U.S. patent application number 09/765745 was filed with the patent office on 2002-09-12 for rotor position estimation for switched reluctance machines.
Invention is credited to Gallegos-Lopez, Gabriel, Rajashekara, Kaushik, Walters, James E..
Application Number | 20020125851 09/765745 |
Document ID | / |
Family ID | 25074366 |
Filed Date | 2002-09-12 |
United States Patent
Application |
20020125851 |
Kind Code |
A1 |
Gallegos-Lopez, Gabriel ; et
al. |
September 12, 2002 |
ROTOR POSITION ESTIMATION FOR SWITCHED RELUCTANCE MACHINES
Abstract
Method and system for estimating rotor position of a switched
reluctance machine is provided. The method allows for estimating
flux linkage across a respective phase of the machine. The method
allows for measuring of magnetization curves at aligned and
unaligned positions of the machine. The method further allows for
computing magnetization reference data between the aligned and
unaligned positions. A storing step allows for storing rotor
position data based on the magnetization reference data. The stored
rotor position data is indicative of rotor position variation as a
function of phase current. A relating step allows to relate the
estimated flux linkage to the magnetization reference data to
determine, for a respective phase current, correspondence of the
estimated flux linkage relative to the magnetization reference
data. A retrieving step allows for retrieving stored rotor position
data when said correspondence is determined. The retrieved rotor
position data is the estimate of rotor position of the switch
reluctance machine corresponding to the respective phase
current.
Inventors: |
Gallegos-Lopez, Gabriel;
(Alexandria, IN) ; Rajashekara, Kaushik; (Carmel,
IN) ; Walters, James E.; (Carmel, IN) |
Correspondence
Address: |
MARGARET A. DOBROWITSKY
DELPHI TECHNOLOGIES, INC.
Legal Staff, Mail Code: 480-414-420
P.O. Box 5052
Troy
MI
48007-5052
US
|
Family ID: |
25074366 |
Appl. No.: |
09/765745 |
Filed: |
January 19, 2001 |
Current U.S.
Class: |
318/701 |
Current CPC
Class: |
H02P 25/089
20160201 |
Class at
Publication: |
318/701 |
International
Class: |
H02P 001/46; H02P
003/18; H02P 005/28; H02P 007/36 |
Claims
What is claimed is:
1. A method for estimating rotor position of a switched reluctance
machine, said method comprising: estimating flux linkage across a
respective phase of the machine; measuring magnetization curves at
respective aligned and unaligned positions of the machine;
computing magnetization reference data between said aligned and
unaligned positions based on the measured magnetization curves;
storing rotor position data based on said magnetization reference
data, said stored rotor position data indicative of rotor position
variation as a function of phase current; relating the estimated
flux linkage to said magnetization reference data to determine, for
a respective phase current, correspondence of the estimated flux
linkage relative to the magnetization reference data; and
retrieving stored rotor position data when said correspondence is
determined, said retrieved rotor position data comprising the
estimate of rotor position of said switch reluctance machine
corresponding to the respective phase current.
2. The method of claim 1 wherein the step of computing
magnetization reference data between said aligned and unaligned
positions of the machine is in accordance with the following
equation:
.psi..sub.ref(p)=[(.psi..sub.a-.psi..sub.u).TM.p+.psi..sub.u],
wherein .psi..sub.a and .psi..sub.u represent the respective flux
linkage at the aligned and the unaligned positions respectively for
the respective phase current, and p corresponds to a numerical
factor having a value between 0.ltoreq.p.ltoreq.1.
3. The method of claim 2 wherein the step of computing
magnetization reference data comprises generating a single
reference magnetization curve corresponding to a single value of
the numerical factor p.
4. The method of claim 3 wherein the step of storing rotor position
data comprises storing rotor position data for said single
reference magnetization curve, said rotor position data being
indicative of rotor position variation as a function of phase
current and said single value of the numerical factor p.
5. The method of claim 2 wherein the step of computing
magnetization reference data comprises generating a family of
reference magnetization curves corresponding to distinct values of
the numerical factor p.
6. The method of claim a wherein the step of storing rotor position
data comprises storing rotor position data for said family of
reference magnetization curves, said rotor position data being
indicative of rotor position variation as a function of phase
current and said distinct values of the numerical factor p.
7. The method of claim 5 wherein the step of generating each
reference magnetization curve p.sub.ref for said family of
reference magnetization curves is based on the following equation:
5 p ref = [ e - u a - u ] ,wherein .psi..sub.a and .psi..sub.u
represent the respective flux linkages at the aligned and the
unaligned positions respectively, and .psi..sub.e represents the
estimated flux linkage, each at the respective phase current.
8. The method of claim 7 wherein the step of retrieving stored
rotor position data further comprises retrieving stored rotor
position data as a function of said distinct values of the
numerical factor p, and wherein each retrieved rotor position data
comprises distinct rotor position estimates of said switch
reluctance machine corresponding to the respective phase current
and respective ones of said family of reference magnetization
curves.
9. The method of claim 2 wherein the step of estimating flux
linkage comprises sensing a voltage V across a respective phase
winding and calculating the phase flux-linkage based on the
following equation: .psi..sub.e=.intg.(V-R*i)dt, wherein R
comprises phase winding impedance and i comprises phase
current.
10. The method of claim 2 wherein the step of estimating flux
linkage comprises estimating a voltage V across a respective phase
winding and calculating the phase flux-linkage based on the
following equation: .psi..sub.e=.intg.(V-R*i)dt, wherein R
comprises phase winding impedance and i comprises phase
current.
11. A method for determining the aligned position of a switched
reluctance machine, said method comprising: estimating flux-linkage
across a respective phase of the machine; relating the estimated
flux-linkage to a reference flux-linkage for said aligned position
to determine, for a respective phase current, correspondence of the
estimated flux-linkage relative to the reference flux-linkage; and
determining said aligned position when the difference between the
estimated flux-linkage and the reference flux-linkage is zero or
within a predefined range about zero.
12. A method for determining the aligned position of a switched
reluctance machine, said method comprising: estimating flux-linkage
across a respective phase of the machine; calculating the
derivative of said flux-linkage; and determining said aligned
position when the value of said flux-linkage derivative is within a
predefined range about zero and/or said derivative changes
sign.
13. A system for estimating rotor position of a switched reluctance
machine, said system comprising: a flux linkage estimator
configured to estimate flux linkage across a respective phase of
the machine; a processor configured to measure magnetization curves
at respective aligned and unaligned positions of the machine; a
processor configured to compute magnetization reference data
between said aligned and unaligned positions based on said
magnetization curves; memory for storing rotor position data based
on said magnetization reference data, said stored rotor position
data indicative of rotor position variation as a function of phase
current; a flux-relating module configured to relate the estimated
flux linkage to said magnetization reference data to determine, for
a respective phase current, correspondence of the estimated flux
linkage relative to the magnetization reference data; and a data
retrieval unit coupled to said memory to retrieve stored rotor
position data when said correspondence is determined, said
retrieved rotor position data comprising the estimate of rotor
position of said switch reluctance machine corresponding to the
respective phase current.
14. The system of claim 13 wherein said processor, in order to
compute magnetization reference data between said aligned and
unaligned positions of the machine, executes the following
equation: .psi..sub.ref(p)=[(.psi.-
.sub.a-.psi..sub.u).multidot.p+.psi..sub.u], wherein .psi..sub.a
and .psi..sub.u represent the respective flux linkage at the
aligned and the unaligned positions respectively for the respective
phase current, and p corresponds to a numerical factor having a
value between 0.ltoreq.p.ltoreq.1.
15. The system of claim 14 wherein said processor is configured to
generate a single reference magnetization curve corresponding to a
single value of the numerical factor p.
16. The system of claim 15 wherein said memory is configured to
store rotor position data for said single reference magnetization
curve, said rotor position data being indicative of rotor position
variation as a function of phase current and said single value of
the numerical factor p.
17. The system of claim 14 wherein said processor is configured to
generate a family of reference magnetization curves corresponding
to distinct values of the numerical factor p.
18. The system of claim 17 wherein said memory is configured to
store rotor position data for said family of reference
magnetization curves, said rotor position data being indicative of
rotor position variation as a function of phase current and said
distinct values of the numerical factor p.
19. The system of claim 17 further comprising a processor
configured to generate each reference magnetization curve p.sub.ref
for said family of reference magnetization curves based on the
following equation: 6 p ref = [ e - u a - u ] ,wherein .psi..sub.a
and .psi..sub.u represent the respective flux linkages at the
aligned and the unaligned positions respectively, and .psi..sub.e
represents the estimated flux linkage, each at the respective phase
current.
20. The system of claim 19 wherein said data retrieval unit is
configured to retrieve stored rotor position data as a function of
said distinct values of the numerical factor p, and wherein each
retrieved rotor position data comprises distinct rotor position
estimates of said switch reluctance machine corresponding to the
respective phase current and respective ones of said family of
reference magnetization curves.
21. The system of claim 14 wherein said flux linkage estimator
comprises a sensor configured to sense a voltage V across a
respective phase winding and a calculator module configured to
calculate said flux linkage based on the following equation:
.psi..sub.e=.intg.(V-R*i)dt, wherein R comprises phase winding
impedance and i comprises phase current.
22. The system of claim 14 wherein said flux linkage estimator
comprises an estimator configured to estimate a voltage V across a
respective phase winding and a calculator module configured to
calculate said flux linkage based on the following equation:
.psi..sub.e=.intg.(V-R*i)dt, wherein R comprises phase winding
impedance and i comprises phase current.
23. The system of claim 21 wherein said flux-relating module
comprises a device configured to generate the difference between
the estimated flux-linkage and a reference flux-linkage for the
aligned position at the respective phase current.
24. The system of claim 23 wherein said flux-relating module
further comprises a comparator configured to generate a pulse when
the value of said difference is zero and/or within a predefined
range about zero.
25. The system of 13 wherein said flux-linkage estimator module
comprises a differentiator configured to generate the derivative of
the estimated flux-linkage.
26. The system of 25 wherein said flux-estimator module further
comprises a comparator configured to generate a pulse when the
value of said derivative is within a predefined range about zero
and/or said derivative changes sign.
27. A computer-readable medium encoded with computer program code
for estimating rotor position of a switched reluctance machine, the
program code causing a computer to execute a method comprising:
estimating flux linkage across a respective phase of the machine;
measuring magnetization curves at respective aligned and unaligned
positions of the machine; computing magnetization reference data
between said aligned and unaligned positions based on said
magnetization curves; storing rotor position data based on said
magnetization reference data, said stored rotor position data
indicative of rotor position variation as a function of phase
current; relating the estimated flux linkage to said magnetization
reference data to determine, for a respective phase current,
correspondence of the estimated flux linkage relative to the
magnetization reference data; and retrieving stored rotor position
data when said correspondence is determined, said retrieved rotor
position data comprising the estimate of rotor position of said
switch reluctance machine corresponding to the respective phase
current.
28. The computer-readable medium of claim 27 wherein the step of
computing magnetization reference data between said aligned and
unaligned positions of the machine is in accordance with the
following equation:
.psi..sub.ref(p)=[.psi..sub.a-.psi..sub.u).about.p+.psi..sub.u],
wherein .psi..sub.a and .psi..sub.u represent the respective flux
linkage at the aligned and the unaligned positions respectively for
the respective phase current, and p corresponds to a numerical
factor having a value between 0.ltoreq.p.ltoreq.1.
29. The computer-readable medium of claim 28 wherein the step of
computing magnetization reference data comprises generating a
single reference magnetization curve corresponding to a single
value of the numerical factor p.
30. The computer-readable medium of claim 29 wherein the step of
storing rotor position data comprises storing rotor position data
for said single reference magnetization curve, said rotor position
data being indicative of rotor position variation as a function of
phase current and said single value of the numerical factor p.
31. The computer-readable medium of claim 28 wherein the step of
computing magnetization reference data comprises generating a
family of reference magnetization curves corresponding to distinct
values of the numerical factor p.
32. The computer-readable medium of claim 31 wherein the step of
storing rotor position data comprises storing rotor position data
for said family of reference magnetization curves, said rotor
position data being indicative of rotor position variation as a
function of phase current and said distinct values of the numerical
factor p.
33. The computer-readable medium of claim 31 wherein the step of
generating each reference magnetization curve p.sub.ref for said
family of reference magnetization curves is based on the following
equation: 7 p ref = [ e - u a - u ] ,wherein .psi..sub.a and
.psi..sub.u represent the respective flux linkages at the aligned
and the/unaligned positions respectively, and .psi..sub.e
represents the estimated flux linkage, each at the respective phase
current.
34. The computer-readable medium of claim 33 wherein the step of
retrieving stored rotor position data further comprises retrieving
stored rotor position data as a function of said distinct values of
the numerical factor p, and wherein each retrieved rotor position
data comprises distinct rotor position estimates of said switch
reluctance machine corresponding to the respective phase current
and respective ones of said family of reference magnetization
curves.
35. The computer-readable medium of claim 28 wherein the step of
estimating flux linkage comprises sensing a voltage V across a
respective phase winding and calculating the phase flux based on
the following equation: .psi..sub.e=.intg.(V-R*i)dt, wherein R
comprises phase winding impedance and i comprises phase
current.
36. The computer-readable medium of claim 35 further comprising
generating the difference between the estimated flux linkage and a
reference flux linkage for the aligned position at the respective
phase current.
37. The computer-readable medium of claim 36 further comprising
generating a pulse when the value of said difference is within a
predefined range about zero.
38. The computer-readable medium of 35 wherein said flux-relating
step comprises generating the derivative of the estimated
flux-linkage.
39. The computer-readable medium of 38 further comprising
generating a pulse when the value of said derivative is within a
predefined range about zero and/or said derivative changes sign.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention is generally related to control for
electromechanical machines, and, more particularly, the present
invention is related to sensorless control techniques for
estimating rotor position in a switched reluctance machine.
[0002] In order to properly operate a switched reluctance machine,
it is generally necessary to determine the rotor position in order
to appropriately commutate the currents flowing in the respective
phase windings of the machine. Various devices may be used to
obtain a measure of rotor position, e.g., resolvers, particularly
when high resolution is required. Other devices that may be used to
determine rotor position include encoders or Hall sensors. However,
such devices and required associated circuitry add incremental
costs and may become sources of single point failure.
[0003] In order to eliminate the need for position sensors, such as
resolvers, encoders, or Hall sensors, sensorless operational
techniques have been developed. Many of such techniques, however,
suffer from lack of consistency due to their failure to account for
machine-to-machine variation when applied to a large number of
machines. Further, in some cases, such techniques require
time-consuming and burdensome individual calibration of the
controller configured to execute such techniques in any given
machine.
[0004] The present invention proposes a new technique for rotor
position estimation for switched reluctance machines. The proposed
technique uses the respective magnetization curves of the machine
for rotor position estimation, and its inputs are measured current
and estimated flux linkage. One desirable feature of the proposed
technique is that it measures the magnetization data of the machine
online and approximates the magnetization data in a substantially
linear manner. Hence the loss of consistency from one machine to
another in high volume manufacturing is not a concern. Also, it is
not necessary to calibrate the controller for each machine
separately.
BRIEF SUMMARY OF THE INVENTION
[0005] Generally speaking, the present invention fulfills the
foregoing needs by providing in one aspect thereof a method for
estimating rotor position of a switched reluctance machine. The
method allows for measuring magnetization curve at respective
aligned and unaligned positions of the machine. The method allows
for estimating flux-linkage across a respective phase of the
machine. The method further allows for computing magnetization
reference data between the aligned and unaligned. A storing step
allows for storing rotor position data based on the magnetization
reference data. The stored rotor position data is indicative of
rotor position variation as a function of phase current. A relating
step allows to relate the estimated flux linkage to the
magnetization reference data to determine, for a respective phase
current, correspondence of the estimated flux linkage relative to
the magnetization reference data. A retrieving step allows for
retrieving stored rotor position data when said correspondence is
determined. The retrieved rotor position data is the estimate of
rotor position of the switch reluctance machine corresponding to
the respective phase current.
[0006] In another aspect thereof, the method allows for estimating
multiple rotor positions by estimating an initial rotor position
using the estimated flux-linkage and phase current. The initial
rotor position is compensated as a function of current to obtain
the final estimated position. In yet another aspect thereof, the
method uses the magnetization curve at the aligned position as a
reference to run the machine sensorless and measure the
magnetization curve at the unaligned position. Alternatively, the
method may estimate the aligned position by detecting a sign change
in the derivative of the flux-linkage or when the value of such
derivative is within a predefined range about zero.
[0007] The present invention further fulfills the forgoing needs by
providing in another aspect thereof, a system for estimating rotor
position of a switched reluctance machine. The system includes a
processor for measuring magnetization curve at aligned and
unaligned positions of the machine. The system includes a flux
linkage estimator configured to estimate flux linkage across a
respective phase of the machine. The system further includes a
processor configured to compute magnetization reference data
between the aligned and unaligned positions of the machine. Memory
is provided to store rotor position data based on the magnetization
reference data. The stored rotor position data is indicative of
rotor position variation as a function of phase current. A
flux-relating module is configured to relate the estimated flux
linkage to said magnetization reference data to determine, for a
respective phase current, correspondence of the estimated flux
linkage relative to the magnetization reference data. A data
retrieval unit is coupled to said memory to retrieve stored rotor
position data when that correspondence is determined. The retrieved
rotor position data comprises the estimate of rotor position of the
switch reluctance machine corresponding to the respective phase
current.
[0008] In one aspect thereof, the system allows for estimating
multiple rotor positions by estimating an initial rotor position
using the estimated flux-linkage and phase current. The initial
rotor position is compensated as a function of current to obtain
the final estimated position. In another aspect thereof, the system
uses the magnetization curve at aligned position as a reference to
run the machine sensorless and measure the magnetization curve at
unaligned position. Alternatively, the system estimates the aligned
position by detecting the change of sign of the derivative of the
flux-linkage or when it becomes zero.
DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a block diagram representation of exemplary
techniques for estimating flux linkage at an aligned position in a
switched reluctance machine;
[0010] FIG. 2 illustrates respective plots of exemplary
magnetization curves of a switched reluctance machine;
[0011] FIG. 3 illustrates respective plots of normalized
flux-linkage as a function of rotor position;
[0012] FIG. 4 illustrates respective plots of variation of the
estimated rotor position as a function of phase current;
[0013] FIG. 5 illustrates a block diagram representation that may
be used for practicing an exemplary embodiment that enables
estimation of a single rotor position in accordance with one aspect
of the present invention; and
[0014] FIG. 6 illustrates a block diagram representation that may
be used for practicing an exemplary embodiment that enables
estimation of multiple rotor positions in accordance with another
aspect of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0015] The present invention proposes a new technique for rotor
position estimation for switched reluctance machines. The technique
uses the magnetization curves of the machine that are a function of
measured current and estimated flux-linkage for rotor position
estimation.
[0016] The principles of the present invention are described in the
context of an exemplary algorithm, and, for the sake of
facilitating understanding, such algorithm is explained in three
conceptual stages as follows:
[0017] First stage: Allows for measuring the magnetization curve of
a polyphase switched reluctance machine at an aligned phase
position, i.e., when the stator poles of that phase are aligned
with the respective rotor poles of the machine. This first stage
may be executed as follows:
[0018] Energize one of the machine phases to provide alignment to
that phase.
[0019] Apply an energization signal to the phase, e.g., a voltage
pulse. Measure and store the phase current and estimated
flux-linkage by eq. (1). The phase impedance R ma be estimated by
calculating the applied voltage and the phase current (V/i). The
phase current and the flux-linkage represent the magnetization
curve at the aligned position. In one exemplary embodiment, one may
execute this step several times and then calculate the average of
the magnetization curve at the aligned position.
.psi..sub.e=.intg.(V-R*i)dt (1)
[0020] Second stage: This stage may be executed while running the
machine sensorless using the magnetization curve at the aligned
position as a position reference. FIG. 1 shows an exemplary block
diagram 100 for conceptualizing the estimation of the aligned
position. This stage may be executed as follows:
[0021] By way of example, any phase to be energized next may be
identified based on the direction of rotation set by the firing
sequence commanded by a machine controller. When the phase is
energized, the phase current is measured, and the flux-linkage
.psi..sub.e is estimated in a processor 102 configured to execute
eq. (1). As shown in FIG. 1, processor 102 mathematically
integrates the difference between the applied voltage, e.g.,
voltage V, and the voltage that develops across the impedance R,
e.g., voltage R*i, such as may be obtained from a
voltage-estimating device 103, such as a device that multiplies the
phase current by impedance R. The difference V-R*i may be obtained
from a summer 104 having respective non-inverting and inverting
terminals to respectively receive the applied voltage and the
voltage across the impedance. For a given current, the
corresponding reference flux-linkage .psi..sub.a at the aligned
position may be retrieved from a memory device, e.g., a look-up
table 106, comprising the values of the reference flux-linkage
derived in the above-described first stage. The difference
.psi..sub.e-.psi..sub.a, as may be obtained from a summer 108, is
used to estimate the aligned position .theta..sub.a. As will be
understood by those skilled in the art, initially the value of the
difference .psi..sub.e-.psi..sub.a may be negative. When the
aligned position is reached, the value of the difference
.psi..sub.e-.psi..sub.a approaches a sufficiently small value,
e.g., zero, so that a pulse is generated by a comparator device 110
configured to generate the pulse upon the value of the difference
.psi..sub.e-.psi..sub.a reaching a predefined range about zero. At
this point that phase is turned off and the next phase in the
energizing sequence is turned on.
[0022] Block 112 illustrates an alternative embodiment for
estimating the aligned position. In this embodiment, a
differentiator 114 receives the estimated flux-linkage .psi..sub.e,
and, when the aligned position is reached, the slope of the
flux-linkage would become zero, and change sign when the aligned
position has been passed, and this would cause a comparator device
116 to be triggered and generate the pulse.
[0023] As suggested above, regardless of the specific methodology
used for estimating the aligned position, the same procedure is
carried out for each phase in the energizing sequence. In this
stage, the machine is run sensorless with the aligned position
estimated in every energy conversion.
[0024] Upon estimation of the aligned position, the turn-on angle
should be set a few mechanical degrees before the unaligned
position, i.e., when the stator poles of that phase are at the
point of least alignment with the rotor poles of the machine. In
one exemplary embodiment, a timer could be used for measuring
elapsed time between any two successive pulses from comparator 110
or 116 to determine the unaligned position relative to the aligned
position. Once the unaligned position is determined, one can then
estimate the flux-linkage at that unaligned position. It will be
appreciated that the flux-linkage at the unaligned position
comprises the minimum value in an entire electrical cycle. While
the machine is driven sensorless, at least two measurements of
position at different current levels at the unaligned position
should be carried out to calculate the magnetization curve at the
unaligned position, which is a straight line. See FIG. 2, wherein
curve 122 represents an exemplary magnetization curve at the
unaligned position.
[0025] It is noted that although in this stage the machine can run
sensorless, the respective phases, however, are energized over the
aligned position. As will readily understood by one skilled in the
art, this could lead to generation of negative torque and would not
be a very efficient method to drive the machine. Thus, this stage
is temporarily used to obtain magnetization data of the machine at
different current levels for the rotor positions to be identified
by the algorithm, as explained in greater detail below.
[0026] Third stage: As suggested above, the concept of rotor
position estimation, as contemplated in one aspect of the present
invention, is based on the magnetization curve of the machine.
[0027] Exemplary magnetization curves of a switched reluctance
machine are shown in FIG. 2. From the foregoing description, it
will be appreciated that, at this stage of the algorithm, the
respective magnetization curves corresponding to the aligned and
unaligned positions have been determined. For example, as shown in
FIG. 2, a magnetization curve 120 represents the curve for the
excited phase when the stator poles of that phase are aligned with
the respective rotor poles of the machine. A magnetization curve
122 represents the curve for the excited phase when the stator
poles of that phase are at the point of least alignment with the
rotor poles of the machine. In one exemplary embodiment, it is
proposed to use as a reference an approximated magnetization curve
124 at an intermediate position. The new reference magnetization
curve is calculated between the aligned and the unaligned position
by eq. (2).
.psi..sub.ref(p)=[(.psi..sub.a-.psi..sub.u).multidot.p=.psi..sub.u].sub.i=-
cnt (2)
[0028] where .psi..sub.a and .psi..sub.u represent the respective
flux-linkages at the aligned and the unaligned position
respectively at a given current, and the factor p is a number
chosen between 0.ltoreq.p.ltoreq.1. In one exemplary embodiment, a
value of factor p close to 0.5 is used because the sensitivity for
rotor position estimation is believed to be the largest under this
condition. It will be appreciated, however, that the present
invention is not limited to any specific value of factor p. The
reference magnetization curve 124 using p=0.5 is shown in FIG. 2
marked with the letter X.
[0029] From FIG. 2, it should be noted that the reference
magnetization curve .psi..sub.ref does not represent a unique
magnetization curve of the machine since curve 124 conceptually
intersects with an infinite number of magnetization curves, better
noticeable after the machine becomes saturated (e.g., above 10A in
the case illustrated in FIG. 2). It should be further noted that
the rotor position angle represented by reference magnetization
curve 124 is a function of current, and the estimated angle tends
to decrease as the current increases. This is better appreciated
with the help of FIG. 3.
[0030] FIG. 3 shows normalized flux-linkage curves as a function of
rotor position. The flux-linkage is normalized at an intermediate
position .theta. by eq. (3). 1 nor ( ) = [ ( ) - u a - u ] i = cnt
( 3 )
[0031] Assuming p=0.5, this would correspond to a value of
.psi..sub.nor=0.5 (e.g. p=.psi..sub.nor). In the exemplary
representation shown in FIG. 3, if .psi..sub.nor=0.5 is the
reference for rotor position estimation, then the estimated rotor
position would vary from about 48 to about 42.5 mechanical degrees
as the value of the current increases.
[0032] The normalized flux-linkage and factor p at zero current can
be calculated for a given machine geometry by eq. (4) 2 p ( ) = - [
u + s + r 2 ] Min ( s , r ) , ( 4 )
[0033] and through straightforward algebraic manipulation of eq. 4,
rotor position .theta. as a function of factor p is determinable by
eq.(5) 3 ( p ) = Min ( s , r ) * p + [ u + s + r 2 ] ( 5 )
[0034] where .beta..sub.s and .beta..sub.r are the stator and rotor
pole arc, and .theta..sub.u represents the unaligned position, and
Min(.beta..sub.s, .beta..sub.r) represents selecting the smallest
of .beta..sub.s and .beta..sub.r. In one exemplary embodiment, the
rotor position angle at zero current may be computed from eq. (5),
and that angle may be used as an initial estimate of rotor
position.
[0035] FIG. 3 shows an exemplary zero-current curve 126 calculated
by eq. (5) and marked with the letter X.
[0036] FIG. 4 shows exemplary variation in rotor position
estimation as a function of current for a family or set of
reference magnetization curves. As shown in FIG. 4, the family of
magnetization values correspond to different values of factor p
from 0 to 1 illustrated with an exemplary step of {fraction
(1/30)}. A magnetization curve 130 marked with the letter X
represents the curve with factor p=0.5. Note that the curves tend
to be linear in a region, such as the region under bracket 132. In
the exemplary illustration of FIG. 4, it can be shown that the
slope is approximately constant for values of current above about
15A.
[0037] In order to calculate the variation in rotor position
estimation as a function of current, the machine is run at least at
two different current levels above the saturation current using the
procedure discussed above in the context of the second stage of the
algorithm. For each current level, the rotor position is calculated
and a linear approximation is obtained for the variation in rotor
position. In one exemplary embodiment, this action may be executed
several times in order to calculate an average value of the rotor
position.
[0038] In one embodiment of the present invention, the proposed
algorithm uses at least one reference magnetization curve, as may
be calculated by eq. (2). An exemplary block diagram 200 of this
embodiment is shown in FIG. 5. As suggested above, when a phase is
energized, the current is measured and the voltage can be either
measured or calculated from the switching signals. The flux-linkage
.psi..sub.e is estimated in processor 102 configured to execute eq.
(1), and the reference flux-linkage .psi..sub.ref is obtained from
a processor 202 configured to execute eq. (2) at a given phase
current. Alternatively, eq. (2) may be stored as a look-up table. A
summer 208 is respectively coupled to processors 102 and 202 to
generate a signal indicative of the difference
.psi..sub.e-.psi..sub.ref. That difference is in return coupled to
a comparator 210 used to identify the reference magnetization curve
Pref. By way of example, initially the value of the difference
.psi..sub.e-.psi..sub.ref may be negative, but such difference
eventually becomes zero when the reference magnetization curve has
been reached and positive when the reference magnetization curve
has been passed. A pulse is generated by comparator 210 upon
detection of the sign change, or upon the value of the difference
.psi..sub.e-.psi..sub.ref reaching zero within any desired margin.
A switch 212 is actuated by the pulse from comparator 210 to allow
retrieval of a reference angle .theta..sub.ref from a look-up table
214 . The reference angle .theta..sub.ref is obtained from look-up
table 214 by using the phase current as an index to the table.
After the reference magnetization curve p.sub.ref has been reached,
the switch is enabled and the estimated rotor position is obtained
.theta..sub.e=.theta..sub.ref. It will thus be appreciated that
look-table 214 contains the rotor position variation as a function
of current (FIG. 4).
[0039] Note that if only one reference magnetization curve is used
then the resolution of the algorithm is one rotor position per
energy conversion. However, the resolution of the algorithm
increases with increased number of reference magnetization curves
(p).
[0040] FIG. 6 shows a block diagram 300 of an embodiment that uses
a set or family of reference magnetization curves. The flux-linkage
.psi..sub.e is estimated as previously described using processor
102. A processor 302 is coupled to receive .psi..sub.e and the
measured phase current to execute eq. (6) in order to generate the
reference magnetization curve p. Alternatively, eq (6) may be
stored as a look-up table. In this embodiment, a two-dimensional
look-table 304 receives the output from processor, i.e, the
reference magnetization curve p and the phase current as respective
indexes from where the estimated position .theta..sub.e is
calculated. 4 p ref = [ e - u a - u ] i = cnt ( 6 )
[0041] At this point, the machine is driven sensorless using the
new reference magnetization curve that allows to compensate for
rotor variation as a function of current.
[0042] The present invention can be embodied in the form of
microprocessor-implemented processes and apparatus for practicing
those processes. The present invention can also be embodied in the
form of microprocessor program code containing
microprocessor-readable instructions embodied in tangible media,
such as floppy diskettes, CD-ROMs, hard drives, or any other
computer-readable storage medium, wherein, when the microprocessor
program code is loaded into and executed by a microprocessor, the
microprocessor becomes an apparatus for practicing the invention.
When implemented on a microprocessor, the microprocessor program
code segments configure the microprocessor to create specific logic
circuits or processing modules.
[0043] It will be understood that the specific embodiment of the
invention shown and described herein is exemplary only. Numerous
variations, changes, substitutions and equivalents will now occur
to those skilled in the art without departing from the spirit and
scope of the present invention. Accordingly, it is intended that
all subject matter described herein and shown in the accompanying
drawings be regarded as illustrative only and not in a limiting
sense and that the scope of the invention be solely determined by
the appended claims.
* * * * *