GENETIC ALGORITHM QUADRATIC PROGRAMMING BASED PREDICTIVE CONTROL FOR MLD SYSTEMS

Transcription

1 G GRH UR PRGRG S PRV R FR SYSS Jan hoas Soin a Jan isson idi ndsia daion og ni Swf gyp Phon : 6 76 Spé F 99 Gif s Yv d Phon : Spé F sson-sévigné d Phon : 99 8 jhh_hoas@yahoo.o {soin.oa jan.isson didi.d}@sp.f sa: h id ogia ynaia foais is an ffiin oding fawo fo hyid syss dsid y dynais ogi and onsains. Fho i aows soving paia pos sh as ono sing fo ap pdiiv sagis. Howv is ain dawa ains h opaion oad d o h Ps o sovd. his pap poposs an anaiv opiiaion hniq asd on gni agoihs ind o P opiiaion poviding sopia soions fo h inay vaias and opia soions fo h oninos vaias spivy in asona i vn wih a ong pdiion hoion. his sagy is appid in siaion o a h ans nha. Kywods: Hyid syss id ogia ynaia syss od Pdiiv ono Gni goihs adai Pogaing opiiaion.. RU any ono pos invov hyid syss inding oh oninos and dis vaias dis vaias oing fo pas dsid y ogi sh as fo ap on/off swihs o vavs. Vaios appoahs hav n poposd o od hyid syss aniy a. 998 i oaa od Pi ns od and ina opnay od. was shown ha oving ogia aions ino ina onsains on ing vaias povids a goa oding fawo ad id ogia ynaia foais poad and oai 999. aows dsiing a ag n of asss of hyid syss. his foais an aso foa and sov paia pos sh as sa siaion o ono and pdiiv sagis in ha sns povid ffiin oos whih na syss o a a dsid fn ajoy. h ain dawa of his foais ains h opaiona dn ad o h opiy of h divd id ng adai Pogaing Ps pos. ndd P's pos a assifid as P-op so ha in h wos as h opiiaion i gows ponniay wih h po si vn if anh and ond hods ay d his i Fh and yff 99. n od o d h opaiona opiy anaiv appoahs hav n dvopd.g. Ssg and ng hoas a. a wh diffn hniqs a sd o d h n of inay opiiaion vaias. n anaiv opiiaion hniq asd on gni agoihs is poposd in a a.. is shown ha h gni agoihs povid sopia soions in asona i vn wih a ong pdiion hoion. Fo his ppos a odifid fo wih ony dis ono aions is divd ha ss in a s adqa fo qadai -pos foais. h ansfoaion of oninos inps o dis vas is asd on fy inign hniqs inding an adapaion of h vaias ss fo a pision. his appoah onsiday ds h opaion i and appas o o ffiv wih ong

2 pdiion hoions as h opaion i inass inay and insad of ponniay wih h n of inay opiiaion vaias. n his diion his pap poposs a sagy soving h opiiaion po ad o od pdiiv ono of hyid syss nd h fo. his hniq oining gni agoihs and qadai pogaing opiiaion G-P povids sopia soion in asona i. s a fis sp h gni agoih is sd o find a sopia soion fo h inay opiiaion vaias. hn a qadai pogaing opiiaion is appid o din h opia soion of h oninos opiiaion vaias nd h onsains iposd y hs inay vaias and h sys isf. vn hogh his hniq povids a sopia ono sqn i ffiiny ds h opaion i ha now inay inass wih h n of inay opiiaion vaias. his hniq appas o o sip han h on in a a. sin i dos no qi odifiaion of h fo aoaion of h nw ais disiaion of h ono aions hogh fy adapiv fi whih as ao % of h goa opaion i a ah iaion. h pap is oganid as foows: Sion givs a if dsipion of h fo fo hyid syss. Gna onsidaions ao od pdiiv ono P and is appiaion o syss a psnd in sion. Sion is ddiad o h gni agoihs. Sion ains as h ain oniion h G-P opiiaion soion. his sagy is appid in sion 6 o a h ans nha. Finay onsions a sad in Sion 7.. h od pis h dsipion of vaios asss of hyid syss i ina hyid syss onsaind ina syss sqnia ogia syss so asss of dis vn syss and non-ina dynai syss wh noninaiis an pssd hogh ogia oinaion. dsis h syss y ina dynai qaions sj o ina inqaiis invoving oh a and ing vaias nd h foowing fo s poad and oai 999 fo o dais: wh: y n { } n { } R R y y y p { } p { } R R a spivy h vos of oninos and inay sas of h sys of oninos and inay on/off ono inps of op signas of aiiay inay and oninos vaias. h aiiay vaias a inodd whn ansaing pposiiona ogi ino ina inqaiis Fig.. { j } { } { } j j j j j ais in a oaind hogh h spifiaion angag HYS as paind in oisi a.. / if a s is/ igia if oninos dynai sys Fig.. od s. a s a. PRV R / od pdiiv ono P has povd o ffiiny ono a wid ang of appiaions in indsy. is apa o ono a ga vaiy of posss inding syss wih ong day is non-ini phas syss nsa syss ivaia syss and onsaind syss aaho and odons Gna onsidaion h ain ida of pdiiv ono is h s of a pan od o pdi f ops of h sys. asd on his pdiion a ah saping piod a sqn of f ono vas is aoad hogh an on-in opiiaion poss whih aiis h aing pfoan whi saisfying onsains. ny h fis va of his sqn is appid o h pan h who pod is pad again a h n saping piod aoding o h ding hoion sagy oh and 996. h os fnion o iniid is gnay a wighd s of sqa pdid os and sqa f ono vas.g. in Gnaid Pdiiv ono GP a a od Pdiiv ono fo syss Fo a sys of h fo h foowing od pdiiv ono po is onsidd.

3 h n i h n sa an qiii pai o a fn ajoy va and h pdiion hoion find h ono sqn oving h sa fo o iniiing h os fnion: in J / / / y / y sj o and onsan fo wh is h ono hoion a h aiiay vaias of h qiii poin o h fn ajoy va aad y soving a P po fo h inqaiy wih h noaion / ˆ in a siia way fo ' h oh inp and op vaias i i > ' fo i and i i i. h qaiy onsains of h fo a sd o pa h ipii vaias in h opiiaion po ading o a P po nd h fo: F in H f sj o p wh h opiiaion vo is: and h n of inay opiiaion vaias is. n h wos as h opiiaion i inass ponniay wih his n Raan and Gossann 99. anh and ond & hniq an sd o sov P po wh h - oinaions a pod hogh a inay sysaiay paiioning h fasi gion ino s-doains and gnaing vaid pp and ow onds a diffn vs of his. Sva ahos ag on h fa ha & hods a h os sssf soving P pos Fh and yff 99.. G GRHS s niond aov h ain dawa of h assia appoah wih h & hniq is h ponnia opiy wih h n of inay opiiaion vaias. was shown in a a. ha h gni agoih as opiiaion hniq an an ffiin soion poviding a ina dpndny ov h inay opiiaion vaias. his sion sais h ain onps of gni agoihs fo fh s fo opiiaion. h oigina onp of gni agoihs was fis inodd in h 97s y John Hoand of h Univsiy of ihigan ay 996; Hap 998. h asi pinip is as foows: a ando n gnao is sd o gna a fini s of ando dsign vaia vos whih a fd o as individas o hoosos. s of individas is ad a popaion. Fo ah individa in h popaion h ojiv fnion va o finss is aad. ndividas wih a high finss a o iy o hosn fo podion. Sing vaias of h hosn individas a hn andoy ad and ossovs wn wo pan individas a pfod on pas of h hoosos. h sing popaion gnaion is hn aind as a asis fo h n opiiaion y. h agoih is soppd af a spifid n of gnaions o a ain onvgn dvopn and h individa ha has podd h s va of h ojiv fnion is onsidd as op. h ning of h G qis h hoi of h vaia yp and ad onds h ossov and aion opaos h popaion si affing h qaiy of h opiaiy h n of aia gni opaions and h inaion iia. n h oigina on gni agoihs wod on individas onsising of inay dsign vaias. ihawi inodd a yp of gni agoih ha wos diy on oninos o foaing poin individas ihawi 996. n fa gni agoihs a a o poss ih inay o oninos individas. Howv vaias of diffn yps gnay anno id d o iiaions of n ipnaions. h assia appoah is o ansf a vaia yps o inay dsign vaias ih piiy o hogh a s infa as i was aid fo h aa Gni goih piiaion ooo G ohop. n his as h va of h oninos vaia is aad as: a in v in. v wh v is h oninos va v is h inay va in h ow vaia ii a h pp ii and h n of is. his disiaion ay ad o a oss of aay hogh qanifiaion of h oninos opiiaion vaias and ay as haing o ovshoos on h spons. o avoid his i was poposd in a a. a fy adapaion of h dis ss of iniia oninos vaias. o an disiaion of oninos vaias h n sion poposs a hniq oining G and P o sov h opiiaion po of qaion.

4 . G-P PZ S PRV R FR SYSS. Sopia soion h fo an win as foows: y 6 h gni agoih is sd o find h sopia soion of h inay vaias of h fo i.. h individas inding h foowing vaias: 7 Fo ah individa a P opiiaion po is sovd o find h osponding opia soion fo h oninos vaias of h fo: F in 8 wh h opiiaion vo inds h oninos vaias ov h pdiion hoion: 9 and y y wh i is a ona ai of i ns of dinsion. h P opiiaion 8 is sovd sj o: a wh: a h soion of h opiiaion po 8 nd h onsains is onsidd as h ojiv fnion va o finss whih has o aad fo ah individa in h G.. pnaion iss n any ass and an aad fo h n sa whih is assd o nown and fo whih is divd fo h G. if so and/o ns dpnd on h oninos ono vaias hn hs vaias and/o hav o opiid. h iniiaiaion of h G has o ind fasi individas i.. individas ading o fasi soion of h P po. his an ahivd y hoosing aong an ipoan n of ando individas ony h fasi ons as iniia popaion.

5 6. PP 6. sipion of h nha h poposd ono sagy is appid on h h ans nha sd y poad a h sipifid physia dsipion of h h ans sys poposd y SY as a sandad nha fo ono and fa dion pos is psnd in Fig. s oan a. 997 fo o dais. h sys onsiss of h ans fid wih wa y wo indpndn pps and aing on ans and spivy. hs wo pps a oninosy anipad fo p o a ai fow. Fo swihing vavs V V V and V ono h fow wn h ans hos vavs a assd o ih opy opnd o osd V i o spivy. h V ana vav onos h noina ofow of h idd an. wi assd in fh siaions ha h V and V vavs a aways osd and V is opn. h iqid vs o onod a dnod h h and h fo ah an spivy. h onsvaion of ass in h ans povids h foowing diffnia qaions: h& V V h& V V h& V V V V wh h ' s dno h fows and is h osssiona aa of ah of h ans. Fo hs pssions a od is divd as in poad a. 999 inoding h foowing vaias: wh: h h h V V V V i hi hv i i i hi hv i i Vi i i V h h i i i i 6. ppiaion of h G-P hniq h poposd ono sagy is appid o h h ans nha wh: V V V V Fig.. SY h an nha sys. n his sys an aad fo and ddd fo and. hs fo h opiiaion vos a: onsid now h spifiaion: saing fo o vs h h ans ing py h ojiv of h ono sagy is o ah h iqid vs h. h. and h.. h G- P opiiaion hniq has n appid in siaion o ah h v spifiaion pviosy givn wih h wo pdiion hoions a popaion si qa o and a n of aia gni opaions qa o. h s is psnd in Fig. fo h h ans vs and in Fig. fo h ono signas v of fis an h v of sond an h Saping insans.... Fig.. Wa vs in h h ans. h Vav posiion opn - os h fow /s -. h inp V V - Saping insans Fig.. onod vaias v of hid an h h v in h h ans h h h Saping insans - - V. h inp V - Saping insans

6 s noid ha h. dos no ospond o an qiii poin. onsqny h sys opns and oss h vavs o ainain h v in h hid an aond h dsid v of.. Fo a opaison ppos wn h assia appoah of P fo syss poad and oai 999 sing h P aa od poad and ignon G wih odifid fo a a. and G-P opiiaion hniq h sa pvios v spifiaion has n onsidd wih. a isas h avag opaion i on a. GH P wih 6 o of a. a opaison wn h assia appoah of P fo syss G wih odifid fo and G-P opiiaion hniq ppoah opaion i s P fo G wih odifid G-P opiiaion hniq US Pvios wo poposd a sagy asd on gni agoih wih fy adapiv fi and odifid fo as an anaiv hniq o appy pdiiv ono fo hyid syss nd h foais. n his pap anoh hniq oining gni agoih and P opiiaion is dvopd whih dos no qi a odifid fo o fy adapiv fi hs ding h opaion i a ah iaion. h G-P hniq offs sopia soion in asona i vn fo ong pdiion hoions. is hfo o onvnin fo syss wih a ag n of inay vaias and ong pdiion hoion as h opaion i inass inay and no ponniay wih h n of inay opiiaion vaias. RFRS poad. and. ignon. iqp.: aa fnion fo soving id ing qadai pogas. hnia Rpo. poad.. ignon and. oai 999. oving hoion siaion fo hyid syss and fa dion. n Podings of h ian ono onfn San igo. poad. and. oai 999. ono of syss ingaing ogia dynais and onsains. n: oaia : 7-7. oh P. and a oand Pédiiv. diions hnip Pais. aniy.s. V.S. oa and S.K. i 998. nifid fawo fo hyid ono: od and opia ono hoy. n: ansaion on oai ono : -. aaho.f. and. odons 999. od Pdiiv ono. Sping. a.w.. ohadi and P.S. ffs 987 Gnaid Pdiiv ono Pa h asi agoih Pa nsions and inpaion. n: oaia : 7-6 ah. oan G.. Jii. Raa J. Povi and. Vani 998. h-an nha s. hnia po opnis poj po 9-7. ay nodion o gni agoihs. hp:// -/vo/hw ai.h. Fh R. and S. yff 99. ia pin wih ow onds fo P anh and ond. hnia po p. of ahais Univsiy of nd Soand. Hap R.. and S.. Hap 998. Paia gni agoihs. Wiy w Yo. ohop K.W.. onpa dsign opiiaion of a is-na anspoaion ahi sing gni agoihs. hsis. ihawi Z Gni goihs aa Ss voion Pogas. Sping Y. a S. J. hoas. and J. isson. Gni agoih asd od pdiiv ono fo hyid syss nd a odifid fo. n: nnaiona jona of Hyid Syss -:-. Raan R. and.. Gossann 99. Raion wn P oding and ogia infn fo hia poss synhsis. n: op and hia ngining : 7-8. Ssg. and S. ng. pia ono of swihd oninos syss sing iding pogaing. n: h F Wod ongss on oai ono. hoas J.. and J. isson a. Pdiiv ono of hyid syss nd a i- foais wih sa spa poyhda paiion. n: ian ono onfn oson US Jn. hoas J.. and J. isson. od pdiiv ono fo hyid syss nd a sa paiion asd appoah SP. n: nnaiona onfn on nfoais in ono oaion and Roois Súa Poga gs. oisi F.. poad and. ignon. Hysd a oo fo gnaing hyid ods. hnia po U- oai ono aoaoy H Zih.