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TORQUE RIPPLE REDUCTION OFSWITCHED RELUCTANCE MOTORS BY

PHASE CURRENT OPTIMAL PROFILINGD.S. schramm B.W. Williams T.C. Green

Department of Electrical and Electronic EngineeringHeriot-Watt universityEdinburgh EH1 2HT, Scotland, U.K.

ABSTRACTOptimal precalculat ion of the position-phase current

pro j i le or current eeding a 4-phase, 4 kW switched reluctancemotor, results in a single input, l inear. decoupled outputtorque control ler, which provides low torque ripple. A bicubicspl ine interpolation was used to model the non-l inearexperimental data. The algori thm is bused 011minimizing boththe average and peak current hence improves the dynamicper formance of the novel six switch, current fed, igbt 4 kW,4 0 k H z inver ter. Test results by ins tuntaneo us speedmeasurement over the speed runge 100-300 pm, ruted torque,open-loop optimizing technique are presented,

1.INTRODUCTIONSwi t ched r el uctance (SR) motor dr i vesare r enowned f or hi gh t orque r i ppl e, hencehi gh noi se and v i br at i on. The torque r i ppl ei s due t o t he non- l i near coupl i ng betweenphase cur r ent , r ot or posi t i on and over l apangl e as wel l as the machi ne desi gn. Byexper i ment a l l y charact er i z i ng t orque f or al langl es and cur rent l evel s , decoupl ed l i nearsyst ems have al l owed torque r i ppl em ni m z at i on [l], [ 2 1 , [ 3 1 .The met hod t o be outl i ned i s anext ensi on of t he met hods r ef er enced, butopt i m zes t he cur r ent over l ap at al l t orquel evel s s o as t o m ni m se t he peak phasec ur r ent . Thi s c ur r ent opt i m zat i oni nc reases t he i nver t er N. m A rat i ng, anda l so mai nt ai ns t or q ue r i ppl e m ni m sat i on t oa hi gher speed, t han can be achi eved byother opt i m z i ng t echni ques . Bet t er dynam cperf ormance r esul t s .2.SWITCHED RELUCTANCE MOTOR DRIVETORQUE CHARACTERISTICSI n non- l i near SR dri ve syst ems t hecommutat i on angl e ( curr ent , hence t orqueproduct i on r educi ng t o zer o i n one phase andi nc reas i ng f r om zero i n another phase) i s

opt i m sed by sel ect i ng an angl e f or a gi vent orque t hat r equi r es the m ni mumcur rent f ora maxi mum possi bl e motor ef f i c i ency. The

commut at i ng phase cur r ent s each pr oducet orque whi ch i s addi t i ve. F i gur e 1 showst he summed i nst ant aneous t or que pr oduced at200 r p m f or a f our - phas e 4 kW SR mot orproduci ng r at i ng t orque ( aver age of 25. 5N. m . The t orque di ps are due t o cur r entcommut at i on, whi l e t he r ounded tops ar e duet o satur at i on and the non- l i near t or queproduct i on natur e when j ust one phaseconduct s .

00 10 20 30 40 50 60 70 80 90P osition (1 O-bit encoder steps)Fi g. 1. I nst antaneous tor que pr oduced at200 r pm by t he 4 kW non- l i near SRMdr i ve.

3.TORQUE LINEARIZATION AND DECOUPLINGThe usual method to l i neari ze anddecoupl e ( LD) t orque i s t o produce by

exper i ment at i on s t at i c t or que-pos i t i oncur ves f o r di f f erent cur r ent l evel s as showni n F i gur e 2 . Thi s dat a i s t hen used to

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generate curr ent - posi t i on cur ves f ordi f f erent const ant t orque r equi r ement s asshown i n Fi gur e 3. The dat a f or one phase( because of symmet r y) i s st ored i n an EPROMas a l ook- up t abl e.I n generat i ng t hi s data i t i s necessar yt o have used a speci f i c commutat i on angl e,

whi ch convent i onal l y i s sel ect ed f r omFi gure 2. The commutat i on angl e i s sel ect edsuch that i f commutat i on occur si nst ant aneousl y then no change i n tor quepr oduct i on woul d r esul t . The l ocus i s thei nt ersect i on of di spl aced t orque cur ves, asshown i n Fi gur e 2. Thi s c r i t e r i a has anumber of f eat ures.F i r st l y t he on- phase cur rent i ncreasesj us t bef or e commut at i on. Thi s wi l l l i m tt he upper speed l i m t of compensati on si ncet he cur r ent has a f i n i t e r ate of changel i m t .Secondl y the requi r ed t orque i sachi eved at hi gher cur r ent s and wi t h l atecommut at i on, whi ch r est r i ct s t he upper speedof operat i on.Last l y , t he peak cur r ent ra t i ng i ss i gni f i cant l y great er t han t he on s t atemean f or a gi ven t orque. When posi t i oncont r ol i s used, t he i nver t er must be r atedf or t he maxi mum experi enced curr ent , whi chi s undul y hi gh at angl es j ust pr i or t ocommut at i on.The ext ent of t hese l i m t at i ons can

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n0 10 20 30 40 50 60 70 80 90P osition ( 1 0- bit encoder steps)F i g. 2 . T or que - p os i t i o n c ur v es f ordi f f er ent c ur r ent l evel s ( A ) .

0 10 20 30 40 50 60 70 80 90P osition ( 1 0-bit e n c o d e r steps)F i g. 3. Cur r ent - pos i t i on c ur ves f ordi f f erent t o rque l evel s ( N. m) .onl y be s l i ght l y modi f i ed by var y i ng themechani cal st ator / r otor pol e desi gn.

4.MODIFIED LD TECHNIQUEThe above l i m t at i ons can be al l evi atedby usi ng F i gure 3 as the basi s f or sel ect i ngt he commut at i on angl e. For exampl e,F i gure 3 shows t hat r ated tor que of 25. 5 N. mcan be produced i nst ant aneousl y f or am ni mumcur r ent of 14. 8 A , at an angl e countof 40 . I f t hi s cur r ent l i m t i s us ed,

dur i ng opt i mal commut at i on t he t orque t otalwoul d f al l t o a m ni mum of 23 N. m at t hebegi nni ng of t he commutat i on peri od. I f t hemaxi mumcurr ent i s i ncr eased t o 16. 5 A , t hen2 5 . 5 N. m can be produced by one or bot hphases t oget her dur i ng commut at i on.I nc i d ent a l l y, a l i m t of 22. 75 A woul d beset i f t he conventi onal appr oach i s used.We now i mpose t he r est r i ct i on t hatdur i ng commut at i on the t or ques changes at aconst ant r ate; t her eby retai ni ng t he t orquel i near i zat i on requi rement at a l l angl es .The of f - l i ne pr ocess t o spec i f y theangl e-curr ent val ues f or a gi ven torque i sas f ol l ows :

( 1 ) The m ni mum cur r ent I f or r equi redt orque T, ( when onl y one phase i spr oduci ng t orque) i s determ ned f r omt he data, based on F i gure 3.

( 2) The angl e r el ated torques f or t wo

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phases ar e summed based on a l i m t ofI , us i ng Fi gure 2. ( 3 ) I f t he summed t orque f al l s bel ow T, ,t h e c ur r ent l i m t I i s i ncrement ed andst age 2 r epeated.( 4 ) The commutat i on per i od i s def i ned by

t he angl es (8 , ,8 , ) at whi ch j ust onephase cur r ent , I , can pr oduce t hesummed t or que T,, wi t h equal cur r ent i nbot h phases at t he cent r al commutat i onpoi nt .( 5) F i gur e 3 i s used t o ensur e that al i near i ncr ease i n tor que can beproduced by t he on- com ng phase. I fnot , t he cur r ent i s i ncrement ed andst age 4 i s r epeat ed to yi el d newcommut at i on angl es.( 6) Data i s generated f or T, . The pr ocessi s r epeat ed f or 255 di scret e t orquel evel s .

To conti nue our exampl e, at r atedt or que, a 16. 5A phase l i m t and commut at i onangl es ( 13, 371, a const ant 25. 5 N. m can bepr oduced, wi t h l i near r ate changes dur i ngcommut at i on as shown i n Fi gur e 4 . Thi s modeof operat i on r epr esent s a 2 7 % reduc t i on i nt he cur r ent r at i ng o f t he i nver t er swi t ches.

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O0 10 20 30 40 50 60 70 80 90P osition (10-bit encoder steps)F i g. 4 . Cur r ent prof i l e and r esul t anttorque: ( a ) and ( b) cur rent i nsubsequent phases; ( c) and ( d) t orqueproduced by phases ( a) and ( b)r espec t i vel y .

spl i ne i nter pol ati on was used to model t henon- l i near experi ment al SRM dat a. F i gure 4shows t he generat ed curr ent pr of i l e andr esul t ant t orque.5.HARDWARE IMPLEMENTATION

Modest EPROM st or age i s r equi r ed,s peci f i cal l y 86 sampl es of 8 bi t s by 256di scr ete t orque l evel s. Phase di spl acementsymmetr y i s used t o cont r ol al l phases f r omt he of one phase st or ed i n t he EPROM.Cont r ol i s per f or med by an EPLD and t heout put cur r ent demand is vi a two D/ Aconvert er s whi ch f eed t he novel curr entcont r ol l ed i nver t er br i dge.6.OPEN-LOOP RESULTS

Fi gure 5 shows t he i nst ant aneous speedof t he non- l i near SRM dr i ve obt ai ned at 200r pm r at ed t orque, 150 V DC r a i l , and thecurr ent i n t wo phases mechani cal l y shi f t edby 90. The very f ast changes on t he speedsi gnal are due to el etr omagnet i c swi t chi ngnoi se. The i nst ant aneous speed measur ementi s a good repr esent at i on of t he SRMi ns tant aneous torque, par t i cul ar l l y i n v i ewof t he t i me dependency on di ps and t ops, andmechani cal osc i l l a t i ons .

F i g. 5. Non- l i near SRM dr i ve: s =i nstantaneous speed ( 50 r pm di v) ; i =phase cur r ent ( 5A/ di v). Ti me scal e:5 ms/ di v.Fi gur e 6 shows t he i nst ant aneous speedand cur r ent wavef orm of t he pr oposedopt i m z i ng- t ec hni que l i near SRM dr i ve f or1 0 0 , 2 0 0 and 3 0 0 r pmwi t h speed var i at i on of1 7 % , 6. 4% and 3 . 9 % r espec t i vel y . For theaver age speed of 2 0 0 r pmt he speed var i at i oni mpr ovement obt ai ned wi t h t he modi f i ed LDt echni que over t he non- l i near SRM dr i ve i s

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( a) 100 r pm Ti me scal e: 10 ms/ d i v;

( b) 200 r pm Ti me scal e: 5 ms/ d i v;

( c ) 300 r pm Ti me scal e: 3 . 3 3 ms/ d i v;F i g. 6. SRM dr i ve torque r i ppl e wi t h t hemodi f i ed LD t echni que: s = speed ( 50r p m d i v) ; i = curr ent ( 5 A/ di v ) .

6. 4%agai nst 38% Hi gher encoder r esol ut i onand c l osed- l oop cont ro l wi l l f ur t her r educet he SRM dr i ve t orque r i ppl e.7.CONCLUSIONS

The pr oposed cur r ent prof i l i ngal gor i t hm r esul t s i n t he hi ghes t poss i bl eN. m A i nvert er r ati ng and an ext endedoper at i ng speed r ange under const ant t or queoperat i on. The t orque out put i s a decoupl eds i ngl e- i nput l i near f unc t i on of t or que i nputdemand. Exper i ment al r esul t s by i ndi r ecti nst ant aneous t or que measurement show t hei mprovement s obt ai ned wi t h t he pr oposedopen- l oop opt i m zi ng techni que. A 300 V DCrai l woul d ext end t hese r esul t s up t o 600r pm.ACKNOWLEDGEMENT

Thanks ar e due t o PWM Dr i ves Ltd f oral l owi ng t he use of PC and graphi cssof t ware, Li ng Dynam c Syst ems f or suppl yi ngi gbt gate- dr i ve boar ds, D. R. Carm chael andJ . G. Paul f o r text cor r ec t i ons .REFERENCES

J . V. Byrne, M. F . McMul l i n, and J . B.O' Dwyer , " A hi gh perf ormance vari abl er el uctance dr i ve: a new br ushl essservo" , i n P roc. Motorcon Conf . ,Chi cago, pp. 147- 160, Oct ober 1985.MG. Egan, J . M. D. Murphy, P. F .Kenneal l y , and J . V. Lawt on, " A hi ghper f ormance var i abl e r el uctancedr i ve: achi evi ng servomotor cont r ol " ,i n Proc. Motorcon Conf . , Chi cago, pp.161- 168, Oct ober 1985.D. G. Tay l or , M. J . Wool l ey, and M.I l i c , "Desi gn and i mpl ement at i on of al i neari zi ng and decoupl i ng f eedbackt r ansf ormat i on f or swi t ched r el uct ancemot or s" , i n Pr oc. 17t h Symp.I ncrement al Mot i on Cont r ol Syst ems andDevi ces , pp. 173 -184, I L , USA, J une1988.

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