U.S. patent application number 12/949371 was filed with the patent office on 2011-03-24 for minimizing magnetic interference in a variable reluctance resolver.
Invention is credited to Cheon Soo Park.
Application Number | 20110068960 12/949371 |
Document ID | / |
Family ID | 42239722 |
Filed Date | 2011-03-24 |
United States Patent
Application |
20110068960 |
Kind Code |
A1 |
Park; Cheon Soo |
March 24, 2011 |
MINIMIZING MAGNETIC INTERFERENCE IN A VARIABLE RELUCTANCE
RESOLVER
Abstract
A resolver apparatus and method are provided. The apparatus
comprises a source generation unit for generating a uni-phase
source signal to excite a resolver, wherein said source generation
unit comprises a low distortion oscillator, a variable phase
shifter, and a capacitive resolver driving network; and a signal
output unit for generating a two-phase output signal, wherein said
signal output unit comprises the resolver, a signal detector and
level adjuster, an angular position measurement unit, and an
angular position compensation unit. The method comprises generating
a source signal to excite a resolver; transmitting the source
signal through a variable phase shifter; transmitting the source
signal through at least one capacitive passive element serially
connected to each coil winding of the resolver; outputting a
displacement signal generated by the resolver to a
resolver-to-digital converter; and converting said displacement
signal into a digital position using the resolver-to-digital
converter.
Inventors: |
Park; Cheon Soo; (Seoul,
KR) |
Family ID: |
42239722 |
Appl. No.: |
12/949371 |
Filed: |
November 18, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12484207 |
Jun 13, 2009 |
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12949371 |
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Current U.S.
Class: |
341/116 |
Current CPC
Class: |
G01D 3/032 20130101 |
Class at
Publication: |
341/116 |
International
Class: |
H03M 1/48 20060101
H03M001/48 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 15, 2008 |
KR |
10-2008-00127309 |
Claims
1. A method for minimizing magnetic interference in a resolver, the
method comprising: generating a uni-phase source signal to excite a
variable reluctance (VR) resolver, wherein the source signal is
transmitted through at least one capacitive passive element
serially connected to each coil winding of the VR resolver, wherein
a two-phase displacement signal generated by the VR resolver is
outputted to a resolver-to-digital converter, and wherein the
displacement signal is converted into a digital position using the
resolver-to-digital converter.
2. The method of claim 1, wherein amplitude and phase of the source
signal is controlled by connecting at least one resistive passive
element in parallel with said capacitive passive element.
3. The method of claim 1, wherein the source signal is phase
shifted using a variable phase shifter.
4. An apparatus for minimizing magnetic interference in a resolver,
the apparatus comprising: a source generation unit for generating a
uni-phase source signal to excite a variable reluctance (VR)
resolver, said source generation unit comprising a low distortion
oscillator, a variable phase shifter, and a capacitive resolver
driving network comprising at least one capacitive passive element
connected to each coil winding of the VR resolver; and a signal
output unit for generating a two-phase output signal, said signal
output unit comprising the VR resolver, a signal detector and level
adjuster, an angular position measurement unit, and an angular
position compensation unit.
5. The apparatus of claim 4, wherein at least one resistive passive
element is connected in parallel with said capacitive passive
element in order to reduce angle displacement measurement error by
controlling amplitude and phase of the source signal.
6. The apparatus of claim 4, wherein the capacitive passive element
is serially connected to each coil winding of the VR resolver.
7. The apparatus of claim 6, wherein at least one resistive passive
element is connected in parallel with the capacitive passive
element.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 12/484,207, filed on Jun. 13, 2009, which
claims the benefit of earlier filing date and right of priority to
Korean Patent Application No. 10-2008-00127309, filed on Dec. 15,
2008, the contents of which are hereby incorporated by reference in
their entirety.
TECHNICAL FIELD
[0002] The claimed subject matter relates generally to
electromechanical systems and, more particularly, to resolver
apparatus and methods for measuring the angular position of a
shaft.
BACKGROUND
[0003] In motor applications, an optical encoder or a resolver may
be used to determine the angular position of a shaft.
[0004] An optical encoder is a device comprising a rotating disk, a
light source, and a photodetector (i.e., a light sensor). The disk,
which is mounted on the shaft, has coded patterns of opaque and
transparent sectors. As the disk rotates, these patterns interrupt
the light projected onto the photodetector and generate a digital
or pulse signal output that is used to determine the angular
position of an object.
[0005] A resolver is a rotary transformer comprising a rotor and a
stator with one or more windings (i.e., a coil). In response to
excitation by one or more source signals, the windings output one
or more sine or cosine signals (i.e., output voltages). The
magnitude of the sine and cosine signals can be used to determine
the angular position of a shaft inserted into the rotor.
[0006] Typically, a basic resolver is used for low resolution
applications, and a multi-pole resolver is used for high resolution
applications. A basic resolver houses two polarity windings in the
stator such that the angular position of the shaft is equivalent to
the mechanical angle of the stator. A multi-pole resolver houses
more than two pole windings in the stator and thus provides more
accuracy than a basic resolver.
[0007] Unfortunately, existing multi-pole resolvers fail to provide
the same accuracy as an optical encoder. In existing multi-pole
resolvers, as the rotation of the rotor increases in speed, the
magnetic flux around the rotor and the windings distorts the sine
and cosine output signals, which decreases the accuracy of angular
position measurements.
SUMMARY
[0008] The present disclosure is directed to minimizing magnetic
interference in a variable reluctance resolver.
[0009] For purposes of summarizing, certain aspects, advantages,
and novel features have been described herein. It is to be
understood that not all such advantages may be achieved in
accordance with any one particular embodiment. Thus, the claimed
subject matter may be embodied or carried out in a manner that
achieves or optimizes one advantage or group of advantages without
achieving all advantages as may be taught or suggested herein.
[0010] In accordance with one embodiment, a resolver apparatus is
provided. The apparatus comprises a source generation unit for
generating a uni-phase source signal to excite a resolver, wherein
said source generation unit comprises a low distortion oscillator,
a variable phase shifter, and a capacitive resolver driving
network; and a signal output unit for generating a two-phase output
signal, wherein said signal output unit comprises the resolver, a
signal detector and level adjuster, an angular position measurement
unit, and an angular position compensation unit.
[0011] In accordance with another embodiment, a resolver signal
processing method is provided. The method comprises generating a
source signal to excite a resolver; transmitting the source signal
through a variable phase shifter; transmitting the source signal
through at least one capacitive passive element serially connected
to each coil winding of the resolver; outputting a displacement
signal generated by the resolver to a resolver-to-digital
converter; and converting said displacement signal into a digital
position using the resolver-to-digital converter.
[0012] One or more of the above-disclosed embodiments in addition
to certain alternatives are provided in further detail below with
reference to the attached figures. The claimed subject matter is
not, however, limited to any particular embodiment disclosed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] Embodiments of the claimed subject matter are understood by
referring to the figures in the attached drawings, as provided
below.
[0014] FIG. 1 illustrates an exemplary multi-pole resolver, in
accordance with one or more embodiments.
[0015] FIG. 2 is a circuit diagram of an exemplary two-phase
excitation, uni-phase output resolver.
[0016] FIG. 3 is a circuit diagram that is electrically equivalent
to the circuit diagram provided in FIG. 2.
[0017] FIG. 4 illustrates the distortion caused by magnetic
interference.
[0018] FIG. 5 is a circuit diagram of an exemplary uni-phase
excitation, two-phase output resolver.
[0019] FIG. 6 is a block diagram of an exemplary apparatus
comprising a uni-phase excitation, two-phase output multi-pole
resolver, in accordance with one embodiment.
[0020] FIGS. 7(a) and 7(b) are circuit diagrams of an exemplary
resolver driving network, in accordance with one embodiment.
[0021] FIG. 7(c) is a circuit diagram of an exemplary resolver
signal level detector and adjuster, in accordance with one
embodiment.
[0022] FIG. 8 is a circuit diagram of an exemplary resolver output
signal stabilizer including a capacitive resolver driving network
(C-network), in accordance with one embodiment.
[0023] FIG. 9 is a circuit diagram that is electrically equivalent
to the circuit diagram provided in FIG. 8, in accordance with one
embodiment.
[0024] FIGS. 10(a) and 10(b) are graphs comparing the waveforms for
cosine and sine signals, respectively, outputted by an ideal
resolver, an existing resolver, an exemplary resolver, in
accordance with one embodiment.
[0025] FIGS. 11(a) and 11(b) are Lissajous graphs of output
waveforms before installing a capacitive resolver driving network
and after installing a capacitive resolver driving network, in
accordance with one embodiment.
[0026] Features, elements, and aspects that are referenced by the
same numerals in different figures represent the same, equivalent,
or similar features, elements, or aspects, in accordance with one
or more embodiments.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0027] In the following, numerous specific details are set forth to
provide a thorough description of various embodiments of the
claimed subject matter. Certain embodiments may be practiced
without these specific details or with some variations in detail.
In some instances, certain features are described in less detail so
as not to obscure other aspects of the disclosed embodiments. The
level of detail associated with each of the elements or features
should not be construed to qualify the novelty or importance of one
feature over the others.
[0028] Referring to FIG. 1, in accordance with one embodiment, an
exemplary multi-pole resolver comprises a rotor, a stator, and a
coil with two or more stator windings. In one implementation, the
resolver may be a variable reluctance (VR) resolver. Each stator
winding in the resolver 100 in FIG. 6 is associated with one or
more sine or cosine signals (e.g., Sin .theta., Sin(.theta.+180),
Cos .theta., Cos(.theta.+180)). Excitation by a uni-phase or
two-phase source signal may induce current to flow through the
stator windings and cause the resolver to output a two-phase or
uni-phase signal, respectively.
[0029] Referring to FIG. 2, a circuit diagram of an exemplary
two-phase excitation, uni-phase output multi-pole resolver. The
waveform of the signal outputted by the resolver may be expressed
as follows:
( V sin .omega. t .times. Sin .theta. ) - ( V sin .omega. t .times.
sin ( .theta. + 180 ) ) = 2 V sin .omega. t .times. Sin .theta. ( V
cos .omega. t .times. Cos .theta. ) - ( V cos .omega. t .times. Cos
( .theta. + 180 ) ) = 2 V cos .omega. t .times. Cos .theta.
##EQU00001## Vout = 2 V sin .omega. t .times. Sin .theta. + 2 V cos
.omega. t .times. Cos .theta. = 2 V Cos ( .omega. t - .theta. ) = 2
V Sin ( .omega. t - .theta. + 90 ) ##EQU00001.2##
[0030] However, the uni-phase sinusoidal signal waveform
sin(wt-.theta.+90) of the output signal prevents the use of a
general purpose resolver-to-digital (R/D) converter since a general
purpose R/D converter needs both sine and cosine reference phases
to process the displacement signal .theta.. To measure the phase
rotation accurately from the uni-phase sinusoidal signal, a very
sensitive phase discriminator is required to track the phase of the
output signals. The other drawback in angular position measurement
from the uni-phase sinusoidal signal arises from the inherently
existing non-linearity of the uni-phase sinusoidal signal itself,
which essentially leads to increased measurement error even for a
very fine displacement. The non-linearity of coil inductance also
contributes to increased error when the resolver rotates at high
speed.
[0031] Referring to FIG. 3, a circuit diagram that electrically
equivalent to the circuit diagram shown in FIG. 2 is provided to
explain the two-phase excitation, uni-phase output resolver in more
detail. As the shaft rotates with .theta., two fundamental
components are considered: the inductance component (Ls) which
varies sinusoidally and the dependent current source component (Is)
which is proportional to the multiplication of inductance component
(Ls) and the applied voltage (Ve). The dependent current source
(Im) induced by the magnetic flux Fm(.theta.) that varies with the
magnetic interference is also considered.
[0032] The resulting electrical characteristic of uni-phase
sinusoidal wave resolver is also a function of driving source (Ve)
frequency and non-linearly dependent on time-varying inductance
which includes the magnetic interference. The output current (Ie)
shown in FIG. 3 may be expressed as provided in Equations (1)
through (3) below:
Ie = Is + Im + 1 ( R 2 + .omega. 2 Ls 2 ) Sin ( .omega. t + .PHI. )
, ( 1 ) Ls = Lo ( 1 + m Sin .theta. ) = Lo ( 1 + m Sin .OMEGA. t )
, ( 2 ) .PHI. = arc tan ( - .omega. Ls / R ) , .OMEGA. : Angular
Speed of Reolver Rotation Angle .theta. , ( rad / sec ) ( 3 )
##EQU00002##
[0033] Ls denotes the inductance of resolver coil, Lo denotes the
intrinsic inductance of resolver coil, Im denotes the sum of all
currents induced by interference flux, Ie denotes the resolver
driving current (output voltage for the case of VR type), m denotes
the ratio between the intrinsic inductance and the flux changes, R
denotes the resistance to detect the output voltage, .theta.
denotes the rotation angle of resolver, Fm(.theta.) denotes the
induced current, and Ve denotes the applied voltage to
resolver.
[0034] Equations (1), (2), and (3) show that even though the
dependency of amplitude variation of the source signal is minimized
by increasing (R.sup.2+.omega..sup.2Ls.sup.2), the amplitude and
phase of the source signal varies as the resolver inductance
varies, especially due to the time varying nature of magnetic
interference.
[0035] FIG. 4 illustrates the distortion caused by magnetic
interference. As described above, the complicated and non-linear
characteristic of magnetic interference in a resolver excited by a
uni-phase sinusoidal wave may be attributed to two factors: self
interference within the same poles and the cross interference
between orthogonal poles. Mechanical distortion may also be added
on top of magnetic interference.
[0036] Self interference comprises: the interference between Sin
.theta. pole and Sin(.theta.+180) pole, which is a function of
K.sup.2*Sin .theta.*Sin(.theta.+180); the interference between Cos
.theta. pole and Cos(.theta.+180) pole, which is a function of
K.sup.2* Cos .theta.*Cos(.theta.+180). Cross-interference
comprises: the interference between Sin .theta. pole and Cos
.theta. pole, which is a function of K.sup.2*Sin .theta.*Cos
.theta.; the interference between Sin(.theta.+180) pole and
Cos(.theta.+180) pole, which is a function of
(K.sup.2*Sin(.theta.+180)*Cos(.theta.+180)); the interference
between Sin .theta. pole and Cos(.theta.+180) pole, which is a
function of K.sup.2*Sin .theta.*Cos(.theta.+180); and the
interference between Sin(.theta.+180) pole and Cos.theta. pole,
which is a function of K.sup.2*Sin(.theta.+180)*Cos .theta..
[0037] The above analysis is based on up to 2nd harmonics, however,
and, depending on the direction of windings, higher order harmonics
may be involved in practice. Therefore, the generalized form of
interference current due to the magnetic flux interference (Im) is
expressed as follows as provided below. K=.zeta.*m(.zeta. is the
magnetic flux coupling ratio; m is the coil inductance change
ratio).
[0038] Interference current through Sin .theta. and
Sin(.theta.+180) pole may be expressed as follows:
Im=2nd harmonic interference+3rd harmonic interference+ . . .
=(K.sup.2*Sin.sup.2.theta.)+(K.sup.2*Sin .theta.*Cos
.theta.)+(K.sup.3*Sin.sup.3.theta.)+ . . . (4)
[0039] Interference current through Cos .theta. and
Cos(.theta.+180) pole may be expressed as follows:
Im=(K.sup.2*Cos.sup.2.theta.)+(K.sup.2*Sin .theta.*Cos
.theta.)+(K.sup.3*Cos.sup.3.theta.)+ . . . , (5)
[0040] In Equations (4) and (5), K is the rate of flux change as
the resolver rotates, which is in the usual range of 0.1.about.0.3,
so that terms beyond 2nd order of K can be neglected. If the
windings are wired in such a way as to minimize the interference
between orthogonal poles, the interference induced current by sine
winding and cosine winding respectively may be simplified as
follows:
Im=(K.sup.2*Sin.sup.2.theta.), (6)
Im=(K.sup.2*Cos.sup.2.theta.), (7)
[0041] Assuming magnetic flux coupling between poles of 100% (no
leakage inductance), K becomes m. In this case, the interference
induced current by sine winding and cosine winding respectively may
be expressed as follows:
Im=(m.sup.2*Sin.sup.2.theta.), (8)
Im=(m.sup.2*Cos.sup.2.theta.), (9)
[0042] Above Equation (1) applies when resolver is not rotating,
however, as resolver rotates with angular speed of .OMEGA., the
resolver inductance (Ls) becomes a time varying function, and the
phase of the source signal, .phi., becomes a non-linear time
varying function. Especially when R.ltoreq.Ls, this phenomenon is
more significant so that resolver output voltage is heavily
dependent on .OMEGA., thereby phase rotation measurement error will
grow.
[0043] Referring to FIG. 5, an exemplary uni-phase excitation,
two-phase output resolver is provided in accordance with one
embodiment, in which driving waveforms are wired in such a way as
to minimize the magnetic induction between orthogonal poles while
maximizing the magnetic induction between the same poles. The
currents i1, i2, i3, and i4 through each pole, Sin .theta.,
Sin(.theta.+180), Cos .theta., and Cos(.theta.+180), respectively,
may be determined using Equation (1) as provided below in Equations
(10) through (13).
[0044] The current through Sin .theta. may be expressed as
follows:
i 1 = [ Lo ( 1 + m Sin .theta. ) + m 2 Sin 2 .theta. + 1 ( R 2 +
.omega. 2 Ls 2 ) ] Sin ( .omega. t + .PHI. ) , ( 10 )
##EQU00003##
[0045] Applying Sin(.theta.+180)=-Sin .theta., the current through
Sin(.theta.+180) may be express as follows:
i 2 = [ Lo ( 1 - m Sin .theta. ) - m 2 Sin 2 .theta. - 1 ( R 2 +
.omega. 2 Ls 2 ) ] Sin ( .omega. t + .PHI. ) , ( 11 )
##EQU00004##
[0046] The current through Cos .theta. may be expressed as
follows:
i 3 = [ Lo ( 1 + m Cos .theta. ) + m 2 Cos 2 .theta. + 1 ( R 2 +
.omega. 2 Lc 2 ) ] Sin ( .omega. t + .PHI. ) , ( 12 )
##EQU00005##
[0047] Applying Cos(.theta.+180)=-Cos .theta., the current through
Cos(.theta.+180) may be expressed as follows:
i 14 = [ Lo ( 1 - m Cos .theta. ) - m 2 Cos 2 .theta. - 1 ( R 2 +
.omega. 2 Lc 2 ) ] Sin ( .omega. t + .PHI. ) , ( 13 )
##EQU00006##
[0048] The Sin .theta. and Cos .theta. waveform of a uni-phase
excitation, two-phase output resolver is distorted significantly
compared to the ideal waveform. For this reason, many existing
resolvers are two-phase excitation, uni-phase output resolvers, as
shown in FIG. 3. However, the magnetic interference in a uni-phase
excitation, two-phase output multi-pole variable reluctance
resolver may be minimized such that a general purpose R/D converter
can be readily and economically utilized to process a two-phase
output signal.
[0049] Systems and methods for obtaining near-ideal Sin .theta. and
Cos .theta. waveforms in a uni-phase excitation, two-phase output
multi-pole variable reluctance resolver are provided below.
[0050] Referring to FIG. 6, an exemplary uni-phase excitation,
two-phase output resolver apparatus is provided in accordance with
one embodiment. A voltage oscillator 200 may provide a source
signal to excite the stator windings in a resolver 600 attached
onto a motor. The signal may be processed by the variable phase
shifter 300 and the amplifier 400 prior to arriving at the output
signal stabilizer 1000. Once the signal arrives at the output
signal stabilizer 1000, the signal may pass through the capacitive
resolver driving network 500 prior to reaching the resolver
600.
[0051] The capacitive resolver driving network 500 may be
implemented as a capacitor (C) network or a resistor-capacitor
(R-C) network as shown in FIGS. 7(a) and 7(b), respectively. A
network including variable resistors to implement a resolver signal
detector and adjuster 700 may be added to the output signal
stabilizer 1000, as shown in FIG. 7(c). The resolver signal
detector and adjuster 700 may output sine and cosine signals to a
resolver-to-digital (R/D) converter 100. The R/D converter 100 may
be implemented using commercially available monolithic integrated
circuits (ICs).
[0052] Referring to FIG. 7(a), in accordance with one embodiment, a
capacitive passive element (e.g., a capacitor) may be serially
connected to each coil winding of the resolver 600. Inserting the
capacitive passive element, however, may cause phase shift between
the R/D converter 100 phase reference and the R/D converter 100
input signal. In accordance with one embodiment, the variable phase
shifter 300 may be implemented to compensate for the above phase
shift.
[0053] Referring to FIG. 7(b), in accordance with one embodiment, a
resistive passive element (e.g., a resistor) may be connected in
parallel to a capacitive passive element to control the amplitude
of an output signal in an effort to improve overall
performance.
[0054] Referring back to FIG. 6, in accordance with one embodiment,
the R/D converter 100 may measure angular position from output
signals provided by the resolver 600 and make more reliable
position data using an encoder signal generator 800 and angular
position compensator 900 and a buffer amplifier. The encoder signal
generator 800 may be implemented using a general purpose processor
or a digital signal processor.
[0055] The angular position compensator 900 may compensate for
angular position measurement error as well as any additional
mechanical/electrical error by applying a linear interpolation or a
direct addition or subtraction method. The position error reference
data used by the angular position compensator 900 may be stored in
Flash memory, ROM, or EEPROM, or other type of memory.
[0056] Referring to FIG. 8, a circuit diagram of an exemplary
resolver output signal stabilizer 1000 is provided in accordance
with one embodiment. The resolver output signal stabilizer
implements a capacitive resolver driving network using a C network,
but it is possible to implement the capacitive resolver driving
network using an R-C network as provided earlier.
[0057] An output signal may processed by the resolver output signal
stabilizer according to the electrically equivalent circuit shown
in FIG. 9. The following equations may respectively be derived from
Equations (1), (2), and (3):
Ie = Is + Im + 1 R 2 + ( .omega. Ls - 1 / .omega. C ) 2 Sin (
.omega. t + .PHI. c ) ( 14 ) Ls = Lo ( 1 + m Sin .theta. ) = Lo ( 1
+ m Sin .OMEGA. t ) ( 15 ) .PHI. c = arc tan ( - .omega. Ls - 1 /
.omega. C R ) .OMEGA. : Angular Speed of Reolver Rotation Angle
.theta. , ( rad / sec ) ( 16 ) ##EQU00007##
[0058] Ls denotes the inductance of the coil, Lo denotes the
intrinsic inductance of the coil, Im denotes the sum of all
currents induced by interference flux, Ie denotes the resolver
driving current (resolver output voltage for VR type resolver), m
denotes the ratio between the intrinsic inductance and the flux
changes, R denotes the resistance to detect the output voltage,
.theta. denotes the rotation angle of resolver, Fm(.theta.) denotes
the induced current, Ve denotes the applied voltage to resolver,
and C denotes the capacitance of the passive capacitive element in
the capacitive resolver driving network.
[0059] Equations (3), (4), and (5) and Equations (14), (15), and
(16) express the steady state response for a sinusoidal AC current,
in which (.omega.Ls-(1/.omega.C)) in Equations (14) and (16) is the
non-linear and time-varying component as the resolver rotates at
angular speed .omega.. The angular speed .omega. of the source
signal is in the range of 10 kHz, while the rotating angular speed
.OMEGA. is in the range of a few hundred Hz even for high speed
applications. Therefore .OMEGA.<<.omega.,
.omega.Ls-(1/.omega.C) in Equations (14), (16) may be respectively
rewritten in terms of the angular speed of .omega. and .OMEGA. as
follows:
.omega.Ls-1/.omega.C.apprxeq..omega.Ls, (17)
.OMEGA.Ls-1/.OMEGA.C.apprxeq.-(1/.OMEGA.C), (18)
[0060] If .omega.Ls-(1/.omega.C) in Equation (14) and (16) is
replaced by Equations (17) and (18), then Equations (14) and (16)
may have the same form as Equations (1) and (3), respectively,
however 90.degree. phase difference in angular speed variation
exists due to the capacitive passive element C.
[0061] The 90.degree. phase difference calculated from the above
derivation indicates that there is 90.degree. phase difference
between the inductance variation by resolver rotation and current
variation by driving source signal. Since the current induced by
the interference flux is caused by the current of driving signal,
the interference current will be the sum of currents having
90.degree. phase difference. Therefore, when capacitive passive
element C is inserted, Equations (8) and (9) may be expressed as
provided below in Equations (19) and (20).
[0062] The interference induced current by sine winding and cosine
winding may be respectively expressed as follows:
Im=(m.sup.2*Sin .theta.*Sin(.theta.+90)), (19)
Im=(m.sup.2*Cos .theta.*Cos(.theta.+90)), (20)
[0063] Using the above equations, the currents i1, i2, i3, and i4
through each pole, Sin .theta., Sin(.theta.+180), Cos .theta., and
Cos(.theta.+180) as shown in Equations (10), (11), (12), and (13),
respectively, may be simplified as provided below in Equations (21)
through (24).
[0064] The current through Sin .theta. may be expressed as
follows:
i1=Lo(1+m Sin .theta.)+m.sup.2 Sin .theta.*Sin(.theta.+180),
(21)
[0065] The current through Sin(.theta.+180) may be expressed as
follows:
i2=Lo(1m Sin .theta.)+m.sup.2 Sin(180+.theta.)* Sin .theta.
(22)
[0066] The current through Cos .theta. may be expressed as
follows:
i3=Lo(1+m Cos .theta.)+m.sup.2 Cos .theta.*Cos(.theta.+180),
(23)
[0067] The current through Cos(.theta.+180) may be expressed as
follows:
i4=Lo(1-m Cos .theta.)+m.sup.2 Cos(.theta.+180)*Cos .theta.,
(24)
[0068] When capacitive passive element C is inserted, in accordance
with one embodiment, Equations (21), (22), (23), and (24) may be
rewritten as provided below in Equations (25) through (28).
[0069] The current through Sin .theta. when capacitive passive
element C is inserted may be expressed as follows:
i1=Lo(1+m Sin .theta.)+m.sup.2 Sin .theta.*Sin(.theta.+180+90),
(25)
[0070] The current through Sin(.theta.+180) when capacitive passive
element C is inserted may be expressed as follows:
i2=Lo(1-m Sin .theta.)+m.sup.2 Sin(180+.theta.)*Sin(.theta.+90),
(26)
[0071] The current through Cos .theta. when capacitive passive
element C is inserted may be expressed as follows:
i3=Lo(1+m Cos .theta.)+m.sup.2 Cos .theta.*Cos(.theta.+180+90),
(27)
[0072] The current through Cos(.theta.+180) when capacitive passive
element C is inserted may be expressed as follows:
i4=Lo(1-m Cos .theta.)+m.sup.2 Cos(.theta.+180)*Cos(.theta.+90),
(28)
[0073] FIGS. 10(a) and 10(b) compare the waveforms of one
embodiment with ideal waveforms and waveforms from output of an
existing resolver. FIGS. 10(a) and 10(b) show graphs of sinusoidal
waveforms (solid sharp line) both for Sin .theta. and Cos .theta.
when Lo=1 and m=0.15 in above equation on top of the ideal
sinusoidal waveform (solid bold line), in which the dotted line
waveform is the one obtained by the conventional method of without
capacitive passive element. It can be clearly seen that the Sin
.theta. or Cos .theta. waveform (solid sharp line) obtained after
connecting capacitive passive element in accordance with the
claimed subject matter is very close to the corresponding ideal
waveform (solid bold line), while conventional Sin .theta. or Cos
.theta. waveform (dotted line) is distorted from the ideal
waveform.
[0074] In FIGS. 11(a) and 11(b), Lissajous graphs are provided to
illustrate the effectiveness of the claimed subject matter. FIG.
11(a) shows the output of a uni-phase excitation, two-phase output
resolver apparatus without an R-C driving network (i.e., an
existing resolver apparatus), while FIG. 11(b) shows the output of
a uni-phase excitation, two-phase output multi-pole resolver
apparatus comprising an R-C driving network (i.e., a resolver
apparatus in accordance with the claimed subject matter).
[0075] In FIG. 11(a), the path traced by Sin .theta. and Cos
.theta. along the x-axis and y-axis, respectively, is severely
distorted. In FIG. 11(b), however, the distortion is almost
entirely removed while the orthogonality between Sin .theta. and
Cos .theta. still holds. Therefore, FIGS. 11(a) and 11(b) show that
the resolver apparatus in accordance with the claimed subject
matter is a significant improvement over the existing resolver
apparatus.
[0076] Advantageously, the resolver apparatus and methods provided
in accordance with one or more embodiments of the claimed subject
matter significantly reduce magnetic interference by directly
connecting capacitive passive elements to each winding of a
resolver. This is possible, in part, because the angular speed
.omega. of the source signal is much bigger than the rotator
angular speed SI Additionally, the capacitance of the passive
capacitive element in resolver driving network and the intrinsic
inductance Lo of resolver coil react at different angular speeds;
that is, Lo reacts dominantly at co, while C reacts dominantly at
SI Moreover, the phase of the current at C is 90.degree. apart from
that of the current at Lo, such that magnetic interference is
orthogonal. Due to this orthogonal property, the magnetic
interference in the resolver is greatly reduced as shown in FIGS.
10(a), 10(b), and 11(b). Even the minor phase error shown in FIG.
10(a) or 10(b) may be easily compensated by the angular position
compensator 900 provided above with reference to FIG. 6.
[0077] In addition to achieving high accuracy, the resolver
apparatus and methods provided in accordance with one or more
embodiments of the claimed subject matter also achieve high
resolution. For example, a resolver with 100 poles, in accordance
with one embodiment, may achieve as many as 6,553,600 divisions per
revolution using the methods provided above, which is more than
65,000 times the number of poles. That is, the resolver may achieve
a multiplication factor of more than 65,000. Compared with the less
than 5,000 multiplication factor achieved by existing practical
interpolation conversion methods, the resolver in accordance with
the claimed subject matter improves resolution by at least more
than an order of magnitude.
[0078] Further, the resolver apparatus and methods provided in
accordance with one or more embodiments of the claimed subject
matter achieve improved performance at an economic cost. For
example, a resolver apparatus may be implemented using a
cost-effective general purpose R/D converter that is configured for
high-speed hardware processing, which may reduce the amount of
software processing time required to determine a digital
position.
[0079] The claimed subject matter has been described above with
reference to one or more features or embodiments. Those skilled in
the art will recognize, however, that changes and modifications may
be made to these embodiments without departing from the scope of
the claimed subject matter. These and various other adaptations and
combinations of the embodiments disclosed are within the scope of
the claimed subject matter as defined by the claims and their full
scope of equivalents.
* * * * *