SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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Motors can produce torque using two independent principles: the first is to use two interacting magnetic fields and the second is to use one magnetic field and a magnetic circuit whose reluctance is a function of rotor position. Some motors use only the first principle, some use only the second, and some motors use a combination of the two. When discussing torque production (and hence, motor control) it is necessary to make these distinctions. Some observations about common existing motors are useful to learn how to categorize them according to saliency. When torque is produced only by the interaction of two fields (called mutual torque), one field is produced by the stator and the other is produced by the rotor; these machines are called non-salient machines. When torque is produced only by the interaction of one field and a variable reluctance element (called reluctance torque), that field is produced by the stator; these machines are called reluctance machines. When a motor uses a combination of these principles (producing both mutual and reluctance torque) it is called a salient-pole machine. For salient-pole machines an additional observation is that the rotor is always salient and the stator may or may not be salient. If only the rotor is salient it is called a singly-salient machine; when both the rotor and stator are salient it is called a doubly-salient machine. To summarize, non-salient machines produce only mutual torque, reluctance machines produce only reluctance torque, and the torque produced by salient-pole machines has both mutual and reluctance components. Induction motors are non-salient; synchronous machines may be salient or non-salient (this is true for both wound-field and PM types); a salient machine generally has a salient rotor; and the only common doubly-salient machine is the switched reluctance motor. In the literature, a cylindrical rotor 1 is one that is non-salient, smooth bore describes a non-salient stator, and smooth airgap describes a non-salient machine (rotor and stator). DC motors have been excluded from this discussion because of the concentration on synchronous machines. There is indeed a difference in saliency between the wound-field and PM types and this saliency does affect operation, although the nature is different because the saliency is in the stator field poles. Many of these aspects have direct parallels to AC machines but cannot be included here. Something else to note is that slotting has been ignored in this discussion. If slotting is considered it is clear that it contributes to saliency because flux paths through the teeth will have lower reluctance than those through the winding slots. One must question where to 1 Cylindrical rotor is found in the literature to mean a non-salient rotor but is also used to refer to a radialflux machine (as opposed to an axial-flux machine, which has a flat “pancake” rotor). 20
draw the line between the solenoidal windings and large slot widths of the switched reluctance machine (whose stator is intended to be salient) and the slots of a non-salient machine (such as a sinusoidal PM synchronous machine) where the slotting causes undesired parasitic effects. Those effects are minimized when the width of the slots are “small” compared to those of the teeth or when there are many slots per pole. As far as the author can tell, for the non-salient PM brushless motors considered in this report, the only effect of slotting that needs to be considered is the cogging torque that results as the rotor magnets attempt to align with the teeth. Armature and Field The categorization based on saliency was presented primarily to discuss torque production and circuit models later in the report. However that categorization also helps illustrate the fact that motors from all three groups must have at least one winding. As a consequence of the mechanical motion of the rotor this winding will have a voltage induced in it—this is the armature winding. It is the induction of a voltage that makes this winding different the other winding that a motor may have (as both windings will create a field). If the motor has a second magnetic field, that field is produced by either a permanent magnet or another winding; this field is usually called the field. If a magnet is used it is called a PM machine; if a winding is used it is called a wound-field machine. In a brush DC motor, the field is produced by the stator; in a synchronous motor, the field is produced by the rotor. (Induction motors are not well described by the words armature and field so the circuits are generally called the stator and rotor circuits, respectively.) Brush DC machines always have the armature wound on the rotor; the armature winding is always called the armature winding (or simply, the armature). Contrarily, all traditional (gridtied) synchronous machines and all brushless machines have the armature wound on the stator. For this reason, the armature winding is often called the stator winding (or simply, the stator). This misnomer is as widely accepted in the vernacular as the phrase “the flow of electric current” and thus will be used in this report. 21
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 and 14: Figure C.13 - Single-turn full-pitc
Page 15 and 16: List of Symbols Symbol Meaning Unit
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: Figure 2.7 - Cross sections of some
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
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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
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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
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The SV as a Vector The first facet
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j0 j0 j0 aˆ 1 0 1 bˆ j e e e
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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
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Ne 1 jj f , t i e i * e 2 2
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distribution that is cosinusoidal i
Page 129 and 130:
3 Ne j t f Ie p 2 2 . This
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j set θ to anything. Taking the re
Page 133 and 134:
epresent any physically-distributed
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lumped-parameter model in this repo
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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
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common choice is to force the power
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As an example, find the SV that cor
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the same magnitude, the projection
Page 149 and 150:
Figure 3.32 - Arbitrary SV referenc
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universal and the choice of convent
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stator’s perspective and at R fr
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The potential discrepancy (p.108) w
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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
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Part III - SV Theory Applied to Sin
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In Equation (3.135) Z has elements
Page 167 and 168:
to use SV theory. It may be helpful
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Figure 3.42 - Coupling between d- a
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R R d R R v Ri Li j Li dt s
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current does not influence the valu
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d v Ri L i e dt d v Ri L i e
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Figure 3.47 - Simulation diagram fo
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e je ), and (2) it was demonstrate
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Overview of Voltage Source Inverter
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In addition to measuring voltages w
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then there would be periods during
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Figure 4.9 - Gating and POLE voltag
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Figure 4.11 - Ideal voltage wavefor
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inverter is called sine-triangle co
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and it offers the fastest dynamic r
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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
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Figure 4.26 - Base SVs showing the
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Figure 4.27 - Transformed voltage w
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also correspond to six-step squarew
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was fed to the SVM inverter as a SV
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Figure 4.31 - Temporal limit of inv
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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
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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
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Figure 5.21 - Flux weakening in the
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appears that this is very much rela
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Stationary and Synchronous Regulato
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stationary regulator had. For compl
Page 255 and 256:
This coupling can be mitigated by m
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educes to two independent circuits,
Page 259 and 260:
D, some of the 120° methods are ap
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d d v Ri Ls i R dt dt The r
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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
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Wisconsin-Madison. [Online]. Availa
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Angle Tracking [175] D. Morgan, “
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Appendix A - Elementary Electromagn
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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
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triangle with an amplitude whose nu
Page 325 and 326:
Returning to Figure C.18 it is clea
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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
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3v 3e 3v v v v v v v 3v AM BM CM A
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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
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