SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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As the ability to control motors progressed, so did the types of motors that could be controlled. One of the many variations that arose was the brushless permanent magnet synchronous (BPMS) motor, which is the subject of this report. Although there were many paths of development that occurred around the world, according to Jahns [108] the BPMS motor evolved from at least two distinct application areas. The first type (call them type-A) were BPMS motors with a rotor cage that would start across the line and then pull into synchronism. In the 1970s integral-horsepower versions were designed that offered excellent efficiency but their high cost prevented widespread acceptance. In the second path of development, permanent magnet (PM) brushed DC servos (call them type-B) began to replace those with field coils in the 1960s, thus eliminating the field loss. According to Jahns, these two development paths converged in the 1970s, where for the first time PM-rotor synchronous motors were driven by solid-state inverters. Before the merger, rotor losses (type-A) and field losses (type-B) had been eliminated, but now rotor inertia was decreased due to the elimination of the starting cage (type-A) and of the armature on the rotor (type-B); this enabled faster maximum acceleration rates. Further, the problems associated with a brushcommutator system (outgassing, mechanical and electrical inefficiency, required maintenance, voltage and current limits, and the impossibility of operating submersed or in explosive environments) of type-B machines were eliminated. According to Jahns, electronicallycommutated motors (ECMs) were developed first, simply because of the simplicity of the control required. Later (late 1970s and 1980s) the sinusoidal variety was developed; this was a significant advancement because it required the phase of the VVVF output waveforms to be controlled in addition to amplitude and frequency (whereas for the induction motor, control of the phase was unnecessary). More about the differences between the ECM and the sine motor will be discussed at the end of Chapter 2. Return again to the beginning of the century to examine modeling. André Blondel introduced two-reaction (or two-axis, or d-q) theory in France before 1900 which was translated into English in 1913 [1]. In the United States this was extended by R.E. Doherty and C.A. Nickle in late 1920s ([2]-[6]) and was more-finalized by R.H. Park in 1929 [7], [8]. Two-reaction theory allowed salient machines to be analyzed and was important in studying machine stability and transient operation (today, almost all such analysis uses the transform). In the middle of the century the “generalized theory of electric machines” ([18], [37, ch.9]) was gaining ground and Kron’s tensor analysis ([13], [14]) was causing a stir, although the author is unsure of the influence of these two theoretical areas. It seems that the “final” step in modeling was the idea of using complex space 2
vector theory to model a machine, which was formalized in 1959 by Kovács and Rácz in Hungary [15]. (Transient phenomena in AC machines had already been documented [16], [17]—it seems that it was the space vector’s complex-valued notation and ability to combine electrical and mechanical quantities that made it of value.) Regardless of any gains in theoretical understanding of the induction motor, it seems that the motor continued to be controlled as described earlier, until the late 1960s when Germans Blaschke and Hasse made some key innovations [19], [20], [21]. It seems that their efforts led to the first control systems that attempted to control the induction motor based on its transient model instead of the steady-state equivalent circuit—they were the first form of “vector control.” Instead of simply generating three-phase voltages of varying frequency and amplitude in order to achieve variable speed operation, the vector control also controlled the phase of the output waveforms. This was the beginning of a revolution that would allow the induction motor to be used in speed control applications requiring dynamic performance, eliminating the need to oversize motors to achieve satisfactory transient performance. Vector control is also known as field oriented control (FOC). FOC can be applied to other AC machines as well and there is benefit in doing this. However, the benefits obtained in applying FOC to a synchronous machine are not the same as those obtained with the induction motor. At the simplest level, vector control of a synchronous machine provides a control structure that makes decoupling control and arbitrary control schemes easier to implement. Due to the fact that the structure performs inherent synchronous frame current regulation, it also affords better steady-steady control at high speeds where traditional “stationary frame” regulators begin to lose gain and phase. In contrast, FOC control tames the dynamics of the induction motor (which are more sluggish than those of the synchronous machine). It seems as if the drastic benefits provided by FOC of an induction motor have been ascribed to the synchronous machine as well, causing some general misunderstanding as to the benefits of FOC. It is interesting to note that according to [100] most major servo drive manufacturers use FOC for sinusoidal drives (as opposed to non-FOC sinusoidal commutation), yet very few advertise this fact. In this case, the servo manufacturers are not contributing to the confusion between FOC of a BPMS motor and FOC and induction motor; it seems that most of the confusion has been caused by the other articles in the popular literature. Additional information on AC motor drives can be found in [64], [75], [81], [92], [93], [94], [95], [96], [97], [99]. 3
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: CHAPTER 1 - Introduction Historical
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
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Part I - Sinusoidal BPMS Motors wit
Page 85 and 86:
grounded-neutral wye or delta conne
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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
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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
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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
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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
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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
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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
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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
Page 169 and 170:
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
Page 195 and 196:
Figure 4.18 - Fundamental gain and
Page 197 and 198:
In the literature this is called th
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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
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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
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Figure 5.3 - Torque control of sinu
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obviously a change in perspective.
Page 235 and 236:
Figure 5.9 - Comparison of referenc
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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)
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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
Page 251 and 252:
Stationary and Synchronous Regulato
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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,
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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
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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
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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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