A sliding mode multimodel control for a sensorless photovoltaic system

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1 48 ounal of Scentfc Inustal Reseach SCI IND RES VO 7 UNE Vol. 7, une, pp A slng moe multmoel contol fo a sensoless photooltac system Ahme Rhf, Zoha Kaous an Naceu BenHaj Baek Aance System aboatoy, Polytechnc School of Tunsa (aboatoe es Systèmes Aancés(SA, Ecole Polytechnue e Tunse, BP 74, 78 a Masa, Tunse Recee 9 Decembe ; ese 4 Apl ; accepte May Ths stuy pesents a slng moe multmoal contol fo a sensoless photooltac panel, whch sets tself as pe the sun poston at eey secon ung the ay fo a peo of fe yeas; then tacke, usng slng moe multmoal contolle an a slng moe obsee, wll tack these postons to make sunays othogonal to photooltac cell that pouces moe enegy. Afte sunset, tacke goes back to ntal poston of sunse. Ths autonomc ual axs sun tacke nceases powe poucton by oe 4%. Keywos: Alttue, Azmuth, Photooltac panel, Sola enegy, Sun tacke Intoucton Photooltac aays ae fxe. In ths way, sola enegy ncent on moules s not optmal ung tme aaton an seasons. Theoetcal stues - show that enegy supple by a photooltac cell euppe by a sun tacke (ST s hghe (-4% than enegy poe by fxe panels (Fg.. A sola panel ( m² fxe to a suface pouces 5 kwh of electcty pe ay. The same nstallaton, f euppe wth a tow axs sun ST -5 (Fg., can poe up to 8 kwh pe ay. Ths stuy pesents spee an poston contol of ST usng slng moe contol (SMC an a slng moe obsee (SMO. Expemental Secton Dual Axs Sun Tacke (ST Moellng A ual-axs tackng system wth two egees of feeom (DOF was use fo followng the sun poston n both alttue an azmuth ectons, keepng the sun s ays nomal to photooltac cell. Opeatonal subset of ST has two DOF, motoze by tow steppe motos, n oe to tack exactly the pescbe sun s path. Mechancal system (Fg. conssts of alttue moto to e hozontal axs, azmuth moto to e etcal axs an photooltac cell (5 mm x mm. It was esgne usng solwoks softwae n the Depatment of Electoncs, Hgh Insttute of Apple Scences an Technologes Sousse (ISSAT so, an ealse n Plexglas pofles n oe to obtan a smple an economc stuctue. Conseng that system opeaton s accomplshe by one of those steppe motos at each tme, mathematcal moel of the pocess n - (ect-uaatue tansfomaton 6 (Fg. 4 woul be gen as t t t t ( R + N ( R + N K ( K f C ( whee R, esstance; nuctance,, neta; N, spn numbe; K, toue constant gan; f, fcton;, angula elocty;, oto poston; an, cuents n - efeental; an an, oltages n - efeental. Conseng x u functon wll be gen as [,,, ] T [, ] T, then moel state *Autho fo coesponence E-mal: ahme.hf@gmal.com x f ( x + gu + p (

RHIF et al: SIDING MODE MUTIMODE CONTRO FOR A SENSORESS PHOTOVOTAIC SYSTEM 49 Fg. Hstogam of sola enegy pouce Fg. Two axs system oentaton Fg. Mechancal esgn of the pocess Fg.

( ges y y y K y + Ry ( y + K K ( y + f y + C N K y ( f + R ( y + f y + C Rf y + K + K + Ny y + C K ( Contolle Desgns Among contolle types teste an mplemente n ST, Hua Shen compae sun tackng

Yousef eelope a ST system wth a fuzzy logc contol fo nonlnea ynamcs of tackng mechansm,. Roth 4 esgne a sola tackng system to measue ect sola aaton.

2 RHIF et al: SIDING MODE MUTIMODE CONTRO FOR A SENSORESS PHOTOVOTAIC SYSTEM 49 Fg. Hstogam of sola enegy pouce Fg. Two axs system oentaton Fg. Mechancal esgn of the pocess Fg.4 Electcal moel n - efeental whee f R N N R K a ( K f f an g as lnea functons. g p C wth In othe way, E. ( coul be gen n a smplest way; conseng y an y, E. ( ges y y y K y + Ry ( y + K K ( y + f y + C N K y ( f + R ( y + f y + C Rf y + K + K + Ny y + C K ( Contolle Desgns Among contolle types teste an mplemente n ST, Hua Shen compae sun tackng effecteness of maxmum powe pont tackng (MPPT algothms wth a contol metho, whch combne a scete contol an a Popotonal Integal (PI contolle to tack maxmum powe ponts of a sola aay 7-. Yousef eelope a ST system wth a fuzzy logc contol fo nonlnea ynamcs of tackng mechansm,. Roth 4 esgne a sola tackng system to measue ect sola aaton. The system was contolle by a close loop seo system compose by fou uaant photo-etectos neee to sense the poston of sun 5,6. Fnally, a sensoless contol test usng SMC, whch s ey solcte n tackng path stues. Hgh Oe Slng Moe Contol (SMC SMC can bng back the system state on slng suface, whee t wll sle along the ese state. Howee, SMC nees a hgh leel of scontnuous contol, whch makes hamful effects on actuatos, known as chatteng phenomenon (CP. As a soluton, esgnng

3 4 SCI IND RES VO 7 UNE of a hgh oe SMC conssts of slng aable eate computng 7-. A secon oe SMC conssts of.. s ( x s ( x an V ( s ss η s wth η > an t V as yapono uaatc functon. Path tackng eo n the ogn s stablze as [,,, ] T [ e, e, e e ] T e, 4 E. (, one gets e e e e 4 e ( Re + N( e e + e + e ( Re + N( e e + e + e Ke ( Ke f e C. Usng (4 whee e, system eo;, efeence cuent n - efeental;, efeence oltage n - efeental, efeence angula elocty; an, efeence oto poston. Fo elocty contol by a secon oe SMC, slng suface s wtten as s µ e + e wth µ >. Fst oe eate of E. (4 ges s µ e + e an s ( Ke f e C ( Ke fe C µ +. In secon phase, to eal wth poston contol pocess, slng suface s consee as s µ µ + e4 + e4 e4 (5 Combnng E. (4 an E. (5 ges s µ e4 + µ e + ( Ke fe C wth µ, µ >. In conegence phase, to bng the system on slng suface, ffeent foms of swtchng contol ae aalable. In ths stuy, the followng wee chosen (U >: u s U sgn( s ; an u s U sgn( s s. Popose Slng Moe Multmoel Contol (SM-MMC Synthess Multmoel appoach epesents an nteestng altenate to SMC poblems, an a poweful tool fo entfcaton, contol an analyss of complex systems. Multmoel pncple makes possble the esgn of a non lnea contol compose by lnea sub contols elate to each sub moel. The pocess contol coul be then euce fom a fuson o a commutaton between ffeent patal contols weghte by eualent altes. In ths sense, seeal methos of altes estmaton [ n N an n( t ] ae aleay ( t epote. These methos ae classfe accong to the moels acuston ways, whch ae elate to pocess knowlege. Ths pape wll apt fo esue appoach fo altes computng as n N (6 y( t y ;,,N (7 whee, alty;, esue; y(t, system s output; an y (t, output of th moel. In oe to euce stubances ue to naeuate moels, altes wee enfoce as enf enf n N j j ( j Nomalze enfoce altes ae gen as enf N enf (8 (9 SM-MMC uses multmoel fuson appoach to euce swtchng contol effect, whch nuces CP -4. To mpoe contol pefomances, Ue Inalhan 5 apple a scete slng moe. In anothe stuy 6, a non lnea contol was consee fo a combat a ehcle to execute agle manoeues. To euce CP, fuzzy moe was apple to a hgh felty sx egees of feeom F-6 fghte acaft moel. In ths stuy, contol appoach consste n cayng out a fuson on slng moe scontnuous contol (Fg. to elmnate o mnmze CP. To aapt the contollng pocess to each sub moel, seeal slng sufaces wee use, each state of a sub moel M was consee to each one of these slng sufaces s (Fg. 5. To ensue SMC exstence, seeal swtchng contol u s elate to each slng suface s wee use. Then, patal contols y of each sub moel wll contbute on altes calculatonas us mn s sgn( s < us us max s sgn( s > (

4 RHIF et al: SIDING MODE MUTIMODE CONTRO FOR A SENSORESS PHOTOVOTAIC SYSTEM 4 Fg.5 Slng moe multmoel contol (SM-MMC stuctue Fg.6 Velocty contol base on a slng moe obsee (SMO Afte that, pocess wll conege to the sum of those sufaces weghte by coesponent altes υ ( S υ s an global contol wll be obtane by ang patals contols u ( u ue + us weghte by N aapte altes compute on lne ( u g ν u wth u e, eualent contol elate to each slng suface. In ths way, to mpoe pefomances of ths contol, a PID slng suface 7-8 was use, an esgne as s t ( x x α ( x x + β + γ ( x x t ( t ( x x ( x x Then, s α + β + γ ( x x t t wth α, β, γ >,,,N, x the ese state an x the eal state. To euce CP, satuaton functon was use to ge s u s λ sat ( Ψ whee u s λ sgn( s f s Ψ s λ Ψ f s Ψ wth λ an thckness. ( Ψ >, Ψ efnes the bounay laye Slng Moe Obsee (SMO Angula eloctes of steppe motos measuements coul ge unelable esults because of stubances that nfluence tachymety senso. Theefoe, angula elocty s estmate usng SMO nstea of senso. Ths opeaton woul ge bette esults an wll euce the numbe of sensos, whch ae ey costly an may hae ha mantenance sklls. SMO can be use n the state obsees esgn, an has the ablty to bng coonates of estmato eo ynamcs to zeo n fnte tme. SMOs (Fg. 6 hae attacte measuement nose eslence, whch s smla to a Kalman flte. CP concene wth slng moe metho can be elmnate by mofyng SMO gan, wthout sacfcng the contol obustness an pecson ualtes 9-4. Obsee poston eo s gen as ε ˆ an angula elocty eo as ε ˆ, wth ˆ estmate poston an ˆ estmate angula elocty. Angula elocty s eual to the poston eate as ˆ ε ˆ ε. In ths case, E. ( coul be t t epesente as ˆ K f ˆ C + ˆ λ sgn( t ˆ ˆ + λ sgn( ˆ t an ε ε ε λ sgn( ε ˆ f ε t t, wth λ, λ > (4 (5 To ascetan state conege to slng suface, one has to efy yapono 6-9 stablty cteon gen by

5 4 SCI IND RES VO 7 UNE Tme, s Tme, s a b Fg.7 Inclnaton angle usng slng moe contol (SMC of: a azmuth moto; an b alttue moto eg/sec eg/sec, eg, eg Tme, s Tme, s a b Fg. 8 Real an obsee angula elocty of: a azmuth moto; an b alttue moto uaatc functon V ε. In ths way, V ε ( ε λ sgn( ε. Then, V < f λ > ε an max system ynamc s gen by ε λsgn( ε when ε.conse now a secon yapono uaatc functon V ( ε + ε. As ε, E. (7 ges V f ε ε ( λ sgn( ε C, then V < f λ > C. max Results an Dscusson Expemental esults wee accomplshe fo a secon oe SMC of E. ( apple on the system (Fg. connecte to a compute though a seal cable RS. Ths eue system contol eoluton, eal an obsee angula eloctes, an, an azmuth an alttue nclnatons, an. Slng suface paametes use wee µ.5, µ. an µ.55. Steppe moto chaactestcs wee as follows: neta moment,.45-4 kg.m ; mechancal toue C,.78 Nm; toue constant K,.4 Nm/A; amatue esstance R,.5 Ohm; amatue nuctance, 8.5 mh; an fcton foces f,.7 Nms/a. Expemental test was consee fo tme exceeng s. Usng secon oe SMC, t was obsee (Fg. 7 that steay state s eache n a shot tme (~5 s. Also, fo the fst test,.48 an.57 ; thus azmuth nclnaton s ey close to alttue nclnaton. Ths fact s elate to ellptc moement natue of sun. Howee, pesence of CP (~. was notce. Real an obsee angula eloctes (Fg. 8 of two axs tacke ae ey close; 8 /s ˆ an 6 / s ˆ. Ths excellent esult s ue to hgh estmaton ualty of SMO. Moeoe, SMC shows ts obustness (Fg. 7

RHIF et al: SIDING MODE MUTIMODE CONTRO FOR A SENSORESS PHOTOVOTAIC SYSTEM 4 Dstubances Contol, u Tme, s Fg.9 Dstubance sgnal Tme, s Fg. SMC eoluton, eg Real an obsee cuent, A Tme, s Tme, s a b Fg.

6 RHIF et al: SIDING MODE MUTIMODE CONTRO FOR A SENSORESS PHOTOVOTAIC SYSTEM 4 Dstubances Contol, u Tme, s Fg.9 Dstubance sgnal Tme, s Fg. SMC eoluton, eg Real an obsee cuent, A Tme, s Tme, s a b Fg. Inclnaton angle usng SM-MMC of: a azmuth moto; an b alttue moto Contol, u, eg Tme, s Fg. Real an obsee cuent of the contol when a peoc stubance sgnal s njecte (Fg. 9 wth a sgnal peo T of 5 s. System oes not eate fom tajectoy an pesee ts eulbum poston. Howee, contol eoluton (Fg., wth no hgh leel but wth shap commutatons feuency, oes not ge Tme, s Fg. SM-MMC eoluton aeuate opeatng contons fo actuatos (both azmuth an alttue motos. As a soluton to these poblems (chatteng an contol oscllatons, system was smulate by PID SM-MMC appoach, esultng n CP elmnaton (Fg.. Also, contol eoluton (Fgs of the

7 44 SCI IND RES VO 7 UNE system ha less commutaton feuency an eache steay state n a ey shot tme, whch pesee obustness of the system an gae goo contons fo actuatos. Conclusons In ths stuy a SMO has been consee to ealuate angula eloctes of steppe motos. Expemental esults showe effecteness of SMC n tackng pocess an ts obustness unless stubances an hgh estmaton ualty of SMO. PID SM-MMC was esgne an pocess smulate. Ths new appoach showe excellent esult n tem of CP elmnaton an contol stablzaton wth peseng contol obustness. Refeences Hua C Shen C, Compaate stuy of peak powe tackng technues fo sola stoage system, n IEEE Appl Powe Electon Conf Expo (Anahem, CA, USA 5-9 Feb 998. ee D S Youn M, Contolle esgn of aable stuctue systems wth nonlnea slng suface, Electon ett, 5 ( Rhf A, Poston contol eew fo a photooltac system: ual axs sun tacke, IETE Tech Re, 8 ( Semma R P Imamua M S, Sun tackng contolle fo multkw photooltac concentato system, n Poc Int Photooltac Sol Enegy Conf (Cannes, Fance 98, McFee R H, Powe collecton eucton by mo suface non flatness an tackng eo fo a cental ecee sola powe system, Appl Opt, 4 ( Nollet F, los e commane pa moe glssants u moteu pas à pas, thess, l Ecole Centale e lle et l Unesté es Scences et Technologes e lle, 6. 7 Sngh B Rajagopal V, Decouple sol state contolle fo asynchonous geneato n pco-hyo powe geneaton, IETE Res, 56 ( Sngh B Kasal G, An mpoe electonc loa contolle fo an solate asynchonous geneato feeng -phase 4-we loas, IETE Res, 54 ( Henanez-Matnez E O, Mena A Olgun-Salnas D, Fast tme oman peoc steay-state soluton of nonlnea electc netwoks contanng DVRs, IETE Res, 57 ( 5-. Rhf A, Stablzng slng moe contol esgn an applcaton fo a DC moto: spee contol, Int Instum Cont Syst (IICS, ( 5-. Yousef H A, Desgn an mplementaton of a fuzzy logc compute-contolle sun tackng system, n IEEE Int Symp In Electon (Ble, Sloena -6 uly 999. Hanmanlu M, Al base goenng technue fo automatc contol of small hyo powe plants, IETE Res, 5 ( Sngh M, Sastaa S Gupta R P, Ientfcaton an contol of nonlnea system usng neual netwoks by extactng the system ynamcs, IETE Res, 5 ( Roth P, Geogeg A Bouno H, Desgn an constucton of a system fo sun-tackng, Renew Eneg, 9 ( Hseh S P, Hwang T S N C W, Twn VCM contolle esegn fo the nutato system wth eolutonay algothme, IETE Tech Re, 6 ( Kamath S, Geoge V I Vyasaga S, Smulaton stuy on close loop contol algothm of type abetes melltus patents, IETE Res, 55 ( Rhf A, A slng moe contol fo a sensoless tacke: applcaton on a photooltac system, Int Cont Theoy Compu Moellng (ICTCM, ( Rhf A, Kaous Z Ben Haj Baek N, A hgh oe slng moe-multmoel contol of non lnea system smulaton on a submane moble, n Int Mult-Conf on Syst, Sgnals Deces (SSD (Tunsa, 4-9 Mach. 9 Rhf A, A eew note fo poston contol of an autonomous unewate ehcle, IETE Tech Re, 8 ( ,. Sellam A, Anouls R, Mh R Ksou M, Slng Moe Contol Appoch fo MPPT of a Photooltac Geneato couple to a DC Wate Pump (TEA, Sousse. Anoso D V, On stablty of eulbum ponts of elay systems, Automat Remote Cont, ( Utkn V I, Vaable stuctue systems wth slng moes, IEEE Tans Automat Cont, ( Rhf A, Kaous Z Ben Haj Baek N, Fst an hgh oe slng moe-multmoel stablzng contol synthess by a sngle an mult slng sufaces of nonlnea systems smulaton on a submane moble, Tans Syst, Sgnals Deces, (n pess. 4 Rhf A, Kaous Z Ben Haj Baek N, Stablzng slng moe-multmoel contol fo nonlnea systems smulaton on an acaft: abus A4, n Int Mult-Conf on Syst, Sgnals Deces (SSD (Gemany,. 5 Kemal Ue N Inalhan G, Desgn of Hghe Oe Slng Moe Contol aws fo a Mult Moal Agle Maneueng DCAV (IEEE, Tukey 8. 6 Z Shu-sheng Q, Analyss an expemental stuy of popotonal-ntegal slng moe contol fo DC/DC conete, Electon Sc Technol Chna, (5. 7 Rhf A, A hgh oe slng moe contol wth PID slng suface: Smulaton on a Topeo, Int Infom Technol, Cont Automat (IITCA, ( -. 8 Rhf A, A slng moe contol wth a PID slng suface fo powe output maxmzng of a wn tubne, Instum Cont, ( Rhf A, Kaous Z Ben Haj Baek N, A hgh oe slng moe obsee: Topeo guance applcaton, Engg Technol, ( -8. Alaybeyoglu A, Ecyes K, Kantac A Dageen O, Tackng fast mong tagets n weless senso netwoks, IETE Tech Re, 7 ( Petells N, Konofaos N Ph Alexou G, Estmaton of a taget poston base on nfae patten ecepton ualty, IETE Tech Re, 7 ( Flota M, Alaez-Salas R, Mana H, Cabal-Yepez E Romeo-Toncoso R, Nonlnea obsee-base contol fo an acte ectfe, Sc In Res, 7 ( 7-5. Saa H, Caon B Tajne M, On the esgn of scete tme epette contolles n close loop conûguaton, AUTOMATIKA, 5 ( Ylm S, A popose neual ntenal moel contol fo obot manpulatos, Sc In Res, 65 (6 7-7.

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