IDENIFIKASI PARAMEER SISEM PADA PAN SIMUAOR SECARA ON-INE Olh : Nimh Dwi Idriti F 5 Jurus i Eltro Fults i Uivrsits Dipogoro Jl. Prof. H. Sudrto, S.H mblg, Smrg E-mil : idri_d@yhoo.com Abstr Idtifisi sistm didfiisi sbgi ush utu mrostrusi modl prmtr plt mllui sprimtl dg mggu dt yg brsl dri msu d lur. Pross idtifisi sutu sistm pd plt dpt dilu dg cr o-li tu lgsug trhubug scr lgsug dg plt. Hsil yg diprolh dri progrm ii dlh di dpt ili prmtr dlm btu modl mtmti. Bd tr lur plt yt d plt modl disbut dg rror. Nili rror digu utu prhitug pd lgoritm MS yitu utu mg-updt prmtr pd plt modl. Mtod prhitug yg digu dlm ugs Ahir ii mggu mtod IIR MS d prgt lu (softwr) yg diprogrm dg mggu Dlphi 6. Pd pguji ord stu dihsil ili prmtr =.74 d b =. d ili rrory dlh.9 Utu pguji ord du dihsil ili prmtr =.967 =.9 d b =.5 b =.64 d ili rrory dlh.4 Utu pguji ord tig dihsil ili prmtr =.7 =.57 =.489 d b =.96 b =.867 b =.867 d ili rrory dlh.8 pguji dilu dg wtu itrsi miliscod. I. PENDAHUUAN Dlm sistm otrol, pgthu plt yg didli diprlu utu mrcg sistm dliy. Alisis ts sutu sistm (tu siyl) lbih mudh ji dithui modl mtmti-prmtri sistm yg brsgut. Utu itu prlu dilu idtifisi prmtr sistm. Idtifisi sistm didfiisi sbgi ush utu mrostrusi modl prmtr plt mllui sprimtl dg mggu dt yg brsl dri msu d lur. Pross idtifisi sutu sistm pd plt dpt dilu dg rl tim tu lgsug trhubug plt scr o-li mupu off-li. Pliti sblumy mgi idtifisi prmtr sistm scr off-li tlh dilu olh Jody Roostdy [8] dg mggu mtod lgoritm gti. Pd pulis ugs Ahir ii pulis mguri mgi pgidtifisi sistm yg dilu scr o-li. Plt sistm yg diigu sbgi lt uji dlh brup plt simultor ord, ord d ord d plt modl yg dircg dlh plt ord, ord d ord. Mtod yg digu dlm ugs Ahir ii mggu lgoritm lst m squr (MS) dg filtr dptif IIR.. uju ugs Ahir uju yg igi dicpi pd tugs hir ii dlh utu mcri ili prmtr dri sutu sistm yg brup plt simultor yg dilu scr o-li (Rl im).. Bts Mslh Dlm pmbut tugs hir ii, utu mgtsi prmslh yg d m pyusu mmbtsi prmslh sbgi briut :. Sistm plt yg digu utu pguji mrup plt simultor dg tgg lur msiml 5 volt.. Pguji dibtsi pd plt yg mmpuyi msu d lur (sigl iput sigl output = SISO).. Pmbut progrm dibtu dg btu Dlphi 6. d prgt tr mu (itrfc Crd) PPI crd 855, ADC & DAC 8 bit. 4. id mmbhs mslh Hrdwr. 5. Algoritm pmbhru dt mggu mtod IIR MS. II. DASAR EORI. Modl Mtmti Sistm Dimi Modl mtmti dri sistm dimi didfiisi sbgi sutu st prsm mtmtis yg mmprstsi dimi sutu sistm scr urt tu plig tid mdti rtristi sistm dimi trsbut. Sbgi lgh wl dlm mglisis sistm dimi dlh dg muru modl mtmtiy. Modl mtmti stip sistm brbd-bd, hl itu trgtug dri ompo-ompo sistm.. Kosp Idtifisi Sistm Idtifisi sistm didfiisi sbgi ush mrostrusi modl prmtri plt lwt ush sprimtl dg mggu dt yg brsl dri msu d lur. D sljuty dihiri dg pross stimsi yg mmbri prmtr optiml yg lbih mjls ttg sistm yg dili. Dg t li pross pgidtifisi sutu sistm mrup gbug dri du ush, yitu ush pmbtu modl mtmti srt pgstimsi ili prmtr yg optiml lwt lgh-lgh sprimtl. Sdg modl mtmti yg brisi prmtr dpt disbut dg pdsripsi prmtri dri plt. Mtod yg srig digu utu mmprir (mgstimsi) dri ili prmtr modl sistm dlh dg ti prmtri. Pd ti ii ili prmtr dri sutu sistm dpt diprolh scr lgsug d mrup solusi yg tpt trutm ji trit dg prj sits o-li tu rl-tim. Hl yg br dg idtifisi prmtri ditry dlh:
. strutur modl d ord sistm. prmtr poliomil iput d output. dly tim 4. rtristi srt dimi ois (gggu.. Algoritm MS Algoritm MS srig digu r pd lgoritm ii sgt sdrh dlm prhitug. Slh stu lgoritm dptif yg srig digu dlh lgoritm MS (st M Squr). Sprti pd lgoritm dptif, mslh utm pd lgoritm MS dlh ovrg dg solusi vctor bobot optimum, dim E dimiiml. Utu mmris ovrgsi MS, mul-mul prhti bhw prir grdit pd : w. w. ˆ (.).. X.. w w prsm lgoritm MS utu mg-updt prmtry dlh: w (.) w X.. Filtr Adptiv Rcursiv IIR Idtifisi ti prmtri di bgi mjdi du yitu o-rursif d rursif. Prosdur stimsi rursif dilu dg osp sbgi briut : (t ) (t) +.f ( ( t ), (t) ) (.) rliht bhw hsil stimsi pd sutu st diprolh dri hsil stimsi st sblumy dg ftor orsi. Pd stimsi rursif tid lgi by mmori yg diprlu, dismpig wtu omputsi yg juh lbih cpt d rltif ttp. Pd stimsi o-rursif sgt tid fisi ji dirlissi dlm btu lgoritm omputr rl-tim, mgigt prlu mmori yg mmbsr dismpig wtu omputsi yg dpt sgt pjg. Utu mcri ftor orsi f ( ( t ),(t) ) trdpt sjumlh mtod srt lgoritm stimsi prmtr mupu strtgi dptsi (orsi) prmtr. Pd tugs hir ii digu lgoritm IIR MS. Hubug tr iput-output pd filtr IIR (Ifiit Impuls Rspos) dlh sbgi briut [] : x( ) ) y( ) b y (.4) ( ) W... b b.. b (.5) U x x.. x y y.. y (.6) d y (.7) y W U (.8) x z b z Gmbr. Filtr dptif rursif y W U (.9) Sprti pd lgoritm dptif, mslh utm pd lgoritm MS dlh ovrg dg solusi vtor bobot optimum, dim E dimiiml. Utu mmris ovrgsi MS, mul-mul prhti bhw prir grdit pd trg sblumy : ˆ W W y = -. y y b y d y. b (.) r pd prsm (.44) dlh sistm rursif m utu ili : y = y x bl l = x bl. y b l (.46) = y y bl b l = y b l (.). l Pggmbr utu ili d dituju pd gmbr (.) dg A ( z ) z d B ( z ) b z (.) l l l Gmbr. Modl IIR MS [] Prosdur stimsi IIR MS dilu dg osp sbgi briut : W W Mˆ (.) l
rliht bhw hsil stimsi vctor bobot pd sutu st diprolh dri hsil stimsi vctor bobot st sblumy dg fctor orsi. Ftor ors disii trdiri dri stimsi grdit ( ˆ ) d lju ovrgsi ( M ).Utu mghitug stimsi grdi digu prumus : ˆ d y.... (.4) Sdg utu mghitug lju ovrgsi mcup pgmbil uur lgh d v.prsm lju ovrgsi dlh : M dig[ µ... µ v... v ] (.5) III. PERANCANGAN. Prgt Krs Prgt rs yg digu dlm pguji ii trdiri ts:. Itrfc Crd (PPI 855). Digitl to Alog Covrtr (DAC 88). Alog to Digitl Covrtr (ADC 84) 4. Uit Ctu Dy 5. Rgi Plt Simultor 6. Komputr Plt Simultor Ord Plt simultor ord yg digu pd pguji tugs hir ii trbtu dri rgi sprti trliht pd gmbr. Gmbr. Plt Simultor Ord Du [] Dg: R, R, R4, R5 = 47 K Ohm R, R6 = 94 K Ohm C, C = F didpt fugsi lihy dlh: Eo( s) 4 G( s) = Ei( s).69s.68s rsfr fuctio dlm ws z dg wtu cupli = ms dlh.9z.58 G ( z) z.764z.446 y d Plt Simultor Ord Plt simultor ord yg digu pd pguji tugs hir ii trbtu dri rgi sprti trliht pd gmbr.4 Gmbr. Blo Digrm Prgt Pguji. Rgi Plt Simultor Plt yg digu dlm pguji ii trdiri dri plt simultor ord, ord d ord. Plt simultor yg digu dlm prcg ii mrup plt simulsi yg dimbg brdsr rgi ltroi dg fugsi lih brod stu, ord du d ord tig yg trdiri dri ompo rsistor d psitor srt ompo tify yitu pgut oprsiol (Op-mp). Plt Simultor Ord Plt simultor ord yg digu pd pguji tugs hir ii trbtu dri rgi sprti trliht pd gmbr. Gmbr. Plt Simultor Ord Du [] Dg R = K Ohm d C = F didpt fugsi lihy dlh: G(s) s rsfr fuctio dlm ws z dg wtu cupli = ms dlh.6 G ( z) z.679 Gmbr.4 Plt Simultor Ord ig []. Prgt u.. Plt Modl Plt modl yg digu utu pguji pgidtifisi dlh plt dg fugsi lih modl propr. Modl propr dlh fugsi lih yg ord pmbilgy lbih cil dibdig ord pybuty. Prsm fugsi lih dri systm yg dimodl utu diidtifisi mrup fugsi lih dlm z.. Plt Modl Ord G ( z ) z b b. Plt Modl Ord z G ( z ) z b z b c. Plt Modl Ord z z G( z) z b z b z b
.. Dt Msu ( x ) Pd pguji ii, tgg yg digu utu pguji dimsu plt simultor d plt modl mllui PC (Prsol Computr).gg yg msu plt simultor dismplig pd tip priod smplig d pd tip wtu itulh lur output diprbhrui. Dt yg msu plt simultor (pd Hrdwr) hrus mlwti DAC trlbih dhulu.. Dt Klur rdpt du mcm dt lur, yitu dt lur dri plt simultor d ) d dt lur dri ( plt modl ( y ). Dt yg lur dri plt simultor dlh lgsug dri pmbc ADC..4 Prosdur Algoritm IIR MS Briut ii dlh lgh-lgh prhitug yg dilu dlm Idtifisi prmtr sistm yg dilu scr o-li dg mtod Algoritm IIR MS ˆ x y ( d y W y l l d l U b b l y.. )[......... [] = b [] = x[-] = y[-] = [ ] = [ ] = (. Mmbc Iformsi output ). Mghitug lur dri plt modl y W y U ( ) b y ( ) x ( 4. Mghitug ili d ili x b d d iput sistm x ) ( ) = ( ) ( ) ( ) ( ) = y ( ) b ( ) ( ) 5. Mghitug ili rror d y 6. Mghitug stimsi grdit ˆ ˆ = - [ ( ) M [ v ] 7. Updt bobot w old w old ) ( ) ] ( ) b b v ( ). Softwr Pduug Softwr (prgt lu) yg digu diprogrm dg mggu bhs pmrogrm Borld Dlphi 6. d ombisi dg bhs Assmblr 888. Progrm ii trdiri ts 6 buh form yitu: Form Pmbu Form Mu Form st DAC 4 Form st ADC 5 Form Pilih Modl & Sumbr 6 Form Hsil IV. PENGUJIAN DAN ANAISA Hsil yg didpt pd progrm idtifisi prmtr sistm pd tugs hir yg di lu scr o-li ii dlh didpt prsm modl mtmtis dri plt yg diuji, dim plt trsbut dlh plt simultor ord, ord d ord. Pguji pd tugs hir ii dilu dg cr mmbri iput DAC d mgmti lur yg trbc pd ADC. ( W W Mˆ M dig[... v... v ] Gmbr.5 Digrm lir prhitug lgoritm IIR MS Sbgi cotoh prhitug utu sistm ord stu dlh : Usul modl ord stu G ( z ) z b G y y ( z ) ( z ) x ( z ) b z ( z ) b z y ( z ) z x( z z ) gh-lgh dlm pross Idtifisi Prmtr dg Mtod IIR MS dlh :. gh wl yg yg prlu dilu dlh mgiisilissi odisi wl, mliputi : X Gmbr 4. Blo Sistm Idtifisi Dri gmbr 4. Siyl iput ( X ) msu plt modl d plt simultor. Plt modl brd dlm progrm computr d plt simultor brd di lur computr. Dt yg lur dri plt simultor ( Yˆ d d ) diurg dg dt yg lur dri plt modl ( Y ) hsily it m sbgi rror ( ). Error trsbut
digu utu prhitug pd lgoritm MS yitu utu mg-updt prmtr pd plt modl. Pguji Sistm Ord Stu Gmbr 4. Siyl hsil pguji sistm ord stu () pd tgg rfrsi volt (b) Pd tgg rfrsi volt (c) Pd tgg rfrsi volt (d) pd iput btu sius () pd iput btu rm..4. Pguji Sistm Ord Du.8.6.4. 5 5 5 Wtu (miliscod) ().5.5.5 5 5 5 Wtu (miliscod).5 ().5.5 5 5 5 Wtu (miliscod).5 (b).5.5.5 5 5 5 Wtu (miliscod) (b).5.5.5 5 5 5 Wtu (miliscod).5 (c).5.5.5.5 5 5 5 Wtu (miliscod) (c).5.5 5 5 5 Wtu (miliscod) (d) gg (Vlt.5.5.5 5 5 5 Wtu (miliscod).5.5.5 5 5 5.5.5.5 (d) Wtu (miliscod) () 5 5 5 Wtu (miliscod) ()
Gmbr 4. Siyl hsil pguji sistm ord du () pd tgg rfrsi volt (b) Pd tgg rfrsi volt (c) Pd tgg rfrsi volt (d) pd iput btu sius () pd iput btu rm. Gmbr 4.4 Siyl hsil pguji sistm ord tig () pd tgg rfrsi volt (b) Pd tgg rfrsi volt (c) Pd tgg rfrsi volt (d) pd iput btu sius () pd iput btu rm. Pguji Sistm Ord ig.8.6.4..8.6.4. 5 5 5 Wtu (miliscod) bl 4. Hsil Prhitug Scr ori No Plt b b b Simultor Ord.6 - -.679 - - Ord.9.58 -.764 -.446 - Ord.5.596.7.8 -.44.5 bl 4. Hsil Pguji Plt Ord Stu ().5.5.5 5 5 5 Wtu (miliscod) (b).5.5.5.5 5 5 5 Wtu (miliscod) (c).5.5.5 5 5 5 Wtu (miliscod) (d).5.5.5 5 5 5 Wtu (miliscod) () No Sumbr Nili Alph Error b Cost(Volt)...6895.49 Cost(Volt)..464.788.8 Cost(Volt)..498.77.6 Sius. -.79.8598.7 Rm. -.6.5848.8 Utu dt pguji pd ili msu yg brbd sprti btu rm d btu sius mmpuyi ili prmtr (ili d b ) yg juh brbd dg ili msu pd siyl stp (iput costt). Pd btu stp (iput costt) dt-dt yg dihsil tu ili prmtry mdti plt sbry. Ji pguji dilu dg btu rm, ili prmtr yg dihsil jug hmpir mirip dg pguji dlm btu stp. Pguji dg btu sius mghsil ili yg brbd dg btu stp tu rm. Prbd ili prmtr ji dilu dg pguji iput stp, sius d rm dlh r pd pguji sius d rm tgg rfrsi msu brsl dri dri progrm, shigg pd wtu mg-updt ili iput sllu brubh. bl 4. Hsil Pguji Plt Simultor b b b Ord.74 - -. - - Ord.97.9 -.5.65 - Ord.7.57.489.96.867.867 Utu Prhitug dri hsil pguji dg prhitug scr tori dpt diliht pd tbl 4. d 4. Dri tbl trsbut trdpt prbd pd ili prmtr yitu tr phitug scr tori d dt hsil pguji. Hl ii dpt dir. Pd pguji yg dilu scr lgsug dg lt simulsi msih by trdpt gggu-gggu shigg hsily tid msiml.. Kmugi msih dy slh dlm pmbut progrm d logi yg di mbil.
. Prgt tr mu (Itrfc Crd) PPI 855 yg trllu ssitiv shigg dg-dg trjdi slh dlm pmbc. Dt-dt lur dri plt sbry () d dtdt lur dri plt modl () utu pguji pd sistm ord stu, ord du d ord tig ji dibtu grfi mghsil grfi yg ssui dg tori, dim utu grfi pd pguji ord stu dpt diliht pd gmbr 4. Utu grfi pd ord du dpt diliht pd gmbr 4. sdg pd ord tig dpt diliht pd gmbr 4.4 V. PENUUP A. Ksimpul Dri hsil pguji d lis trhdp progrm Idtifisi Prmtr Sistm dpt ditri bbrp simpul sbgi briut :. ju covrgc pd lgoritm IIR MS sgt brpgruh dlm mtu bsry ili prmtr.. Smi cil lju covrgc m wtu yg dibutuh utu mg-updt ili prmtr smi lm.. Utu mdpt ili prmtr dri plt yg diuji, dim hsily mdti plt sbry m digu btu iput costt (stp). 4. Pd pguji ord stu dihsil ili prmtr =.74 d b =. d ili rrory dlh.9 pguji dilu dg wtu itrsi miliscod. 5. Pd pguji ord du dihsil ili prmtr =.967 =.9 d b =.5 b =.64 d ili rrory dlh.4 pguji dilu dg wtu itrsi miliscod. 6. Pd pguji ord tig dihsil ili prmtr =.7 =.57 =.489 d b =.96 b =.867 b =.867 d ili rrory dlh pguji dilu dg wtu itrsi miliscod. 7. Smi lm wtu itrsi pd wtu pguji m ili prmtr yg dihsil smi bgus. B. Sr Sr-sr yg dpt dimbil dri hsil pguji d lis yg tlh dilu dlh: Sotwr d Hrdwr pd ugs Ahir ii sudh dpt diplisi sbgi modul Prtium Estimsi d Idtifisi Prmtr Sistm. Prlu dimbg sbuh prgt rs yg lbih bi dg plisi yg lbih by. Utu pgmbg mcob prhitug lgoritm dptiv dg mtod li sprti RS tu JS (Jrig Syrf iru). 4 Mcob dg plt yg modl mtmtis blum dithui sm sli d lbih ompl, sprti pd motor DC DAFAR PUSAKA. Bodr, Rldi : Prbdig Kirj Algoritm MS d Algoritm Gti Utu Filtr Adptif Pghilg Nois, ugs Ahir, Uivrsits Dipogoro, Smrg,.. Dimitris G. Joh : Pmross Siyl Digitl, Prhllido, Jrt: 997.. Hriyoo A. jorogoro : Idtifisi Prmtr Sistm, Jurus i Fisi, Istitut ologi Bdug, 996. 4. Ifchor Emmul d Jrvis Brri: Digitl Sigl Procssig, Addiso Wsly, 99. 5. Ktsuhio Ogt : Modr Cotrol Egirig, Prtic-Hll, Eglwood Cliffs, NJ. 6. Kdir, Abdul : Dsr Pmrogrm Dlphi 5 Jilid, P. Adi Offst, Yogyrt,. 7. Kdir, Abdul : Dsr Pmrogrm Dlphi 5 Jilid, P. Adi Offst, Yogyrt,. 8. soo, Edi : Distributd Cotrol Systm, Jurus i Fisi, Istitut ologi bdug, 994. 9. rt jug : Systm Idtifictio : hory for th Usr, Prtic-Hll, Ic., Eglwood Cliffs, Nw Jrsy, 987.. Roostdy, Jody : Pgidtifisi Prmtr Fugsi Alih Sistm Pd Plt Simulsi Ord ig D Empt Dg Mtod Algoritm Gti, ugs Ahir, Uivrsits Dipogoro, Smrg,.. Styw, Edwi Yuli : Modul Pltih Kdli ogi Fuzzy, ugs Ahir, Jurus i Eltro, Uivrsits Dipogoro, Smrg,.. Widrow, B. d Strs, S : Adptiv Sigl Procssig, Prtic-Hll, Eglwood Cliffs, NJ, 985.., h Studt Editio of MAAB High- Prformc Numric Computtio d Visuliztio Softwr, Vrsio 4 Usr s Guid, Prtic-Hll, Eglwood Cliffs, NJ, 995. Mgthui/Mgsh Pmbimbig I Sumrdi, S. M NIP. 5 67 Nimh Dwi Idriti, lhir di Purbligg Fbruri 979. Srg sdg mylsi SI i Eltro Uivrsits Dipogoro thu dg ostrsi i Kotrol. Smrg, Agustus 4 Mgthui/Mgsh Pmbimbig II Iw Stiw, S.M NIP. 8 8