APPLICATION OF A PRECISE ANALOGUE IN SOLVING THE FUZZY PROBLEM OF OPTIMAL CONTROL FOR THE HYDRATION BLOCK

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1 WORLD SCIENCE ISSN APPLICAION OF A PRECISE ANALOGUE IN SOLVING HE FUZZY PROBLEM OF OPIMAL CONROL FOR HE HYDRAION BLOCK Associated Professor Elchi Melikov Azerbaija, Baku, Azerbaija State Oil ad Idustr Uiversit Abstract. I the article, based o a corehesive aalsis of the fuctioig features of the techological istallatio for roductio rolee glcol, a hsicall justified stateet of the otial cotrol roble for a hdratio block with idistictl described states is forulated. he obtaied roble is a otiizatio roble with fuzz araeters, for which the origial ethod of trasitio to a clear aalogue for the fuzz costrait sste usig (L-R)-reresetatio of fuzz ubers is roosed. Kewords: otial cotrol, fuzz iforatio, techological istallatio, recise aalog, (L- R)-reresetatio. Itroductio. his article is devoted to the roductio of rolee glcol, which is widel used i various idustries, i articular, as a workig fluid i hdraulic sstes, raw aterials i the roductio of atifreeze, varish ad aits, a oisturizer of tobacco i the food idustr, etc. Here we cosider the atheatical stateet of the cotrol roble for the hdratio block oeratig i fuzz iforatio ad the trasitio fro a fuzz sste of costraits to a recise aalog. Ivestigatio of the techological rocess of rolee glcol roductio showed that due to the strog sesitivit of both the quatitative ad qualitative idices of the target roduct to the chage i the regie araeters of each of the, the solutio of the cotrol roble usig kow classical ethods is ot alwas ossible [, ]. O the other, at the reset tie easurig istruets used for the autoatio of techological istallatios, which are obsolete both orall ad techicall, ake it iossible to obtai objective ad real iforatio about the rocess uder cosideratio usig these eas. I eistig local autoatio sstes, the absece of soe qualitative aalzers does ot allow oitorig for the ai idicators of the rolee oide hdratio i rolee glcol ad the variatio i outut araeters, the values of which var over a wide rage. he carried out researches have show that fuzz relatios betwee the coditios of restrictios o the doais of variatio of the cotrol araeters at the boudaries of the rocess regie, disturbig effects ad outut coordiates akes it iossible to use ol deteriistic odels for otial cotrol of the techological rocess uder cosideratio. I this coectio, there is the eed to develo fuzz algoriths ad atheatical odels for the roductio rocess of rolee glcol havig the abovedescribed features [3, 4]. For this urose, i the article uder cosideratio, oe of the fuzz regressio ethods, the estiatio ethod E D [5], was used to develo the above atheatical odels, which akes it ossible to costruct a atheatical odel uder the coditios of a assive eeriet. Stateet of the roble. Suose that X 0,, X,..., X are fuzz variables that take values o the set of all fuzz ubers F ( R ), ad assue that there is a liear relatioshi, i.e.: X 0 X... X () where i, ( i, ) are ukow real coefficiets ad X, ( ) 0, если если I. () Ad let htt://ws-coferece.co/ 4(3), Vol., Aril 08 3

2 WORLD SCIENCE ISSN E E( X ) E( X ) (3) i E( X ) ad E( X ) fuzz estiate for the value of D, resectivel, where are the etroies of the j th fuzz observable value ad the j th X * i X ij i. Here we cosider the etro of fuzz sets ( E( X ) X ( ) d ), the ebershi fuctio of which is also a fuzz set. R he criterio for solvig the roble of estiatig the coefficiets,..., is the coditio for iiizig itegral deviatio the etro estiated values of the deedet variable fro the etro of its observed values: ( ) ( i ( ) ( ), * * E E E E... j j (4) o coditio D( X, Xˆ ) h (5) j * * 0 j 0 j Here D is the degree of roiit for the fuzz ubers, h is soe give roiit stadard ( h 0, ), which is chose i accordace with the requireet of the roble: * * * = iij, j,. i * * It is kow that to fid ukow real coefficiets,..., the above-stated roble ca be trasfored ito a series of liear rograig robles. Whe costructig fuzz regressio odels, the hdratio block of the rocess for the roductio of rolee glcol is cosidered as a object whose iuts are: the cosutio of orolee ( ) ad the cosutio of water vaor ( ) ; cotrol actios: teerature i the hdrator ( u ), ressure i the aaratus ( u ) ad the ratio of the flow of water vaor to the feed of the orolee sulied to the hdrator; outut araeters: secific gravit ( ) ad quatit of orolee ( ) (see the Figure ). Fig.. Structural diagra of the hdrator as a odelig object Whe odelig, cotrol variables were assued to be fuzz variables. Without a doubt, i this case the variables ad will also be fuzz: 4 4(3), Vol., Aril 08 htt://ws-coferece.co/

3 WORLD SCIENCE ISSN , 75 0, ,093( 5.7)( 93.7) 73,569.5 u ; 3.97 ( u 7.) ; u u (6) (7) Whe costructig fuzz regressio odels for the hdrator, the ters for the araeters cosidered are show i able. able. Paraeters of hdratio odels i the rolee glcol roductio Paraeters eerature i the hdrator () Pressure i the hdrator (P) he ratio of the water vaor flow to the flow of the orolee (F/F) ers a b a b a b Sall Middle Big As ca be see, because of the fuzz of soe variables ad costraits, the otial cotrol roble over the rocess of roducig rolee glcol is a roble of fuzz otiizatio ad to solve it is ecessar to use the trasitio fro fuzz costraits to their recise aalogue. For this urose, the article uses (L-R)-resetatio of fuzz ubers. I view of the foregoig, the stateet of the otial cotrol roble for the rocess uder cosideratio ca be writte i the followig for: 0, 75 0, ,093( 5.7)( 93.7) 73,569.5 u a; 3.97 ( u 7.) ; u u (8) (9) (0) u 5 () 60 u 80 () (3) (4) 4 6 (5) Costructig a recise aalogue for solvig the cotrol roble. Whe odelig the state estiates of the hdratio block, the fuzz-uber (L-R) -te ebershi fuctios are writte i the followig for: htt://ws-coferece.co/ 4(3), Vol., Aril 08 5

4 WORLD SCIENCE ISSN a u L u a, 0 ( u) A u a R u a, 0, where L is the left reresetatio; R is the right reresetatio; a is the average value of the fuzz uber; ad, resectivel, the right ad left fuzziess coefficiets. L ad R are icreasig fuctios o the iterval 0,. Fuzz ubers (L-R) -te are writte i the for: А ( а,, ). he, usig the (L-R)-reresetatio, the objective fuctio ad the costrait sste (8) - (5) ca be rereseted i the followig for: F F F,,,, a (6) 0.75,, ( 5.7)( 93.7) ( u 4.9) 0.079,.5( 4.9),.5( 4.9) ; (7) u u , ( 7.) , ( 7.) ; ,, 3.97( u 7.) ,,,,.036,,,, u,, 5,, P P P P (8) ; (9) ; (0) P P 60,, u,, 80,, ; () ; () ; (3). (4) 4 6 akig ito accout the ricile of costructig a aalogue for the etreu of the fuzz objective fuctio, the criterio (6) ad the costrait sste (7) - (4) ca be rereseted as follows: 6 4(3), Vol., Aril 08 htt://ws-coferece.co/

5 WORLD SCIENCE ISSN F a, (5) F i, (6) F a, (7) ( 5.7)( 93.7) ( u 4.9) 0.079, u u , ( u 7.) (8) (9).5( 4.9), (30) ( 7.) , (3) ( 4.9), (3) ( 7.) , (33) , (34) u 5, (35) 60 u 80, (36), (37), (38), (39), (40), (4), (4) , (43) , (44) htt://ws-coferece.co/ 4(3), Vol., Aril 08 7

6 WORLD SCIENCE ISSN (45) 4 6 hus, the above sste of costraits (5) - (45) describes a ulticriteria oliear roble of vector otiizatio for the hdratio block of rolee glcol roductio uder icolete iforatio, the solutio of which ca be carried out b kow vector otiizatio ethods. Coclusios. he hsicall justified roble of otial cotrol for the hdratio block of the rolee glcol roductio, described b fuzz atheatical odels, is cosidered. For the uerical solutio of the forulated roble, a origial ethod of trasitio fro fuzziess to a recise aalogue for the sste of costraits i the cotrol roble is roosed. REFERENCES. I. R. Efediev, I. A. Mustafaev,. M. Magerraova. Develoet of otial cotrol algoriths for the techological rocesses of rolee glcol roductio (Stateet of the roble ad atheatical aalsis of otiizatio algorith). News of Higher echical Schools of Azerbaija. No. (8), (00).. I. R. Efediev, I. A. Mustafaev,. M. Magerraova. Develoet of otial cotrol algoriths for the techological rocesses of rolee glcol roductio (Algoriths for solvig otiizatio robles based o the Lagrage ethod). News of Higher echical Schools of Azerbaija. No. 3 (9), (00). 3. I. A. Ibragiov, I. R. Efediev, V.. Kositski, E. A. Melikov. Prisiles of costructio of self-learig autoatic cotrol sstes for cole techological rocesses i coditios of deficiet iforatio, Dokl. Akad. Nauk SSSR, vol. CCCXX (6) (99), I. A. Ibragiov, I. R. Efediev, V.. Kositski, E. A. Melikov. he desig of selflearig fuzz cotrol sste. Secod Euroea Cogress o Itelliget echiques ad Soft Coutig, Aache, Gera, Seteber 0-3, 994, Proceedigs, vol., Z. Y. Wag, S. N. Li //Fuzz Sets ad Sstes 36 (990), (3), Vol., Aril 08 htt://ws-coferece.co/

S. A. ALIEV, Y. I. YELEYKO, Y. V. ZHERNOVYI. STEADY-STATE DISTRIBUTIONS FOR CERTAIN MODIFICATIONS OF THE M/M/1/m QUEUEING SYSTEM

S. A. ALIEV, Y. I. YELEYKO, Y. V. ZHERNOVYI. STEADY-STATE DISTRIBUTIONS FOR CERTAIN MODIFICATIONS OF THE M/M/1/m QUEUEING SYSTEM Trasactios of Azerbaija Natioal Acadey of Scieces, Series of Physical-Techical ad Matheatical Scieces: Iforatics ad Cotrol Probles 009 Vol XXIX, 6 P 50-58 S A ALIEV, Y I YELEYKO, Y V ZHERNOVYI STEADY-STATE