I|ll|l|||||lI|||||||||||||I|l||||||||||||||||l|||||||||||||||||||llllllll
`USC|'067567S7B2
`
`(12) Ulllted States Patent
`Marcinkiewicz et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 6,756,757 B2
`Jun. 29, 2004
`
`(54) CONTROL SYSTEM AND METHOD FOR A
`R0’l‘A'l‘lNG El.E(.I’I‘ROMAGNET[C
`MACHWE
`
`6,498,449 B1 * 12/2002 Chen el al.
`5,498,451 B1 * 1242002 Boules et al.
`FOREIGN PATENT DOCUMENTS
`
`3is.~'434
`3'l8.~'tS6l
`
`H?
`
`1061640 A
`12/2000
`OTHER PUBLICATIONS
`TELE Kyoon Ha et al, “Simple and high—performance drive of
`switched reluctance motors for
`low—cost applications,”
`Industrial Electronics, 1997, ISIE. ’97', Proceedings of the
`IEEE International Symposium on Guimaraes, Portugal Jul.
`7_11’ 1997’ New York’ NY, Use. IEEE’ Usfllul‘ 7. 1997‘ pp.
`631-636, XP0126S098 ISBN (Hs03—3935—3.
`
`(List continued on next page.)
`
`Primary E.mmt'rter—--Rina Duda
`Assistant Examr'ner—Eduardo Colon Santana
`(74) Attorney, Agent, or Fr'rm—-Howrey Simon Arnold &
`White LLP
`(57)
`
`ABSTRACT
`
`A system and method for controlling a rotating electromag-
`netic machine. The rotating machine, such as a permanent
`magnet motor or switched reluctance motor,
`includes a
`stator having a plurality of phase windings and a rotor that
`rotates relative to the stator.Adrive is connected to the phase
`windings for energizing the windings. The control system
`includes an estimator connectable to the machine for receiv-
`
`ing signals representing the phase winding voltage and rotor
`position. The estimator outputs parameter estimations for an
`electrical model of the machine based on the received
`Voltage and rotor position. A torque model receives the
`parameter estimations from the estimator to estimate torque
`for associated rotor position-phase current combinations of
`the machine. A controller outputs a control signal
`to the
`drive in response to a torque demand and rotor position
`signals and the torque model. In certain embodiments, a
`solver uses the torque model to generate energization current
`profiles according to desired machine behavior, such as
`smooth torque andfor minimal sensitivity to errors in rotor
`p95iti9I1 II1fl5Hn=IH6HI-
`
`35 Claims, 3 Drawing Sheets
`
`(75)
`
`Inventors: Joseph G. Mai-cinktewlcz, St. Charles,
`l:£fli:,lJEI]u(,)l\E1I|J(§l;aeI I. Henderson, St.
`
`(73) Assignee: Emersflfl Electric Company, 51- L0‘-11.51
`M0 (US)
`_
`_
`_
`_
`Subject 10 any CllSClalJIlC.'t', the term Of lhls
`patent is extended or adjusted undcr 35
`o.s_c_ 154(b) by 0 days.
`
`_
`( ‘ ) Notice:
`
`(21)
`
`(22)
`(65)
`
`A9131. N0-I 10/153.414
`.
`,
`Filed‘
`
`May 21’ 2002
`Prior Publication Data
`US 2003/0213444 Al Nov. 27, 2003
`
`H02P 71300
`Int. Cl.-"
`(51)
`318/4.32; 318,434; 3185701
`(52) U.S. Cl.
`313/700, 701,
`(53) Fiem of Search
`31g,'551_ 7i'_é:'jI;¢31, 550, 501, 721, 302,
`305, 305, 309, 533, 509, 254, 307, 432,
`510, 303, 333, 4391 133; 323/320.354
`
`References Cited
`_
`‘
`H-3 PATENT DOCUMENTS
`4,961,033 A 4. 10/1990 M,,,_.Mim.,
`533,775 A 4=
`5/1993 Mongeau
`5,488,280 A
`H1996 Langreck
`5,569,994 A
`10/1996 Taylor et al.
`5,834,918 A * 11f1998 Taylor etal.
`5,841,262 A * 11/1998 Tang
`5,852,355 A “ 1211998 Turner ......... ..
`5 962 999 A
`10,1999 Nakamum E1 at
`6,002,234 A
`121.1999 Ohm e,al_
`63053364 A
`12,-1999 Acamley
`6,262,550 B1
`712001 Kilman et :11.
`6,304,052 B1 * ioootii
`()'Mea.ra et at.
`6,452,357 B1 *
`912002 Iahlrorten
`
`..
`..
`
`.
`
`313/595
`313/432
`318/805
`3183700
`-- 313/501
`
`’
`
`318/432
`“ 318,729
`318/632
`I: 318/565
`3l8f7€]D
`313/721
`
`
`
`(SG)
`
`!..-....-.-..........!
`
`
`
`-................_._._.J
`
`act:-0:14:39
`
`BOM Exhibit 1041
`
`BOM v. Nidec
`
`|PR2014—01 121
`
`BOM Exhibit 1041
`BOM v. Nidec
`IPR2014-01121
`
`1
`
`

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`US 6,756,757 B2
`Page 2
`
`OTHER PUBI_IC.A'I'IONS
`
`Quo Qingding et al, "Neural network adaptive observer
`based postion and velocity scnsorless control of PMSM,”
`Advanced Motion Control, 1996. AMC ’96—M]E. Proceed-
`ings, 1996. 4th International Workshop on MIE, Japan Mar.
`18-21, 1.996, New York, NY, USA, IEEE, US Mar. 18,1996,
`pp. 41-46, XP01016-4178 ISBN: 0-7803-3219-9.
`International Search Report for International Application
`No. PCT/USO3/15773, Oct. 6, 2003.
`Krause et 211, Analysis of Electric Machinery, 1986, Chapter
`One pp. 1-31.
`
`:11, Numerical Mathematics, 2000, Chapter
`Quarteroni et
`Sever pp. 281-287.
`W'elIstead ct al, Self—Tuning Systems, 1991, Chapter Three
`pp. 71-91.
`Akhiezer et 211, Theory of Linear Operators in Hilbert Space,
`1993. pp. 10-17.
`Chapman et a], Design and Precise Realization of Optimized
`Current Waveforms for an 8/6 Switched Reluctance Drive.
`Jan. 2002.
`
`* cited by examiner
`
`2
`
`

`
`U.S. Patent
`
`Jun. 29,2004
`
`Sheet 1 of3
`
`US 6,756,757 B2
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`
`15/
`
`2
`
`3
`
`

`
`U.S. Patent
`
`Jun. 29,2004
`
`Sheet 2 of3
`
`US 6,756,757 B2
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`mm.....m._.o...mwma4
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`4
`
`
`

`
`U.S. Patent
`
`Jun. 29, 2004
`
`Sheet 3 of3
`
`US 6,756,757 B2
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`5
`
`

`
`US 6,756,757 B2
`
`1
`CONTROL SYSTEM AND METHOD FOR A
`ROTATING ELEC'I‘ROM.AGNE'l'lC
`MACHINE
`
`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`
`The invention relates generally to the control of electro-
`magnetic rotating machines such as permanent magnet,
`switched reluctance and hybrid machines thereof, and more
`particularly,
`to adaptive, smooth torque control of such
`machines.
`
`2. Description of Related Art
`Many electromagnetic machines in general, and electric
`motors employing permanent magnets in particular, exhibit
`torque irregularities as the rotor rotates with respect to the
`stator,
`the coils of which are typically energized with a
`sinusoidal waveform. Such irregularities are referred to as
`“torque ripple.” These torque irregularities may be caused
`by the physical construction of a given machine. For
`example, they may result from the use of hearings to support
`the rotor. In addition, because of the electromagnetic char-
`acteristics of machines that employ magnets, the rotor tends
`to prefer certain angular positions with respect to the stator.
`Torque irregularities resulting from the electromagnetic
`characteristics of an electromagnetic machine are commonly
`known as “oogging” irregularities and the resultant non-
`uniform rotation of the rotor or non-uniform torque output is
`known as “cogging." Cogging is either current independent
`or current dependent. The first component is noted When the
`machine is spun unenergized. The second component
`is
`present when current fiows—tl:ie cogging grows as the
`magnitude of the stator currents increases.
`In rotating electromagnetic machines employing penna-
`nent magnets, cogging most often results from the physical
`construction of the machine. irregularities due to the mag-
`nets can result, for example, from the magnets being incor-
`rectly placed upon or in the rotor, or Erorn. some irregularity
`about how the magnets are energized. Moreover, the utili-
`zation of rotors having discrete north and south outer poles
`results in a circumferential distribution of magnetic flux
`about the rotor circumference that is not smooth, but choppy.
`Additionally. the stators commonly used with such machines
`are formed in such a way that the magnetic fluxes generated
`by the stator windings provide a flux distribution about the
`stator circumference that is not smooth. The combination of
`such rotors and stators, and the accompanying non-smooth
`flux distributions, produces undesired irregularities in the
`torque output of such machines. Rotor output non-
`uniformities may also be produced by back emf harmonics
`produced in certain machiries.
`Obtaining smooth torque is further complicated by other
`factors. For instance, manufacturing variances between
`motors makes it dillicult,
`if not
`impossible,
`to apply a
`common solution to a group of motors. Such manufacturing
`variance includes the placing or misplacing of magnets upon
`the rotor (if surface mounted), variance introduced by the
`magnetizing process itself and irregularities in the stator coil
`windings. Other causes of variance include instances when
`the magnets are damaged or chipped. Further, variations
`exist even within individual motors. For example, variations
`typically exist between a motor’s phases and over
`the
`motor’s full mechanical cycle. Moreover, motor behavior
`changes over time as the motor ages.
`The phase windings of certain types of electromagnetic
`machines are energized at least in part as a function of the
`
`2
`
`instantaneous rotor position. Accordingly, such machines
`often use a rotor position sensor that provides an output
`indicating rotor position relative to the stator. A controller
`uses this in formation to produce control signals that are used
`to energize and de-energize the phase windings. Errors in the
`measurement of the angular position of the rotor also
`contribute to torque ripple.
`For many motor applications a slight non-uniformity in
`the rotation of the rotor caused by torque irregularities is of
`little or no consequence. For example,
`in large motors
`driving large loads, slight variations in the output torque will
`not significantly affect the rotor speed and any slight varia-
`tions in rotor speed will not significantly affect the system
`being driven by the machine. This assumes that the torque
`variation as the machine turns is small compared to the load.
`In other applications, where the rotation of the rotor or the
`torque output of the motor must be precisely controlled or
`uniform, such non-uniformity is not acceptable. For
`example,
`in servomotors used in electric power steering
`systems and is in disk drives, the rotational output of the
`rotor or the torque output of the motor must be smooth and
`without significant variation.
`Prior art approaches to reducing the undesirable conse-
`quences of torque irregularities in electromagnetic machines
`have focused on relatively complex rotor or stator construc-
`tions designed to eliminate the physical characteristics of the
`machines thatwould otherwise give rise to the irregularities.
`While the prior art machine Construction approaches can
`result in reduction of torque irregularities, the approaches
`require the design and construction of complex rotor and
`stator components, such complex components are typically
`Lliilicult to design, dillicult to manufacturer, and much more
`costly to produce than are conventionally constructed com-
`ponents. Moreover, many of the physical changes required
`by such prior art solutions result in a significant reduction in
`the efliciency or other performance parameters of the result-
`ing machines over that expected of comparable conventional
`machines. Thus, many of the prior art attempts to reduce
`torque irregularities do so at
`the cost of machine perfor-
`mance.
`
`Attempts to reduce torque ripple that focus on motor
`control schemes, rather than motor construction, have also
`been undertaken. For example, various learning or iterative
`schemes, based on either experimental procedures or Well
`known physical relationships concerning motor voltages,
`currents and angular positions have been attempted. These
`attempted solutions often make assumptions concerning the
`behavior of the motor, such as motor flux being described by
`a linear relationship, or considering the elIect of mutual liux
`insignificant. Still further, prior solutions to torque ripple
`typically ignore the effect of motor sensitivity to inaccura-
`cies in angular measurement. To increase accuracy in posi-
`tion measurement. the use of sophisticated position sensors
`has been attempted, but this increases the machine's com-
`plexity and cost.
`Thus, a need exists for a control system that addresses the
`shortcomings of the prior art.
`
`SUMMARY OF THE INVENTION
`
`invention. a system for
`In one aspect of the present
`controlling a rotating electromagnetic machine is presented.
`The rotating machine, such as a permanent magnet motor or
`switched reluctance motor. or some hybrid of the two,
`includes a stator having a plurality of phase windings and a
`rotor that rotates relative to the stator. A drive is connected
`to the phase windings for energizing the windings. The
`
`Ln
`
`1U
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`15
`
`IdUr
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`30
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`SD
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`60
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`I'.i5
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`6
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`

`
`US 6,756,757 B2
`
`3
`control system includes an estimator connectable to the
`machine for receiving signals representing the phase wind-
`ing voltage, current and rotor position. The estimator outputs
`parameter estimations for an electrical model of the machine
`based on the received voltage, current and rotor position.
`The electrical model is a mathematical model that describes
`electrical behavior of the machine as seen at
`the motor
`terminals.
`
`A torque model receives the parameter estimations from
`the estimator. The torque model is developed via a math-
`ematical transform of the electrical model, and describes
`torque characteristics of the machine. Using the parameters
`received from the estimator.
`the torque model estimates.
`torque for associated rotor position-phase current combina-
`tions. A controller has input terminals for receiving a torque
`demand signal and the rotor position signal. The controller
`outputs a control signal to the drive in response to the torque
`demand and rotor position signals and the torque model. In
`certain embodiments, a solver uses the torque model to
`generate energization current profiles according to desired
`machine behavior, such as smooth torque and/or minimal
`sensitivity to errors in rotor position measurement. It is to be
`noted in particular that the solver can be so defined that the
`solution possesses particular properties. It may be desired to
`deal with only the most significant components of cogging
`or torque ripple, a result of motor drive cost considerations.
`Such a solution can be achieved.
`Some parameters of the torque model are unobservable
`via information immediately available from the machine
`terminals. For example, in machines employing permanent
`I1'1.‘1gneLs, it is not mathematically obvious how changes in
`the machine current and voltage, as the rotor spins, indicate
`or measure the interaction of the machine’s magnets with
`themselves. In accordance with further aspects ofthe present
`invention, a method of determining a non-load dependent
`cogging torque is provided. The rotor is spun unloaded at a
`predetermined angular velocity and the motor terminal volt-
`age and current are measured. Rotor positions associated
`with the voltage and current measurements are determined,
`and a lirst mathematical model is developed based on the
`measured voltage and rotor position to describe electrical
`behavior of the machine. The first mathematical model is
`mathematically transformed to develop a second mathemati-
`cal model to describe torque characteristics of the machine.
`The windings are then energized such that the rotor holds a
`predetermined position against the cogging torque, and the
`cogging torque is calculated for the predetermined position
`via the second mathematical model.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`Other objects and advantages of the invention will
`become apparent upon reading the following detailed
`description and upon reference to the drawings in which:
`FIG. 1 is a block diagram of an exemplary rotating
`electromagnetic machine system in accordance with
`embodiments of the present invention;
`FIG. 2 is a block diagram illustrating an electromagnetic
`machine control system in accordance with embodiments of
`the present invention;
`FIG. 3 is a chart illustrating an exemplary integration path
`for evaluating an integral giving coenergy used in embodi-
`ments of the invention;
`FIG. 4 illustrates current profiles generated for a smooth
`torque solution in accordance with the present invention;
`and
`
`FIG. 5 illustrates torque ripple for a machine controlled in
`accordance with aspects of the present invention.
`
`5
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`40
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`45
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`55
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`60
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`4
`While the invention is susceptible to various modifica-
`tions aud alternative forms, specific embodiments thereof
`have been shown by way of example in the drawings and are
`herein described in detail. It should be understood, however,
`that the description herein of specific embodiments is not
`intended to limit
`the invention to the particular
`forms
`disclosed, hut on the contrary, the intention is to cover all
`modifications, equivalents, and alternatives falling within
`the spirit and scope of the invention as defined by the
`appended claims.
`
`DETAILED DESCRIPTION OF TIIE
`INVENTION
`
`Illustrative embodiments of the invention are described
`below. In the interest of clarity, not all features of an actual
`implementation are described in this specification. It will of
`course be appreciated that in the development of any such
`actual embodiment, numerous implementation-specific
`decisions must be made to achieve the developers’ specific
`goals. such as compliance with system -related and business-
`related constraints, which will vary from one implementa-
`tion to another. Moreover, it will be appreciated that such a
`development elfort might be complex and time-consuming,
`but would nevertheless be a routine undertaking for those of
`ordinary skill in the art having the benefit of this disclosure.
`Turing to the drawings and,
`in particular, to FIG. 1, a
`system 10 constructed according to certain teachings of this
`disclosure is illustrated. Among other things, the illustrated
`system 10 actively controls the electric power supplied to an
`electromagnetic machine such that
`the negative conse-
`quences of torque irregularities that would otherwise be
`produced by the machine are reduced or eliminated.
`The system 10 includes an electromagnetic machine 12
`and a drive 14 that provides electric power to the electro-
`magnetic machine 'l2. The machine 12 shown in FIG. 1 may
`comprise,
`for example,
`a permanent magnet motor, a
`switched reluctance motor, or a hybrid motor (permanent
`magnet and switched reluctance combination). The machine
`12 is of conventional construction that includes a rotating
`component (a rotor 1211) and a stationary component (a
`stator 1212). Wound about the stator are a number of ener-
`gizable phase windings 12c which may be energized through
`the application of electric power to motor terminals 15, 16,
`17.
`
`The drive 14 is coupled to provide electric power to
`terminals 15, 16 and 17 of the machine 12. The drive 14
`receives control inputs from a control system 13. Which is
`coupled to receive feedback from the machine 12. in terms of
`rotor position information 18 and energization feedback 19.
`Other feedback information may he provided to the control-
`ler 13. While the drive 14 is illustrated in exemplary form as
`providing three power terminals to the machine 12, it should
`be understood that more or fewer power terminals may be
`provided to accommodate motors or machines with greater
`than three phases, less than three phases or if various types
`of inverters (e.g., with neutral connections) are used.
`The energization feedback 19 provides an indication of
`the operational characteristics of the machine 12 and may,
`for example, include feedback concerning the currents flow-
`ing in the stator windings andfor the voltages at the terminals
`15, 16 and 17. The position and energization parameters may
`be detected through conventional detectors such as standard
`rotor position detectors and standard currcntfvoltagc sen-
`sors. Altcrnative embodiments are envisioned in which the
`rotor position and feedback parameters are not detected
`directly but are calculated or estimated through known
`
`7
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`

`
`US 6,756,757 B2
`
`5
`techniques. For example, embodiments are envisioned
`where only the terminal voltages are known or sensed along
`with the Currents flowing through the stator windings of the
`machine 12 and the sensed current and voltage values are
`used to derive rotor position information.
`'lhe control system 13 also receives input command
`signals 11 that correspond to a desired output parameter of
`machine 12 such as rotor speed, output torque, etc. As
`described in more detail below, the drive 14 controls the
`application of electric power to machine 12 in response to
`the control system 13 in such a manner that the diflicrence
`between the input command signal 11 and the corresponding
`output of the machine 12 is minimized.
`In certain
`embodiments, the control system 13 also actively controls
`application of power to the machine 12 as a function of rotor
`position in such a manner to achieve a desired behavior of
`the machine 12 meeting one or more criteria in categories
`including, for example, torque ripple, cogging torque, angu-
`lar sensitivity, harmonic content, etc. The use of the control
`system 13 to actively achieve desired machine behavior, as
`opposed to attempting to achieve such behavior through
`complex rotor or stator constructions, results in a better
`performing system in that, for example, conventional, low
`cost machines and machine construction techniques may be
`used.
`
`An electromagnetic machine system 100 in accordance
`with an exemplary embodiment of the present invention is
`shown in FIG. 2. The machine system 100 includes a control
`system 13, which may be implemented by an appropriately
`programmed digital Controller, sttch as a digital signal
`processor (DSP), microcontrollcr or microprocessor.
`The control system 13 includes an input terminal 11 that
`receives, for example, a signal representing the torque
`demanded of the motor 12. Torque is a function of current
`and angle; hence, for any particular rotor angle there is a set
`of appropriate currents that will produce the desired torque.
`Based on the rotor angle and the required torque, appropriate
`current values are sent to the drive 14, which in turn provides
`the necessary voltage to the motor 12 to meet the current
`demand.
`
`Rotor position feedback 18 and energization feedback 19,
`such as the motor terminal voltage and current, are provided
`to an estimator 30. In accordance with mathematical "good
`practice,” the voltage and current values may be
`non'nalizcd—the measured values are divided by the maxi-
`mum expectcd value. The estimator 3|} calculates motor
`parameters such as angular speed and the time derivatives of
`the phase currents. These values are used to derive and
`update a first mathematical model that describes the elec-
`trical behavior of the motor 12. The structure of the electrical
`model is such that it can accurately represent electrical
`machine characteristics such as resistance, back electromag-
`netic Eorce (“HEMP”), self and mutual inductance, cogging,
`etc., depending on the type of machine 12 employed.
`The parameters calculated by the estimator 30 are passed
`to a torque model 32 of the motor 12. The torque model 32
`is developed by mathematically transforming the electrical
`model in an appropriate manner, dictated by the electromag-
`netic physics of the motor 12,
`into a second model
`that
`describes the torque characteristics of the machine 12. Since
`the electrical model co-ell'1cicnt.S flow naturally into the
`torque model 32, by constructing an aocuratc electrical
`model of the motor 12,
`the torque characteristics of the
`motor 12 are also known. For example, the torque model
`may describe the torque produced for any combination of
`phase current and rotor position in the normal operating
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`envelope of the machine. Thus, using the values calculated
`by the estimator 30, an estimate of motor torque can be
`calculated for any current-angle combination.
`The torque model 32 is interrogated by a solver 34, which
`calculates the required currents, or solution curves, accord-
`ing to some desired motor behavior and the known behavior
`of the motor 12 (as regards current and angle).
`'l'hus, the
`controller 36 provides the appropriate current for a given
`rotor angular position to achieve the desired output torque
`40 or other output parameter, and further, to achieve the
`output parameter in accordance with the desired machine
`behavior. For example, the desired machine behavior may
`include the operating characteristics of the motor 12 meeting
`one or more criteria in categories including cogging torque,
`torque ripple, angular sensitivity of the solution to angular
`error and harmonic content of the solution curves. In the
`particular system 100 shown in FIG. 2, the solver 34 output
`is stored explicitly as a lookup table accessible by the
`controller 36. The torque demand 11 and rotor angle is
`applied to the lookup table to determine the appropriate
`phase current value to be applied to the phase windings via
`the driver 14. In other embodiments, the output of the solver
`3-4 is in an analytic form, derived by fitting a function to the
`calculated numerical values.
`
`Since the electrical model used by the estimator 3|] is
`algebraic in nature, the estimator 30 can be allowed to run
`for some time period operating upon not necessarily sequen-
`tial data before a new set of parameter estimates are released
`in to the torque model 32.At this point the solver 34 can then
`recalculate the necessary lookup tables 36. Once fully
`calculated, the new lookup tables can then replace those
`tables currently in use. Many of these operations can be
`background tasked;
`that
`is,
`they can occur as and when
`computational resources are available. This is one of the
`advantages of an algebraic motor rnodel—it is not intricately
`wrapped up in the time variable.
`Torque can be estimated via ooenergy or field energy,
`though calculating torque via coenergy results in simpler
`expressions. Thus, the estimate of output torque 40 can be
`calculated using only feedback available from the machine
`terminalsr—such as the tenninal voltage and current and the
`rotor position—to estimate the pyrameters of resistance and
`flux linkage. The following disclosure is generally provided
`in terms of a three phase hybrid motor, though the model
`form can be generalized into different
`types of rotating
`machines having any number of phases by one skilled in the
`art having the benefit of this disclosure.
`It
`is common in many applications to utilize what is
`known as a balanced three phase feed. In such systems,
`when a three-phase motor is used, the sum of the three phase
`currenLs will equal zero. Hence, the o.|3-l-'rarnc of Reference
`(FOR) can be used. If balanced feed is not used,
`it
`is
`necessary to use the abc-FoR. The rr.B-FoR is considered
`first.
`
`The electrical model may have the form of a product of
`polynomial expressions in current and angle. Typically,
`those for angle will involve trigonometric functions. The
`currentpolynomials may also be orthogonal and may be one
`of any number of suitable polynomial
`types. For more
`complex machines, an orthogonal model form may be
`appropriate. With the first model structure disclosed herein,
`it is assumed that flux linkage models are expressions that
`are products of polynomial terms involving phase currents
`and trigonometric polynomials of mechanical angle. Models
`using orthogonal functions are discussed further later in this
`specification. Generally, the following nomenclature is used
`in this disclosure:
`
`8
`
`

`
`US 6,756,757 B2
`
`7
`¢ is the phase index, ranges over defined set of numbers
`{l,.2r3. .
`.
`. } or equivalent letters {a,h,c,
`.
`.
`. }
`a,b,c are phase names, equivalent to 1,2,3 when numeri-
`cally referenced
`
`ot,fi,0 are o.[5 Frame of Reference (FOR) labels
`
`its, is the phase :1) flux linkage
`p,P .
`,
`. q,Q .
`.
`. r,R .
`.
`. n,N are summation indexes and
`maximum index values
`
`sin( ), cos( ) are trigonometric functions
`
`gwqm, hwqm are model parameters
`ia,i‘,,iC are variables representing (15 frame of reference
`currents
`
`JD
`
`15
`
`lwlfi are maximum values of a|3-frame of reference
`currents encountered in the coenergy integral
`ia,ib,i¢ are variables representing abc-frame of reference
`currents
`
`Ia,I,,,lG are maximum values of abc-FoR currents encoun-
`tered in the coenergy integral
`
`if is the current flow associated with the fictious rotor
`circuit modelling the presence of a magnet
`V‘, is the phase tp voltage
`
`RW,R«,,RWfi are resistance values associated with phase
`
`S‘, is solution sensitivity
`
`8
`
`I:
`
`:'.,t9(tn
`r'at9t'2)t
`
`1'a(9(N_l,l
`='fi(9(13)
`mats):
`
`J',ql3(N)J
`
`frame of reference current values
`is the vector of all
`across the set of discrete angle values
`l(n+1),l(n) are the {n+I)’1h and n’th iterated current
`VBCIOIS
`
`AI(n) is the calculated change in current vector at n’th
`interval
`
`.
`cpfl=(0 .
`vector
`
`. LI 'I‘((-l(k),ia(k),ifi(lt)) 0 .
`
`. .0) is the k’th torque
`
`. 0 S(6(k),i[,(l<),i¢,(k)) 0 .
`.
`,.,,=(o .
`sensitivity vector
`
`.
`
`. 0) is the ma
`
`A 2
`
`#51‘;
`
`Ifim
`
`is the dilfererttial of x with respect to it
`B is the rotor angle
`(1) is the rotor angular velocity
`t is time t
`
`ms is coenergy
`dis is X infintesimal
`
`are stacked torque vectors
`
`.35
`
`s =
`
`¢'5t
`
`ti5sN
`
`
`
`are stacked current vectors
`Assuming that
`the model structure for each machine
`phase (:11) is identical, the general form of the flux model
`using the nt|3-FoR is;
`
`I f(x) dx is the integral of f(x) with respect to X
`(3
`
`2.1, =
`
`Efl-RV» ---3
`
`P
`E
`so
`
`Q
`E
`q. o
`
`if; -
`
`R
`E
`no
`
`1'; -
`
`ff,
`
`N
`r|:D
`
`lgpmm - 5it'l[.rt -9) + ltqgpqm -cnstrz-:91]
`
`t1)
`
`is the partial derivative of function f('.) with respect to x
`D1, .
`.
`. ,D,; are components of the coenergy integral, along
`defined path
`T is motor or true torque
`00:") is the remainder associated with n’th order and
`higher terms of the Jacobiatil matrix
`
`S0
`
`.13 is the ij’th entry of the Jacobian
`F,{xl, .
`.
`. ,xM) is the i’th function ofvariables xl, .
`ox is delta 2:
`
`.XM
`
`.
`
`.
`
`hxmw is the new value of delta x, or change in x
`xnm, X0“ are new and old values of X calculated during
`Newton iterative process
`T“. is estimated torque, directly from the terminal vari-
`ables
`
`cog
`T
`is torque which cannot be calculated directly using
`terminal variables
`
`Such a model allows for a non-linear relationship between
`phase current and flux as well as mutual effects between any
`two or more phases. As noted above, for the purposes of the
`present disclosure it is assumed that model structure is
`invariant with respect to phase, although this need not be so.
`Contiguous powers of polynomial current and angle har-
`monic need not be used, as is the case in Equation (1). For
`example, consider the following:
`
`:
`
`(2)
`
`fir
`g
`,
`P-Pt
`
`.
`1;“
`
`tn"
`
`_
`-Hat
`
`Pu
`“V
`.,
`1
`.
`E _ If - 2‘ (g¢,,,,,, -smtrr-6)+ h¢,,,,,,, -cosln -9)]
`n=.u|
`ten
`
`1‘; -
`
`65 where the indexing sets:
`-
`P=(P1sP2; -
`-
`- sP.s'-) r=(r1sr25 -
`[l=(‘l1sP2s -
`-
`- -qr) “=(nts1'12s -
`
`- srU*)
`~
`~ ant»)
`
`9
`
`

`
`US 6,756,757 B2
`
`9
`need not contain contiguous integers. In fact, most. practical
`applications will have this form.
`Relatively simple models of the form presented in Equa-
`tion (2) that are suflicienlly accurate can he obtained. Model
`structure can he allowed to vary between phases if so
`desired. This variation upon defining model structure has a
`significant impact upon the computational complexity of the
`associated algorithms. Some model components will be
`present as a result of manufacturing variance and would not
`he suggested by a theoretical consideration of the motor
`design. Further, model complexity can vary greatly between
`motors of different design. For example, a permanent mag-
`net motor design with the express intent of reducing
`cogging, typically through the use of skew, may only require
`a very simple model
`to accurately predict
`torque.
`It
`is
`generally desirable to avoid models that are over or under
`determined.
`
`10
`
`15
`
`The abc-FoR currents can be transformed into all-FoR
`currents using the following transform:
`
`‘L0
`
`-continued
`
`R
`
`N
`
`F“
`
`mo
`
`[gwqm - slum-9] +ftdW,,. -costar -9])
`
`+
`
`P
`E
`pun
`
`Q
`i§-Zt%-
`F0
`
`Jr
`E
`.=t
`
`J
`[rrfl Fray]
`
`ht
`
`rr=|}
`Z (g‘,m,, -sin(n»li'j + fzwqm -contra-3)!
`
`+
`
`9
`E
`[J30
`
`lg
`
`<2
`
`q=n
`
`R
`N
`g 5:, m.n.(g¢Pqm.m._;(,,.g)_
`7:“
`":‘
`
`h.,,..,,,1 - si_u1n- 9))
`
`The imaginary rotor current (i.) is nominally constant and
`its time derivative is zero. Hence, from Equations (5) and
`(7)=
`
`1
`1
`0
`1
`_
`F; = 34 ‘é-5 I
`-2-1 an I
`
`.
`Z’,
`
`t3]
`
`v,=R,,+t,-R,,,+:I,.R,¢.+2,.i_,,.tr,,,,‘,_,+
`
`(8)
`
`P
`d
`2 [p'E§—l'E‘ai
`VI
`
`Under the balanced feed assumption. the third phase current
`is zero. It is known that phase voltage (v,,) is defined by
`
`30
`
`0
`
`q=0
`
`R
`N
`1%-Zr}tzltgwpqn,-5in(r:-3)+h,,,,,,,,-ccstn-9),!--~+
`;=u
`":0
`
`33:5,-R¢+‘%.l¢
`
`'4]
`
`P
`p=o
`
`Q
`d
`"5'Zl*“?l'n l
`q=1
`
`where R“, is the phase resistance. Thus, using the tlfi-FUR:
`
`d
`_
`_
`_
`_
`V¢=R,9+ig‘R,h+1!,I':l'i¢g‘l-l¢‘1fi'Rfl,-13+EM
`
`'
`
`1'5)
`
`It should be noted that there are more resistance terms in
`Equation (5) then is necessary from the perspective of how
`electric circuits operate. Such additional terms allow for the
`presence of test data olfsets and the like to be directly
`compensated for‘, otherwise the estimator will set redundant
`terms to zero.
`
`It is also known that angular velocity (no) is defined by:
`
`d
`aa=afi'
`ctr
`
`50
`
`6
`[J
`
`R
`N’
`2fl-Z[gwqm-sin(n-H)+h¢W.,,-cns{n-t?))---+-
`_=u
`mo
`
`P
`Z:'':
`p-U
`
`0
`
`539
`
`2
`
`r-0
`
`N
`gm n [g,,,,,,,.,, coslrz 6']-
`““
`
`fl¢.,,i.,,_ -si.n(rt - 09))
`
`4-0
`
`45
`
`In embodiments employing a switched reluctance
`machine, there is no imaginary rotor current state as there
`are no rotor magnets with which this state is associated,
`hence:
`
`10
`
`From Equati