Artificial Bee Colony-Based Design of Optimal On-Line Self-tuning PIDController Fed AC Drives

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1 Fom the SelecteWoks of nnovatve Reseach Publcatons RP na Wnte Decembe, 04 Atfcal Bee Colony-Base Desgn of Otmal On-Lne Self-tunng PDContolle Fe AC Dves nnovatve Reseach Publcatons, RP na, nnovatve Reseach Publcatons Essamun A. Ebahm Avalable at: htts://woks.beess.com/na/3/

2 ntenatonal Jounal of Engneeng Reseach (SSN: )(onlne),( )(Pnt) Volume No.3, ssue No., : Dec. 04 Atfcal Bee Colony-Base Desgn of Otmal On-Lne Self-tunng PD- Contolle Fe AC Dves Essamun A. Ebahm Powe Electoncs an Enegy Conveson Deatment Electoncs eseach nsttute, El-tah Steet, 6 Dokk,, Cao, EGYPT essamun@yahoo.com Abstact n ths ae, an otmzaton metho base on the foagng behavo of a colony of honey bees n natue was oose. An otmze moel fo Pootonal ntegal Devatve (PD)- see contolle of 3-hase M ves was ntouce to aat the constant gans of ths classcal contolle. To enhance obustness of ths contolle, an onlne algothm fo self-tunng of PD contolle-aametes was oose. Exemental wok was ntouce usng DSP an test esults wee obtane fo seveal see tajectoes of -egee of feeom M ve an comae wth conventonal PD contolles. eywos Atfcal Bee Colony Otmzaton, ftness, Objectve functon, Scout an Onlookes, nucton Moto JER@04. ntoucton The ootonal-ntegal- evatve (PD) contolles have been wely use n nusty fo many yeas. Unfotunately, obustness an otmzaton not be acheve wth ths contolle ue to uncetanty of lant, an system nonlneaty. The Zegle an Nchols tunng metho s mostly use to comute otmal PD gans fo the lant une cetan oeatng ont. f the aametes of the lant ae change ue to uncetanty o nonlneaty, the contolle becomes not obust an not n otmum state. Patcle Swam Otmzaton (PSO) (E. A. Ebahm et al, 03), o gem of ntellgent (as ant colony otmzaton ACO (Q. Zeng an G. Tan, 007) an bactea foagng BF, (A. Oshba an E. Al, 04) technques have nse as technques fo otmal esgn of PD contolles. One such a algothm s the Atfcal Bee Colony (ABC) algothm that oose by (aaboga n 005). Most atcles suggest off-lne esgn fo PD-contolle aametes an then use n on-lne contol. n ths ae, authos have eveloe an otmzaton oceue base on the foagng behavo of an atfcal bee colony. The foagng behavo s eceve as a mnmzaton metho an an otmzaton famewok that use n esgnng of nect fel-oente (FO) vecto contol of nucton moto contolle. The oose ABC technque s use n on-lne self-tunng of PD- contolle aametes to acheve otmzaton. Ths oose ntellgent contolle s abbevate an known as (ABC-PD) contolle. Ths ae s oganze as follows: Secton ntoucton, Secton eals wth mathematcal moellng of fel-oente vecto-contol of M, objectve functon an ABC algothm. Secton nclues test esults an comason stuy.. Mateal an Methoology A. Mathematcal Moel of fel-oente M The ynamc state equatons of a 3-hase M can be escbe n a fxe stato -q fame (D. W. Novotny an T. A. Lo,996) as follow: [ Rs + X] ν s ν ( X) = ν XM ν q XM ( ). X) [ Rs + X] XM ). XM XM ( XM) [ R + X] X ( ). XM) s X M X ). b q [ R + X]. P Te = ( λs 3 3 P 3 P Lm ) ( ) ( λ s = Lm q s = λ q s L λ ) O, m T e = J + B m + T (3) l t R = = (4) e * e * * * sl ( S s ) = e * e * L s τ s The moto eveloe toque can be ectly elate to () () e* fom eqn. () as: 3 P L m e * * e e * e * T e = λ = T λ (5) L The schematc agam of FO-M ve wth the oose see contolle s shown n fgue (E. A Ebahm, 00). B. Fomulaton of Objectve Functon Atfcal bee colony (ABC) tunng algothm s use to get the otmum values of gans fo the PD-contolle base on see eo. All the atcles of oulatons ae ecoe fo,,. The contolle esgn s fst eafte as an otmzaton oblem whee the objectve functon comses ynamc esonse secfcatons. Page 807

3 ntenatonal Jounal of Engneeng Reseach (SSN: )(onlne),( )(Pnt) Volume No.3, ssue No., : Dec Fo each onlooke bee {Select a soluton X eenng on P Pouce soluton ft Aly geey selecton ocess} X Calculate the value 9. f thee s an abanone soluton fo the scout. Then elace t wth a soluton whch wll be anomly ouce by () 0. Memoze the best soluton so fa. cycle= cycle+. Untl cycle=mcn Whee, X eesents a soluton, ft s the ftness value of X, X ncates a neghbo soluton of X, obablty value of the algothm. P the P an MCN s the # of maxmum cycle n Fgue. Close-loo see contol of an M base on nect fel-oente contol Two objectve functons ae oose. The fst one uses ntegal Tme Absolute Eo (TAE). TAE s chosen as an objectve functon because of ts avantage n oucng smalle oveshot an oscllatons. Equaton 6 eesents the fst objectve functon as: 0 * TAE = ( t e ( t ) ) t (6) (An\O) the secon objectve functon can be eesente as: Mnmze F ( φ ) = + t (7) Subject to the constant: φ the set of contolle Whee, JER@04 s mn, an * φ φ max, whee φ eesents e( t ) = (8) n an off-lne contol of M ve, equatons (6-8) wll be use as objectve functons to otmze the ntal gans of the oose contolle. C. Atfcal Bee Colony (ABC) Otmzaton n ABC moel, the colony conssts of thee gous of bees: emloye, onlookes an scouts (A. au an S. Goya, 0) - Pseuo-coes of the ABC algothm (Teooovc et al.,0). Loa samles of contolle aametes. Geneate the ntal oulaton x, =,,... FS 3. Evaluate the ftness ( ft ) of the oulaton 4. set cycle to 5. eeat 6. Fo each emloye bee {Pouce soluton X by usng eqn. (). Calculate the value ( ft ) by usng eqn. (0).Aly geey selecton ocess} 7. Calculate the obablty values ( P ) fo the solutons ( X ) by eqn. (9) - Detale Exlanaton fo the Algothm n the algothm, fst half of the colony conssts of emloye atfcal bees an the secon half consttutes the onlookes. The numbe of emloye bees s equal to the numbe of foo souces (# of solutons n the oulaton). At fst ste, the algothm stats by ntalzng all emloye bees wth anomly geneate foo souces (solutons), whee SN enotes the sze of oulaton. Each soluton x, =,,... FS s a D-mensonal vecto. Whee D s the numbe of otmzaton aametes. Hee, n ths stuy, D- eesents the PD-contolle aametes to be otmze..e., D = [ ] Afte ntalzaton, n each teaton of all gven cycles, evey emloye bee fns a foo souce neghbouhoo of ts cuent foo souce an evaluates ts necta amount,.e. ftness). n geneal the oston of foo souce s eesente as: X = X, X,..., X ). ( D th Afte the nfomaton s shae by the emloye bees, onlooke bees go to the egon of foo souce at X base on the obablty P = FS k = ft P etemne as: ft k Whee, FS s total numbe of foo souces. Ftness value (9) ft s calculate usng: ft = + f ( X ) (0) Hee, f X ) s the objectve functon, n ths stuy, an objectve ( functon s TAE etemne fom equaton 6 an /o F (φ ) that etemne fom eqn. 7. The onlooke fns ts foo souce n the egon of X by usng the followng equaton: X = X + ( X X ) () j * j kj Page 808

4 ntenatonal Jounal of Engneeng Reseach (SSN: )(onlne),( )(Pnt) Volume No.3, ssue No., : Dec. 04 Whee, k (,,3,... FS ) such that k an j (,,3,... D ) ae anomly chosen nexes, s a unfomly stbute anom numbe n the ange [-,]. The value of eetemne numbe of cycles s an motant contol aamete of the ABC algothm, whch s calle lmt fo abanonment. Assume that the abanone souce s X an J {,,... D }, then the scout scoves a foo souce to be elace wth X. Ths oeaton can be exesse (. Vvekananan et al, 0 an M. çelk et al, 0) n the followng elaton: j X j j j = X + an 0,)( X X ) () mn ( max mn D. On-lne tunng of ABC-PD contolle The tunng ocess eens on the ate of change of eo sgnal an ts value. The sequence of ogam suboutne algothm can ntouce as a flow chat of fgue. n the flowchat, thee ae thee categoes fo eo values: e (t ) > e. e(t)< max e. mn e e(t) mn e max Yes Tune Only ntalzaton No s e(t)> e(max)? s e(t)< e(mn)? Fgue. Flow chat of ABC-PD on-lne Contolle. Test Results an Tables A comute ogam was wtten n MATLAB (m-fle) to mlement (Mathwok Co., 0) the oose contolle esgn base on bees colony concet.,,, can be efne as: No Tune,, Retun Yes Tune Only θ ( FS, D) =.. S.. S.. S Whee FS= no of foo souces, an D s the aamete otmze. n ths wok, D=3, S=0, an the contolle aametes ae boune as: {0, }, { 0, }, ABC algothm was max max selecte by tal an eo an the followng table () nclues these aametes: Table. Paametes of bee foagng algothm The oose contolle was ale on an M ve as a test machne whch all aametes ae shown n table (). Table () Moto aametes Rate lne voltage (Y-connecton) 380V Rate lne cuent. A Rate owe 05W fequency 60 Hz No of oles 4 oles Stato an oto esstances 6.5 Ω,.0 Ω Stato an oto leakage Ω,30.75 Ω eactance s Magnetzng Reactance X m 46.0 Ω Moment of neta fo Roto J g. m The off-lne esults fo that otmze contolle aametes ae obtane n fgue 3(a). As shown n ths fgue, the bees movement s lotte aganst,, axes. Fom the convegence chaactestcs t s seen that all bees convege to a sngle ont smla to all woke bees convege to the best flowe atch n natue. The gah of fgue 3 s a clea ncaton that the oose algothm tuly mtates the foagng behavou of bees. The otmalty of the bees algothm n yelng qualty solutons wth faste convegence ate eaches at the 39th cycle of the ogam teaton. At the en of these teatons, the otmze values of the ABC-PD oose contolle ae obtane as follows: = 7, =. 33, an fnally = Numbe of Colony Sze=N 0 Numbe of Foo Souces ( S=N/) 0 Maxmum Numbe of Cycles 50 Theshol Pobablty 0.75 Numbe of Otmze Paametes 3 JER@04 Page 809

5 ntenatonal Jounal of Engneeng Reseach (SSN: )(onlne),( )(Pnt) Volume No.3, ssue No., : Dec. 04 (a) ntal values (a) Wth ABC-PD Contolle (b) wth tunng Fgue. 3 Bees movements along,, an axes These aametes ae obtane fo ste-nut of see-efeence tajectoy- fo test machne - These otmze values fo the contolle that obtane above, ae use as ntal values fo the oose on-lne ABC-PD contolle to test the obustness of the contolle n -DOF tackng contol. Seveal tajectoes n -DOF ae oose to test the contolle obustness. Fgue 3(b), shows the bees movement to otmze the aametes of contolle at cetan oose tajectoy. Pont n that fgue, eesents anothe necta souce that bees move to t. Ths ont s an oeatng ont fo the oose contolle to tack the oose tajectoy. The tune contolle aametes at that oeatng ont ae: = 34, =. 48, an fnally = 0. 0 Fgues (4,5,6,7) show the squae-wave, taezoal, tangle, an snusoal tajectoes wth self-tune aatve contolle an wth conventonal PD- contolle. Sol lne eesents the efeence an ashe lne s the actual see tajectoy. Also, on ght han, the outut wth ABC-PD contolle (a) an on the left-han (b), ncate the tajectoy wthout contolle. Fom these fgues, the moto une the oose contolle, can tack the oose tajectoes an matches wth the efeence see values wthout evaton. But, the classcal o tatonal PDcontolle wth fxe values wthout aataton cannot be able to tack the oose tajectoes. Also, ths algothm was wtten n Bolan C++ an coe to an executable fle that ves an exemental g nclues: a test machne, an a Texas DSP- TMS30C30 Ca an GBT-ntellgent owe nvete moule. JER@04 (b) Wth classcal PD contolle Fgue. 4 Squae wave see tajectoy (a) Wth ABC-PD Contolle (b) Wth classcal PD contolle Fgue 5. Taezoal see tajectoy Page 80

6 ntenatonal Jounal of Engneeng Reseach (SSN: )(onlne),( )(Pnt) Volume No.3, ssue No., : Dec. 04 V. Concluson (a) Wth ABC-PD Contolle The foagng behavo of a colony of bees s exlote to evelo an otmzaton algothm an the same s use to esgn off-lne aametes of self-tune self-aatve PD-contolle fe nucton moto ve. These otmze values ae use n the oose ABC-PD contolle to make t obust though tackng contol. The obustness of the contolle was teste by oosng seveal see efeence tajectoes. All oose tajectoes, the moto succeee to tack them n -DOF wthout evaton. But, the moto fale to follow the escbe tajectoes when alyng conventonal classcal PD- contolle wth fxe aametes. So, by usng the oose ABC-PD contolle, the contolle becomes a obust wth self-aatve self-tune aametes. Also, t oves excellent ynamc esonse at all oeatng onts. Refeences (b) Wth classcal PD-contolle Fgue 6. Tangula see tajectoy (a) Wth ABC-PD contolle. H.. Abul-ghaffa, E. A. Ebahm an M. Azzam, Desgn of PD Contolle fo Powe System Stablzaton Usng Hyb Patcle Swam-Bactea Foagng tmzaton, WSEAS Tansacton on Powe Systems, ssue, Volume 8, Januay( 03), Q. Zeng an G. Tan," Otmal esgn of PD contolle usng mofe ant colony system algothm", EEE Th nt. Conf. on Natual Comutaton (CNC07), 4-7 Aug. (007), Chna.. A. S. Oshaba an E. S. Al Bactea Foagng: A New Technque fo See Contol of DC Sees Moto Sule by Photovoltac System, WSEAS Tansacton on Powe Systems, Volume 9, (04), v. D. aaboga, S. Okem, an C. Oztuk, "Cluste base weless senso netwok outng usng atfcal bee colony algothm", nte. Conf. on Autonomous an ntellgent, AS0, June -3, 00, Povoa e Vazm, Potugal. v D. W. Novotny an T. A. Lo, Vecto contol an ynamcs of AC ves, Claenon Pess, Oxfo,( 996). v Essamun A E, "Atfcal neual netwok-base tackng fel-oente vecto-contol of 3-hase nucton moto sevo ves", Ph D.Thess, Cao Unvesty 00. v. A. au an S. Goyal, "A bee colony otmzaton algothm fo coe coveage test sute otzaton", nt. Jounal of Engnneng Scence an Technology (JEST), Vol. 3 No. 4, Al (0). v. Vvekananan et al., "Atfcal bee colony algothm fo g scheulng", Jounal of Convegence nfomaton Technology, Vol. 6, No. 7, July (0). x. D. Teooovc et al., "Bee colony otmzaton: The alcatons suvey", ACM Tansactons on Comutatonal Logc, (0), Pages -0. x. M. çelk et al, "Atfcal bee colony ata mne", 0 ntenatonal Symosum on nnovatons n ntellgent Systems an Alcatons (NSTA), 5-8 June (0). x. Mathwok Cooaton, Matlab/ Smulnk 0b, Use s Gue, USA ( 0). (b) Wth classcal PD contolle Fgue 7. Snusoal see tajectoy JER@04 Page 8