143184865-BLDC-Motor-Modelling-and-Control-A-Matlab-Simulink-Implementation
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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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i3 6= 0 ⇒
u12 = v12 − (e1 − e2 ) =
Vs − e 1 + e2
u23 = v23 − (e2 − e3 ) =
−e2 + e3
u31 = v31 − (e3 − e1 ) = −Vs − e3 + e1
u12 = v12 − (e1 − e2 ) =
i3 = 0 ⇒ u23 = v23 − (e2 − e3 ) =
u31 = v31 − (e3 − e1 ) =
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u31 = v31 − (e3 − e1 ) =
Vs − e 3 + e1
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u31 = v31 − (e3 − e1 ) =
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1
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2
1
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ic 6= 0
ic = 0
ib 6= 0
ib = 0
ia 6= 0
ia = 0
ic 6= 0
ic = 0
ib 6= 0
ib = 0
ia 6= 0
ia = 0
60◦ − 120◦
120◦ − 180◦
180◦ − 240◦
240◦ − 300◦
300◦ − 360◦
vab − eab
Vs − e a + eb
Vs − e a + eb
−ea + eb
1
(Vs − ea + ec )
2
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1
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2
−Vs − ea + eb
−Vs − ea + eb
−ea + eb
1
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2
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1
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1
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2
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1
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C
B
A
B
D2
D3
D6
D2
D5
Vs
Vs
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60o - 120o
B
A
B
D5
D2
D1
D4
Vs
120o - 180o
180o - 240o
C
B
B
D1
Vs
240o - 300o
D5
Vs
A
D6
C
A
C
D4
D3
A
C
D4
D3
D6
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−
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3
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+
−
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+
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60◦ − 120◦
120◦ − 180◦
180◦ − 240◦
240◦ − 300◦
300◦ − 360◦
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ia 6= 0, ic = 0
ia = 0, ic 6= 0
ia = 0, ic = 0
ic 6= 0, ib 6= 0
ic 6= 0, ib = 0
ic = 0, ib 6= 0
ic = 0, ib = 0
ib 6= 0, ia 6= 0
ib 6= 0, ia = 0
ib = 0, ia 6= 0
ib = 0, ia = 0
ia 6= 0, ic 6= 0
ia 6= 0, ic = 0
ia = 0, ic 6= 0
ia = 0, ic = 0
ic 6= 0, ib 6= 0
ic 6= 0, ib = 0
ic = 0, ib 6= 0
ic = 0, ib = 0
ib 6= 0, ia 6= 0
ib 6= 0, ia = 0
ib = 0, ia 6= 0
ib = 0, ia = 0
vab − eab
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1
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2
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A
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60o - 120o
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A
C
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A
C
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D5
D4
D6
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i3
e2
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vd3
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Z
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60◦ − 120◦
120◦ − 180◦
180◦ − 240◦
240◦ − 300◦
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ia 6= 0, ic 6= 0
ia 6= 0, ic = 0
ia = 0, ic 6= 0
ia = 0, ic = 0
ia 6= 0, ib 6= 0
ia 6= 0, ib = 0
ia = 0, ib 6= 0
ia = 0, ib = 0
ib 6= 0, ia 6= 0
ib 6= 0, ia = 0
ib = 0, ia 6= 0
ib = 0, ia = 0
ib 6= 0, ic 6= 0
ib 6= 0, ic = 0
ib = 0, ic 6= 0
ib = 0, ic = 0
ic 6= 0, ib 6= 0
ic 6= 0, ib = 0
ic = 0, ib 6= 0
ic = 0, ib = 0
ic 6= 0, ia 6= 0
ic 6= 0, ia = 0
ic = 0, ia 6= 0
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Signal
Generator
Abs1
Vs
Constant
Position
Iref
Iref step
i
>=
Vs
Current controller
Relational
Operator
chop
Firing Signals
Firing Signals
Vs
Control block
DC source
voltage
Idc
1/2
Gain
uab,ubc
Vs
Inverter block
uab,ubc
Position
iabc
BLDC motor block
|u|
Abs
wrzpeva1¤Ã~Hx Õgjnpej¶mas7nVlgjevnpq®h³hgja9i
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s7nplmgjehnVq{q{a9eo­nVe1c>s@ingjnpebeha9va9lmgjat§wrl¡CúûGEª¤k a4a9vw{zVlºhgcfehgvm³¦va9qra9sugjw{lz|c
a9vw{evatevw{vagvwrika t o­npegjas7eheva9lmgt¤\evnpi gjdc½gc1s7nVlvg©clg α wr a7gja7eviw{lat
re
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cf
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tre
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kp = αe L
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ki = αe R.
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kp = 2.00 · 103
ki = 2.75 · 105
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CúûGE¢£cfl¥dcf>cK¨VnVq¬gcfzVa©cfgve©c½gjw{nVlq{nsj²Úgjdc½gq{wrikw{gvgja|a9i4cl¥at¨npq{g©czpa
gjn ±6 V vn>gjdc½ggva4s7npibdcehw{jnpl§yTw¬gj§gjakgvevw¾clzpq¾ceyc9¨a@yw{qrq#zpw¬¨a4s7npeveva9sug
eva7jq¬gjt¤Â wrzpeva ¤rö9vntyT1gvaa9q{atsugjehw¾s9cqgvnVev¶maV¤Â$a4eva9o­a7eva9l¥s7a4gvnVev¶ma cfl¥
gjaq{nmcºhgja7b)w{1hgjw{q{q 0.2 mN m ggjakgjnpej¶a¤¥¥sgjdc½gjw{nVl)w{1q¾cfevzpa9egvdclºw{l
gjaTm³hgja7eva9vw{$s7nplmgvevnpq~¤Z$aehacfjnplo­npegvwrw{gjdc½ggvaa9q{atsugjehw¾s9cq¼³ldcfiwrs7$ceha
¨a9e ³ o cfhgTsunVibdcfeva9 yw{gv>gja yw{gjs©w{lzo­evat¶a9l¥su³¤
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0.2
0.15
0.1
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0
0.05
0.1
0.15
t (s)
0.2
0.25
0.3
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w{lz>o­evat¶a9l¥su³yw{qrqZbevn¥s7akq{a9v¨pcehw¯c½gjw{nVl§wrlKs7eveha9lmg1cfl¥¦gva9eva9o¯nVeva@vinngja7e
gjnpej¶aV¤Z$aevngjnpevb a9at4w{vnylw{l´¥zVeha¤röpöcl¥w{go­npq{qrntyTgvaT©cfiaTs7eh¨Va
cf$gjavb a9atÂw{l>gjam³vgva9eva9vw{s7nVlgjevnpq®jsja9iaV¤
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5
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4.5
4
Mech. speed (rpm)
3.5
3
2.5
2
1.5
1
0.5
0
0
0.05
0.1
0.15
t(s)
0.2
0.25
0.3
w{zVeva=¤röpö(H$npgvnVe$vb a9atÂw{lÂbyTißgjnpej¶mas7nVlmgvevnpq®auÝb npvat>gvnc«qrncvgva9b
ia (A)
0.5
0
−0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0
0.05
0.1
0.15
0.2
0.25
0.3
0
0.05
0.1
0.15
t (s)
0.2
0.25
0.3
ib (A)
0.5
0
−0.5
ic (A)
0.5
0
−0.5
wrzpeha=¤röt~HxZdcvas7eheva9lmgvwrlÂbyi gvnVev¶mas7nplmgjehnVqµauÝb nVvat gjn4c@q{nmchgja9b
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w{gja«©cfiakcf a9o­npeva«gc x\$vb a9at¦s7nVlgjevnpq{qra9e¥c a9a9lKcatµ¤$a«vb a9at
s7nplmgjehnVq{q{a9ebdcfe©cfia7gja9ehcehaka9evw¬¨at¦vw{lz>vwrikwrq¾cfeevacfvnVlw{lzco¯nVegjaks7eheva9lmg
s7nplmgjehnVq{q{a9ebdcejcika7gja9ehwrº
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kp = αω J
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a7b a9l¥nplkgjaa9jw{eva9kevw{ja gjw{ianpo gvavb a9at¼¤\ eva7a$¨Vcfq{a9npo yTw{q{q
agvevαw{atωÂa9evap¤ a´¥evhg¨pcq{aic²pa9gjajb a9a9sunVlmgvevnpq cfo cfhgcfgva1s7αeωheva9lmg
s7nplmgjehnVq¸gjavats7npl¥ic²pa9 w{g l¥eva9gvwrika9 jq{nty$a7ecl¥gvaq¯cfhg ¨pcq{a9 ic²pa9
w¬ggva9l>gjw{ia9vqrnty a9et¤
ki = αω kf
|u|
Signal
Generator
Abs1
Vs
Constant
wm ref
wm step
wm
Position
I ref
Speed
controller
Iref
i
Vs
Current controller
>=
Relational
Operator
chop
Firing Signals
Firing Signals
Vs
Control block
DC source
voltage
Idc
1/2
Gain
uab,ubc
Vs
Position
uab,ubc
wm
iabc
Inverter block
BLDC motor block
|u|
Abs
wrzpeva1¤{öt÷~Hx Ívb a9atsunVlmgvevnpq®h³hgja7i
a7ghgjw{lz
αω = αe
zVw¬¨a7gvao­npqrq{ntyTw{lzbdcejciaugja9ev&H
kp = 1.10 · 10−5
ki = 3.03 · 10−4
aeha9o­a9eha9l¥s7avb a9at§wr 20,000 rpm c a9o­npevaV¤ w{zVeva¤rö7ùÂvntyTgjdc½ggja7ja
s7nplmgjehnVqbdcfe©cfia7gva9evFbehn¥suacji4cq{qn½¨Va9evvnmnpgFw{l«vb a9at@cl¥gja9eha$cfqrvncbb aceh
gjn a#jnpia#hgvacp³hg©cfgvaa7evevnpet¤/ w{zVeha9F¤{öcl¥1¤rö9ûvnty·gja#a9q{atsugvevwrstcqVgjnpej¶a
cfl¥gjaTb¥cvas7eveha9lmgv¤Z aTbyiØgH³4su³s7qraTw{ö9p ?lmgjw{qdgvaTvb a9at4evacs©a9
gjakeva9o­a7eva9l¥s7ak¨Vcfq{aV¤$abdcfvas7eveva9lgjjnty gvdc½g1w¬ggcf²Va9nplq{³ºcf nVg1npla
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2.5
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2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
t(s)
3
3.5
4
4.5
5
−3
x 10
w{zVeha=¤rö7ùH$npgvnVe$jb a7atÂw{lbVyTi vb a9ats7nplmgvevnpq/cfglnq{ncpº¡ α
ω
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£
0.7
0.6
Te (mNm)
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
w{zVeha=¤röt~H#\q{atsugjehw¾stcfqµgjnpej¶maw{lÂbyi vb a9atsunVlmgvevnpq/c½glnq{ncpº¡ α
ω
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£
a7ghgjw{lz α = 0.01α eva9vq¬gj@wrlc|i=¥s©vqrnty a9e@eha9jb nplvacf@jntylwrl ´¥zpeva
¤rö¤# aωs7nplmgjehnVq{q{a9eebdcejciaugja9evTcfevalnty
kp = 1.10 · 10−7
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a
i (A)
0.5
0
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
b
i (A)
5
−3
x 10
0.5
0
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
−3
x 10
0.4
c
i (A)
0.2
0
−0.2
−0.4
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
wrzpeva1¤{ötû~HxZdcvas7eveha9lmgvw{lÂbyi vb a9atÂs7nVlgjevnpq/c½glnkqrnc)¡ α
ω
= αe
£
ki = 3.03 · 10−6
a9evaw{@ln¦n¨Va9evvnng@a9evag«gvavgvacp³·hg©cfgvaa9evevnpe«eha9icfwrlt¤¦=´¥zpeva9
¤rö9ÿcl¥¤röjny1gjabyTi nVb a9ejcfgvwrnpl a9zpwrlTevw{zpmgc½ggjahgcfehgTw{lnVeva9egjn
vq{nynyl>gjaehwrvanpo/gjavb a9atµ¤
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w{$gjnmno cfvgTcfl¥
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gjehnVqµbde cejcika7gja9ehTcαevaω = 0.1αe
kp = 1.10 · 10−6
ki = 3.03 · 10−5
rw zpehak¤ vntyTTgjdc½ggva9va=bdcejciaugja9evzpw{¨Va« augvgja9eTeva9vq¬gjt¤$a9eva@cbb aceh
gjn alnn¨a9ehvnng=g1gja9ehaw{@c>ji4cq{qhgjac³Kvg©cfgva4a9evevnpet¤Â`vw{lz¦cÂq{nVlzpa9e
vw{i«q¾cfgvwrnplgjw{iaeva7¨Vacfqrgvdcfggja9eva1w{ckvicfqrqn¨a9ehvnngcfl¥Âgva1hgjac³Âhgc½gja
a9ehevnVe ats7npia91ji4cq{q{a9egj¥clºgva4a9evehnVeva9a9l)w{l)´¥zpeva¤ ¤> w{zVeha9@¤ öcfl¥
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Fw{zpeva$¤ ÷TjntyFntygjah³hgja9iQehacpsgj gvncq¯cfevzpaq{nmc=hgja9b=npo 0.23 mN m
yw¾sj=wr/gvaicÝw{i«iQs7nplmgvwrlnp qrncgjdc½gZstcfl= a cfbbq{wratgjngjaingjnpet¤ a
vb a9atÂevnpbw{s7npljwra9ejcq{aV¤
KMLONQPSR TVU,Y Ka_a\^R U¹_¸
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14000
12000
Mech. speed (rpm)
10000
8000
6000
4000
2000
0
0
0.5
1
1.5
2
2.5
t(s)
3
3.5
4
4.5
5
−3
x 10
w{zVeva=¤rö-H$npgvnVe$vba7atÂw{lbVyTi vb a9ats7nplmgvevnpq/cfglnq{ncpº¡ α
ω
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£
0.45
0.4
0.35
Te (mNm)
0.3
0.25
0.2
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0.1
0.05
0
0
0.5
1
1.5
2
2.5
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3
3.5
4
4.5
5
−3
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wrzpeha¤rö9ÿH#Zqratsgjevw¾cfq¼gvnVev¶mawrl byTißvb a9at s7nplmgjehnVq®c½g$ln@q{nmcK¡ α
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i (A)
0.2
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0
−0.2
−0.4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
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−3
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0.4
i (A)
0.2
b
0
−0.2
−0.4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
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0.1
c
i (A)
0
−0.1
−0.2
−0.3
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
wrzpeva1¤röHxZdcvas7eheva9lmgvwrlÂbyi vb a9atÂs7nVlgjevnpq/c½glnkqrnc)¡ α
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4
2.5
x 10
Mech. speed (rpm)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
t(s)
3
3.5
4
4.5
5
−3
x 10
w{zVeha=¤ H#ngjnpe$jb a9a9Âw{lbVyTi vb a9atÂs7nplmgjehnVqcfglnq{nmc)¡ α
ω
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£
£
KMLONQPSR TVU,Y Ka_a\^R U¹_¸
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0.6
Te (mNm)
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0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
wrzpeha1¤ ö(H\q{atsugvevwrstcfq¼gjnpej¶maw{l>byi vb a9at>s7nVlgjevnpqc½gln@q{nmcK¡ α
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a
i (A)
0.5
0
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
b
i (A)
5
−3
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0.5
0
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
−3
x 10
0.4
c
i (A)
0.2
0
−0.2
−0.4
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
wrzpeva1¤øV¥HxZdcvas7eveha9lmgjw{lÂbyTi vb a9atÂs7nVlmgvevnpq/c½glnq{ncpº¡ α
ω
= 0.1αe
£
£
KMLONQPSR TVU,Y Ka_a\^R U¹_¸
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4
2.5
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Mech. speed (rpm)
2
1.5
1
0.5
0
0
0.001
0.002
0.003
0.004
0.005
t(s)
0.006
0.007
0.008
0.009
0.01
wrzpeha¤øp÷~HZngjnpe#vb a9atwrlbyi vb a9at4sunVlmgvevnpqc½gic½Ýwri=i'q{nmcvgva9b¡ α =
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ab npvw¬gjw{nVlsunVlmgvevnpqrq{a9e$wrcflnpgva9ex#s7nplmgjevnpq{qra7eTcfvntylÂw{l ´¥zVeha¤øù¤# a
s7nplmgjehnVq{q{a9estcfllnpgT a¨a9e ³Âo¢chgT atstcfva1wro\cfln¨a9ehvnngTns9s7eht¥gjanplq¬³ yct³
gjn«zpn@s7q{nVva9e nylgvn=gjaeha9o­a9eha9l¥s7acflzVq{aTy nVqr agjn«eha7¨a9ehjaTgjaevngjnpejb a7atµ¤
wr«qrsingjnpe«ikna9qnma9@lng@vbb npehg«jb a7at eha7¨a9eh©cq¸¤¦$as7nVlgjevnpq{qra9e«w{
gja7eva9o­npevai4cpavq{nygjnkbeva7¨Va9lmgcflÂn½¨Va9evvnmnpgt¤
|u|
Signal
Generator
Abs1
Vs
Constant
thetam step
thetam ref
wm ref
thetam
Position
controller
wm ref
wm
Position
I ref
Speed
controller
Iref
i
>=
Vs
Current controller
Relational
Operator
chop
Firing Signals
Firing Signals
Vs
Control block
Inverter block
DC source
voltage
Idc
1/2
Gain
uab,ubc
Vs
uab,ubc
Position
thetam
wm
iabc
BLDC motor block
|u|
Abs
Fw{zpeva1¤øùHx Íb nVvw¬gjw{npls7nplmgjehnVqµv³vgva9i
as7nplmgjehnVq{q{a9e#bdcfe©cfia7gva9ev\vatka9ehaTcfeva$nVgcw{latk³@vw{lzgja gjevw¾cfqdclka9evehnVe
ia7gvnµ¤#`vw{lz
kp = 6.59
cfl¥
ki = 9.10 · 10−8
zpw{¨Va9/gvazVnmn1eha9vq¬gjt¤ Fw{zpeva¤øVvnty/gjaevngjnpeFclzVq{a c½g lnTq{ncpnVb a9ejcfgvwrnpl®¤
aeha9o­a9eha9l¥s7acflzpqraw{ 3600◦ ¤\ aa7evevnpew{ nplq¬³ co­e©csugvwrnpl npo/c=a7zVeva7aV¤\ wrzpeva
¤ û1vnygva©cfiagjw{lzyTa7lgjaTicÝw{i«iØs7nplmgvwrlnVq{ncp¦¡
£
w{cfbbq{w{atcfg$gjahg©cehgt¤# aeva9vq¬gjTcfevawra9lmgvw¾stcfq¼yTw¬gjÂbe©csugjwrstcfq{q{³ 0.23
¿9a9evnkmN
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4000
3500
3000
θm (deg)
2500
2000
1500
1000
500
0
0
0.5
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1
1.5
wrzpeva1¤ p~H#ngjnpeTcflzpqrawrlÂbyi b npvw¬gjw{nVls7nplmgvevnpq/c½glnkqrncp
4000
3500
3000
θm (deg)
2500
2000
1500
1000
500
0
0
0.5
t(s)
1
1.5
wrzpeva1¤øpû~H$ngjnpeTcflzVq{awrlÂbyi b npjw¬gjw{npls7nplmgjehnVqcfgicÝw{i«i qrnc
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Position Firing Signals
Iref
Iref step
i
Vs
Current controller
Control block
Firing Signals
Vs
uab,ubc
Inverter block
uab,ubc
Position
idc
BLDC motor block
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5
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4.5
4
Mech. speed (rpm)
3.5
3
2.5
2
1.5
1
0.5
0
0
0.05
0.1
0.15
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0.2
0.25
0.3
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0.2
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0.3
0
0.05
0.1
0.15
0.2
0.25
0.3
0
0.05
0.1
0.15
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0.2
0.25
0.3
0.2
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wm step
wm
Position Firing Signals
I ref
Speed
controller
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i
Vs
Current controller
Control block
Position
Firing Signals
Vs
uab,ubc
uab,ubc
wm
idc
Inverter block
BLDC motor block
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2.5
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3
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4
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0.5
0.3
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T (mNm)
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0.2
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1
1.5
2
2.5
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3
3.5
4
4.5
5
−3
x 10
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2
2.5
3
3.5
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4.5
b
i (A)
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0.5
1
1.5
2
2.5
3
3.5
4
4.5
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0.4
c
i (A)
0.2
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−0.4
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
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14000
12000
Mech. speed (rpm)
10000
8000
6000
4000
2000
0
0
0.5
1
1.5
2
2.5
t(s)
3
3.5
4
4.5
5
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0.1
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0
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
x 10
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0.4
0.2
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1.5
2
2.5
3
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4
4.5
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0.4
b
i (A)
0.2
0
−0.2
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0.5
1
1.5
2
2.5
3
3.5
4
4.5
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0.05
c
i (A)
0
−0.05
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−0.15
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
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KMLONQPSR TVU,Y Ka_a\^R U¹_¸
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4
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Mech. speed (rpm)
2
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1
0.5
0
0
0.5
1
1.5
2
2.5
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3
3.5
4
4.5
5
−3
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e
0.7
0.6
Te (mNm)
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
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0.2
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1
1.5
2
2.5
3
3.5
4
4.5
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5
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b
0
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1
1.5
2
2.5
3
3.5
4
4.5
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0.4
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c
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−0.4
0
0.5
1
1.5
2
2.5
t (s)
3
3.5
4
4.5
5
−3
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4
2.5
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Mech. speed (rpm)
2
1.5
1
0.5
0
0
0.001
0.002
0.003
0.004
0.005
t(s)
0.006
0.007
0.008
0.009
0.01
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0.6
0.4
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0.3
0.2
0.1
0
0
0.001
0.002
0.003
0.004
0.005
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0.006
0.007
0.008
0.009
0.01
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thetam step
thetam ref
wm ref
thetam
wm ref
wm
Position
controller
Position Firing Signals
Iref
I ref
i
Speed
controller
Control block
Vs
Firing Signals
Vs
uab,ubc
Inverter block
Current controller
uab,ubc
Position
thetam
wm
idc
BLDC motor block
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4000
3500
3000
θm (deg)
2500
2000
1500
1000
500
0
0
0.5
t(s)
1
1.5
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4000
3500
3000
θm (deg)
2500
2000
1500
1000
500
0
0
0.5
t(s)
1
1.5
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0.06
0.05
0.045
0.04
0.09
0.0905
0.091
0.0915
0.092
0.0925
t (s)
0.093
0.0935
0.094
0.0945
0.095
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0.26
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T (mNm)
0.24
0.22
0.2
0.18
0.09
0.0905
0.091
0.0915
0.092
0.0925
t (s)
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