U.S. patent application number 10/442440 was filed with the patent office on 2004-11-25 for method and apparatus for reducing sampling related errors in a modulating waveform generator used with a pwm controller.
Invention is credited to Kerkman, Russel J., Seibel, Brian J..
Application Number | 20040232902 10/442440 |
Document ID | / |
Family ID | 33097981 |
Filed Date | 2004-11-25 |
United States Patent
Application |
20040232902 |
Kind Code |
A1 |
Seibel, Brian J. ; et
al. |
November 25, 2004 |
METHOD AND APPARATUS FOR REDUCING SAMPLING RELATED ERRORS IN A
MODULATING WAVEFORM GENERATOR USED WITH A PWM CONTROLLER
Abstract
A method and apparatus for use with a controller that samples a
command frequency and provides modulating waveforms to a PWM
inverter as a function of the sampled command frequency, the
inverter also receiving a carrier signal having a carrier
frequency, the method for reducing distortions in the modulating
waveforms that result from sampling characteristics of the
controller, the method comprising the steps of sampling the command
frequency at a sampling frequency to generate a series of sampled
signals, integrating the sampled signals to generate a phase angle,
identifying a correction angle as a function of the sampling
frequency, adding the correction angle to the phase angle to
generate a corrected phase angle and using the corrected phase
angle to generate the modulating waveforms to be provided to the
PWM inverter.
Inventors: |
Seibel, Brian J.; (Grafton,
WI) ; Kerkman, Russel J.; (Milwaukee, WI) |
Correspondence
Address: |
Susan M. Donahue
Rockwell Automation Inc., 704-P
1201 South Second Street
Milwaukee
WI
53204
US
|
Family ID: |
33097981 |
Appl. No.: |
10/442440 |
Filed: |
May 21, 2003 |
Current U.S.
Class: |
323/284 |
Current CPC
Class: |
H02M 7/53873 20130101;
H02M 7/53875 20130101; H02P 27/08 20130101 |
Class at
Publication: |
323/284 |
International
Class: |
G05F 001/40 |
Claims
What is claimed is:
1. A method for use with a controller that samples a command
frequency and provides modulating waveforms to a PWM inverter as a
function of the sampled command frequency, the inverter also
receiving a carrier signal having a carrier frequency, the method
for reducing distortions in the modulating waveforms that result
from sampling characteristics of the controller, the method
comprising the steps of: sampling the command frequency at a
sampling frequency to generate a series of sampled signals;
integrating the sampled signals to generate a phase angle;
identifying a correction angle as a function of the sampling
frequency; adding the correction angle to the phase angle to
generate a corrected phase angle; and using the corrected phase
angle to generate the modulating waveforms to be provided to the
PWM inverter.
2. The method of claim 1 wherein the step of identifying a
correction angle includes identifying the correction angle as a
function of both the sampling frequency and the command
frequency.
3. The method of claim 2 wherein the step of identifying a
correction angle includes identifying the correction angle as a
function of the ratio of the command frequency to the sampling
frequency.
4. The method of claim 3 wherein the step of identifying a
correction angle .delta. includes solving the following
equation:.delta.=.omega..sub- .eT.sub.s/2where .omega..sub.e is the
command frequency in radians/second and T.sub.s is the sampling
period.
5. The method of claim 4 wherein the sampling frequency is
identical to the carrier frequency.
6. The method of claim 4 wherein the sampling frequency is twice
the carrier frequency.
7. The method of claim 1 wherein the sampling frequency is
identical to the carrier frequency.
8. The method of claim 1 wherein the sampling frequency is twice
the carrier frequency.
9. The method of claim 1 wherein the step of using the corrected
phase angle to generate the modulating waveforms includes the steps
of: receiving two synchronous voltage command signals;
mathematically combining the voltage command signals and the
corrected phase angle to generate two phase corrected voltage
command signals in the stationary frame of reference; and
converting the two phase corrected voltage command signals to three
phase command signals.
10. The method of claim 9 further including the step of identifying
a voltage magnitude correction value as a function of the sampling
frequency and wherein the step of mathematically combining the
voltage command signals and the corrected phase angle includes
combining the voltage command signals, the corrected phase angle
and the voltage magnitude correction value.
11. The method of claim 10 wherein the step of combining the
voltage command signals, the corrected phase angle and the voltage
magnitude correction value includes the steps of: multiplying the
voltage magnitude correction value by the two synchronous voltage
command signals to generate the corrected two voltage command
signals; performing a stationary to synchronous conversion on the
corrected phase angle to generate a two by two stationary matrix;
and multiplying the corrected two phase voltage command signals by
the two by two stationary matrix to generate the two phase
corrected voltage command signals in the stationary frame of
reference.
12. The method of claim 10 wherein the step of identifying a
voltage magnitude correction value as a function of the sampling
frequency includes the step of identifying a voltage magnitude
correction value as a function of both the sampling frequency and
the command frequency.
13. The method of claim 12 wherein the step of identifying a
voltage correction magnitude value V.sub.corr includes the step of
solving the following equation: 4 V corr = 1 sin c ( e T s / 2 )
where .omega..sub.e is the command frequency in radians/second and
T.sub.s is the sampling period.
14. A method for use with a controller that samples a command
frequency and receives two phase synchronous command voltages and
provides modulating waveforms to a PWM inverter as a function of
the sampled command frequency and command voltages, the inverter
also receiving a carrier signal having a carrier frequency, the
method for reducing distortions in the modulating waveforms that
result from sampling characteristics of the controller, the method
comprising the steps of: sampling the command frequency at a
sampling frequency to generate a series of sampled signals;
integrating the sampled signals to generate a phase angle;
modifying the phase angle as a function of the ratio of the
operating frequency to the sampling frequency to generate a
corrected phase angle; modifying the two phase command voltages as
a function of the ratio of the operating frequency to the sampling
frequency to generate corrected two phase voltage command signals;
mathematically combining the corrected two phase voltage command
signals and the corrected phase angle to generate two phase voltage
command signals in a stationary frame of reference; and converting
the two phase voltage command signals in the stationary frame of
reference to three phase signals to be provided to the PWM
inverter.
15. The method of claim 14 wherein the step of modifying the phase
angle includes solving the following equation to identify a
correction angle:.delta.=.omega..sub.eT.sub.s/2and adding the
correction angle to the phase angle and wherein the step of
modifying the two phase command voltages includes the step of
solving the following equation to identify a voltage magnitude
correction value Vcorr: 5 V corr = 1 sin c ( e T s / 2 ) and
multiplying the voltage magnitude correction value V.sub.corr by
the two phase command voltages, where .omega..sub.e is the command
frequency in radians/second and T.sub.s is the sampling period.
16. A controller that receives a command frequency and provides
modulating waveforms to a PWM inverter as a function of the command
frequency, the inverter also receiving a carrier signal having a
carrier frequency, the controller for reducing distortions in the
modulating waveforms that result from sampling characteristics of
the controller, the controller comprising: a sampler for sampling
the command frequency at a sampling frequency to generate a series
of sampled signals; an integrator for integrating the sampled
signals to generate a phase angle; a correction angle determiner
for identifying a correction angle as a function of the sampling
frequency; a summer for adding the correction angle to the phase
angle to generate a corrected phase angle; and a processor using
the corrected phase angle to generate the modulating waveforms to
be provided to the PWM inverter.
17. The apparatus of claim 16 wherein the step of identifying a
correction angle includes identifying the correction angle as a
function of both the sampling frequency and the command
frequency.
18. The apparatus of claim 17 wherein the correction angle
determiner identifies a correction angle by identifying the
correction angle as a function of the ratio of the command
frequency to the sampling frequency.
19. The apparatus of claim 18 wherein the correction angle
determiner identifies a correction angle .delta. by solving the
following equation:.delta.=.omega..sub.eT.sub.s/2where
.omega..sub.e is the command frequency in radians/second and
T.sub.s is the sampling period.
20. The apparatus of claim 19 wherein the sampling frequency is
identical to the carrier frequency.
21. The apparatus of claim 16 wherein the sampling frequency is
identical to the carrier frequency.
22. The apparatus of claim 16 wherein the processor receives two
phase synchronous voltage command signals and includes a combiner
that mathematically combines the voltage command signals and the
corrected phase angle to generate two phase corrected voltage
command signals in the stationary frame of reference and a
converter that converts the two phase corrected voltage command
signals to three phase command signals.
23. The apparatus of claim 22 further including a voltage magnitude
correction value determiner for identifying a voltage magnitude
correction value as a function of the sampling frequency and
wherein the combiner mathematically combines the voltage command
signals, the corrected phase angle and the voltage magnitude
correction value.
24. The apparatus of claim 23 wherein the combiner includes a
multiplier that multiplies the voltage magnitude correction value
by the two phase synchronous voltage command signals to generate
corrected two phase voltage command signals, a stationary to
synchronous converter that performs a stationary to synchronous
conversion on the corrected phase angle to generate a two by two
stationary matrix and a multiplier that multiplies the corrected
two phase voltage command signals by the two by two stationary
matrix to generate the two phase corrected voltage command signals
in the stationary frame of reference.
25. The apparatus of claim 23 wherein the voltage magnitude
correction value determiner identifies a voltage correction
magnitude value Vcorr by solving the following equation: 6 V corr =
1 sin c ( e T s / 2 ) where .omega..sub.e is the command frequency
in radians/second and T.sub.s is the sampling period.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] Not applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] Not applicable.
BACKGROUND OF THE INVENTION
[0003] The field of the invention is pulse width modulated (PWM)
controllers and more specifically a method and apparatus for
modifying modulating signals as a function of a carrier frequency
and/or an electrical operating frequency to minimize sampling
related errors in phase shift and magnitude.
[0004] One type of commonly designed induction motor is a three
phase motor having three Y-connected stator windings. In this type
of motor, each stator winding is connected to an AC voltage source
by a separate supply line, the source generating currents therein.
Often, an adjustable speed drive (ASD) will be positioned between
the voltage source and the motor to control motor speed.
[0005] Many ASD configurations include a PWM inverter consisting of
a plurality of switching devices and a controller for controlling
the inverter. Referring to FIG. 1, an exemplary inverter 9 has six
switches 12-17. The switches 12-17 are arranged in series pairs
between positive and negative DC buses 48 and 49, each pair forming
one of three inverter legs 39, 40, and 41. Each switch includes a
high speed semiconductor switching device in inverse parallel
relationship with a diode. For example, diode 23 is associated with
switch 12. Similarly, diodes 25, 27, 24, 26 and 28 are associated
with switches 14, 16, 13, 15 and 17, respectively.
[0006] A controller 11 is linked to each switch by a separate
control line. For example, controller 11 is linked to switch 12 via
line 51. Similarly, controller 11 is linked to switches 13, 14, 15,
16 and 17 via lines 52, 53, 54, 55 and 56, respectively. Controller
11 controls the on and off cycles of the switches 12-17 via lines
51-56.
[0007] Referring still to FIG. 1, each leg 39, 40 and 41 is linked
to a separate one of three motor terminals 31, 30 32, respectively.
Referring specifically to leg 39, by triggering switches 12, 13 on
and off in a repetitive sequence, terminal 31 and winding 36 linked
to leg 39 receives high frequency DC voltage pulses. Similarly,
each of legs 40 and 41 are controlled to provide pulses to
associated terminals 30 and 32 and hence to windings 35 and 37.
[0008] Referring to FIG. 2, an exemplary sequence of high frequency
voltage pulses 60 that inverter 9 might provide to terminal 31 can
be observed along with an exemplary low frequency alternating
fundamental voltage 62 and related alternating current 69. By
varying the widths of positive portions 63 of each high frequency
pulse relative to the widths of negative portions 64 over a series
of high frequency voltage pulses 60, a changing average voltage
which alternates sinusoidally is generated. The changing average
voltage defines the low frequency alternating voltage 62 that
drives motor 19. Low frequency alternating voltage 62 in turn
produces low frequency alternating current 69 that lags the voltage
by a phase angle .PHI.. By triggering switches 12 and 13 in a
regulated sequence, inverter 9 is used to control both the
amplitude and frequency of voltage 62 that eventually reach the
stator windings (e.g., 36).
[0009] Referring to FIG. 3a, representative waveforms used to
generate trigger signals for leg 39 are illustrated. As well known
in the art, a carrier signal or waveform 67 is perfectly periodic
and operates at what is known as a carrier frequency f.sub.c. A
command or modulating voltage waveform 68 is sinusoidal, having a
much lower frequency f.sub.e and a greater period than carrier
signal 67.
[0010] Referring also to FIGS. 3b and 3c, an upper trigger signal
72 and a lower trigger signal 74 corresponding to a comparison of
waveforms 67 and 68 and for controlling the upper and lower
switches 12, 13, respectively, can be observed. The turn-on
t.sub.u1, t.sub.u2 and turn-off t.sub.o1, t.sub.o2 trigger times of
the upper and lower signals 72, 74 come from the intersections of
command waveform 68 and carrier waveform 67.
[0011] When command waveform 68 intersects carrier waveform 67
while carrier waveform 67 has a positive slope (i.e. during periods
T.sub.p), upper signal 72 goes OFF and lower signal 74 goes ON.
When command waveform 68 intersects carrier waveform 67 while
carrier waveform 67 has a negative slope (i.e. during periods
T.sub.n), upper signal 72 goes ON and lower signal 74 goes OFF.
Thus, by comparing carrier waveform 67 to command waveform 68,
trigger times are determined.
[0012] Early control systems operated using only a single carrier
signal frequency which, at the time, addressed most application
requirements and was suitable given inverter switching limitations.
As switching technology has evolved, however, much higher switching
speeds have been realized and hence a much greater range of carrier
signal frequencies are now available. With control system evolution
it has been recognized that carrier signal frequency can have
various advantageous and disadvantageous affects on system control
and that, therefore, different carrier frequencies are ideal for
different applications. For example, harmonic content in a PWM
system has been known to generate audible noise in certain
applications. The harmonic content in a PWM system can be altered
to some degree by altering the carrier frequency and hence audible
noise can typically be tuned out of a system via carrier frequency
changes.
[0013] As another example, increased carrier frequency sometimes
results in reflected voltages that have been known to damage system
cabling and/or motor windings (see U.S. Pat. No. 5,831,410 titled
"Apparatus used with AC motors for eliminating line voltage
reflections" which issued on Feb. 12, 1997 for a detailed
explanation of reflected waves). As one other example, when carrier
frequencies are increased the number of switching cycles are
similarly increased and overall switching losses (e.g., switching
losses occur during each switching cycle) and system heating are
also increased. As yet another example, as carrier frequency is
increased ripple current in the resulting waveforms is reduced
appreciably. Thus there are tradeoffs that have to be understood
and accounted for when selecting carrier frequency for specific
system configurations and applications.
[0014] There are many systems today that allow carrier frequency to
be altered to address application specific requirements. In
addition, there are several applications where carrier frequency is
altered on the fly as a function of other operating parameters and
intended control requirements. For one example of an application
where carrier frequency is altered on the fly, see U.S. patent
application Ser. No. 09/956,781 titled "Method and Apparatus for
Compensating for Device Dynamics by Adjusting Inverter Carrier
Frequency" which was filed on Sep. 20, 2001 and which is commonly
owned with the present invention.
[0015] Unfortunately, under certain circumstances, on the fly
carrier frequency changes have been known to cause system
disturbances. To this end, FIG. 4 illustrates an exemplary q-axis
torque producing current I.sub.qe and a resulting single phase
current I.sub.ws where a carrier frequency f.sub.c is altered at
time .tau..sub.1 from 3 KHz to 4 KHz. As illustrated, when the
carrier frequency is altered at time .tau..sub.1, a noticeable
current disturbance occurs which shows up in single phase current
I.sub.ws most noticeably as a magnitude change. Although less
noticeable, a phase change also occurs at time .tau..sub.1.
[0016] Disturbances like the one illustrated in FIG. 4 occur
because of the way in which modulating waveforms are generated for
comparison to carrier signals. In this regard, an exemplary
modulating waveform generator 200 is illustrated in FIG. 5. The
generator 200 receives a command frequency signal .omega..sub.e in
radians/second and two phase synchronous d and q-axis command
voltage signals V.sub.qe and V.sub.de (e.g., from a synchronous
current frame regulator) and uses those signals to generate three
phase modulating waveforms for use by a PWM inverter (see 217). To
this end, generator 200 includes a sampler 202, an integrator 204,
a synchronous to stationary transformer 206, a multiplier 208, a
two-to-three phase converter 210 and a carrier frequency selector
211. Although illustrated in FIG. 5, carrier signal generator 213
and PWM inverter 217 are not part of the modulating waveform
generator.
[0017] As its label implies, carrier frequency selector 211 is used
to select the carrier frequency f.sub.c either manually or, in the
case of more sophisticated systems, automatically, as a function of
sensed system operating parameters (e.g., component temperatures,
sensed ripple/harmonics, etc.). The carrier frequency f.sub.c is
provided to each of carrier signal generator 213 and sampler 202.
Signal generator 213 uses frequency f.sub.c to generate a high
frequency carrier signal (e.g., 67 in FIG. 3a) that is provided to
inverter 217 for comparison as described above.
[0018] In the embodiment described here, it is assumed that sampler
202 is programmed to sample the command frequency .omega..sub.e
once per carrier period. Thus, the sampling frequency f.sub.s is
equal to the carrier frequency f.sub.c and sampler 202 samples
frequency .omega..sub.e every period T.sub.s where period
T.sub.s=1/f.sub.c. The sampled values are provided to integrator
204 which outputs the integrated value as a phase angle
.theta..sub.e. The integrator output is a stepped signal as
illustrated at 212 where the output value changes every sampling
period T.sub.s.
[0019] Stepped phase angle signal .theta..sub.e is provided to
synchronous to stationary converter 206 which generates a 2.times.2
matrix 219 of values in the stationary frame of reference. The two
phase synchronous voltages V.sub.qe and V.sub.de form a 2.times.1
matrix 221 and are multiplied by 2.times.2 matrix 219 thereby
generating two phase stationary frame voltage command values 223
(see also 229 ). Converter 210 converts the two phase stationary
frame voltage command values to three phase modulating signals that
are in turn provided to PWM inverter 217 for comparison to the
carrier signal.
[0020] Referring to FIG. 6, an exemplary ideal fundamental
modulating waveform 68 is illustrated along with a sampled or
discretized modulating waveform signal 91 that may be produced by
multiplier 208 illustrated in FIG. 5. Waveform 68 corresponds to a
waveform that would result if the sampling period T.sub.s was a
zero or near zero duration.
[0021] Referring also to FIG. 7, a small segment of waveform 68 is
illustrated along with two separate associated discretized or
sampled waveform signals 91 and 93 where the sampled signals
correspond to different sampling frequencies. Sampled signal 91
corresponds to a 4 kHz sampling frequency while signal 93
corresponds to an 8 kHz sampling frequency. In addition to
waveforms 68, 91 and 93, FIG. 7 also illustrates separate
fundamental components of modulating waveforms associated with
sampled signals 91 and 93. In FIG. 7, fundamental component 95
corresponds to the 4 kHz sampling signal 91 while fundamental
components 97 corresponds to the 8 kHz sampling signal 93.
[0022] A simple analysis of FIG. 7 makes clear that the fundamental
component of a modulating waveform generated using sampled values
of the command frequency .omega..sub.e is phase shifted by an error
angle. In FIG. 7, the phase shift error corresponding to
fundamental component 95 is identified as .DELTA..sub.1 while the
error corresponding to fundamental component 97 is identified as
.DELTA..sub.2. In addition, although not easily observable in
either of FIGS. 6 or 7, the fundamental components 95 and 97
associated with sampled signals 91 and 93 have lower magnitudes
than ideal waveform 68.
[0023] While existing commutation algorithms have been developed to
compensate for processing delays intrinsic in any electronic
components, these algorithms generally do not contemplate
compensating for distortion due to sampler related phase and
magnitude errors. In many applications where carrier to operating
frequency ratios are much greater than unity these commutation
algorithms provide suitable results. Unfortunately reflected wave
requirements, thermal regulation algorithms and wide speed
operation render the great than unity ratio assumption questionable
at best.
[0024] While reduced modulating waveform magnitudes and phase
shifts from ideal waveforms are problematic generally, the affects
of these errors on load control are most pronounced when operating
frequency or carrier frequency changes occur (see again FIG. 4
where carrier frequency was altered at time .tau..sub.1). Referring
again to FIG. 7, as described above, when the carrier frequency
f.sub.c and hence the sampling frequency f.sub.s is 8 kHz, the
resulting modulating waveform has a fundamental component 97 and
when the carrier and sampling frequency f.sub.s are 4 kHz, the
resulting modulating waveform has a fundamental component 95. Thus,
a carrier frequency change from 8 to 4 kHz or from 4 to 8 kHz
results in a fundamental component phase shift identified as
.DELTA..sub.3 in FIG. 7. Similar phase shifts occur when other
carrier frequency changes occur. While errors occur in the
resulting fundamental components as illustrated in FIG. 7, it
should be appreciated that distortions occur in other harmonics in
the resulting waveforms and should to be corrected.
[0025] Thus, there is a need for a controller that can accurately
compensate for distortions that occur when carrier frequency used
with a PWM controller is altered and to essentially eliminate
sampling related phase and magnitude errors.
BRIEF SUMMARY OF THE INVENTION
[0026] It has been recognized that the magnitude of the error that
results from the sampling/discretizing process is a function of the
ratio of the carrier frequency f.sub.c to the electrical operating
frequency f.sub.e. In this regard, experiments have shown that when
the ratio of carrier frequency f.sub.c to operating frequency
f.sub.e is large, the magnitude of the phase error resulting
therefrom is relatively small and when the ratio is relatively
small the magnitude of the phase error resulting therefrom is
relatively large. Similarly, when ratio f.sub.c/f.sub.e is small,
the phase distortion that results from a carrier/sampling frequency
change is appreciable. Thus, in at least some embodiments of the
invention, phase correction is facilitated by tying a correction
angle to the carrier or sampling frequency or to the ratio of the
carrier frequency to the operating frequency.
[0027] It has also been recognized that the magnitude error in a
modulating waveform generated through sampling is also related to
the carrier frequency/operating frequency ratio. Thus, in at least
some embodiments of the invention, in addition to a phase
correction operation, inventive systems also implement a magnitude
correction operation where the magnitude correction is a function
of the operating and carrier frequencies.
[0028] Consistent with the above, the invention includes a method
for use with a controller that samples a command frequency and
provides modulating waveforms to a PWM inverter as a function of
the sampled command frequency, the inverter also receiving a
carrier signal having a carrier frequency, the method for reducing
distortions in the modulating waveforms that result from sampling
characteristics of the controller, the method comprising the steps
of sampling the command frequency at a sampling frequency to
generate a series of sampled signals, integrating the sampled
signals to generate a phase angle, identifying a correction angle
as a function of the sampling frequency, adding the correction
angle to the phase angle to generate a corrected phase angle and
using the corrected phase angle to generate the modulating
waveforms to be provided to the PWM inverter.
[0029] In some embodiments the step of identifying a correction
angle includes identifying the correction angle as a function of
both the sampling frequency and the command frequency. More
specifically, the step of identifying a correction angle may
include identifying the correction angle as a function of the ratio
of the command frequency to the sampling frequency. Even more
specifically, the step of identifying a correction angle d may
include solving the following equation:
.delta.=.omega..sub.eT.sub.s/2
[0030] where .omega..sub.e is the command frequency in
radians/second and T.sub.s is the sampling period.
[0031] In some cases the step of using the corrected phase angle to
generate the modulating waveforms includes the steps of receiving
two phase synchronous voltage command signals, mathematically
combining the voltage command signals and the corrected phase angle
to generate two phase corrected voltage command signals in the
stationary frame of reference and converting the two phase
corrected voltage command signals to three phase command
signals.
[0032] Some embodiments further include the step of identifying a
voltage magnitude correction value as a function of the sampling
frequency and the step of mathematically combining the voltage
command signals and the corrected phase angle may include combining
the voltage command signals, the corrected phase angle and the
voltage magnitude correction value. Here, the step of combining the
voltage command signals, the corrected phase angle and the voltage
magnitude correction value may include the steps of multiplying the
voltage magnitude correction value by the two phase synchronous
voltage command signals to generate corrected two phase voltage
command signals, performing a stationary to synchronous conversion
on the corrected phase angle to generate a two by two stationary
matrix and multiplying the corrected two phase voltage command
signals by the two by two stationary matrix to generate the two
phase corrected voltage command signals in the stationary frame of
reference.
[0033] The step of identifying a voltage magnitude correction value
as a function of the sampling frequency may include the step of
identifying a voltage magnitude correction value as a function of
both the sampling frequency and the command frequency. More
specifically, the step of identifying a voltage correction
magnitude value Vcorr may include the step of solving the following
equation: 1 V corr = 1 sin c ( e T s / 2 )
[0034] The invention also includes a method for use with a
controller that samples a command frequency and receives two phase
synchronous command voltages and provides modulating waveforms to a
PWM inverter as a function of the sampled command frequency and
command voltages, the inverter also receiving a carrier signal
having a carrier frequency, the method for reducing distortions in
the modulating waveforms that result from sampling characteristics
of the controller, the method comprising the steps of sampling the
command frequency at a sampling frequency to generate a series of
sampled signals, integrating the sampled signals to operating
frequency to the sampling frequency to generate a corrected phase
angle, modifying the two phase command voltages as a function of
the ratio of the operating frequency to the sampling frequency to
generate corrected two phase voltage command signals,
mathematically combining the corrected two phase voltage command
signals and the corrected phase angle to generate two phase voltage
command signals in a stationary frame of reference and converting
the two phase voltage command signals in the stationary frame of
reference to three phase signals to be provided to the PWM
inverter.
[0035] Moreover, the invention includes a controller that receives
a command frequency and provides modulating waveforms to a PWM
inverter as a function of the command frequency, the inverter also
receiving a carrier signal having a carrier frequency, the
controller for reducing distortions in the modulating waveforms
that result from sampling characteristics of the controller, the
controller comprising a sampler for sampling the command frequency
at a sampling frequency to generate a series of sampled signals, an
integrator for integrating the sampled signals to generate a phase
angle, a correction angle determiner for identifying a correction
angle as a function of the sampling frequency, a summer for adding
the correction angle to the phase angle to generate a corrected
phase angle and a processor using the corrected phase angle to
generate the modulating waveforms to be provided to the PWM
inverter.
[0036] These and other objects, advantages and aspects of the
invention will become apparent from the following description. In
the description, reference is made to the accompanying drawings
which form a part hereof, and in which there is shown a preferred
embodiment of the invention. Such embodiment does not necessarily
represent the full scope of the invention and reference is made
therefore, to the claims herein for interpreting the scope of the
invention.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0037] FIG. 1 is a schematic diagram of a controller and a PWM
inverter which incorporates the present invention;
[0038] FIG. 2 is a graph illustrating high frequency pulses and a
resulting low frequency alternating voltage applied to a stator
winding by a PWM inverter;
[0039] FIG. 3a is a graph illustrating exemplary waveforms used by
a PWM inverter to produce the high frequency pulses shown in FIG.
2, FIG. 3b and FIG. 3c are graphs illustrating PWM trigger
signals;
[0040] FIG. 4 is a plot illustrating various current waveforms;
[0041] FIG. 5 is a schematic illustrating a modulating wave
generator;
[0042] FIG. 6 is a plot illustrating an ideal modulating waveform
and a sampled or discretized modulating waveform that results from
a sampling process performed by the generator of FIG. 5;
[0043] FIG. 7 is a graph similar to FIG. 6, albeit illustrating a
smaller section of the waveforms of FIG. 6 and illustrating sampled
waveforms corresponding to two different sampling frequencies;
[0044] FIG. 8 is an equivalent schematic of the waveform generator
of FIG. 5;
[0045] FIG. 9 is an equivalent schematic of the waveform generator
of FIG. 8;
[0046] FIG. 10 is an equivalent representation of the waveform
generator of FIG. 9, albeit in the frequency domain;
[0047] FIG. 11 is a magnitude plot of errors that result from
operation of the generator illustrated in FIG. 5 at various command
frequencies and at two different carrier frequencies;
[0048] FIG. 12 is a phase error plot generated using the waveform
generator of FIG. 5 and corresponding to various operating
frequencies and two different carrier frequencies;
[0049] FIG. 13 is a schematic diagram similar to the diagram of
FIG. 5, albeit incorporating the present invention;
[0050] FIG. 14 includes two different plots, each of the plots
illustrating an ideal modulating waveform and a sampled or
discretized modulating waveform generated via the inventive
waveform generator illustrated in FIG. 13;
[0051] FIG. 15 is a plot similar to FIG. 7, albeit illustrating an
ideal modulating waveform and a discretized waveform associated
with an integer high to low carrier change with the inventive
compensation system activated; and
[0052] FIG. 16 is a plot similar to FIG. 15, albeit illustrating
waveforms associated with a low to high non-integer carrier change
with the inventive compensation system activated.
DETAILED DESCRIPTION OF THE INVENTION
A. Theory
[0053] To correct for the sampling related phase and magnitude
distortions as described above, first, the source of the errors has
to be determined and then the error magnitudes have to be quantized
and tied to some determinable operating parameters. In order to
study the source and magnitudes of the phase and magnitude errors,
exemplary modulating waveform generator 200 (see again FIG. 5) can
be represented in a complimentary form in the frequency domain.
[0054] Referring to FIGS. 5 and 8, the sampler 202 and integrator
204 of FIG. 5 can be replaced by an equivalent combination
including an integrator 212, an ideal sampler 214 and a zero order
hold (ZOH) block 216 (e.g., the well known sinc function). In FIG.
8 components 206, 208, 210, 211, 213 and 217 are identical to
similarly labeled components in FIG. 5. Referring also to FIG. 9,
sampler 214 and ZOH block 216 can be moved to the right of the
vector product operation corresponding to block 208 to configure
equivalent time domain configuration 221.
[0055] Configuration 221 of FIG. 9 can be represented in the
frequency domain by the schematic illustrated in FIG. 10 which
shows how the modulating waveform generating process evolves in the
frequency domain. To this end, the two phase modulating signals
which include sine wave pulses are convolved by convolver 222 with
the ideal sampler which is represented by an infinite series of
impulses to generate an infinite series of impulses that are
provided to multiplier 224. Here, note that multiplication in the
time domain corresponds to convolution in the frequency domain.
[0056] The infinite series of impulses are next multiplied by the
ZOH function at block 224--the process represented by block 224 is
not a convolution since the ZOH operation is a convolution in the
time domain. The output of block 224 is an infinite number of
impulses modulated by the sinc function decreasing in amplitude and
increasing phase shift with increasing frequency. The fact that the
amplitude decreases with increasing frequency indicates that the
disturbances in the modulating waveform that occur when changing
the carrier frequency on the fly are associated closely with ZOH
multiplier block 216 (see again FIG. 9).
[0057] To quantify the ZOH related disturbances, magnitude and
phase plots of errors can be generated. To this end, assume
sampling and carrier frequencies that are identical (e.g., 2 kHz)
so that the PWM registers are updated once per carrier cycle. Here,
the frequency spectrum of sampled modulating signals used to
perform a duty cycle conversion will be the composite signal at the
output of the ZOH block (FIGS. 9 and 10). The magnitude of the
output signal (FIG. 10) is the product of the sampled modulating
signal and the magnitude response of the ZOH. The phase of the
output signal is the sum of the modulating signal phase and the
phase of the ZOH.
[0058] Consistent with the above discussion, error magnitude and
phase plots, FIGS. 11 and 12, respectively, have been generated for
various command frequencies and carrier/sampling frequencies so
that a visual representation of the errors can be examined. In
FIGS. 11 and 12, plots are provided for 1 KHz and 2 KHz sampling
frequencies and for a range of command operating frequencies.
[00581 Referring to FIGS. 11 and 12, some general observations can
be made. First, with high carrier frequencies, the errors
corresponding to operating frequencies within the typical range of
OHz 400 Hz are negligible. Second, the phase shift illustrated in
FIG. 12 is linear and follows the classical sinc function. Third,
low carrier frequencies f.sub.c or higher operating frequencies
f.sub.e (low f.sub.c/f.sub.e ratios) produce a disturbance in
magnitude of the signal provided to the PWM inverter and ultimately
to the output of the PWM inverter. Fourth, the magnitude of the
distortions is related to the ratio f.sub.c/f.sub.e such that, as
ratio f.sub.c/f.sub.e is decreased, the magnitude of the
distortions is increased.
[0059] Thus, in general, phase shift and magnitude errors due to
sampling characteristics can be compensated by generating
correction signals that are a function of the sampling period
f.sub.s. More specifically, the correction values should be made a
function of both the sampling period f.sub.s and the commanded
operating frequency f.sub.e.
[0060] Here, in at least one embodiment of the invention, a phase
correction angle .delta. to be added to the synchronous frame angle
.theta..sub.e can be generated by executing the following
equation:
.delta.=.omega..sub.sT.sub.c/2 (1)
[0061] Period T.sub.s=1/f.sub.s=1/f.sub.c and therefore Equation 1
can be rewritten as: 2 = e 2 f s ( 2 )
[0062] Examining Equation 2, it can be appreciated that the
magnitude of correction angle .delta. is tied to the ratio of
f.sub.c/f.sub.e such that when ratio f.sub.c/f.sub.e is low and
hence greater phase distortion can be anticipated, Equation 2
yields a relatively larger correction angle .delta. and, when ratio
f.sub.c/f.sub.e is relatively high and hence relatively less phase
distortion can be anticipated, Equation 2 yields a smaller relative
correction angle .delta.. To this end, assuming a constant command
frequency .omega..sub.e, if a sampling frequency f.sub.s (i.e.,
f.sub.c) is 8 kHz, the correction angle .delta. will be less than
if the sampling frequency f.sub.s is 4 kHz. Referring again to FIG.
7, distortion .DELTA..sub.2 corresponding to an 8 kHz sampling
frequency is smaller phase distortion .DELTA..sub.1 corresponding
to a 4 kHz sampling frequency (e.g., the difference is
.DELTA..sub.3) and therefore Equation 2 results in the appropriate
relative correction.
[0063] The magnitude distortion can be compensated by multiplying
the two phase synchronous frame voltage values V.sub.qe and
V.sub.de by a correction voltage value Vcorr determined by solving
the following equation: 3 V corr = 1 sin c ( e T s / 2 ) ( 3 )
B. Implementation of Correction
[0064] FIG. 13 is a schematic similar to the schematic of FIG. 5
except that correction hardware consistent with at least one
embodiment of the invention has been added. Components in FIG. 13
that are similar to the components of FIG. 5 are identified by
identical numbers. In addition to the components of FIG. 5, the
embodiment of FIG. 13 includes phase and magnitude error
determiners 230 and 232, respectively, a summer 234 and a
multiplier 236. Determiner 230 receives each of the command
frequency and the carrier frequency (e.g., the sampling frequency
in a once per carrier cycle sampling system) and uses those values
to solve Equation 1 above (e.g., T.sub.s=1/f.sub.s=1/f.sub.c).
Similarly, determiner 232 receives each of the command operating
frequency and the carrier frequency and uses those values to solve
Equation 3 above. The 6 and Vcorr values are provided to summer 234
and multiplier 236, respectively.
[0065] As in the case of FIG. 5, sampler 202 samples command
frequency .omega..sub.e once per sampling period and provides the
sampled values to integrator 204. Integrator 204 integrates the
received signals and provides a phase angle output .theta..sub.e to
summer 234. Summer 234 adds correction angle .delta. to phase angle
.theta..sub.e and thereby generates a corrected phase angle which
is provided to synchronous to stationary converter 206. Converter
206 transforms the corrected phase angle to a 2.times.2 matrix in
the stationary frame of reference which is provided to multiplier
208.
[0066] Multiplier 236 multiplies corrected voltage value Vcorr and
the two phase voltage value V.sub.qe and V.sub.de to generate
corrected two phase voltage values that are provided as a 2.times.1
matrix to multiplier 208. Multiplier 208 multiplies the received
values thereby generating corrected two phase stationary d and q
axis command voltages V.sub.ds and V.sub.qs that are provided to
converter 210 for two-to-three phase transformation. The output of
converter 210 is provided to PWM inverter 217.
[0067] C. Experimental Results
[0068] A simple verification of the correction is possible by
examining the fundamental component of a sampled command signal
generated using the configuration of FIG. 13 and using operating
parameters identical to those used to generate the waveforms of
FIG. 6. FIG. 14 illustrates the results of this examination and
includes an ideal modulating waveform 68 and a sampled waveform 240
that is generated by the waveform generator of FIG. 13. As
illustrated, when the present invention is employed, the
fundamental component of the modulating waveform generated using
the stepped sampled waveform 240 is in phase with the ideal
modulating waveform.
[0069] The correction concepts described above facilitate
essentially distortion free high to low or low to high carrier
frequency changes. In addition, the concepts can be used to
facilitate non-integer ratios of carrier changes. FIG. 15 shows the
case of an integer high to low carrier change. The FIG. 15 plot
shows an ideal commanded modulating waveform 68 and a phase
corrected sampling waveform 250 at 8 kHz which is shifted to 4 kHz
at time .tau..sub.2. FIG. 16 shows a low to high non-integer
carrier change from 2.5 kHz to 6 kHz that occurs at time
.tau..sub.s. Both of the carrier change examples in FIGS. 15 and 16
were accomplished without disturbing the phase or magnitude of the
fundamental modulating waveform generated.
[0070] It should be understood that the methods and apparatuses
described above are only exemplary and do not limit the scope of
the invention, and that various modifications could be made by
those skilled in the art that would fall under the scope of the
invention. For example, while the invention is describe above as
one wherein the sampling and carrier frequencies are identical, it
should be appreciated that the periods may be different. For
instance, the sampling period in some embodiments may be twice the
carrier period. Experiments using a sampling period that is twice
the carrier period have generated results similar to the results
described above.
[0071] In addition, while Equations 1 and 3 above include
algorithms that have been found to be particularly useful, other
algorithms based on operating and carrier frequency ratios and
indeed simply on carrier frequency are contemplated. Moreover,
while the system is described above as one wherein both phase and
magnitude correction are employed, other embodiments are
contemplated wherein only phase error correction is
implemented.
[0072] To apprise the public of the scope of this invention, the
following claims are made:
* * * * *