SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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Figure 2.27 – Simulation diagram of general motor. The figure shows the relationships developed in this chapter. The torque function is the “cascade connection” and the bEMF function is the “feedback connection” between the electrical portion and the mechanical portion. The coupling exists via the magnetic medium (rotor-stator flux linkage). Note that the bEMF acts as a disturbance in the voltage-to-current conversion and the load torque acts as a disturbance in the electromagnetic-torque-to-velocity conversion. These relationships are derived from first principles so there is essentially no simpler model of a motor. That is, the torque production, bEMF generation, and their relationship will exist in any motor in a way very similar to that shown. Thus, this model could represent a brush DC motor (in that case the torque and bEMF functions would be constants). Here, it will be used to represent a single winding in a BPMS motor and it will be called the “phase model.” If a per-phase model is used for each phase, three of them combined can be used to represent a three-phase motor; this is called the “phase-variable model” and is shown in Figure 2.28. 48
Figure 2.28 – Phase-variable simulation diagram of general motor. Clearly, each phase contributes to the overall torque production, thus torque production of a three-phase motor cannot be investigated unless all three phases are considered. Additionally, each winding has mutual inductive coupling with the other windings. The duality between torque and bEMF would then suggest that the circuit of each phase could not be investigated unless all three phases are considered. This is true but for a wye-connected motor it turns out that this coupling can be removed by replacing the simple inductance with the “synchronous inductance” Ls (Appendix B). Thus, the phase-variable model shows that torque is produced by all three phases but the electrical circuits are not coupled. However, it is vital to note that the applied voltages are the line-neutral voltages (this directly follows from the previous electrical model; combining three models (such as that shown in Figure 2.18) the “ vt () ” is by definition the line- neutral voltage). This means that the model is correct only for applied three-phase voltages that 49
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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
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 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: General Electromechanical Models Th
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
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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
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In the literature this is called th
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voltage will be below (above) the b
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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
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Checking sextant s 23 again for thi
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SVM Implementation The block diagra
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has been made of using THI in the S
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different triplen signal would be i
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Similarly, when the modulation inde
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Summary and Conclusion The two-leve
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CHAPTER 5 - Field Oriented Control
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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.
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Figure 5.9 - Comparison of referenc
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variables to the stationary referen
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Figure 5.13 - Torque control of sin
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To analyze a salient machine one mu
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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
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Stationary and Synchronous Regulato
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stationary regulator had. For compl
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This coupling can be mitigated by m
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educes to two independent circuits,
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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
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Figure 6.6 - Full state feedback (o
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State-Space Model of BPMS Motor A s
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Figure 6.9 - FOC block diagram. The
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loop). A second way to implement th
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knowing the rotor position from ini
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[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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