PROSIDING ISBN : 978-979-65-8-7 T-6 PANDUAN DAN KENDAI KAPA TANPA AWAK DENGAN MENGGUNAKAN METODE MODE PREDICTIVE CONTRO (MPC) DAN AKAR KUADRAT-UNSCENTED KAMAN FITER (AK-UKF) Tayatl Aan, Sban, Inttt Tnolo Spl Nopb, Sabaya tayatlaan@alo, ban@atatata Abta St nal paan al tal paa apal tanpa awa Paa pnltan n banan t tan nt apal tanpa awa ala t nal an ta Maala taa ala nal apal aala plaaan lntaan an pnan lntaan Mto yan naan nt nntan nal apal aa ttap paa lntaannya aala to Mol Pt Contol (MPC) MPC anat oo nt pnan lntaan ana MPC ba p otpt a t Unt naba aatan nal yan a apat nan MPC, tat ol an paat ol yan ta pat abat anan lnnan lat/naa apal ta nan nnaan to Aa Kaat-Unnt Kalan Flt (AK-UKF) Mto AK-UKF paan pnbanan a to Unnt Kalan Flt (UKF) nan nplntaan a aa aat Sa n apat pna al ta, ba ala al tnat aa apn wat opta yan naan Mol apal yan naan paa pnltan n aala apal natat nan nal paa on yaw, apal natat paan apal yan l jla nal yan lb banya bannan nan jla atatonya Dna apal jlaan nan nnaan St-Fnt a nan nnan lan otpt plaaannya Paat ol yan ta yat na apal ta pnabaan aa paa Da al ta yan apat a la nan nnaan AK-UKF aan naan baa npt nal (on yaw) Sla a nal an ta nnjan alan a nal yan apat Kata n: MPC, AK-UKF, Knal, Eta, Kapal PENDAHUUAN Inona paan naa at an paan naa plaan tba na, yan a p ta wlayanya aala latan Dala paya njaa tan wlaya paan plan at t ptaanan aanan yan at Sala at paya yan tla laan aala nan nnatan patol paan Inona Unt nn paya patol paan Inona tnt aja btan altta (alat taa t ptaanan) yan aa, ontonya aala apal Maala pntaan ala Sna Naonal Matata an Pnan Matata nan ta Kontb Pnan Matata an Matata ala Mbann Kaat G an Swa" paa tanal Nob Jan Pnan Matata FMIPA UNY
PROSIDING ISBN : 978-979-65-8-7 Kapal nan baa alat yan ba paa paan lat yan l 6 ajat bbaan ala ba yat, way, a, oll, pt, an yaw (Fon, 999) yan apat lat paa Gaba Paa aala n aabl yan nalan anya ala a ajat bbaan yat an yaw nan a a way, a, oll, pt ta bpna paa an apal Kapal yan a aala apal natat ana jla aabl yan ontol lb banya apaa jla yan nalan ol atato (O Ryo an Sn, ) Atato aala ba alat yan naan nt nontol ba an ata t Maala taa ala nal apal aala tajtoy tan an pat ollown (Enanao an Paol, ) Tajtoy tan na paa a baaana apal laa jal nnya, anan pat ollown btjan naaan apal nt nt jal yan nnan Tajtoy tan anat tantn paa ol n anan pat ollown lb nn nt plnta pat pt panan (an) an pnnalan apal (Xao,, ) Gaba Ena ajat bbaan a apal Pbanan pnltan nna nal apal pat ollown an btaba n wat Banya pnatan yan nalan ala bbaa ltat, antaanya pnnal batppn yan naan Enanaao an Paoal () paa waana ala a an Sjtn an Fon () nt nontol apal aa baa paa baan lntaan yan nnan, ta pnnal tat an otpt ba yan naan Do an Pan () nt nan apal paan natat nt lntaan yan aa paa patan aj ontan nan nabaan anan lnnan Paa aala n, naan ol pt ontol (MPC) nt nnalan apal tanpa awa na po apal apat nt lntaan yan aapan Plan tn nal MPC anaan nal n apat nanan t ltaabl Pnltan n oan paa ontol on yaw yan tja ana paan apal latan Aa npt nal lb aat aan laaan ta tat ol an paat yan ta pat yat pnabaan aa apal paa a aa ( ) nan nnaan to Aa Kaat-Unnt Kalan Flt (AK-UKF) Mto AK-UKF paan pnbanan a to Unnt Kalan Flt (UKF), ana AK-UKF nt Tolb an Apl () pnya tnat aaan lb ba apaa UKF Da al ta tbt naan baa nptan nal MPC Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 5
PROSIDING ISBN : 978-979-65-8-7 MODE MATEMATIKA PERGERAKAN KAPA Mol atata apal natat paa paan, way, an yaw nan ontan aala baa bt (Xao,, ): y o o o o () nan : = ppnaan paa aa a y = ppnaan paa aa a way = St yaw taap b b = Kpatan = Kpatan way = Kpatan yaw,, = pnabaan aa paa paan, way, an yaw, = pa taan ona abat paan way an yaw = on yaw Kana paa lntaan apal tnjan baa bt : Gaba Kana paa lntaan apal Paa aba, paan lntaan yan tla ta M paan poy otoonal a tt P apal paa paan jaa panjan lntaan antaa Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 5
PROSIDING ISBN : 978-979-65-8-7 bbapa tt ttap paa lntaan an M n an t paan to noal an to nan paa M paan jaa anta M an P, paan t antaa t an X b Malan t paan patan total apal paan t antaa patan an patan total Baaan paat ata, naa apal paa Paaan () tanoaan baa bt: t n t o t t () nan paan onta o paan lnnan lntaan pa tt M, paan t laan an tt tbanan t () aala, Klaan n paa pat ollown ana yan aapan aala o antaa lntaan apal an lntaan yan nnan aa nan nol Baaan Paaan () apatan bawa a tablan nan Saa atat l at bawa nnaan t an paa paaan () a nja at paaan, nt t nan lan laannya (otpt-nton) nan pnnan baa bt w an () nan lal ontan pot Sbtt Paaan () Paaan t (), na pol Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 5
PROSIDING ISBN : 978-979-65-8-7 n w t t o w w t n w o w t t n w o w t () w MODE PREDICTIVE CONTRO (MPC) UNTUK SISTEM NONINEAR Paaan t nonlna (Cn,, ): y (5) n nan R aala to aaan, aala npt, an y aala otpt Fn objt ban baa bt: J T T yˆ t wˆ t yˆ t wˆ t (6) nan T aala wat p, ŷ t aala p laan an t nyal n p Knal npt t optal npt û t, T (), aa: ŵ aala ban baa nla awal paa nal nan nn n objt paa paaan t t ˆ nt Opta paa MPC nonlna ban ol toa bt : Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 5
PROSIDING ISBN : 978-979-65-8-7 Toa (Cn,, ) : Patan t nonlna (5) an anaan laan paa ntal p pan nan nnaan pan t taylo apa o l nan paan ajat lat Unt o nal l, opta ala MPC nonlna nan nan n tjan (6) baa bt : t KM w t (7) nan M R ban baa bt : t w t w M (8) w t nan K R, al K at pat K,,, (9) nan R,,, Sbt Paaan (8) an (9) Paaan (7) aa pol t w w t () nan,,, aala ba ptaa paa at bt : T ll l, yan ban baa ll,, l l, l, l () l,, l,, l () T j (), j! j! j ' nan T aala wat p an l aala o nal Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 5
PROSIDING ISBN : 978-979-65-8-7 Dajat lat t btjan nt nntan npt a ala t Dn (Cn, ) : St nonlna (5) ataan pnya ajat lat ja : () nt tap ptaan an () Dajat lat paa t nonlna (5) ataan nan nan ba (wll n) ja ajat latnya aa nt tap Kta ajat lat ta nan nan ba aa Spaya apat aa t paa Paaan (5), naan tnan nan nnaan atan anta Dn (Mntan,, 8): Tnan nan baa al al ata aa tl: nan nan atan baa tnan n ata to Eln a tnan aala: n Dn [7]: Yan a nan n aala: n n nan n atan baa tnan -n n ata to PEMBAHASAN Baaan Paaan () aa t tbt apat tl bal baa bt: nan Z T w, npt nalnya aala Dan n an otptnya o ( ) w Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 55
PROSIDING ISBN : 978-979-65-8-7 Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 56 o n o n Inpt nal paa MPC nonlna yan na paa Paaan () aa pol () Sna pol tnan nya baa bt o n n n Sa nan Dn aa t pnya ajat lat Maa aan a nla a baa bt :
PROSIDING ISBN : 978-979-65-8-7 Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 57 o n o n n o n n o o n n Klaan n aa tnan apa aala Inpt nal paa Paaan () apat tl baa bt :
PROSIDING ISBN : 978-979-65-8-7 Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 58 } o n n n o o n n o n o an n o an { Paat pnnal MPC yan naan aala T=75 t, l=6 Paa ptnan Paaan ()-() apatan nla 65, an 67, PENERAPAN MPC DAN AK-UKF PADA KENDAI DAN PANDUAN KAPA TANPA AWAK Knal MPC nt nnalan apal aa nt lntaan yan bpa lnaan nan ja-ja 8 Knal ta nan nta tat na an paat, paat yan aan ta aala paat pnabaan aa apal paa paan Eta laan nan nnaan to AK-UKF (Aa Kaat Unnt Kalan Flt) nan nla paat paa Tabl, an alota AK-UKF ajan paa Tabl Hal la pnapan MPC an AK-UKF paa nal an panan apal tanpa awa paa Gaba nnjan bawa lntaan apal (lntaan wana ja) apat nt lntaan lnaan (lntaan yan nnan wana a) nan ja-ja 8 nan ba
y () PROSIDING ISBN : 978-979-65-8-7 Eo otpt po an aa paa Gaba an 5 nnjan bawa o otpt onn paa nla nol a wat an a at t, al n nyataan bawa apal ba a nan lntaan yan nnan RMSE (Root Man Sqa Eo) nt o otpt po an aa aala 998 Tabl Nla awal aabl an paat Vaabl an Paat Nla Awal Eo otpt po ( Z ) Eo otpt aa ( ) a Kpatan way (), / Kpatan Yaw () a/ Po S () Po Sway (y) St Yaw ( ),57 a Paat pnabaan on bat paa ( ) ntaan Kapal Tanpa Awa nan MPC-AKUKF 8 6 ntaan yan Dnnan MPC-AKUKF Gaba ntaan Kapal nan Knal MPC an Eta AK-UKF Eta paat pnabaan aa apal paa paan ( ) tabaan paa tat ol na apal, nan alan pnabaannya l paaan baa bt,5 - -8-6 - - 6 8 () - - -6-8 Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 59
Z () PROSIDING ISBN : 978-979-65-8-7 6 8 6-6 8 6 8 Gaba Eta Eo Otpt Po nan AK-UKF 6 8 () (a) 6-6 8 6 8 Gaba 5 Eta Eo Otpt Aa nan AK-UKF 6 8 6 6 8 6 8 wat (ala : t) Gaba 6 Eta Pnabaan Mon Bat paa S nan AK-UKF Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 6
PROSIDING ISBN : 978-979-65-8-7 Da al la nnjan bawa nal MPC paan nal yan ba nt pnan lntaan paa apal tanpa awa an ta nan AK-UKF l tnat aa ta an wat opta yan pat Tabl Alota Mto AK-UKF (Tolb an Aplan, ) Mto AK-UKF Mol t an ol pnan + =, + w = H(, ) + ~ N, P ; w ~ N, Q ; ~ N, R Inala Paa aat = = E P = E[ T ] Mntn Fato Coly S a: S = ol P a = E a = E T S a a = ol P Unt {,,, N} Htn Sa Pont: T P a = E a a T = a χ a = a ± γs Dnan γ = + λ, an λ = α + κ Taap p (t pat) χ = w ] = F[χ, χ W = χ, Mntn Fatoa QR S a: S = q( W (χ :, ) Q ) Mntn Upat Fato Coly S a: S = olpat([s, (χ, ), W ]) Z = H[χ ] = = W Z, Taap o (ant pat) Mntn opo QR S a: S = q( W (Z :, ) R ) Mntn Upat Fato Coly S a: S = olpat ([S, (Z, ), W ]) = ] P = [W [χ, ][Z, ] T κ = (P /S T )/S = + κ (Z Z ) Mntn at U: U = κ S Mntn Upat Fato Coly S a: S = olpat ([S, U, ]) P P w P Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 6
PROSIDING ISBN : 978-979-65-8-7 KESIMPUAN Pnnal Mol Pt Contol an AK-UKF apat tapan nt nnalan a apal natt nan ba Hal n tlat a al la yan nnjan bawa a apal anya btan wat an at t aa apat nt lntaan yan aapan DAFTAR PUSTAKA Cn, WH, Balan, D J, an Gawtop, PJ, Optal Contol o Nonlna Syt: a pt ontol appoa, Atoata, Vol 9 () 6-6 Cn, WH, Analyt Pt Contoll o Nolna Syt wt ll-n Rlat D, IEEE Pn Contol Toy Applaton, Vol 8 () 9-5 Do KD an Pan J, Stat- an otpt-ba obt pat-ollown ontoll o natat p n St-Fnt a Oan Ennn, : 587-6, Enanaao an Paoal (), Coban tajtoy tan an pat ollown o an at Fon I T(999), Gan an Contol o Oan Vl, Jon Wly & Son O Ryo S an Sn J (), Pat ollown o natat an a l n ln-o-t ba ol pt ontol, Oan Ennn, 7, 89-95 Mntan, I, Bat, AI, Ctl, NA, an Cana, E, Optal Contol o Wn Eny Syt Jan: Spn (8) Sjtn R an Fon TI, Nonlna ann an ontol o p Pon o Oan MTS/IEEE Conn an Ebton, : 88-85 Tolb, M an Ena, A (), Sa Aa Kaat paa Unnt Kalan Flt nt Mnt Tjanya Ka paa Alat Pna Pana, Mat T, Jan Matata, ITS Xao, W, Baoa, Z, Dyn, C, Han, w, (), Aapt Analyt Mol Pt Contoll o Pat Follown o Unatat Sp, Pon o t t Cn Contol Conn, Jly -, Yanta, Cna Sna Naonal Matata an Pnan Matata FMIPA UNY Yoyaata, Nob MT - 6