Hybrid Fuzzy Convolution Model Based Predictor Corrector Controller

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Hbrd Fzz Covolo Model Bed Predor Correor Coroller Jáo ABOYI Árád BÓDIZS Lo AGY Fere SZEIFERT Dere of Chel Eeer Cbere Uver of Vezré P.O.Bo 58 Vezré H-80 HUGARY E-l: bo@b.ve.h Abr. Th er ree ew fzz odel bed redve orol lorh. The rooed redor orreor oroller bed o hbrd fzz odel whh o of fzz ed e odel d deede le reoe odel. The rel-e orol of lboror-zed he e hoe oler e d for he deoro of he rooed orol lorh. The rel how h he rooed lorh ble of oroll he oler roe h oere over wde re.. Irodo Ree er hve weed rd rowh he e of fzz lo oroller for he orol of roee h re ole d bdl defed. Mo fzz oroller develoed l ow hve bee of he rle-bed e where he rle he oroller e o odel he oeror reoe rlr roe o. A lerve roh e fzz or vere fzz odel roe orol ld he e odel d defo e. The oe of odel bed redve orol (MBPC) h bee herlded oe of he o f orol develoe ree er. The wde re of hoe of odel rre redo horzo d ozo rer llow he deer o el lor MBPC o h lo. The MBPC bed o fzz odel develoed o de hve bee of he T-Seo e where he fzz odel erole bewee ler e vr (LTI) odel []. Th er ree lerve ehod for de fzz oroller h re bed o he hbrd fzz ovolo odel of he roe. The rooed odel roh e h he roe deqel odeled wh ler d d oler. Th ool eoered drl roee h dllo d H erlzo. Bee of he re of he olere be effevel reoved fro orol roble llow le orol lorh ed of ooll eve oler ror oe wh he MBPC lo. Therefore he rooed MBPC re bed o redor orreor oroller hee. The rel-e orol of lboror-zed he e hoe e d for he deoro of he rooed orol lorh. The er orzed follow: The dero of he hbrd fzz odel eo. Seo 3 del wh he redor orreor oroller. The e d reeed eo 4. Seo 5 offer he relev olo.

. The Hbrd Fzz Covolo Model The rooed odel oe e h he dl e be odeled obo of oler ed e d d r. The o obvo rereeo be ve b he follow dree ovolo odel: ( ) ( ( ) ) ( ) 443 K () ede 4 444 4444 3 r d r A r o fro e he ovolo h o hdle of he le reoe odel d he - ( ) vle over he odel horzo. A eh l he ovolo lled b K( ) ed e whh deed o ed e.. The Sed-e r Fzz Model Sed-e odel bll dvde o wo le: heoeolol d erl. Pheoeolol odel lo ow fr-rle or ror odel re bed o hel derd of he derl h d her of he roe heoe. Whle derble o develo heoeolol odel ofe here o ffe derd of he derl hl d hel heoe. Bed o hee odero he ed e behvor of he e derbed b zero-order T-Seo [] or rod- r e fzz odel whh be forled b e of rle follow: where r... r f A d... d A he d... : ()... deoe he e of rle he ber of [.. ] T veor o ll of he fzz odel. A ( ) he... M -h eede fzz e referr o he - h whoe eberh fo re deoed b he e bol he fzz vle where M he ber of he fzz e o he -h do. Le he fr elee of he veor he ed e d he oer reer hv effe o he ed e o. Bed o h odero he fzz odel reree oler fo f (... ). U fzz feree bed o rod--rv ve he fl o of he fzz odel ferred b he wehed vere of he d... : M... M.. M M... β β d.. where he weh β > 0 le he overll rh vle of he.. h rle.. lled β ( ).. A eh fzz l vle:... Trlr eberh fo were eloed for (3)

A A (4) where deoe he ore of fzz e A For odel d orol roe he bewee f... (5) h o be deered. Th e he roble of he vero of he fzz odel. I h d he vero ehod rooed b Bb e l. w led [3]. Bed o he fzz odel he ed e of he ovolo odel be deered follow: f K... (6) A ve obervo he rl dervve of he fzz odel (Ble odel) be olved: Γ Γ...... l d A K (7) Γ oherwe 0 f (8). The D Pr (The Ile Reoe Model) The d r of he odel bed o ered -o d d ror owlede bo he roe d. Th owlede be rereeed b he rede e drbo of he e. For ele he de o of oo erfel ed oer h de fo of he redee e drbo: () τ τ τ ϕ e! (9) where he ber of he elee of he de d τ he redee e. I o e he reer d τ be el deered or be fed bed o he ered le-reoe odel. The dree le reoe (IRM) odel be lled follow: ) ( ) ( ϕ ϕ (0) where deoe he l e he h dree e-e d he odel horzo.

3. The Covolo Model Bed PCC Corol The redor orreor oroller (PCC) belo o he fl of odel bed redve oroller. The redor-orreor rle le wo ooe whh leol. Thee re he redo of he roe o bed o he roe odel d he orreo of he odel reer o he b of ered d fer he orol o [4]. The lorh r fro he f h e he vle of he orolled vrble d evell he e-o over he redo horzo () re ow. Th he vle of o be led he ervl [ ] be deered b er redo rle. Afer l he orol o he vle of he reded o be lo deered. The relzed orol o ed o lle he odeled roe o whh eloed o he odel error h ed o ree he odel r. The orol d he orreo rle defe he PCC. The orol rle: w where w deoe he reqred e-o he h dree e d deoe he redo horzo. The orreo rle: ε - - where deoe he ered roe o. I order o lle he vle of he ed e referee o vle he vle of he fre e-o ed w. U he fzz odel vero lorh he be el oed fro b eqo 5. Th he orol o of PCC he h l be forled : ε K where K h o be oed wh eqo 6. B he orreo rle (b he odel error) () he follow relo obed: ε K ( w ) () w K Forll h el P oroller wh b where he d he b vr e. I bl e h he le reoe odel ( ) he orol ove ( - ) d he ( ) ed e -o r re ow o he whole oer ervl. The PCC oroller h wo reer. Thee re he odel horzo d he redo horzo. The odel horzo h o be eql wh he el e of he roe. The redo horzo reree he e whh he orolled vrble h o be eql - o he be of he orol rle - wh he e-o. (3)

4. Rel - Te Eere The oroller w ofred o rr o eerre orol lboror le elerl wer-heer. The he dr of he roe how fre. 33.5 T o T o He T PC 33.5 CVO CVC PCL-8 T CV F q Fq wer Fre. The hee of he hl e The wer oe fro he wer ele o he heer hroh orol vlve (CV) before of flow-re er flow re F d le eerre T. e he wer e hroh r of el e o rrde heer. The rrde heer re led rllel. Eh oher hve erfore of W. The orol o he o eerre T o of he herl e dered vle b d he he orol l of he rrde heer dffere herl e flow re. The ed e o T o deed ol o he herl e flow-re F d he ed e. The fzz odel el reree h reloh: r (4) : f F A d A he d Se for ood odell erfore 4 d 7 eede fzz e o vere were lzed. Fre. how he rfe rereeo of he ed-e fzz odel. 50 40 T 30 0 0 0.5 0 50 60 F 70 80 90 Fre. The rfe rereeo of he fzz odel of he ed-e behvor The f of eqo 9 d 0 o ered le-reoe rve hree dffere flow-re led o he hoe of. Th be ereed below: q q e( q ) e( q ) where q fo of he flow-re [5] e deoe he l e d he h dree e-e. (5)

Fre 3 how he erfore of he oroller der led oe-free odo d rel-e lo. The rel how h he rooed lorh ble of oroll he oler roe h oere over wde re. 6 35 e [ ] 4 e [ ] 30 5 0 0 50 00 50 00 50 300 350 400 450 500 [T0e] 0 0 50 00 50 00 50 300 350 400 450 500 [T0e] [0-] 0.8 0.6 0.4 0. 0 0 50 00 50 00 50 300 350 400 450 500 [T0e] [0-] 0.8 0.6 0.4 0. 0 0 50 00 50 00 50 300 350 400 450 500 [T0e] Slo 6 60 Rel-e 0 60 Fre 3. Sled d rel-e lo-re orol erfore The heved orol erfore h beer h he ol PID oroller d he ler odel bed DMC oroller [5]. 5. Colo Th er reeed he ble of he lo of fzz ovolo odel redor orreor orol of deled d drbed reer e wh oler fere. The rel-e orol of lboror-zed he e hoe e d for he deoro of he rooed orol lorh. Referee [] Le D. A. Kdh S. Lo-re Predve Fzz Corol Tr ICheE 74 (996) o. A. 77-88. [] T T. Seo M. Fzz Idefo of Se d Alo of Model d Corol IEEE Tr. o Se M d Cbere 5 (985). 6-3. [3] Bb R. Fzz Model d Idefo Ph.D. The Delf Uver of Teholo 997. [4] Szefer F. Chov T. L.????? Coer he. E. 6/S (99). 97-04. [5] Bódz Á. Model Predve Corol of Chel Proee Ph.D. The Uver of Vezré Vezré Aowledee The fl or of he Eövö Sholrh d he Hr Mr of Clre d Edo (PFP-VE-MK-30-997) d he Hr See Fodo (OTKA T0357) rel reed.

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