SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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discussed in this report. Good references (which often contain useful information aside from overmodulation techniques) include [141], [142], [143], [144], [145], [146], [147]. The ease of implementation varies wildly with control methods, especially SVM because of the large number of implementation strategies. To review the innumerable varieties would be nearly impossible; surveying the latest articles in the literature would be a better starting point. There are numerous articles regarding the effects of dead-time and their mitigation [138], [139], [140]. Although it is a fundamental issue that may bear much importance, it is nonetheless an entire subtopic (much like the optimal switching problem) and would require a literature review to gain an understanding of the nature and magnitude of the problem and its remedies. In addition to the simple blanking time the turn-off and turn-on characteristics differ between transistor types and may be a function of load. A similar and related problem is the compensation for nonconstant DC link voltages (which can result from using too small a bulk capacitor, improper decoupling, commanding a very large step in torque, and so on). The remaining three topics are somewhat different because they are more complicated and are influenced by many factors (although the switching algorithm seems to be the dominant one). Switching loss is proportional to the switching frequency and depends on the switching algorithm; it is also a function of loading. Voltage and current harmonics should be divided into the baseband and switching harmonics. Baseband voltage harmonics will cause baseband current harmonics, which produce torque ripple. They should not be encountered as long as operation is restricted to the linear region. Voltage switching harmonic content is determined by the switching scheme but may also vary with modulation index. It seems to be a concern associated primarily with EMI. Current switching harmonics are a function of the load inductance; the copper and core losses they induce are functions of the particular motor design. Of all the topics discussed here, these last three were investigated the least due to their complexity. References to begin with might include [70], [148], [149], [150], [151], [152]. 206
CHAPTER 5 - Field Oriented Control of BPMS Motors This chapter develops the concept of field oriented control as applied to the brushless permanent magnet synchronous motor. In the first section some relevant terminology is discussed. The next section returns to torque control in a synchronous machine. The concept of current phasing (from Chapter 2) is used to develop the concept of torque control from the perspective of the rotor frame using ideal current sources. The same concept is then developed again, first using a practical sine-triangle PWM inverter and then using an SVM inverter. The resulting system is precisely the rotor-flux-oriented FOC that is commonly used to control BPMS motors. Toque control of salient machines and field weakening are then briefly discussed. The third section examines current control in FOC and to reveal the concept of the synchronous frame current regulator. This section will show how the synchronous regulator improves performance over the stationary regulator and will show how the motor under FOC can be modeled. 207
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SENSORLESS FIELD ORIENTED CONTROL O
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Table of Contents List of Figures..
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CHAPTER 5 - Field Oriented Control
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List of Figures Figure 2.1 - Radial
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Figure 3.29 - Arbitrary space vecto
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Figure 4.44 - ZS components of some
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Figure C.13 - Single-turn full-pitc
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List of Symbols Symbol Meaning Unit
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Abbreviations ACIM AC induction mot
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Superscripts * commanded value ref
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CHAPTER 1 - Introduction Historical
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vector theory to model a machine, w
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publications and magazines, and Int
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elationship between SVM and other P
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CHAPTER 2 - Fundamentals of Electri
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Preliminaries In reading the litera
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Taxonomy of Motors There is any num
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characteristics (the DC load curren
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torque component, sturdily construc
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Figure 2.7 - Cross sections of some
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draw the line between the solenoida
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These texts generally attribute the
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N B A B Y x(t) (2.6) The induc
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extended to the rotational case lat
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present analysis). When this is tru
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Figure 2.16 - Components of total f
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As aforementioned a spatial analysi
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clear the meaning, but the reader i
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Figure 2.20 - Elementary brushless
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called the per-phase torque functio
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Expressing bEMF in terms of the bEM
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Equation (2.44) is the component of
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d R( r) ke( r) kt( r) sin( r) (2.
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General Electromechanical Models Th
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Figure 2.28 - Phase-variable simula
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Trapezoidal and Sinusoidal BPMS Mot
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Figure 2.29 - Back-EMF and drive cu
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Figure 2.31 - Back-EMF and drive cu
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3 KT Ke 2 (sinusoidal) K 2 K (tra
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control scheme must keep sinusoidal
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with misconceptions. The primary is
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Part I - Sinusoidal BPMS Motors wit
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grounded-neutral wye or delta conne
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N e f A ( ) i 2 N e f B ( ) i 2
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Figure 3.7 - Developed view at zero
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Figure 3.9 - Developed view showing
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Although Equations (3.6) or (3.7) a
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direction. The contributions always
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sinusoidal electrical variable will
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Figure 3.14 - Cross section of two
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3 N e (3.6): f ( , t) I p cos(
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In the previous chapter the per-pha
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peak value is represented as an upp
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Figure 3.21 - Time relationship bet
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another and thus could be placed in
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more widely understood theory (such
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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
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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
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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
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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(
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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
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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
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: Summary and Conclusion The two-leve
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
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Control Systems, Linear Analysis [4
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[77] J.M.D. Murphy, F.G. Turnbull,
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Machine Modeling, Analysis [103] J.
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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
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First the self-flux-linkage of an i
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vAN R iA LM iA eA d v R i
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Figure B.3 - One-half of the flux p
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Equations (B.27) and (B.28) are for
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Fundamental Relationships Figure C.
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Figure C.3 - Sinusoidal winding den
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manufactured compared to the steppe
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phase winding of Figure C.4 will ha
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Distributed N Fp i 2 (C.5) Figu
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alanced machine only odd harmonics
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sinusoidal windings with a sinusoid
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0, and since the direction of inte
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That the rotor-stator flux linkage
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Figure C.17 - Summary of rotor-stat
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Figure C.19 - Amplitudes of harmoni
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triangle with an amplitude whose nu
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Returning to Figure C.18 it is clea
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torque will describe the torque pro
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However, Equation (D.2) is incorrec
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the same order as the PS set (arran
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Implications of the ZS Component Th
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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
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Equation (D.25) and instantaneous q
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If a ZS component could possibly be
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xA X1cos( t) X3cos(3 t) X5cos(5 t)
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Figure D.11 - 3-D base vectors of 1
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the Clarke transform is used. Howev
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Appendix E - Park Transforms This a
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Appendix F - Useful Mathematical Re
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335
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