udit Ler iR Ve ioe (Up-caR - 33 =L) =O © p= Ba — yea FY 78 stppls Kvt to leep-& la dio, ~ eg +Ve =O = cu | 2 La my —Va +e =o Sg = Vig oe + a V2 eps vob wate note A ip tig = We So “ae 2 | | ma tq 2 Oke |. dy = fe ou + bom © The Atate equations rare zg =" Rhyoy — Yyseg + yu = ~ hay + he Un 33 = Vey 4+ Ve xe %. ws" | fet wy choose Ue cutpuk vos the Votlinge, vaciass R. jo, Ys Rr =2R Me. alate model is sa] (8/4, Oo -Yrl foe Yo Pa Ye. Ye o {Fs oo y-[R o af xy 3 —— Chicin the slate. meelel 4 the electrical Ayptem Aheor Lele + 2 Tye Ss oY yf ALcliben Ae A? ; Y ne 7), kee ip =oey -®e& Bs ov Q- Ve ==¢9 <0 Apply Kel wok necle A - Thies w Si, — 2 We -(Yegie\=e —O cle _2s 2 10. =0 S-2y- RO 4B HE sey at! wd oS ee =the abo + a 2B Apply Kuk to dest Leap 7®@ He -10 +3 cli ole +25 10 435 =0 | =" Y3%Q +10/, —>@) Va ek oa a o The plate eqitations care; ay = fara + 10/y ay = Yo - lea + '%e -Sfe fot the eulpuk Ge dhe currant flowing Amough 40 |Acoialon + Ye We atlo 2 -ve 4 zy | +12 = a 410 ya The. atate, meclel is; Bp [Oo — Ys |) oa 7 Va © |f{to ce] | Ye Ya “le Yo | Ye[o m7 fy lo | Ek Ip] ) Find Me inte apace Acprerontetion ay te ccseutt shexon Biles Tee Vs cad the input cand ise vas the ofp. bk in | = ap 4 cde | 2@ = Yor — Yee > —=@ Apply RvE ee Ihe euler Joop bNa -hdil ov. =0 ——=@) | a | Un Lay, - he = O U-ssg = Lea dy =f + Ly —= © The tate. equakions vate; Mya Yo + YU Se = Ye - Veo we | Giver Une: the fox Cin, curseak Auough © ie [Be output » Ys ix = Veo oe a “The plate medel is , ERR SIS: V=[o va] =I | PS] a a Q) ovetey De plate. model fos the nofigone chewn Lolo . of aos" i vst) iF =F Wi Se Bolalion — rea none ist) Men S00 Z(t “oO IS Vel =U 5 1s (= Uz dipply rer at: nee A Soop = OG yp oca 4-9 > @ sippy vL lo Leep | Ve — bit. +Ve = 0 -® Up = Lay +o = 0 “Sr = Yea thy, —=@ >® (~~ Z=1*) The abate equations axe; ay = ak BQ = OY - fy +02 Bp = MQ +, | Zot tho eutpuk Ge Voltage cress fr Asaiator | J. = Vo = 90 the atale medel is ; ell fe oe | Nsfo i] fy [2 —— ———— Q) Ehtain the rae medel ef the circuit shove felow » iit = ave & vO Z Solution he i= Ve =-0 VED =U(E =U App y kel vak nade A Ne 7 RQ Se, LL VOL) Ne at Re 1 J L v Yaa Ry | i ‘ | Ve + belt +ika —O ~G) { ate | Hq +L oy 40h =O i Fd | | | SS ~ Roy, oy + Vp =e —=@) The plate equolion in ; sy = “R2f sey + YL ota Pe = -Ye sa — Yer eta + Yew,V Lee the eutput Ge Vollage acer Ri and Ra - Ve ViED-Ne = U-5%Q Ya = [Ra = ocr The. plata model is; Hi ew RE “le-Ele oo ) Blain the slate pesee morte of dhe ayslorn gine Belews Cohee OF 7 UR care inpubs cand Moo Me vdee eutpue h Solutio & A & by, Be We le vo Ne ERC ua | Apply Keb vk acde A iprig = ode _ SO ce \e, oa Fea = OOS oe HY Yea 5 apply FNL Ae UL. to doop ! 2 _—_—=-© vy obi, 11 “Ra (i) ME . Sey Rq — aha 7 =O ie, Uy - bit — oR , 5S us — sey (Ry tPA) — Baa HT \ at _ RAKED =e —2. xg Be Ta ay 1 Le Apply KML do sep 2 1a stadia Ug vNe +P Cy +is) =0 =) jos Sa R, “La tg — Ug +2 + Ra (oq +268) =O Dia + Lacy —Ug +203 +5e Ra Hoa hh —O 2082 — 22 (Pe 2a) —0%+V2 dbocrn | \ . Zi _— (Rat Rs) ia OO ee ry u —® Loe Y= Ry soar = ® Nase = ctafg —___>® Ma = (ipiad) Ry = GervoeRa = Pade + >%— —=) the ptate equations vars; og = ecu t Ya ora a = Re — (Rat) el a pe > SB ora ~ Ta ta + Ua, —Raiag ~ 1 a, 41, ZTE SF hy Se) = (RPS) oy, cy “The plete model is; (Rt RED ast =! - va a i =a {Ps yo 1 . Vv tr | - | Re (Rat PS) _y diac f ay ‘| te Ta bglF@/*]o Y, n Q Se \ - fe Vo o || od (=~ - a Ry ° 27 fax Ya} =| Ry Ro © || =e Ys] [2 RL 0 | |e Mechanical Translation 8y,tam. fase merlel of rochanical thanaletion dypltin ein be ebtained dy using thea aria clorrerds « Pood, Spring Bash - fo when wa force. is capplicd Lo vo rrechantcol ranslation ayptern ak iy Sppexd Ly Sppering fesees due, to meus , friction vand elanticiby of the. ayplero he. dijfersati equetion “gevesning tho. ayer are elteuned Ay writing foe bsolanec, equakiors alt Yarwous neeles in cle pystun. R. ecociixe vopplying Alate Variable nethed for | oP Ninel tartan Ayptars « r Sep 1 fox each node in the pyslem ena diyeuntial | equakien ean be named by wetting Lhe Pum 4 applied fore do the Sum or eppong fo Step 2 t Amign displacement ko each nede vane haw 1 fie bedly diagram fo each nede- Bip 7 Fen cach peatedy diagam rite ene diffeuntio! equation hy equating dhe sum &! capplicd forces to dhe pum &. appoeng former 1” ebp y+ cheese ca min" numéer G& rtate Wariables The, cchetee, of alate Yariables are clinplacernent, Velecity on caceeleration - Zep 5 3 fe physical Maniables in vdiyfoentiol equation wae, teplaceel By state Yariates cane the eqns vas. rccaranepd Tar 1% opeler ah fevordval eqn. “ther. equ. .cenilttute the atate” eqn of He Alm. The inpubs ate cLappoliod pis wand outpals vee, displacement ; Velecty on cacceleratiorn 4 the edurite! redoo Siep 6 | ‘frelems : Q) Conatuct Ihe stale meetel ef mechanical pysteme aheor ov & o io ly yf ts By Faghedas scliagore ¢f 1 ee) - Mi “By newtens rceend Law, the i Cc balance eg. iy - PCE) = Froy 1 + A =O “ 2 d ju =e T Sy a Bide (4:43) + K(Y-Y2) | ato; + Gy - ees ky KYg ry bon fructedy diaguan 6 (fore Lolane ean bj oa -bfba + fin + fea 4 =O =& fa [roe Ee 4. 8) St (ei) FORTE \ Yate HM (Yo-¥=O “nog de aye Crete A _ o TS 4B) Se - OEE +8! 4 kas +E Ye HY =O 2, mada 4 (6,464) die — BSL 4 (eas ei)ya - =e de aE ae __ det us choose ) = =vlE)=U Dass 2a =S2 3 oes = jae dye j FLED =V(E) egp (D) ==> Us ro 523 +0) Xa - Bitcy + Ka - Ka m9, + Bi seq - KL: é TB RABE oe EE oc + Hy ° 5) bo = pogtta + (@riOx) acy - By 2ea-+ Chat K oa —kiea =O xy = Bue 4Gi_- KOK) op Ky ee xy = VEE). ory Gh aoe, + COA or ky sj20 56 oKT sep s Sh vide elt ae ole in, 1 => _ =O WS, oy ate vate _ lve “de aE fay SQ = OH —_®) Zoe the vdisplacements Yard Ya be te epg Hh ager, VAs 2 Yo aa Oe + fe. Atala model is; oe ° ° \ a Pe © © © \\\ery Ly f° 3 |" & oe trey v 23\ Veo Kifoy -Prfoy | % SY [foe low 3, -CHey yl fi oe | (A [e)-t: 1 © O\let th ay oO @) Oblatn the alate. mealtel of mechanicol pustom Arhreon > - ’ : in ig: by cehoosnd muy 4 Ue. plate Meatadles , Le pti Vo Lot fe Prod? fh drrrererr fi rrr rrrert po pistion Solution 4) forchetss cliegyaro 01 Bo ce. folance. egn in; moe feo, +f + kg =o > O 7 ro By AK Y, + a (Yi =e be wor. (kit ky) - Keto =0 ——— =@ (Fucbedy tagaro ef neds: ous Pouce. Balance eqn 5 Ee neck —te frat B= 0 —_ 9 Ka yc: +6282 <0 Ke Ya- Kad Oss =o ——=-® Jot: up cheese j oy a9, ja =82 7 3 =u 5 FID-U CD =P pope + (kt Keyra ~ Kae <9 (DA Kara — Kae + BOQ =O em a Ka oy kK —_= 22 = ae Oe © loweT 5 74 ay a act. ck ee top = = @ Jor Gy © Ya Be the of >®) Wes 5 Ug= ma’ © The tele medal is; mt 5 ° \ oe - col=] Ka -K2/aolfaaha} of u Po Geom wf, 0 |pal fo oR meelel &. the mechanical dyslera Phe B) Eber the tale | © f° cppeee a oe ‘he We e - to) You bs Ga yon bots = VEO ___ se (Solution fove Calance eqn 25 fray + fs Fea =e =) vivcey Ba ae Casea) 0 -o Kee 1 Rg cbt _ By loro ale “te ~@ Jracdedy idiagsara ef a , ; . fore. Galance. can 12 5 fosate Cid a fra + Fiat) ———>@ | p foe tor U=ma a 402. (mA) +8) ta mpg A244 Bn JOR _ Bac 4; dleto ates SPE + Ga oe oe +6: — 9) foe up cheese; SHS 7 cg =a 5 aoa = aL js ae j RD=0 a—> 11 5B + K 54 + Ba xg - Bacey =0 1B = TK oy —— =, — sy ——>@© 1D) > UshMgry +Barty — Bacts +B) sey bo Vict = Boy — (Bre) 4ti0 — Ss poe 8 (ENED cry tog 4 -@ KT; 9g = Act “aE ' key ey = St 7) = Acta ae tej oty = 2 =&) Jot the o]ps fo sa and 2° " Yy =o ard Yo =o __ fi) "The plate model is; ® ty ° . ' oe . ° sty]. 0 x 2 S o Hees ; Ey hry = Peay, 844] oxy 4 ° U ™ = o By i Yon 7 (B02. if thos a? || cea Vieve Yi] fio © Sly wl le 1 © off? 3 ®) cbtavin the plate Apacs medel Gf the mecharicol ogptire & hewn 40 13 ' Solution fuabedss edliegyorn #1 a fo i e—-fin force. balance. equation 19; = f | Fray + Fy + Fort Pa Ae = © __ = < =f e ate aoa 7 Oa +B, Ge * @ st (20-22) + Kady + KC2t 3D = O At da _adx em =o Monat (BiAQ) SE ere 4 CAKES 8 ‘ i 30 c DQ Fciney eiagioro 22 pee More. halanes. eg ib; bo» — Ie froa +f + fea the = FD — +6) 2 fk 2, rag + © he Gea) 4 82 GE Ged =O ten ve 7 (e162) se den + Koa — Ky =F(D =O fol wy cheers, Bye pea a 5 joey =A 5 FED = Of = o— myst 4 (BU Mery — Bers 4 (44+) 9@ —Key =o Sty TR oe — CKD Foy) pS a t9By oe 0D ony => = baa 63+ (Pi +A2 20 —Bory + koe — Kom = Y =K_ 5g + oa — (RABE) se5 4. Ba omy +, a © aE” ote) es 5 hq = , do a det | tes Seq = tu ——_=O Jot tha wlisplacernents fe the elp- oY <1) Ya =241 = See Tho stale medel is ; par) oO ° t oO 5 oy D ay Ss =|o ° ° ' 2 1| 0 dy og Mog HER | | hog : Hh OR, ty “BH L™] LO wl ff eo © Mle Jo “lo to © Ifo 2g my | Poechanical Rotational _Ayiter @ fe asic: model of mechanical splotional ryptn lean fe edtainel Gy vroing Shue Basic elements, > ine .lvee mars oy moment of ir o, o> Actational dash. - pot + > hetalionel apaing (Shen ai torque wp} ied bb Lo mechanic Xctationcl sytem , ek te eppeced by epprring xapes due to moment os inceti fiction vand elasticchy 4 the aystern « Bocce for .applying Atal. Shariable mathod for mechanical ___ Actotional ayo Step 1 + fev each nede in dhe ayylem one £E van be. Joned 4y equating the passe Of applied konques to Lhe | pie & eppeing foxes « Arp 8 + Amigo van cangular displacement to each nede cand dats a peecedy ediagars - Asp 3 ' Cheese vo miamuro Awaler gf tak variates « Sip ithe pryical variables in ne caw Atplaced by Ata \ariablos cand the eqns cae camanged ras five ower DE. Fhens eqns veonstitute the slate” eqn. x the Ayptero + Bip S The tnpub vase the capplitel Logue cand the eucgputs vars cdisplacernent , Veleety oy ccicceletatinn - Pera ®) Pctewnine Uke alate, medol of cermeture ventolled ide mator i / TO \ of. Soluhion hi cfhe varmatiae ccontuetted AC motion 2yeed contre Aygtee 2s Ahewe elec CL i Ione : vp , ) {ae | fol) The equivialent cetienit of taimatus. fs shown Lele: je fo ke Ye ~ se, Applying Ku we art No ~ ia Re. toll -q,-0 Va = laR +La +e ae Oo Fergus Le Be molto is proportional fo the ect ef flue ane cuuenk . jue ip constant , the ‘Aoique wy Preportional to ja alone: Vet ia toh. ke = Loge. constant The mechanical oyster of the motor dp ahaon ip fig voad the De cqateriuy fhe rrechanical Aystern af the metos io uguen, Belen - | Tea ae | Te + Ade =y — "© The back em) va de machine to prspostional to apd pe an; ep ~ ae “eb = Kb boyy ——— ® Loh) kb do hack errs, veomstank Sub (0) in () {)—~ Va = taka doch 4 Keble. +~® Sub (2) to (SD - 2, : (Ds wae, vade. eke le. ——2~ © foe Ws choose ig U2iand @ cao olale Vanaéles . Le sig jaa = C7 = 48. joys© jVord (DS Vasari +laqy + Keo ot = xy ~ ore + Yn VU —- @ OS Tae +806 = kL oS oq = KE 2c, —- Boca ——® = ts (ok -T 5 aa= © des = de “de ae ins Sty — oq fot the celertteel ep fe us) javand ©» de; Gyala=P1 3 YorlS =m j Yar E =" The vtate mete) iv gree by ; Ba] [R/e Khe SV) (he “=| Kefs - Pfs colle Jt) 5 JO 3) fo i Ofloe, oO 3 Sal > 33 — —_ = pierdiagar cn echauin vay Ahewn below (Bit 78 ts ] Yio. g) ass Solu The feted ccontsclled pe motos spree veontuel system. to Aline to ts . | fhe dexgue gf ve ede mele is paupautional Z8 |pigduct 4 five cand catmiatie scent » Sines the carmatue unk io veenstank in the ayter ; dhe torge in neportiiona! de jes calene , But fsx © prspetional to field cuntent + <1 of if T= ky ip ——S | oho. Rig = iteaguo. uconatant - The mechanical Aypleire ef Ihe erobos jo dhoun Jn {ig vand the DE egevering the mechanical ryplere ¢ the motor io given (cna > de 4 Bho. =T te all @ (2). and (8) 40 vet @9) ~y co. clo_ — ue | Bae = Re, ig. - ~® Jet ws choose i judvand @ cap Ue alate Variable. , sik juqsus=4d0 jag-€ a Np Hoe eq rating, ( Oa * * aed =U = hoy, 4 Ee uo 6 OS Wag 4+ Bo = ky co Sy = Ky cy Bog —>© 6o-K-T i mer © | ep = =-<6_ tp =O inj og => Lek the idesied ofp ba us card 6- J Yysuoama You © HS © She alate neeelol ai] (-8/4 = -(s Sy |= “Ws oe Ba cIP®. W O 1 OTe Re : | Eay _ ee he Gleek veliagrr rcpunentalior dhe mm do Ahan beter. P 4 a “(hy eH ye spe ry late, Space Reprventabion Usin pment _ Spats Reppsentation Using ne pwc Mastatles ars sclofined wan thse _portreula Lstate. \ariatles tohieh ane 0 . uystorn. Variabtes cand its uderimatives , | The Alata. model rai phase Vartables wan Le cosily idetermined if, the pyalem meelel io valeady know li 2 ae equation On branafer foretion: for | Te saducntages _ in choosing phase Variables Is blaze. Dpace medelLing axe ; f —> Uni rare Vlariattes the system model ean fa tunitl adiscatly 4 inspection pe Aho. algerertiad equation egevewning dhe aypter « : > The phase Vasialles Jrovides wo Mae Joliveen. the transfer junction cctenign vafppreach wand dim. -cleman design, fajpreach., he. udisadantage. 40 cheering phase Variables i tt , the phase Vattatles sate net physical ‘ables op the system and thowewe ase ack auailable, is pregibBiernat rere centrel fauxpeses « ; TDetheds ef medelling va Ayslem. aa Phase Variables foe, case thus methods uscel jor modelling a dystem. using phase Variables . | Consicler “Lhe. petiag oH oncler cljsertiol equal ‘relating Yo eulput YD te the input Ul: % xa Ayston « oe (o-D. -2. on . Yaar y + ag yy... tang S+an445 +a0¥ =bu . ——_—__> () By cheesing tho. output Yy vanel thelr ictercvai wah Atnfo CaunGle. . toe c4eb qed | omead a) | (n-l- . ne 6 &=y 5 oe = en. Aubdtituting fhe ptate Mastables in the cligferorihal equation egevemning dhe Aystem. » we gee A+R +Ag App. FAR=9 34 An-+4 Wy +ANWY = bY . = = (2) “ly STARRY = Any Mg — Oya Mem TAD AH — UX bu fh . (5) he state. equation. G the Dystem Ue. Oy = 2cQ : % = % X41 = Xn Be = ma AP = MH Aya — MAEM + bt on vasanging the abe: equations in dhe endtuice 1 [sy oO 100 -oO| | 0 | | a O- oO |=] Seq o ol oO = a | | xs Oo Oo O+-:-0 = oa, ° | |. = }+/0| [io] | | O 8 OF TP | Xn ram AHO TUT oer b “Here the malice A fas a Vou ppectal fowrn- Ge Fun fall 1's ip the Upper ie 1 ite desk 20w ib compat Lard oy the neqatie cenffictents op the oniginol diffoveritiol conation cand “all ether elements vare. Gio. This jew ¥ matux Aw Kneun vas U elle nel. that the B matic fas the Dpeciality, that call ibs elemerls eoceept the last element Late, ga. Fhe etatput Ging x24) the output equation is given bys : | | Y=[fo 0....4] oj (os) Y=cx | Conniclot the fetterrsing OM onclor cel ifererol eof governing the eulpak Ye) fe the input uw 4 a austen | & ind: : Yeon Va a Yan bo O 4b, UP BU (i) lok n= m= 8 Yard +aah+asy = bo Ve by Ua be U4 bgU 7 (SD) om Tokeng Laplace ranyloun. g De aleve equation with Be.o initial enditiens , Wwe ope : 3 2 6 > E WD+A SF YES) 4AQS YES) +03 YD = be SULD + b/ SVD +bg SUS) +bg UE) > (3) ( Nap aas 48) CA) » (bet 1 hot hig Lhasa | 4 a ved. bos VIA by Sh be 70 ulay m1 AQst4 age yay J (hot bib + ba/, : S14 Us 4097.2 09/5") Sy bbe ay bo: bo 4 b/s 4. bb: | | ~ (“Js = Ga/.? — asf) - ‘ - + ({D | From. ranons e forruite » the Danafer jordin g “J ka aye tem ky ugpuen. , TIS) = A Aye An 3) dohere = qa ua . [acter Ce = path gin oy Ka Jor cased poth — | An = A for that prowe of dhe upaph. tahich is | net touching lh Jowoonel path - | A = |= (Sum G call incliaticta) Joep Gpird) + | [num ef gp fprcducls ey wall pororible | combinations % twe nen - fouehing desps) | The Laanates poretion & a ays waits Jou Jour feathes vond wuth thee fediact leaps ib egisert by , | tesa P+ he +P + Pu _ => (4) 1= (Py + Fa +2) on vampasing equations (Drand (4) tus age | G=be5 Pasbis ; Ps = bale 3 Gs beaf8 (As Gs 5 Pig = 49/9 3 Fis =-03/g Al signal feo guph ean Be ceonstisseted Jon fo 4y stem sep reser 4y da Lranaper uncion vas Ehak « legn (D+ She signal fire As veonsteurcted Auch Bhol Aya} cand call lecps ate, ouching doops . Loe us carsiqn Atale, Vvartables at the. eutpul © cach integrator un the Arigna few gap cand fhe [dowalives of the slab. Yariniles mull fe wvadetle vak the input ef each Anita roto» - be | _ | - b an Ln . Spee o> vo) & BNE ST aN ST aK 7 “yes) _ —ty -a3 | She tate equations uae posed by summing wall the ‘inceming pignals te the nodes, where “Kalucs Lonesponds Le fs iclextuaive % Dlate Variables + |. By duumming 4yp the incoming Algnals to nede oy) we gt | be af ay = 3% Hby0— 04 (Ba + bo) | me eNO Sy = ase +oxg + (by bot Te + (® ‘By dummiog Up the ancoming dignals do rede. fq tue cqpk a bad tod gq = 23 +h_U — Ag at bov) me zy Wg = TAQaY-+o03 4+-(bg-abe)t s =f) By durmung typ the ineerning Aignals de pedo %, be ype lav 83 = bo V—Ga(ia+bo’) aa 103 = Gay 4 (hs -Agbo)e bg0 BNL = Its) [ny Or vasan ng the lak. equations cand the. ul equations in dhe matue form tea ue t e “ay 1 olf by-aibo |= |-ag 9 1 \lag\+ | by - Aa bo fv] x3 -a, 0 0 || bg - Gabo Y=[1 0 o] Es" [be] vu a ee) feahel = 3 (Cpnbollalle Ganonical_f (enseler the fetlewiing A onder cclferccitial equals exnt the. tok l i ugereaning Culpul Y(E lo the input vib) oH wa Ayystorn « D- (n-D. (y-9)- >) a YIAUYFARY HAY = by S Eb Oe: Lb \Lok Osre= 3 7 2 Yaa +aady +A3gy = bl V+ 04 bg0 +bgV . =~ (3 | en take Laplace. ransom ¥ the. cabeve equation duit See india) ccenditions Fle cqek | SV +LSAYID Lagsy(D+4ay(D = be SvlD+ | | by su + Lgsvls) + bs v052.5 (Frastyagqs FAS) = (bod +s +bosthQv | yea _ bod pbs + ba S+b3 ots) S74QS* 4AQS+A3 4) ) | dou x5) YS | u(s) HC) Htohoe 5 XS) | _ old” Biastyaas 103 © st) land VQ bo st bs" 4 bos + bs | xfs. | on crow multiplying equation (SD , we pe xD (P+ 3 +aa8 +03) =) KDI EMCD aS’ + *(DAgQs 40g xD = OC) ® en. tareing invewe faplace banfown. 4 dha above equadien Le ge x + Sy +g x +Ag% =U — 319) Lok the stab. Variables fe og ,009 03 & toh 5 om acy wand Ma [Io) 2 YD =x CSS bo ++ Ij" X08) +} og 5x09) +h xIld => [ul) en taking tnyeue faplace. Lansfoun. 4 tha above equibi we gt ~ Y= body +b by oq +Abasq +bgoq ———_= I? on Aubstiluting the stale variables in eqwatidn (18) tue ype : J= bo S +himg + bac + basa ~—_ (15) Pur 3 = —AaEe —aQ% — ayaa $V 40 equation 1) Ys be Fagay —aQ9Q ~Ayo%3 0) -blo10%9 -Foada + ba ths (bs ~Aakeayen, (bg Ag boang + (loy-cu bey Hel (0) The equation (1) ia the. euetput equation en weusaanging the state equations cand culpul equaitsin lin the matua pom » We get | Sl fo 1 o fey o | fol=fo oo 1 |lag\4| ofu | fe] frag -ag -cu]] oc \ | | Y= [Cbg-agbo) (bg-agbo ane + [be] U ceed | | | | DP [ieblemés @) Comstuick va ptake medel for va syste vcharactiriged De cdypartial equatinn pe 2 ay a +6003, ant 464 40 =O. Also gue Hee. Glock veliaguam daprrentation 4 Atala mechl. Selution ee Jot ws choese Nand theis eloxtualives vs Atal The Ayplom is governed by atl erelos \carialles « alyjorential equection vanel no Lhe number of rtaln Vaxiat wlio ate thee + “Lok the slate Variables be a4 ,2¢q 13% a3 + oye Y eV ade cy %= YY dy 7 gee =? te Hd 3 = ey | : “Ginter, APY Ry > 1 +693, +N 46440 20 2b Gey +11XQ + Bog HY =O | | | ac | 1 Dem — 60K, — Ileg — 6% -O The state equations are ; ay =at9 MH =O 2 = — Gay -llat~y — Gy -U Hew »Y= @upuk 7 Bue Yao en cauanging the. atotc equations wand output a OD ! of o at ~}o oOo Ife} +} ofu | | | Sef |-6 tl 8) /% I y=-L!o0 o] E oy) eee } The Llects wcliaguam. “4 the Ayptem us hewn. dele: aS | The Llects cliaguam. of deo Pyptom 4 Ahown lolow -U “aL > ts, atte oy et Pear Yau 8) Prove thak the. unique Alate, Apaco_meclel ef va system ip not (Solubioo | Je peeve that the plate. apace, meee] Go |dystam. we ack Linigue 1 conmstclar va system, luhese Langa fencer is phawn below. Srs+ as +l Trocler de prove tha tive velfperent muthocls wae ive (Fo 01 mot. rrethels ean fe velone.) cane :(i) / Toethed CD Giron NOS) IO uts) Sys +astl en wer ruutti plying the. vabeve equator y 4x wt yea(seustas+D = 100d - 0 5 YS) 4+ UVES) +} Q9YC3) +03) = 10 VI) ‘S47 _4 lawing weve lap taco. Danifonn 1 be “get Yaaijeayey stou ———__+@) Job tus vdine. Alaltu Variables vas poles, B4=Y 7 %a=Yo joy ay jequiction () —> re +4oeg + QoQ +ory =10V 3 = — OY - Qaxg — Area +10U o Ake. tate. equations we, . . ‘ Brace (suas 5 Si Ge Um ASS % =33 ( ayeyg ; : Soy = Y nog 9-38 (yay 5 dow 2d jc Gacy 9 = —TEY— Qorg — Uoeg +1000 The. eulpuk equation is Wace - “The alata model in the malice, fown ia; oy Oo. 1 o [Pay oO | |ag}~]o o «lle, )+]olU wl fa -2 -4/ fey] [lo y= [lo OlRy me “3 Cane : (i!) | oetheed (D ytsd \o 5 7. Grineo, CIS) eansttastl Foyt. 0/3 | ots) | Joao V (-uls-2/o-'f5*) | he nignal flew graphs Jos the valloue Ahanefer jc \ean Le econoluteled uaa dlewn delow « Te plate. equations we. ebtatnce by dumming the ithcorning nignals to the anu oH the tule grate... + The dtate equations ARG ; | ¢ oo ay = HOt ICQ oy 4 ac) ay. 3 Whe Jy = ~QaYy 42a -2 lov ay Re 2.3 = Ty +100 The eukpuk equate in Yay: eubpuk equation 46 Vou Te alata medel g the aystero uo matrice jor db geen by ; BE Sehr * ml=|-2 Oo | aT ey” From the vateve mathods ib is ucleos thet “the alate medel ebtained in net Aame Jor the ugixen | : pyslem - Hence. tL scan be proved that. the slab Ajaee. medel gt Ayetem. As nek unique: | | . 2) The stake diagram 6 va linear ayptem ia gun Lele losign abate vaxrables cand obtain stale rieelol- wd Ly 4 : ~ Yes) a: | eee | ‘Belution | Since thee use 3 inttagreitous pL ban werriga hue. Atale Variables . T2 Yts)

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