SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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BPM brush/brushless PM ECBM electronically commutated brushless motor ECDCM electronically commutated DC motor EDCM equivalent DC motor PMAC permanent magnet AC PMBDC permanent magnet brush/brushless DC PMDC permanent magnet DC PMSM permanent magnet synchronous motor SPM sinusoidal/surface/synchronous PM SPMSM surface PM synchronous motor SMPMSM surface mounted PM synchronous motor Most of these acronyms are unsuitable because they are ambiguous or contradictory. There seems to be an emerging trend in the popular literature: BLDC is used to refer to a trapezoidal motor and; PMSM is used to refer to a sinusoidal motor. But even within that trend there is much inconsistency. Additionally there is little consistency among motor manufacturers, but it is sometimes observed that motors meant to be driven with 120° currents are called “brushless DC” (BLDC) motors whereas motors meant to be driven with sinewave currents are called “brushless AC” (BLAC) servos. In surveying several motor manufacturers’ websites, some have two separate links (akin to BLDC and BLAC) that do point to two separate product lines, indicating the possibility of two different motors. Others have two separate links (akin to BLDC and BLAC) that point to the same product; in this case there is obviously only one motor type. Others have a single link, indicating that there is only one motor type offered by that manufacturer. As mentioned in the section on taxonomy, the motors considered in this report are all synchronous, brushless, AC, and they all employ permanent magnets. Thus this report has used trapezoidal and sinusoidal (or the shorter trap and sine) to describe the two common variants of the BPMS (brushless permanent magnet synchronous) motor, with the understanding that both types are synchronous and AC. There are many alternative definitions of AC and DC motors that have advantages (a good example is [69, p.1.3]), but most tend to unnecessarily segregate the brushless motors into the trap or sine types. It is the author’s opinion that the difference between trap and sine BPMs is surrounded by more misunderstanding and confusion than any other subject in the field of brushless motor control (the second-place award goes to the distinction between vector- and field-oriented- control). Magazine and online articles, internet discussion forums, datasheets, and application notes are often filled 60
with misconceptions. The primary issues are machine construction, current control, and “torque ripple,” with secondary issues being efficiency, “harmonics,” and audible noise. While some references are weakly worded (as if the authors are uncertain of their claims), it is not difficult to find sources with clear wording from both extremes of each issue. For example, “there is absolutely no difference between sine and trap motors,” and “sine and trap motors are entirely different machines.” Or, “sine and trap machines require different types of current commutation,” versus “either motor may be driven by similar means.” Or, “motor and drive types may be mixed,” versus “mixing motor and control types may cause serious issues.” Without field experience it is difficult to determine the truth regarding each issue. The largest difficulty seems to be that the amount of popular literature exceeds the amount of academic literature (concerning this issue). The author has found that although there are excellent resources to help a newcomer distinguish the difference, it takes a steady research effort to locate these resources, it takes time to work through and comprehend these resources, and it is very difficult to “unlearn” solid misconceptions. Some references include [68], [69], [63], [65], [76]. The author’s understanding is summarized here. Sine and trap motors may be constructed a number of different ways but as far as torque production and bEMF generation is concerned, the motors differ only in the shape of the rotor-stator flux linkage. This difference can be created by changing the way the winding is distributed in the stator slots, by adjusting the magnetic design (airgap and tooth/slot dimensions), by adjusting the construction of the rotor and physical shape of the rotor magnets, and by adjusting the magnetization profile of the magnets [68], [69]. As shown earlier, the bEMF/torque function is the derivative of the rotor-stator flux linkage with respect to rotor position and in the general case torque is produced as shown in Figure 2.28 and Equation (2.54). It is clear that the fundamental mechanism by which torque is produced is identical regardless of the type of motor. If a motor can be categorized as trap or sine—and ideal drive currents are forced into it—the motor will produce “ideal” torque. There is much misinformation about the possibility or impossibility of driving a motor with non ideal current waveforms. Quite simply, either type of motor (or any arbitrary motor not fitting either classification) can be driven by any arbitrary current waveform. The torque produced in each case will be different, the efficiency will be affected, and the performance of the current controller will be affected; these issues will be discussed later. 61
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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
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: control scheme must keep sinusoidal
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
Page 119 and 120: 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
Page 125 and 126: 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
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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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