Design of ANFIS Controller for DC-DC Step-Down Converter. DA-DA Gerilim Azaltan Konvertörler için ANFIS Denetleyici Tasarımı

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1 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Desgn of ANFIS Controller for DC-DC Step-Don Converter Ömer Deperloğlu a, Uçman Ergün b ve Gür Emre Güraksın c a Afon Kocatepe Unverst, Engneerng Facult, Bomedcal Engneerng Department, Afonkarahsar, Turke e-posta: b Afon Kocatepe Unverst, Engneerng Facult, Electronc & Communcaton Engneerng Department, Afonkarahsar, Turke e-posta: c Afon Kocatepe Unverst, Engneerng Facult, Computer Engneerng Department, Afonkarahsar, Turke e-posta: Gelş Tarh: 8 Nsan 0; Kabul Tarh: Maıs 0 Abstract In ths paper, a general purpose Adaptve Neuro Fuzz Inference Sstem (ANFIS) controller for dc-dc stchng converters s researched. It has been proved that ANFIS controllers are capable of appromatng an real contnuous control functon a compact set to arbtrar accurac. In partcular, an gven lnear control can be acheved th a ANFIS controller for gven accurac. For ANFIS, the presented approach s general and can be appled to an dc-dc converter topologes. Smulaton of buck converter results demonstrated that the converter can be regulated th a good performance even thought subjected to nput dsturbance and load varaton. Ke Words: ANFIS, Fuzz logc control, dc-dc converters, stch-mode converters. DA-DA Gerlm Azaltan Konvertörler çn ANFIS Denetlec Tasarımı Özet Bu makalede, DA-DA Buck Konvertörler (gerlm azaltan) çn, genel amaçlı Uarlamalı Snrsel Bulanık Mantık Çıkarım Ssteml denetlecler araştırılmıştır. ANFIS denetleclern, herhang br sürekl gerçek kontrol fonksonun çözümünde etenekl olduğu spatlanmıştır. Özellkle ANFIS denetlec le verlen herhang br doğrusal denetmde arzu edlen kesnlkte gerçekleştrleblr. ANFIS çn bahs geçen aklaşım geneldr ve herhang br DA-DA konvertör topolojsne ugulanablr.yapılan Smülason sonuçları konvertörün grştek bozulmalara ve ük değşmlerne rağmen çıkış gerlmn düzenledğn göstermektedr. Anahtar Kelmeler: ANFIS, Bulanık mantık kontrol, DA-DA konvertör, Anahtarlamalı tp konvertörler.. Introducton DC-DC converters are the poer electronc crcuts that convert the DC voltage to dfferent DC voltage level and mostl produce regulated output. In general, these crcuts are classfed as stched-mode DC-DC converters. (Hart, 997; Mohan et. al., 995; Lander, 993). In some resources, the are called as stchng-mode regulators (Rashd, 988) or DC-DC chopper (Gürdal, 997, Bradle, 987). Man probablstc methods have been developed over the past several decades, and are no beng used more del n poer sstem operatons and plannng to deal th a varet of uncertantes nvolved. Eamples of these uncertantes are equpment outages, load forecast uncertantes, eather condtons, uncertantes n the avalablt of basc energ and operatng consderatons (Sngh and Wang, 008). The DC- DC converters have been controlled successfull for ears b usng the analog ntegrated crcut technolog and lnear sstem desgn technques. Wth begnnng of operaton of sem-conductve materals as a stch, the converter process could be defned th seres of lnear connectons. The 7

2 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs appled technques can be used to obtan lnear average models th a good approach to sectonal behavors of the sstem. Recentl, researches make studes about applcaton of the fuzz logc prncples on control of DC-DC converters. Controllng of the DC- DC converters th fuzz logc controller has been tred to be developed through the orld-de researches. (Ba et. al., 003; Elmas et. al., 009; So and Tse, 996; Ln, 995; Mattavell et. al., 997; Ln, 997; Leva et. al., 997). The control acton n the fuzz logc controller s determned b means of evaluaton of the group of smple language rules. Development of rules requres the sstem that s beng controlled to be full comprehensble. Hoever, t does not requre the mathematcal model of the sstem. Consequentl, technque s general and for ths reason, a control schema developed for an tpe of DC-DC converters can also be easl appled on other tpes (Ba et. al., 003). The ANFIS can smulate and analss the mappng relaton beteen the nput and output data through a learnng algorthm to optmze the parameters of a gven fuzz nference sstem (FIS). It combnes the benefts of artfcal neural netorks (ANNs) and FISs n a sngle model. Fast and accurate learnng, ecellent eplanaton facltes n the form of semantcall meanngful fuzz rules, the ablt to accommodate both data and estng epert knoledge about the problem, and good generalzaton capablt features have made neuro-fuzz sstems popular n the last fe ears (Daldaban and Ustkouncu, 009). Because of these fascnatng features. In ths paper, controllng of a buck converter b means of an ANFIS controller s consdered. The fuzz logc control rules and membershp functons of the sstem have been establshed. A smulaton stud of the sstem control th the ANFIS controller n C programmng language has been made.. Adaptve Neuro Fuzz Inference Sstem The fuzz nference sstems and mult-laer perceptrons are specal samples n ver general calculaton studes of adaptve netorks. ANFIS s a class of adaptve netorks that s functonall equal to fuzz nference sstem. The ANFIS sstem that means a adaptve netork-based fuzz nference sstem or an adaptve neural fuzz nference sstem conssts of ntals of ts orgnal name; Adaptve Netork-based Fuzz Inference Sstem or Adaptve Neuro Fuzz Inference Sstem (Gupta et. al., 997). Meanhle, n some resources, ANFIS s defned as the TSK fuzz rules and neuro-fuzz controller. TSK means Sugeno fuzz model or Takag, Sugeno, Kant fuzz logc model (Ln and Lee, 996). It s also called as hbrd neural netorks (Jang et. al., 997). It s a method that depends on the prncple of adjustment of fuzz control parameters th neural netorks from methods of combnaton of fuzz logc and artfcal neural netorks. In fact, the fuzz nference sstem s stronger than the mult-laer perceptron. For nstance, some unque features of ANFIS controllers can be defned;. Learnng ablt,. Parallel processng, 3. Structured nformaton representaton, 4. Better ntegraton th other control desgn methods. The mult-laer perceptron also has the features gven n st and nd but not the features gven n the 3rd and 4th... The ANFIS Archtecture To easl understand the archtecture of fuzz nference sstem n structure of ANFIS, f t s consdered that t has to nputs as and and one output as z, the to fuzz If-then rules for the frst degree Sugeno fuzz model ll be as n equaton. 8

3 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Rule : IF Rule: IF A and B A and B Then f pq r Then f pq r () In the equaton, =, and j=, ; and represents the nput varable, output varable, A, A the lngustc terms of sub modes together th the membershp functon, p, q, r R ; f j (, ) represents the coeffcents of lnear equatons. The output of. node n L laer s gven as O l,besdes,all nodes n the same laer have the same node functon. In fgure, the Sugeno tpe fuzz nference method th to nputs and to rules s gven. f=f(,) corresponds to the neest functon n result and to frng strength n A and B fuzz sets, and all the outputs are obtaned th eghted average. Mn or proc A B X Y f =p +q +r A B f =p +q +r X X Y f f f f f f eghted average Fgure. Sugeno tpe fuzz nference th to nputs and to rules In Fgure, the ANFIS archtecture that s equal to the Sugeno tpe fuzz nference th to nputs and to rules s seen. The node functons that belong to each laer n the ANFIS archtecture and so, functons of laers are gven belo respectvel. Laer : Each node n ths laer s an nput node here eternal sgnals are transferred to other laers. Laer : Each node n ths laer behaves lke the membershp functon of A () and the degree of ts output characterstcs conforms to that characterzes A. So, t s an adaptve node th ts node functon and the node outputs are as n equaton., for o 3,4 for o,, ( ) A B ( ) () Here, and are nputs to. node and A or B - are lngustc labels lke less-more that combne th ths node. In other ords, o, s the membershp degree of fuzz set A lke A=A, A, B and the gven nput determnes the membershp degree that corresponds to the quantt determnant A for or. Here, an desred membershp degree can be used. In general, bellshaped membershp functons (mamum = and mnmum = 0 ) s used and the result functon s gven n equaton 4. 9

4 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Laer Laer Laer 3 Laer 4 Laer 5 Laer 6 A A W N f f B B W N f Fgure. The ANFIS archtecture that s equal to the Sugeno tpe fuzz nference th to nputs and to rules ( ) A b c a c A ep a b (3) (4) here, {a, b, c } s the parameter set havng the adjustment parameters. Wth changng of values of these parameters, the value of bell-shaped curve functon also changes. So, varous structures of membershp functons for the fuzz set A are ehbted. The parameters n that laer are called as antecedent parameters. Laer 3: Each node n ths laer s labeled th and t ponts out the multpler of all nputtng sgnals. In other ords, the output of ths node s a product of all sgnals and t sends the obtaned product to outsde. The output of node can be epressed as n equaton 5. o 3, A B ( ) ( ),,. (5) The output of each node represents the frng strength of one rule. An of T-norm operators that realze the generalzed fuzz AND can be used as a node functon for nodes n that laer. Laer 4: Each node n ths laer s labeled th N and a normalzed frng strength of one rule s calculated. As t s seen n equaton 6, the frng strength of. rule for. node s equal to total of frng strength of all rules. o,, (6) 4, Laer 5: Each node n that laer s an adaptve node th the node functon. Each node calculates the values of eghted results. The output functon of node s gven n equaton 7. o f ( p q r ) 5, (7) Here, s the output of laer 4 and a normalzed frng strength. The adjustment parameter set s requred to adjust the {p, q, r }. Parameters n that laer correspond to consequent parameters. Laer 6: In that laer, there s onl one node and s labeled th. Ths means the total of all consequent sgnals for the hole sstem. Wth 0

5 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs total of all sgnals, the result gven n equaton 8 s obtaned. f overall output o6, f (8) So, a model ANFIS structure that s functonall equal to Sugeno fuzz nference model s defned. The structure of the netork s not full constant. Establshment of the netork and separaton of the node functons accordng to ther dutes can be elected arbtrarl dependng on hat s ensured b each node n ever laer and ther modular functonalt. It can be easl passed from the Sugeno tpe ANFIS to the Tsukamoto tpe ANFIS. Generall, these to tpes are used. For the ANFIS correspondng to the Mamdan tpe fuzz nference, the Ma-Mn composton and result can be obtaned b means of the Center of Gravt Defuzzfcaton Method for output. Hoever, ths s ver dffcult and comple for the Sugeno or Tsukamoto tpe ANFIS. Besdes, t does not make a sgnfcant contrbuton to the learnng ablt and approachng poer. Adjustment and updatng of the adjustment parameters n the ANFIS archtecture s onl possble th backpropagaton method. Besdes, the Kalman flter method can also be used to fnd the result parameters of ANFIS (Fullér, 995; Nauck and Kruse, 997). For ths process, all the result parameters are arranged as a vector n form of p q r p q r T,,,,, and th Kalman flter method, t can be obtaned as belo n equaton 9. ( () () n) () () () () () () () () () () () () () () () () () () p q () d r () d p q d r (9) [((k), (k)), d(k)] k=,,, n used n the equaton s the k. educaton part and besdes, ( k ) ( k ) and s the output of laer 4 that s ( k ) ( k ) combned th, nputs... Applcaton of the hbrd learnng method to ANFIS When values of antecedent parameters n the ANFIS archtecture are constant, from end to end output can be epressed as lnear combnaton of the result parameters. For the ANFIS archtecture th to nputs and to rules gven n Fgure, the f output can be rertten as n equaton 0. f ( ) p ( p q f r ) ( ) q f ( p q r ) r ( ) p ( ) q r (0)

6 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Here, the p, q, r, p, q, r result parameters are lnear. So, the hbrd learnng method can be drectl appled to ANFIS. Here, node outputs of the hbrd learnng method are dspersed forard up to Laer 5 durng ther forard pass and the consequent parameters are defned th least squares method. In backard pass, the error rates propagate backard and the antecedent parameters are upgraded b the gradent descent. So, the defned consequent parameters are the most approprate hen the antecedent parameters are constant. For ths reason, as the hbrd forecast decreases the research space dmensons of the orgnal backpropagaton method, the speed drecton toards to a one pont s speeder. These passes are brefl gven n Table. Table. To passes n the hbrd learnng method for ANFIS Forard pass Backard pass Antecedent Constant Gradent descent parameters Consequent Least squares Constant parameters method Sgnals Node outputs Error rates The learnng mechansm n Sugeno tpe ANFIS does not requre addton for defnton of membershp functons. So, the lngustc and objectve defntons of badl defned concepts are not moved. In that case, t ma be thought that the decson s left to the user. In prncple, f the nput and output data set s ver bg, the membershp functons must be adjusted full. In contrar, f the data set s ver small and does not cover suffcent nformaton about the target sstem, t represents sgnfcant nformaton that does not reflect on the membershp functons data group defned b people. For ths reason, the membershp functons must be kept constantl durng learnng processes. If the membershp functons are constant and the result pece can be adjusted, Sugeno ANFIS can be consdered as a functonal connecton netork. Here, the rased representatons of nput varables can be obtaned th membershp functons. These rased representatons are defned b ves of eperts ho kno the sstem ver ell b beng produced th product models outsde or functonal epanson. The updatng of formulas for the antecedent and consequent parameters completel depends on the hbrd learnng rule. 3. The Sample ANFIS Applcaton For DC-DC Converters In ths secton, control of a buck converter th ANFIS controller s defned. The fuzz logc control rules and membershp of the sstem have been establshed. The smulaton stud of controllng of the sstem th ANFIS controller has been made n C programmng language. In fgure 3, the schema of closed loop ANFIS controller sstem for DC- DC buck converter s gven. The control nput mpulsng rate of converter n the sstem s d. The error s represented th e and defned n equaton. e=v ref -V o () Here, V o s the output voltage of DC-DC converter and V ref s the desred output voltage. The change or dervatve of error s represented th de and for the k. step, t s as n equaton. du(k)= e(k)-e(k-) () Output of the fuzz control algorthm s the change or ncrease amount n dut rato du(k). The dut rato d(k) s obtaned as n equaton 3 here dut rato n prevous phase s added to the change calculated n k. samplng tme. d(k) = d(k-) + du(k) (3)

7 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Fgure 3. The schema of close crcut ANFIS controller sstem for DC- DC buck converter. 3.. Values of the Smulated Converters The elements of buck converter and ts necessar values are elected as n Table. The state varables of the crcut accordng to these elected values are as n Equatons 4, 5 and 6. 0 A A ; (4) 3.. PI Controller ht Current Control for Buck Converter For purpose of comparson, the step-don (buck) converter as frstl operated th current controlled PI controller. After several trals, the most approprate PI controller coeffcents ere found as follos. Gan for current control β : 0. Integral tme constant T : 400 Stchng frequenc F s : 5000 Hz B ; B=0 ; (5) C=C=[ 0 ] (6) The calculaton step n smulaton s taken as ts= Besdes, reference value for the above values s elected as V ref =5 V. The values of buck converter nput voltage Vn= 50 V, output voltage Vref=5 V, nductance L= mh, capactor C=00 F, equvalent load resstance R= 4, stchng frequenc fs= 5 Kh. The output voltage obtaned as a result of the smulaton and bobbn current are gven n fgure 4 and 5 respectvel Buck Converter Control th ANFIS The control model n fgure as appled same to the buck converter gven n table. The ntal membershp functon group that changes n [-00, 00] nterval of the sstem s seen n fgure 6. 3

8 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Fgure 4. Inductor current for PI controller Fgure 5. Output voltage for PI controller 4

9 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs µ() Intal Membershp Functon X Fgure 6. The ntal membershp functons Once the controller s operated and the consequent parameters are used as antecedent parameters, after total 0 learnng epochs, t ma fnd necessar parameters for the membershp functons and rules. The step szes curve durng the learnng epochs s gven n fgure 7. As far as the learnng epoch s advances, the step sze decreases lke a stars step. For ths reason, the decreasng ncreasng rates of parameters durng learnng decrease th step sze. 0. Step Sze ss Learnng Epochs Fgure 7. Ptch measure accordng to learnng ccles The Gaussan Bell or bell curve membershp functon gven n equaton 4 has total three parameters as a, b and c. As the determnant of three membershp functons for A and B sets s 5

10 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs =,, 3, the total parameter number n both sets s 6. The number of p, q and r parameters of rules sampled n equaton 7 s 3 = 9 for to nputs and three membershp functons. Ths sstem establshed b calculatng the parameters as used to fnd the dut rato of buck converter of hch characterstcs gven above. The smulaton stud of fuzz logc controller obtaned th adaptve neural fuzz nference method and the buck converter as made and the obtaned curves are gven n fgures belo. Whle the load at output durng operaton s 4, t s decreased half after ms and made. The output voltage aganst the sad load change s affected less than other method. In fgure 8, a curve of crcut operaton current and n fgure 9, a curve of converter output voltage s gven. The curves obtaned as a result of the applcaton ndcate that the ANFIS controller reaches to the reference value faster than the PI controller and s affected from load changes lesser than t. 4 Inductor Current I (A) t(s) 0-3 Fgure 8. Inductor current for ANFIS controller 6

11 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Output Voltage Vo (V) t(s) Fgure 9. Output voltage for ANFIS controller 4. Smulaton Results and Dscusson In the controller desgn realzed n ths stud, the adaptve fuzz control or neural-fuzz control as used. In short, th ths method that ma be defned as combnaton of learnng ablt of artfcal neural netorks th nference mechansm of fuzz logc, t as amed to ncrease adaptveness of the sstem. Consequentl, b usng the neuro fuzz nference sstem th 3 membershp functons and 9 rules called as ANFIS, an Adaptve controller as desgned and appled to a buck converter. From the eperments made for purpose of comparson, t as determned that the ANFIS controller s more effectve and faster than the PI controller. The ANFIS controller reaches to the reference value faster than the PI controller and s affected from load changes lesser than t. Besdes, an Adaptve fuzz logc controller that s at least to tmes faster and more senstve than the controllers made th onl fuzz logc control or artfcal neural netorks n references (So and Tse, 996; Ln, 995; Daldaban and Ustkouncu, 009) as realzed. As seen from the Fgures the output voltage V o s kept almost constant under large nput voltage or load changes. 5. Conclusons Ths paper has focused on an ANFIS controller for DC-DC converters. The desgn of ANFIS controller for DC-DC converters has descrbed and computer smulaton s made. As t s stated prevousl, n fact there s a combned dffcultes seres n the desgn of fuzz logc controller. The common bottleneck n dervaton of fuzz control rules s that t often takes much tme; t s dffcult and requres epert knoledge and eperence related to the sstem. For ths reason, eperts have to remove dffcultes and decrease the adaptveness ablt and learnng ablt of fuzz sstems. In that case, the frst thng that must be done s to beneft from the learnng ablt of artfcal neural netorks. Electon of learnng method, dut knoledge feld and naturalt of avalable nformaton are 7

12 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs determned. Recent studes attempt to combne fuzz logc, artfcal neural netorks and genetc algorthm to understand learnng n dversfcaton of applcatons. The common approach s to use Genetc Algorthms (GA) n dervaton of parameters of fuzz or adaptve netorks. Though the structures and algorthms of Artfcal Neural Netorks are comple, t s knon that the conform to dnamc behavors of phscal sstems. On the other hand, t s sad that GA s especall convenent n comple nformaton areas. So, t can be used for structuralsm n fuzz or neural netorks sstems and parameter adaptaton. Hoever, to fnd convenent solutons ma take ver long tme. Ths s a ver poerful learnng approach that possesses the advantages of values pecular to these three methodologes. In follong studes on controllng of converters, ths method ma be consdered for ts more poerful learnng and more effectve response ablt. References Hart, D. W.,997, Introducton to Poer Electroncs, Prentce Hall Internatonal Inc, U.S.A.. Mohan, N., Undeland, T. M., Robbns, W.P.,995, Poer Electroncs: Converters, Applcaton and Desgn, Second edton, John Wle & Sons, Neork. Lander, W. C.,993, Poer Electroncs, Mc Gra-Hıll, London. Rashd, M. H., 988, Poer Electroncs Crcuts, Devces and Applcaton, Prentce- Hall Int. Inc, Ne Jerse, USA. Gürdal, O., 997, Güç Elektronğ, GÜTEF, Ankara. Bradle, D. A., 987, Poer Electroncs, VNR (nternatonal) Co. Ltd., London. Sngh, C., Wang L., Role of Artfcal Intellgence n the Relablt Evaluaton of Electrc Poer Sstems, Turk J Elec Engn, Vol.6, No.3, 008, 89-00,, Ba, O., Deperloglu, O., Elmas, C., 003,Fuzz control of dc-dc converters based on user frendl desgn, Internatonal Journal of Electroncs, vol.90, no.7, pp Elmas, C., Deperloglu, O. and Saan, H. H., 009, Adaptve fuzz logc controller for DC DC converters, Epert Sstems th Applcatons, Mar 009, Vol.: 36 Issue: p- p: So, W-C., Tse, C. K., 996, Development of a fuzz logc controller for DC/DC converters: Desgn, computer smulaton, and epermental evaluaton, IEEE Transactons on Poer Electroncs, Vol., No:, 4-3. Ln, B-R., 995, Poer converter control based on neural and fuzz methods, Electrc Poer Sstems Research, 35, Mattavell, P., Rossetta, L., Spazz, G. and Tent, P., 997, General-purpose fuzz controller for DC-DC converters, IEEE Transactons on Poer Electroncs, Vol., No:, Ln, B-R., 997, Analss of neural and fuzzpoer electronc control, IEE Proc. -Sc. Meas. Technol., Vol. 44, No:, Leva, R., Martnez-Salamero, L., Jammes, B., Marpnard, J. C., and Gunjoan, F., 997, Identfcaton and control of poer converters b means of neural netorks, IEEE Transactons on Crcuts and Sstems-: Fundamental Theor and Applcatons, Vol. 44, No:8, Daldaban, F., Ustkouncu, N., 009, Inductance Estmatng of Lnear Stched Reluctance Motors th the Use of Adaptve Neuro-Fuzz Inference Sstems, G.U. Journal of Scence, (): Gupta, T., Boudreau, R.R., Nelms, R. M. Ve Hung, J. Y., 997, Implementaton of a fuzz controller for DC-DC converters usng an nepensve 8-b mcrocontroller, IEEE transacton on ndustral electroncs, Vol. 44,No. 5, October,

13 Deperloğlu, Ergün ve Güraksın/ AKÜ Fen Blmler Dergs Ln, C.-T., George Lee, C. S., 996, Neural Fuzz Sstems, Prentce Hall PTR, Ne Jerse, USA. Jang, J.-S. R., Sun, C.-T., Mzutan, E., 997, Neuro-Fuzz And Soft Computng, Prentce- Hall Inc., Ne Jerse, USA. Fullér, R., 995, Neural Fuzz Sstems, Ábo Akadem, Ábo. Nauck, D., Kruse, R., 997, Neuro-fuzz sstems for functon appromaton, Otto-von- Guercke-Unverst of Magdeburg, Magdeburg, German. 9

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