SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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Figure 5.23 – Field weakening controller. In summary, it has been shown that for a nonsalient rotor, torque control consists of setting id 0 and controlling the torque according to T KT iq. For a salient rotor both i d and i q must be controlled. Separate control of the “torque-producing” and “flux-producing” components of the stator current is possible using the FOC control structure, and this may be used to achieve flux weakening. However, for a salient rotor the torque control and the field-weakening control are not independent of one another. In addition to these fundamental ideas, several have been overlooked and the subject of flux weakening is far more complicated than presented here. Indeed, many of the details and interactions are beyond the author’s present understanding. First, it seems that the control of the two components of airgap flux is coupled in a synchronous machine (see [78, ch.5]) and it appears that this is the same as armature reaction flux [78, pp.249- 250]. Second, as hinted by the key phrase above, “to the extent that the stator MMF creates flux in the airgap,” the stator MMF is not always capable of truly weakening the magnet flux. This is because the magnet has a relative permeability of near unity, thus the airgap is effectively very large [78, pp.250], [87, p.96], [68, p.103]; in salient machines the effect is more pronounced [69, p. 4.18]. This also has something to do with the discussion of internal permeance of the magnet, as discussed in Chapter 2, and it is the same as saying the armature reaction is small or that the synchronous reactance/inductance (Appendix B) is small. The degree to which field weakening can occur thus depends on the motor’s airgap, magnets, and saliency. If a BPMS motor does not experience flux weakening with a negative d-component of stator current, the question arises as to what happens when the stator current SV is advanced like that. It 228
appears that this is very much related to the concept of “phase advance” in ECM motors but an investigation of the subject is beyond scope. Articles on field weakening show plots with many circles, ellipses, and hyperbolas indicating various limits. Understanding field weakening and/or current advancing would require a separate study. References that look to contain good information are [78, ch.9], [109], [110], [111], [112], [113], [114], [115], [116]. Synchronous Current Regulation The FOC control structure has been developed by building upon the understanding of torque control (via phasing) because it is the most intuitive way to gain an understanding of how a space vector is regulated in the rotor frame. However, aside from the “motor control” aspect (determining the angle of i in accordance torque and field weakening) it is clear that the control structure is accomplishing current regulation in the rotor reference frame. Further, the same structure could be used to control any three-phase currents relative to some general reference frame (other than the rotor), such as the reference frame attached to a voltage space vector representing a bus on the grid. Whether it is the rotor frame in a synchronous motor, a grid voltage frame, or the reference frame of the magnetizing flux linkage in an induction motor, they will all be turning at the synchronous frequency as seen from the stationary frame (in the steady state). The idea of controlling a space vector in such a frame has come to be called synchronous frame regulation, or simply synchronous regulation. 41 The concept had been introduced previously by Schauder and Caddy [153] but it seems that Rowan and Kerkman were the ones who developed the concept in their widely-cited paper [154]. The main advantage of the synchronous regulator is that the compensators are in the synchronous frame. This removes them from the cyclic variation of the input error signal in order to prevent the increasing phase lag and magnitude droop that occurs with increasing frequency. In addition, the structure allows the bEMF to be offset and the decoupling of the motor’s d- and q- circuits to be accomplished more easily [107]. In the first subsection the stationary and synchronous 41 The terminology can be a bit confusing at times because the “synchronous” frame of an induction motor deals with the rotating excitation provided by the stator while the rotor slips by at an asynchronous speed. Therefore, various names could be used to refer to the “synchronous regulator” and its coordinates depending on the situation. Examples include: dq-, synchronous-, rotor-, or excitation- frames/coordinates. In other words, the rotor reference frame is a synchronous frame in a synchronous motor but it is not a synchronous frame in the induction motor (but the excitation frame is a synchronous frame). 229
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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
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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
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: Figure 5.21 - Flux weakening in the
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
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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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