BLDC Motor Modelling and Control – A Matlab /Simulink ...

BLDC Motor Modelling and Control – A Matlab®/Simulink® Implementation

– Master Thesis work by Stefán Baldursson –

May, 2005

Institutionen för Energi och Miljö International masters program in Electric Power Engineering CHALMERS TEKNISKA HÖGSKOLA Göteborg, Sverige, 2005 Examinator: Torbjörn Thiringer

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D1

D3

D4

D5

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B

B

A

A

A

A

C

C

C

C

C

A

D6

B

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120o - 180o 180o - 240o

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Vs

Vs

Vs

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i3 6= 0⇒

v12 = Vsv23 = 0v31 = −Vs

i3 = 0⇒

v12 = Vsv23 = 1

2(−Vs + e1 + e2 − 2e3)

v31 = 12(−Vs − e1 − e2 + 2e3)

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i3 = 0⇒

v12 = −Vsv23 = 1

2(Vs + e1 + e2 − 2e3)

v31 = 12(Vs − e1 − e2 + 2e3)

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i3 6= 0⇒

u12 = v12 − (e1 − e2) = Vs − e1 + e2

u23 = v23 − (e2 − e3) = −e2 + e3

u31 = v31 − (e3 − e1) = −Vs − e3 + e1

i3 = 0⇒

u12 = v12 − (e1 − e2) = Vs − e1 + e2

u23 = v23 − (e2 − e3) = 12(−Vs + e1 − e2)

u31 = v31 − (e3 − e1) = 12(−Vs + e1 − e2)

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i3 6= 0⇒

u12 = v12 − (e1 − e2) = −Vs − e1 + e2

u23 = v23 − (e2 − e3) = −e2 + e3

u31 = v31 − (e3 − e1) = Vs − e3 + e1

i3 = 0⇒

u12 = v12 − (e1 − e2) = −Vs − e1 + e2

u23 = v23 − (e2 − e3) = 12(Vs + e1 − e2)

u31 = v31 − (e3 − e1) = 12(Vs + e1 − e2)

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12(−Vs + ea − eb)

60 − 120ib 6= 0 −ea + eb Vs − eb + ecib = 0 1

2(Vs − ea + ec)

12(Vs − ea + ec)

120 − 180ia 6= 0 −Vs − ea + eb Vs − eb + ecia = 0 1

2(−Vs + eb − ec) Vs − eb + ec

180 − 240ic 6= 0 −Vs − ea + eb −eb + ecic = 0 −Vs − ea + eb

12(Vs + ea − eb)

240 − 300ib 6= 0 −ea + eb −Vs − eb + ecib = 0 1

2(−Vs − ea + ec)

12(−Vs − ea + ec)

300 − 360ia 6= 0 Vs − ea + eb −Vs − eb + ecia = 0 1

2(Vs + eb − ec) −Vs − eb + ec

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0o - 60o

D3D2

Vs

A

BC

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60o - 120o

D5

D2

D1D4

D5

B B

B

A

A

A

C

C

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120o - 180o 180o - 240o

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vab − eab vbc − ebc

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12(Vs + ea − eb)

ia = 0, ic 6= 0 12(−Vs + eb − ec) Vs − eb + ec

ia = 0, ic = 0 0 0

60 − 120

ic 6= 0, ib 6= 0 −Vs − ea + eb −eb + ecic 6= 0, ib = 0 1

2(−Vs − ea + ec)

12(−Vs − ea + ec)

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ic = 0, ib = 0 0 0

120 − 180

ib 6= 0, ia 6= 0 −ea + eb −Vs − eb + ecib 6= 0, ia = 0 1

2(Vs + eb − ec) −Vs − eb + ec

ib = 0, ia 6= 0 12(−Vs − ea + ec)

12(−Vs − ea + ec)

ib = 0, ia = 0 0 0

180 − 240

ia 6= 0, ic 6= 0 Vs − ea + eb −Vs − eb + ecia 6= 0, ic = 0 Vs − ea + eb

12(−Vs + ea − eb)

ia = 0, ic 6= 0 12(Vs − eb + ec) −Vs − eb + ec

ia = 0, ic = 0 0 0

240 − 300

ic 6= 0, ib 6= 0 Vs − ea + eb −eb + ecic 6= 0, ib = 0 1

2(Vs − ea + ec)

12(Vs − ea + ec)

ic = 0, ib 6= 0 Vs − ea + eb12(−Vs + ea − eb)

ic = 0, ib = 0 0 0

300 − 360

ib 6= 0, ia 6= 0 −ea + eb Vs − eb + ecib 6= 0, ia = 0 1

2(−Vs + eb − ec) Vs − eb + ec

ib = 0, ia 6= 0 12(Vs − ea + ec)

12(Vs − ea + ec)

ib = 0, ia = 0 0 0

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ia = 0, ic = 0 0 0

60 − 120

ia 6= 0, ib 6= 0 −Vs − ea + eb Vs − eb + ecia 6= 0, ib = 0 1

2(−ea + ec)

12(−ea + ec)

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ia = 0, ib = 0 0 0

120 − 180

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2(eb − ec) −eb + ec

ib = 0, ia 6= 0 12(−ea + ec)

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ib = 0, ia = 0 0 0

180 − 240

ib 6= 0, ic 6= 0 −ea + eb −Vs − eb + ecib 6= 0, ic = 0 −ea + eb

12(ea − eb)

ib = 0, ic 6= 0 12(−Vs − ea + ec)

12(−Vs − ea + ec)

ib = 0, ic = 0 0 0

240 − 300

ic 6= 0, ib 6= 0 −ea + eb −eb + ecic 6= 0, ib = 0 1

2(−ea + ec)

12(−ea + ec)

ic = 0, ib 6= 0 −ea + eb12(ea − eb)

ic = 0, ib = 0 0 0

300 − 360

ic 6= 0, ia 6= 0 Vs − ea + eb −eb + ecic 6= 0, ia = 0 1

2(eb − ec) −eb + ec

ic = 0, ia 6= 0 Vs − ea + eb12(−Vs + ea − eb)

ic = 0, ia = 0 0 0

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0 0.05 0.1 0.15 0.2 0.25 0.3−0.2

−0.1

0

0.1

0.2

i b (A)

0 0.05 0.1 0.15 0.2 0.25 0.3−0.2

−0.1

0

0.1

0.2

t (s)

i c (A)

wrzp eha¤úùH\xZdcvas7 eheva9lmgvwrlm³hgva9eva9vwgjnpej¶m as7nplmgvevnpqauÝbnpvatgjn@cqnmchgja9b

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ÷Vû

ÓsÔÄÓð M W Y®Y Ø [R E ò[ G wrzp ehaK¤ ºvntyTgjaq¾singjnpeyTw¬gj cºm³hgja9eha9vwrvba9atÏs7nplmgjehnVqqa9et¤Q abevwl¥s7wbqa=wvwiwrq¾cfegjngja1npla=wlgjagjnpej¶ a=s7nVlgjevnpq/js©a7ia«a9js7evwatwlgvabevau¨wrnp vatsugvwrnpl®¤a9eha=gva«ehnpgvnVevba9at|wo­a9gjngva«eva7q¯c9³qrns©²¤$a= bba9ecfl¥Kgja4qny a9e1qwiw¬gj1nVogva4eva9q¾c9³Kqns©²ºcfeva4wlºgjw«s9cvagja4vba9atºeva9o­a7eva9l¥s7a¨pcq aÂbqr cl¥Úiwl dcqonVoTgjaÂm³vgva9eva9vw4¥cl¥ yTwrgjeva9vbatsugjw¬¨a7q³¤ ayw¾gvÂnVo/gvam³hgja9eha9vwrdcfl¥>wrlnty

1%npo/gjaeha9o­a9eha9l¥s7avba9atµ¤

$abnpvwgvwnVlvwrzpldcfq$s7nV q¾ a vat·gjn§s9cqrs7 q¾cfgvagjaevngjnpe«vba7at g@gvacsugj dcfq®evngjnpevba9at>w vat>a9evaweva9sugjq¬³>vwl¥s7aw¬gwTcqevac³Âct¨pcfwrq¾cfqao­evnpi gvahgc½gjauªvbdcs7aqns©²¤/n4stcfqrs7 q¯c½gjagjabnpvwgvwrnpljwzpldcq®o­evnpi gvaevngjnpejba9a9|cfl¥gja7l·s9cqrs7 q¾cfgvagjavba9atºo¯evnpiÕgjabnpvwgvwrnpl)vwrzpldcfqZy$np qrºaclº llatsua9j©cfeh³s7npib gc½gjwnpldcq# eja9l®¤be©csugjwrs7aVya9l)wibqra7ia9lmgvwrlzjba9a9cfl¥ºbnVvw¬gjwnVls7nplmgjehnVq¸wzpªeva9vnVq gvwrnplbnpjw¬gjwnplva9lvnVehcfeva vatµ¤

Relay

Firing Signals

Vsuab,ubc

Inverter block

Vs

DC sourcevoltage

Position

chopFiring Signals

Control blockuab,ubc

Position

wm

BLDC motor block

Fwzp eva1¤ø~H#³hgja9eha9vwrvba9atÂs7nVlgjevnpq®h³hgja9i wrzp eha|¤øû§vntyTkgvaÂevngjnpekjba7atya9lc¦qrncÚgvnVev¶m aÂwcbbqratÓc½g

0.01 s¤

a¦eva9o¯a9eva9l¥sua§vba9atÏw20,000 rpm

cfl¥gva¦icfzplwgv ¥a¦nVogja¦qncpÏwgjaicÝwi« i s7nplmgjwl np qrncpcfqrqnty$atX¡

0.23 mNm£¤ßs9cl aºva9a9lwl gja

´¥zp evaVgjao­ehat¶m a9l¥su³>nVo gja1vba9atehwrbbqra9Twl¥s7evacfva9co¾gja9egva1qncphgva9b®¤ wrs©dcflzpa«npo\o­evat¶ a9l¥su³>yTwqqFa=wlm¨a9hgvwrzcfgvat|wl¦vatsgjwnVl§¤ ù¥¤ a«vba9a9|nty$a7¨Va9ethgc9³ yw¬gjwlÂgjam³hgja9eha9vwrdcfl¥cfevnp l¥gjaeha9o­a9eha9l¥s7a¨pcfqr ap¤

Fwzp eva¤yvntyTgjaa9qatsugvevwrstcqgjnpej¶m ap¤\$agjnpej¶ aevwbbqa9cehavgvevnplzcfl¥gjejclvwa9lmgvq³¦zpncqqZgja«yc9³§ntyl§gjn>¿9a9evngjnpej¶m aV¤k^a9o¯nVehakgvakqnmc§wr1cfbbqrwatµgja«gjnpej¶m a@wrnplq¬³¦ldcehevnty'jbw²Va7 gya9l§gja@qrncKw1cfbbqrwatµµgjaklnVl¿9a9ehngjwiaknVogjakba9evwnKats7nVika91q¾cfevzpa9egvdclKgva¿9a9ehnÂgvwrikaV¤4$asªqrwl²§s7 eheva9lmgwTlnpgTvntyTla7eva1 gTwgTwTbevnpbnVegjwnVldcfqgjngjaa9qatsugjehw¾stcfqgjnpej¶ a«cfl¥dcgva©cikao­ehat¶m a9l¥su³>s7nplmgja7lmg¤# wzV eha1¤úÿkvny$gjabdcfva1s7 eveva9lgjt¤

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ÷,

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

Fwzp eva1¤úûH#ngjnpevba9at>wl³hgja9eva7jwvba7atsunVlmgvevnpq®auÝbnpvat>gvnc«qrncpvgva9b

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

0.1

0.2

0.3

0.4

0.5

0.6

0.7

t (s)

T e (mNm

)

wrzp eha¤y-H\\qatsugvevw¾cq¥gjnpej¶m aTwlm³hgja9eha9vwrvba9ats7nVlmgvevnpqauÝbnVvatgjn«cqnmchgja9b

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ÷Vÿ

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02−0.5

0

0.5

i a (A)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02−0.5

0

0.5

i b (A)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02−0.4

−0.2

0

0.2

0.4

t (s)

i c (A)

wzV eha=¤øÿ~HxZdcvas7 eveha9lmgjwlÂm³hgja9eha9vwrvba9atÂs7nplmgjevnpq®auÝbnVvatgjnc«qnmchgja9b

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ÷¦ , *?-=:«./0 -=6ªl>byi s7nVlgjevnpqgjainpgvnVe w gj ehlatnplcfl¥n»§cfgc=wrzp>e©c½gjaV¤\ as©nVbbwlzo­ehat¶m a9l¥su³ºw1´Ýat) g1gjaqa9lzgj·npo gja g!³ºsu³s7qaa9ba9l¥«npl)gvas7nplmgjehnVqa9ehevnVe9¤ ao csuggjdc½ggjao¯evat¶m a7l¥su³Kw´ÝatKic²pa9´¥qgva9evwlznpo$cps7np hgjwrscfl¥a9qatsugjehnVi4czpla7gjwrslnpwvaacfvwra9e9¤Ü$ahyw¬g©s©wlz)o­ehat¶m a9l¥s³wsunViiknVlq¬³Óp½!kHz

cfl¥ vwl¥s7agjaingjnpev« vat a7eva>s9clnpba9e©c½gja>cfgk¶ wgvawzVvba9at¼Zgjao­ehat¶m a9l¥su³ws©npja9lcf

kHz¤

ÓwðaÓ]Ô Õ [»ò$P Y [R E ò[ G as7 eveha9lmg$s7nplmgjehnVqhgjejcfgva9zp³4v zVzpa9hgjatwl×Cú÷GEyc ehwra#¤³a9js7evwatwrlvatsugvwrnpl¤röp¤röp¤\a9eva$gva©cikas7 eveha9lmgva9lvwrlzia7gjnkwr vatkjngvdcfgnplq¬³knplaTs7 eheva9lmgs7nplmgjehnVqqa9eFwFla7atatµ¤F wzV eha$¤'Tvny gva s7nplmgvevnpqh³hgja9i¤ abdcfva s7 eheva9lmgvcfevas7nplm¨a9egjat«gjn1cflkat¶m w¬¨Vcfqa9lmgsªqrwl²@s7 eveva9lg\¨Vcfq aV¤Z wrZ¨Vcfq aw#v gjejcpsgjato­ehnVi?ceha9o­a9eha9l¥s7a¨pcq a stcfqrs7 q¾cfgvat«o­ehnVigvagvnVev¶m aeha9o­a9eha9l¥s7a$cfFwl«vatsugvwrnplk¤öV¤öV¤ as7 eheva9lmg/a9ehevnpe/w/o­atgjncs7 eveha9lmg s7nVlgjevnpqqra9e cl¥gjanp gjb g npogvas7nplmgjehnVqqa9ew s7npibdcfevat4gvn@cgjevw¾cflzV q¾cfeyct¨VaV¤Z$anp gjb g npoµgvas7npibdcfe©c½gjnpewr c1wrzpnpeqny vwrzpldcfq¼yTwrs©Âva9eh¨a7cfTcks©npbbwlzvwrzpldcfq®o­npe$gjawlm¨a7ehgja9e9¤

Idc

SignalGenerator

>=

RelationalOperator

Iref step

Firing Signals

Vsuab,ubc

Inverter block

1/2

Gain

Vs

DC sourcevoltage

Irefi Vs

Current controller

Position

chopFiring Signals

Control block

Vs

Constant

uab,ubcPosition

iabc

BLDC motor block

|u|

Abs1

|u|

Abs

wrzp eva1¤Ã~HxÕgjnpej¶m as7nVlgjevnpq®h³hgja9i

as7 eheva9lmgs7nVlgjevnpqqra9e$wrTckx#s7nVlgjevnpqqra9eTcfl¥>w¬gja7jwzplwdcfvat>nVlc@s7 eheva9lmgs7nplmgjehnVqqa9eo­nVe1c>s@ingjnpebeha9va9lmgjat§wrl¡CúûGEª¤k a4a9vwzVlºhgcfehgvm³¦va9qra9sugjwlz|ca9vwevatevwvagvwrika

treo­npegjas7 eheva9lmgt¤\evnpi gjdc½gc1s7nVlvg©clg

αewr a7gja7eviwlat

cf

αe =ln 9

tre

¡¸¤ø£cfl¥gjas7nplmgjehnVqqa9ebdcejciaugja9evo¯nVqqny cf

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ù

kp = αeL¡¸¤ú÷m£

ki = αeR.¡¸¤ ù£

aja7qratsgjatÂehwrvagvwriawr0.1 ms

yw¾sj³wa9qr

kp = 2.00 · 103

ki = 2.75 · 105

a4sunVlmgvevnpqrqa9e1cqvn va9dcs©²Hstcfqrs7 q¯c½gjwnplºgjn>beva7¨Va9lmgwlmgja9zpe©c½gjnpeyTwl¥ b¡¢va9aCúûGE¢£cfl¥dcf>cK¨VnVq¬gcfzVa©cfgv e©c½gjwnVlqnsj²Úgjdc½gqwrikwgvgja|a9i4cl¥at¨npqg©czpagjn ±6 V

vn>gjdc½ggva4s7npibdcehwjnpl§yTw¬gj§gjakgvevw¾clzp q¾ceyc9¨a@ywqrq#zpw¬¨a4s7npeveva9sugeva7j q¬gjt¤Â wrzp eva¤rö9vntyT1gvaa9qatsugjehw¾s9cqgvnVev¶m aV¤Â$a4eva9o­a7eva9l¥s7a4gvnVev¶m acfl¥gjaqnmcºhgja7b)w1hgjwqq

0.2 mNm ggjakgjnpej¶ a¤¥ ¥sgj dc½gjwnVl)w1q¾cfevzpa9egvdclºwl

gjaTm³hgja7eva9vw$s7nplmgvevnpq~¤Z$aehacfjnplo­npegvwrwgjdc½ggvaa9qatsugjehw¾s9cq¼³ldcfiwrs7$ceha¨a9e³o cfhgTsunVibdcfeva9ywgv>gjaywgjs©wlzo­evat¶ a9l¥su³¤

0 0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

t (s)

T e (mNm

)

wzV eha=¤rö9H#\qatsugjehw¾stcfqµgjnpej¶m awlÂbyi gvnVej¶ as7nplmgjevnpq®auÝbnVvatgjn4c@qnmchgja9b

wr«s9cl·ava9a9l)m³ºs7nVikbdcehwrlzgja4bdcfjas7 eveva7lmgj=wl)´¥zp eva9@¤rötcfl¥ ¤ ù¥¤ as©npbbwlz@lng©s©a9 zpn«i« ¥s©a9a9ba9ewrlgjabyiØjs©a9iap¤Z wrzpa9e ywgjs©wlz>o­evat¶ a9l¥su³ywqrqZbevn ¥s7akqa9v¨pcehw¯c½gjwnVl§wrlKs7 eveha9lmg1cfl¥¦gva9eva9o¯nVeva@vinngja7egjnpej¶ aV¤Z$aevngjnpevba9at4wvnylwl´¥zV eha¤röpöcl¥wgo­npqqrntyTgvaT©cfiaTs7 eh¨Vacf$gjavba9atÂwl>gjam³vgva9eva9vws7nVlgjevnpq®jsja9iaV¤

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ù¥ö

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 104

t(s)

Mec

h. s

peed

(rpm

)

wzV eva=¤röpö(H$npgvnVe$vba9atÂwlÂbyTißgjnpej¶m as7nVlmgvevnpq®auÝbnpvat>gvnc«qrncvgva9b

0 0.05 0.1 0.15 0.2 0.25 0.3−0.5

0

0.5

i a (A)

0 0.05 0.1 0.15 0.2 0.25 0.3−0.5

0

0.5

i b (A)

0 0.05 0.1 0.15 0.2 0.25 0.3−0.5

0

0.5

t (s)

i c (A)

wrzp eha=¤röt~HxZdcvas7 eheva9lmgvwrlÂbyi gvnVev¶m as7nplmgjehnVqµauÝbnVvatgjn4c@qnmchgja9b

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ùm

ÓwðaÓð M W Y®Y Ø [R E ò[ G a bVyTi vba9at«s7nplmgjevnpqh³hgja9iQwZvntyTl«wl«´¥zp eha¤rö9÷¤F a s7 eveha9lmg\s7nplmgjehnVqqa9ewgja«©cfiakcfa9o­npeva« gcx\$vba9at¦s7nVlgjevnpqqra9e¥ca9a9lKcatµ¤$a«vba9ats7nplmgjehnVqqa9ebdcfe©cfia7gja9ehcehaka9evw¬¨at¦ vwlz>vwrikwrq¾cfeevacfvnVlwlzco¯nVegjaks7 eheva9lmgs7nplmgjehnVqqa9ebdcejcika7gja9ehwrlºCúûGEª¤\$abdcfe©cfia7gva9evTcfevastcfq¾su q¯c½gjatcf

kp = αωJ¡¸¤ø£

ki = αωkf¡¸¤úûm£

cfl¥αω

a7ba9l¥nplkgjaa9jweva9kevwja gjwianpogvavba9at¼¤\ eva7a$¨Vcfq a9npoαω

yTwqqagvevwatÂa9evap¤ a´¥evhg¨pcq aic²pa9gjajba9a9sunVlmgvevnpq cfo cfhgcfgva1s7 eheva9lmgs7nplmgjehnVq¸gjavats7npl¥ic²pa9 wg l¥eva9gvwrika9 jqnty$a7ecl¥gvaq¯cfhg ¨pcq a9 ic²pa9w¬ggva9l>gjwia9vqrnty a9et¤

Idc

wm step

wm refwm I ref

Speedcontroller

SignalGenerator

>=

RelationalOperator

Firing Signals

Vsuab,ubc

Inverter block

1/2

Gain

Vs

DC sourcevoltage

Irefi Vs

Current controller

Position

chopFiring Signals

Control block

Vs

Constant

uab,ubcPosition

wmiabc

BLDC motor block

|u|

Abs1

|u|

Abs

wrzp eva1¤öt÷~Hx Ívba9atsunVlmgvevnpq®h³hgja7i

a7ghgjwlzαω = αe

zVw¬¨a7gvao­npqrqntyTwlzbdcejciaugja9ev&Hkp = 1.10 · 10−5

ki = 3.03 · 10−4

aeha9o­a9eha9l¥s7avba9at§wr20,000 rpm

ca9o­npevaV¤ wzV eva¤rö7ùÂvntyTgjdc½ggja7jas7nplmgjehnVqbdcfe©cfia7gva9evFbehn ¥suacji4cqqn½¨Va9evvnmnpgFwl«vba9at@cl¥gja9eha$cfqrvncbbacehgjna#jnpia#hgvacp³hg©cfgvaa7evevnpet¤/ wzV eha9F¤öcl¥1¤rö9ûvnty·gja#a9qatsugvevwrstcqVgjnpej¶ acfl¥gjaTb¥cvas7 eveha9lmgv¤Z aTbyiØ gH³4su³s7qraTwö9p? lmgjwqdgvaTvba9at4evacs©a9gjakeva9o­a7eva9l¥s7ak¨Vcfq aV¤$abdcfvas7 eveva9lgjjnty gvdc½g1w¬ggcf²Va9nplq³ºcfnV g1nplaevngjnpeeha7¨npq gjwnVl>gjnkevacs©Âhgjac³hgc½gjaV¤

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ù÷

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

wzV eha=¤rö7ùH$npgvnVe$jba7atÂwlbVyTi vba9ats7nplmgvevnpq/cfglnqncpº¡αω = αe

£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

t (s)

T e (mNm

)

wzV eha=¤röt~H#\qatsugjehw¾stcfqµgjnpej¶m awlÂbyi vba9atsunVlmgvevnpq/c½glnqncpº¡αω = αe

£

a7ghgjwlzαω = 0.01αe

eva9v q¬gj@wrlc|i= ¥s©vqrnty a9e@eha9jbnplvacf@jntylwrl ´¥zp eva¤rö¤# as7nplmgjehnVqqa9ebdcejciaugja9evTcfevalnty

kp = 1.10 · 10−7

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ùVù

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5

i b (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

t (s)

i c (A)

wrzp eva1¤ötû~HxZdcvas7 eveha9lmgvwlÂbyi vba9atÂs7nVlgjevnpq/c½glnkqrnc)¡αω = αe

£

ki = 3.03 · 10−6

a9evaw@ln¦n¨Va9evvnng@a9eva g«gvavgvacp³·hg©cfgvaa9evevnpe«eha9icfwrlt¤¦=´¥zp eva9¤rö9ÿcl¥¤röjny1gjabyTi nVba9ejcfgvwrnpla9zpwrlTevwzpmgc½ggjahgcfehgTwlnVeva9egjnvqnynyl>gjaehwrvanpo/gjavba9atµ¤

`jwlzαω = αe

w$gjnmno cfvgTcfl¥αω = 0.01αe

wvqny1vnαω = 0.1αe

wr vata9eha1cTcksunVibehnVikwrvaV¤# aeva7j q¬gjwlz4s7nplmgjehnVqµbdcejcika7gja9ehTceva

kp = 1.10 · 10−6

ki = 3.03 · 10−5

wrzp ehak¤ vntyTTgjdc½ggva9va=bdcejciaugja9evzpw¨Va«augvgja9eTeva9v q¬gjt¤$a9eva@cbbacehgjnalnn¨a9ehvnng= g1gja9ehaw@c>ji4cqqhgjac³Kvg©cfgva4a9evevnpet¤Â`vwlz¦cÂqnVlzpa9evwi« q¾cfgvwrnplgjwiaeva7¨Vacfqrgvdcfggja9eva1wckvicfqrqn¨a9ehvnngcfl¥Âgva1hgjac³Âhgc½gjaa9ehevnVeats7npia91ji4cqqa9egj¥clºgva4a9evehnVeva9a9l)wl)´¥zp eva¤ ¤> wzV eha9@¤ öcfl¥¤ p@vnty gvaa9qra9sugjevwrsgjnVev¶m a1cfl¥gjabdcfva1s7 eheva9lgjeva9vbatsugjw¬¨a7q³¤

Fwzp eva$¤ ÷TjntyFntygjah³hgja9iQehacpsgj gvncq¯cfevzpaqnmc=hgja9b=npo0.23 mNmyw¾sj=wr/gvaicÝwi« iQs7nplmgvwrl np qrncgjdc½gZstcfl=a cfbbqwratgjngjaingjnpet¤ a

vba9atÂevnpbws7npljwra9ejcqaV¤

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ùm

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

2000

4000

6000

8000

10000

12000

14000

t(s)

Mec

h. s

peed

(rpm

)

wzV eva=¤rö-H$npgvnVe$vba7atÂwlbVyTi vba9ats7nplmgvevnpq/cfglnqncpº¡αω = 0.01αe

£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

t (s)

T e (mNm

)

wrzp eha¤rö9ÿH#Zqratsgjevw¾cfq¼gvnVev¶m awrlbyTißvba9ats7nplmgjehnVq®c½g$ln@qnmcK¡αω = 0.01αe

£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ùû

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4i b (A

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.3

−0.2

−0.1

0

0.1

t (s)

i c (A)

wrzp eva1¤röHxZdcvas7 eheva9lmgvwrlÂbyi vba9atÂs7nVlgjevnpq/c½glnkqrnc)¡αω = 0.01αe

£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

wzV eha=¤ H#ngjnpe$jba9a9ÂwlbVyTi vba9atÂs7nplmgjehnVqcfglnqnmc)¡αω = 0.1αe

£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ù-

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

t (s)

T e (mNm

)

wrzp eha1¤ ö(H\qatsugvevwrstcfq¼gjnpej¶m awl>byi vba9at>s7nVlgjevnpqc½gln@qnmcK¡αω = 0.1αe

£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5

i b (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

t (s)

i c (A)

wrzp eva1¤øV¥HxZdcvas7 eveha9lmgjwlÂbyTi vba9atÂs7nVlmgvevnpq/c½glnqncpº¡αω = 0.1αe

£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ùÿ

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

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0.1αe£

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Idc

thetam stepwm refwm I ref

Speedcontroller

SignalGenerator

>=

RelationalOperator

thetam refthetam wm ref

Positioncontroller

Firing Signals

Vsuab,ubc

Inverter block

1/2

Gain

Vs

DC sourcevoltage

Irefi Vs

Current controller

Position

chopFiring Signals

Control block

Vs

Constant

uab,ubcPositionthetam

wmiabc

BLDC motor block

|u|

Abs1

|u|

Abs

Fwzp eva1¤øùHxÍbnVvw¬gjwnpls7nplmgjehnVqµv³vgva9i

as7nplmgjehnVqqa9e#bdcfe©cfia7gva9ev\ vatka9ehaTcfeva$nVgcwlatk³@ vwlzgja gjevw¾cfqdclka9evehnVeia7gvnµ¤#`vwlz

kp = 6.59cfl¥

ki = 9.10 · 10−8

zpw¨Va9/gvazVnmn1eha9v q¬gjt¤ Fwzp eva¤øVvnty/gjaevngjnpeFclzVqa c½g lnTqncpnVba9ejcfgvwrnpl®¤ aeha9o­a9eha9l¥s7acflzpqraw

3600¤\ aa7evevnpew nplq¬³co­e©csugvwrnplnpo/c=a7zVeva7aV¤\ wrzp eva

¤ û1vnygva©cfiagjwlzyTa7lgjaTicÝwi« iØs7nplmgvwrl nV qncp¦¡0.23 mNm

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ p

0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

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θ m (d

eg)

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0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

t(s)

θ m (d

eg)

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Iref step

Firing Signals

Vsuab,ubc

Inverter block

Irefi Vs

Current controller

Position Firing Signals

Control block uab,ubcPosition

idc

BLDC motor block

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ V

0 0.05 0.1 0.15 0.2 0.25 0.30

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0.1

0.15

0.2

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t (s)

T e (mNm

)

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0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 104

t(s)

Mec

h. s

peed

(rpm

)

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ p÷

0 0.05 0.1 0.15 0.2 0.25 0.3−0.2

−0.1

0

0.1

0.2

i a (A)

0 0.05 0.1 0.15 0.2 0.25 0.3−0.2

−0.1

0

0.1

0.2

i b (A)

0 0.05 0.1 0.15 0.2 0.25 0.3−0.2

−0.1

0

0.1

0.2

t (s)

i c (A)

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ ù

ÓöjÓð M W Y®Y Ø [R E ò[ G a@vba9at¦s7nVlmgvevnpqqra9e vat¦a9eva«wrgja«©cia@sunVlmgvevnpqrqa9egjdc½gyc vat¦o¯nVegvabyiQvba9at«s7nplmgjehnVq¸¤F wzV eva$¤ø÷övnty gja#ynVqah³hgja9i¤ aeva9o­a7eva9l¥s7avba9atwhgvwrqq

20,000 rpmcl¥gja©cfia1x\s7nplhgcflmgjTcfeva vatµ¤

wm step

wm refwm I ref

Speedcontroller

Firing Signals

Vsuab,ubc

Inverter block

Irefi Vs

Current controller

Position Firing Signals

Control block uab,ubcPosition

wmidc

BLDC motor block

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Fwzp eva9¤ø÷Vµ¤ø÷pûcl§¤ú÷,kjnty gja«©cfia«s7 eh¨Va9Tya9l|gja«s7nplmgjehnVqqa9ewica@¨a9e³¦vqrntyý¡

αω = 0.01αe£u¤@$akeva9v q¬gj1ceha@gjak©cfia4cyTw¬gj§gvakbyTi

s7nplmgjehnVqµauÝs7a9bggvdc½ggjagvnVev¶m awi= ¥s©Âvinmnpgva9et¤Fwzp eva9¤ú÷Vÿ¤ø÷(4cl¥¤úùVvnty gjaeha9v q¬gj$ya9lÂgja1s7nplmgjehnVqqa9ewica

o cfhgja9e|¡αω = 0.1αe

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0.23 mNm£u¤\$aatsuevacfvawlÂvba9at>wrs7nplvw¾a9e!

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ V

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0

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

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αω = αe£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

t (s)

T e (mNm

)

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αω = αe£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ pû

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5i b (A

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

t (s)

i c (A)

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αω = αe£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

2000

4000

6000

8000

10000

12000

14000

t(s)

Mec

h. s

peed

(rpm

)

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£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸

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0

0.05

0.1

0.15

0.2

0.25

t (s)

T e (mNm

)

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αω = 0.01αe£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.2

0

0.2

0.4

0.6

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

i b (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.15

−0.1

−0.05

0

0.05

t (s)

i c (A)

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αω = 0.01αe£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ pÿ

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

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£

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

t (s)

T e (mNm

)

wrzp eha1¤ø÷(~HZqra9sugjevwrstcfq¼gjnpej¶m awrl¨Vcfevw¾cfqrasªqwrl²4¨VnVq¬gcfzpavba9at>s7nplmgvevnVq®c½glnqnmcº¡

αω = 0.1αe£

KMLONQPSRTVU,Y Ka_a\^RU¹_¸ (

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.2

0

0.2

0.4

0.6

i a (A)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.5

0

0.5i b (A

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10−3

−0.4

−0.2

0

0.2

0.4

t (s)

i c (A)

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αω = 0.1αe£

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.5

1

1.5

2

2.5x 104

t(s)

Mec

h. s

peed

(rpm

)

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αω = 0.1αe£

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0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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T e (mNm

)

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thetam stepwm refwm I ref

Speedcontroller

thetam refthetam wm ref

Positioncontroller

Firing Signals

Vsuab,ubc

Inverter block

Irefi Vs

Current controller

Position Firing Signals

Control block uab,ubcPositionthetam

wmidc

BLDC motor block

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0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

t(s)

θ m (d

eg)

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KMLONQPSRTVU,Y Ka_a\^RU¹_¸ û

0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

t(s)

θ m (d

eg)

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