SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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From the summary above, it can be understood that the history of motor control spans more than a century and is very multifaceted. To understand where the material in this report fits into the overall picture, some points should be summarized. The realization of AC motor control via the generation of variable voltage and frequency current (using solid-state devices) was a landmark achievement. This was followed by the development of power devices that could be turned off at will, which allowed PWM to become a reality. In the beginning this was used to create VVVF induction motor drives. At some time, a line-start permanent magnet synchronous motor was introduced but it was not used in variable-frequency applications. In addition, an electronicallycommutated (thus brushless) permanent magnet machine was devised. Eventually the concept of a sinusoidal permanent magnet synchronous machine was combined with an inverter to yield an adjustable-speed AC drive without brushes, capable of servo-like performance. The electronically commutated motor also served in this capacity, with the distinct advantages of using less expensive shaft position sensors and power electronics; due to the lower cost and simplicity of the system, the technique is still used today. Separate from all of this, vector control allowed linear control over the torque produced by an induction motor; this eventually allowed the induction motor to be used in servo-like applications as well where it was previously not possible. The vector control scheme can be applied to other motors and it provides distinct benefits, but these benefits are not the same as those achieved with the induction motor. All methods of synchronous machine control and all methods of vector control (of any machine) require knowledge of the rotor flux, which can be obtained directly or indirectly from a shaft sensor. There are many benefits to eliminating the shaft sensor, yielding so-called sensorless control. The original purpose of the research that led to this report was to investigate the advantages and disadvantages of the sensorless FOC of a BPMS motor. This involved learning the fundamentals of brushless motor operation; since this is not taught in most curricula the initial sources of information were application notes written by servo motor and servo drive manufacturers, and by manufacturers of silicon devices (ASICs, MCUs, DSPs) involved in motor control. The motor drive literature was naturally lacking on the details of how the controls were implemented internally, and the silicon device literature was geared toward the implementation in a particular device and was lacking in theory. All of that literature would be useful for practical applications of the manufacturer’s product, but it is not useful to learn theory. In addition, this literature is very lacking in performance data. Manufacturers are quick to list benefits of using their products, but often these claims are misleading at best. This literature (as well as all articles in trade 4
publications and magazines, and Internet articles) will be called the popular literature in this report. The popular literature was abandoned in hopes of finding more detailed information in the academic literature (which is defined here to consist of textbooks, conference proceedings, and technical journals). However, it was quickly discovered that textbooks in motor control are generally written at an advanced level and most articles investigated such advanced or detailed topics that they were of little help in learning the theory. The bulk of the research then was learning the fundamental theory of brushless motor operation and control in order to be able to interpret the academic literature to gain a better understanding and to find answers to specific questions. Therefore, the first purpose of this report is to summarize what has been learned in terms simple enough that the average technical person can gain an understanding of the field. The second purpose has been to establish a collection of useful references. In addition to investigating the fundamentals mentioned, it was found that the modern academic literature is written in terms of space vector theory, thus this had to be learned as well. Additional topics of importance were found to be the Clarke and Park transforms, reference frame theory, the modifications that must be made to traditional synchronous machine theory in order to describe BPMS motors, state-space control systems, state observer theory, and three-phase inverter control techniques. The report is meant to highlight the pertinent issues and present the author’s present understanding; it is not meant to be a comprehensive treatment that is complete. As each topical area is brought to a close, additional references are listed so that the reader can resume study where the author left off. 5
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: vector theory to model a machine, w
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
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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
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
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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
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
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universal and the choice of convent
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stator’s perspective and at R fr
Page 155 and 156:
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
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
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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
Page 185 and 186:
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
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
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also correspond to six-step squarew
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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
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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
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