SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

More documents

Recommendations

Info

List of Tables Table 4.1 – States and corresponding pole voltages of 180° inverter..........................................178 Table 4.2 – Inverter states (pole voltages) expressed in complex components; k=c=2/3............182 Table 4.3 – Line-neutral voltages expressed in complex components.........................................184 Table 4.4 – Magnitude of space vectors of three-phase quantities. .............................................188 Table 4.5 – Maximum ma referenced to SPWM linear limit (R).................................................202 Table 4.6 – Maximum ma referenced to THI linear limit (T). .....................................................202 Table 4.7 – Maximum ma referenced to fundamental obtained in squarewave mode (F). ..........203 Table 4.8 – Maximum ma referenced to magnitude of six-step basis space vector (S). ..............203 Table 4.9 –Maximum modulation indices defined using peak, L-N,VDC, k=2/3.........................204 xiv
List of Symbols Symbol Meaning Units D diameter [m] Y length [m] G airgap length [m] b friction [N·m·s/(rad)] J inertia [kg·m 2 ] v applied voltage [V] g total induced EMF [V] e back-EMF [V] i current [A] R reluctance [A(·turn)/Wb] = [1/H] R resistance [ohm] L,M inductance [H] = [Wb/ A(·turn)] f,F MMF [A(·turn)] stator flux linkage [Wb(·turn)] S component of stator flux linkage due to stator current [Wb(·turn)] (stator self flux linkage) R component of stator flux linkage due to rotor flux [Wb(·turn)] , (rotor-stator flux linkage) flux [Wb] B flux density [Wb/m 2 ] = [T] H magnetic field strength [A/m] μ magnetic permeability [H/m] T torque (developed electromechanical) [N·m] TL load toque [N·m] t time [s] xv
Page 1 and 2: SENSORLESS FIELD ORIENTED CONTROL O
Page 3 and 4: Table of Contents List of Figures..
Page 5 and 6: CHAPTER 5 - Field Oriented Control
Page 7 and 8: List of Figures Figure 2.1 - Radial
Page 9 and 10: Figure 3.29 - Arbitrary space vecto
Page 11 and 12: Figure 4.44 - ZS components of some
Page 13: Figure C.13 - Single-turn full-pitc
Page 17 and 18: Abbreviations ACIM AC induction mot
Page 19 and 20: Superscripts * commanded value ref
Page 21 and 22: CHAPTER 1 - Introduction Historical
Page 23 and 24: vector theory to model a machine, w
Page 25 and 26: publications and magazines, and Int
Page 27 and 28: elationship between SVM and other P
Page 29 and 30: CHAPTER 2 - Fundamentals of Electri
Page 31 and 32: Preliminaries In reading the litera
Page 33 and 34: Taxonomy of Motors There is any num
Page 35 and 36: characteristics (the DC load curren
Page 37 and 38: torque component, sturdily construc
Page 39 and 40: Figure 2.7 - Cross sections of some
Page 41 and 42: draw the line between the solenoida
Page 43 and 44: These texts generally attribute the
Page 45 and 46: N B A B Y x(t) (2.6) The induc
Page 47 and 48: extended to the rotational case lat
Page 49 and 50: present analysis). When this is tru
Page 51 and 52: Figure 2.16 - Components of total f
Page 53 and 54: As aforementioned a spatial analysi
Page 55 and 56: clear the meaning, but the reader i
Page 57 and 58: Figure 2.20 - Elementary brushless
Page 59 and 60: called the per-phase torque functio
Page 61 and 62: Expressing bEMF in terms of the bEM
Page 63 and 64: Equation (2.44) is the component of
Page 65 and 66:
d R( r) ke( r) kt( r) sin( r) (2.
Page 67 and 68:
General Electromechanical Models Th
Page 69 and 70:
Figure 2.28 - Phase-variable simula
Page 71 and 72:
Trapezoidal and Sinusoidal BPMS Mot
Page 73 and 74:
Figure 2.29 - Back-EMF and drive cu
Page 75 and 76:
Figure 2.31 - Back-EMF and drive cu
Page 77 and 78:
3 KT Ke 2 (sinusoidal) K 2 K (tra
Page 79 and 80:
control scheme must keep sinusoidal
Page 81 and 82:
with misconceptions. The primary is
Page 83 and 84:
Part I - Sinusoidal BPMS Motors wit
Page 85 and 86:
grounded-neutral wye or delta conne
Page 87 and 88:
N e f A ( ) i 2 N e f B ( ) i 2
Page 89 and 90:
Figure 3.7 - Developed view at zero
Page 91 and 92:
Figure 3.9 - Developed view showing
Page 93 and 94:
Although Equations (3.6) or (3.7) a
Page 95 and 96:
direction. The contributions always
Page 97 and 98:
sinusoidal electrical variable will
Page 99 and 100:
Figure 3.14 - Cross section of two
Page 101 and 102:
3 N e (3.6): f ( , t) I p cos(
Page 103 and 104:
In the previous chapter the per-pha
Page 105 and 106:
peak value is represented as an upp
Page 107 and 108:
Figure 3.21 - Time relationship bet
Page 109 and 110:
another and thus could be placed in
Page 111 and 112:
more widely understood theory (such
Page 113 and 114:
other methods, although it has clos
Page 115 and 116:
The SV as a Vector The first facet
Page 117 and 118:
j0 j0 j0 aˆ 1 0 1 bˆ j e e e
Page 119 and 120:
j j ee 1 cos( ) (3.45) 2 3 j t x
Page 121 and 122:
Notice that the amplitude of the MM
Page 123 and 124:
Figure 3.27 - Equivalent MMF produc
Page 125 and 126:
Ne 1 jj f , t i e i * e 2 2
Page 127 and 128:
distribution that is cosinusoidal i
Page 129 and 130:
3 Ne j t f Ie p 2 2 . This
Page 131 and 132:
j set θ to anything. Taking the re
Page 133 and 134:
epresent any physically-distributed
Page 135 and 136:
lumped-parameter model in this repo
Page 137 and 138:
x kCx (3.75) abc The set of varia
Page 139 and 140:
phase variable axes; three axes in
Page 141 and 142:
The component MMFs act away from th
Page 143 and 144:
common choice is to force the power
Page 145 and 146:
As an example, find the SV that cor
Page 147 and 148:
the same magnitude, the projection
Page 149 and 150:
Figure 3.32 - Arbitrary SV referenc
Page 151 and 152:
universal and the choice of convent
Page 153 and 154:
stator’s perspective and at R fr
Page 155 and 156:
The potential discrepancy (p.108) w
Page 157 and 158:
x cos( r) sin( r) xd x sin(
Page 159 and 160:
It must be emphasized that we have
Page 161 and 162:
in relative time like an oscillogra
Page 163 and 164:
Part III - SV Theory Applied to Sin
Page 165 and 166:
In Equation (3.135) Z has elements
Page 167 and 168:
to use SV theory. It may be helpful
Page 169 and 170:
Figure 3.42 - Coupling between d- a
Page 171 and 172:
R R d R R v Ri Li j Li dt s
Page 173 and 174:
current does not influence the valu
Page 175 and 176:
d v Ri L i e dt d v Ri L i e
Page 177 and 178:
Figure 3.47 - Simulation diagram fo
Page 179 and 180:
e je ), and (2) it was demonstrate
Page 181 and 182:
Overview of Voltage Source Inverter
Page 183 and 184:
In addition to measuring voltages w
Page 185 and 186:
then there would be periods during
Page 187 and 188:
Figure 4.9 - Gating and POLE voltag
Page 189 and 190:
Figure 4.11 - Ideal voltage wavefor
Page 191 and 192:
inverter is called sine-triangle co
Page 193 and 194:
and it offers the fastest dynamic r
Page 195 and 196:
Figure 4.18 - Fundamental gain and
Page 197 and 198:
In the literature this is called th
Page 199 and 200:
voltage will be below (above) the b
Page 201 and 202:
Figure 4.24 - Instantaneous phase-A
Page 203 and 204:
Figure 4.26 - Base SVs showing the
Page 205 and 206:
Figure 4.27 - Transformed voltage w
Page 207 and 208:
also correspond to six-step squarew
Page 209 and 210:
was fed to the SVM inverter as a SV
Page 211 and 212:
Figure 4.31 - Temporal limit of inv
Page 213 and 214:
Figure 4.34 - SVM overmodulation re
Page 215 and 216:
Checking sextant s 23 again for thi
Page 217 and 218:
SVM Implementation The block diagra
Page 219 and 220:
has been made of using THI in the S
Page 221 and 222:
different triplen signal would be i
Page 223 and 224:
Similarly, when the modulation inde
Page 225 and 226:
Summary and Conclusion The two-leve
Page 227 and 228:
CHAPTER 5 - Field Oriented Control
Page 229 and 230:
torque production; this is called d
Page 231 and 232:
Figure 5.3 - Torque control of sinu
Page 233 and 234:
obviously a change in perspective.
Page 235 and 236:
Figure 5.9 - Comparison of referenc
Page 237 and 238:
variables to the stationary referen
Page 239 and 240:
Figure 5.13 - Torque control of sin
Page 241 and 242:
To analyze a salient machine one mu
Page 243 and 244:
Figure 5.16 - Torque functions: (a)
Page 245 and 246:
Figure 5.19 - Buried permanent magn
Page 247 and 248:
Figure 5.21 - Flux weakening in the
Page 249 and 250:
appears that this is very much rela
Page 251 and 252:
Stationary and Synchronous Regulato
Page 253 and 254:
stationary regulator had. For compl
Page 255 and 256:
This coupling can be mitigated by m
Page 257 and 258:
educes to two independent circuits,
Page 259 and 260:
D, some of the 120° methods are ap
Page 261 and 262:
d d v Ri Ls i R dt dt The r
Page 263 and 264:
section a state-space model for the
Page 265 and 266:
Figure 6.6 - Full state feedback (o
Page 267 and 268:
State-Space Model of BPMS Motor A s
Page 269 and 270:
Figure 6.9 - FOC block diagram. The
Page 271 and 272:
loop). A second way to implement th
Page 273 and 274:
knowing the rotor position from ini
Page 275 and 276:
[11] E. Clarke, Circuit analysis of
Page 277 and 278:
Control Systems, Linear Analysis [4
Page 279 and 280:
[77] J.M.D. Murphy, F.G. Turnbull,
Page 281 and 282:
Machine Modeling, Analysis [103] J.
Page 283 and 284:
THI, SVM, SPWM [127] J.A. Houldswor
Page 285 and 286:
Wisconsin-Madison. [Online]. Availa
Page 287 and 288:
Angle Tracking [175] D. Morgan, “
Page 289 and 290:
Appendix A - Elementary Electromagn
Page 291 and 292:
L i (A.8) S SS S SR S SS SR (A.9
Page 293 and 294:
First the self-flux-linkage of an i
Page 295 and 296:
vAN R iA LM iA eA d v R i
Page 297 and 298:
Figure B.3 - One-half of the flux p
Page 299 and 300:
Equations (B.27) and (B.28) are for
Page 301 and 302:
Fundamental Relationships Figure C.
Page 303 and 304:
Figure C.3 - Sinusoidal winding den
Page 305 and 306:
manufactured compared to the steppe
Page 307 and 308:
phase winding of Figure C.4 will ha
Page 309 and 310:
Distributed N Fp i 2 (C.5) Figu
Page 311 and 312:
alanced machine only odd harmonics
Page 313 and 314:
sinusoidal windings with a sinusoid
Page 315 and 316:
0, and since the direction of inte
Page 317 and 318:
That the rotor-stator flux linkage
Page 319 and 320:
Figure C.17 - Summary of rotor-stat
Page 321 and 322:
Figure C.19 - Amplitudes of harmoni
Page 323 and 324:
triangle with an amplitude whose nu
Page 325 and 326:
Returning to Figure C.18 it is clea
Page 327 and 328:
torque will describe the torque pro
Page 329 and 330:
However, Equation (D.2) is incorrec
Page 331 and 332:
the same order as the PS set (arran
Page 333 and 334:
Implications of the ZS Component Th
Page 335 and 336:
Figure D.6 - Neutral voltage of loa
Page 337 and 338:
3v 3e 3v v v v v v v 3v AM BM CM A
Page 339 and 340:
components of source voltage sum to
Page 341 and 342:
Equation (D.25) and instantaneous q
Page 343 and 344:
If a ZS component could possibly be
Page 345 and 346:
xA X1cos( t) X3cos(3 t) X5cos(5 t)
Page 347 and 348:
Figure D.11 - 3-D base vectors of 1
Page 349 and 350:
the Clarke transform is used. Howev
Page 351 and 352:
Appendix E - Park Transforms This a
Page 353 and 354:
Appendix F - Useful Mathematical Re
Page 355:
335
show all

SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Create successful ePaper yourself

Delete template?

Save as template?