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BACKGROUND OF THE INVENTION
The present invention relates generally to motor control and deals more
specifically with apparatus and a related method to compensate for torque
ripple in a permanent magnet electric motor.
The use of a permanent magnet motor is generally well known with typical
motor system applications including a combination of a permanent magnet
alternator and an inverter drive whose output driving signal is
synchronized to the rotor position. Such a motor is known in the art as a
brushless DC drive motor and its configuration is somewhat similar to a
conventional commutator type DC motor having a separately excited field
winding. It is also known to excite the motor with an inverter drive
output signal having a simple rectangular pulse waveform to cause the
motor to operate at a speed which is substantially proportional to the
magnitude of the DC voltage from which the inverter operates. The torque
produced will be generally proportional to the DC current. It is further
known to excite the motor with a pulse width modulated (PWM) inverter
drive voltage to replicate the performance of a variable DC voltage driven
motor.
The class of conventional brushless DC motors have advantages and
disadvantages compared to the conventional commutator type DC electric
motor, particularly when comparing the torque ripple and noise is that is
generated. The conventional brushless DC motor produces large torque
ripple which is due primarily to the relatively small number of phases
driving the electric motor compared to the relatively large number of
commutator bars on a conventional commutator type DC electric motor. The
noise produced by a conventional brushless DC electric motor tends to be
high as a result of the high torque ripple and also due to the relatively
quick transitions of the phase commutation and pulse width modulation
(PWM) steps in the driving voltage waveform.
It is desirable to reduce the torque ripple and noise generated by an
electric motor particularly in applications wherein generated noise is of
a great concern. Such an application might be for example, the propulsion
of an undersea vehicle. Of particular importance as a source of noise is
torque ripple which has a direct and difficult to interrupt path for
transmission to the water through which the undersea vehicle passes.
One known approach to reduce torque ripple and noise in a brushless DC
motor is to create a field flux and an armature current both of which are
distributed approximately as a sinusoidal function of an angle and to then
operate the inverter drive and filter the output of the drive in such a
way to create an applied drive voltage which is substantially a sinusoidal
function of time. The performance of a brushless DC motor approximates
that of a AC electric motor with this approach. Although the torque ripple
and noise are reduced, the approach is generally unsatisfactory due to the
increase in size of the electric motor and the reduction in the power
output achieved. In addition, the above method to reduce torque ripple and
noise is somewhat limited due to the difficulty, complexity and often
inability to approximate the desired waveforms.
It is a general aim therefore of the present invention to provide a
permanent magnet electric motor and a solid state power inverter
combination to precisely control output torque and to minimize noise
generation.
It is a further aim of the present invention to permit the selection of
motor magnetics based on high torque production rather than minimum noise
generation.
It is a further aim of the present invention to provide noise reduction by
controlling the current waveform driving the electric motor.
SUMMARY OF THE INVENTION
In accordance with the present invention, apparatus and a related method
for controlling torque and torque ripple in a multiple-phase permanent
magnet axial-field motor is presented. An input current signal
representative of the electrical current required to excite the motor
windings to cause the motor to produce a desired torque output is provided
as an open loop control signal for direct torque control or as an error
signal from some external control system. A table of values corresponding
to a compensation factor at each of a number of angular shaft positions of
the motor is stored in a memory device for subsequent retrieval. Each
compensation factor defines for each of the number of angular shaft
positions, a modifying value to be applied to the input current signal to
cause the motor to produce a substantially ripple free torque output by
compensating for ripple contributing sources such as for example, noise,
cyclical variations in load torque dependent on shaft position and other
systematic variations dependent on shaft position.
The input current signal as modified in accordance with the compensation
factor modifying value at each of the number of angular shaft positions
provides a second current command signal. A table of multiplying values
corresponding to a current amplitude factor at each of a number of angular
shaft positions of the motor is stored in a memory device for subsequent
retrieval and application to the second current command signal to produce
a current regulation control signal.
A driving current for each phase of the motor is generated in response to
the current regulation control signal at each of the number of angular
shaft positions whereby the output torque of the motor is at the desired
magnitude and with a ripple free characteristic.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other features will become readily apparent from the
following written description and the drawings wherein:
FIG. 1 is a somewhat schematic functional block diagram illustrating the
general method and apparatus of the present invention.
FIG. 2 is a schematic representation of the armature windings in a
conventional DC brushless motor.
FIG. 3 is a schematic representation of the armature winding in the motor
of the present invention.
FIG. 4 is a waveform showing the back electromagnetic force (EMF) of a
typical permanent magnet motor at a given speed.
FIG. 5 shows a sinusoidal command current waveform and the computed
pulse-by-pulse response waveform of the inverter circuit.
FIG. 6 shows a torque output waveform corresponding to the sinusoidal
command current control waveform of FIG. 5 wherein the torque output
exhibits a high torque ripple.
FIG. 7 shows the sinusoidal command current waveform modified in accordance
with the present invention and the resultant pulse-by-pulse response
waveform of the inverter circuit.
FIG. 8 shows a torque output waveform corresponding to the command current
waveform modified as shown in FIG. 7 wherein the torque ripple is
substantially eliminated.
FIG. 9 illustrates the difference in output power between the corrected
current command signal and sine current command signal average output
power.
FIG. 10 is a flowchart illustrating one embodiment of the method of the
present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
To more fully appreciate the features and benefits of the control system
embodying the present invention and as illustrated in schematic block
diagram form in FIG. 1, it is beneficial to take notice of the following
information. The usual normally accepted philosophy in the design of an
electric motor places great concern and consideration to minimize output
variations with changes in shaft position. In contrast to normal design
consideration, the present invention permits an electric motor to be
designed to provide high performance and high torque generation with only
secondary considerations, if any, given to output variations as a function
of shaft position.
In the present invention, electrical current which is injected into the
motor from a high bandwidth current controller is controlled to achieve
the intended output torque and also to control the generation of noise
through torque ripple control and other known noise reduction means.
An electric motor which may be utilized with the present invention is
preferably of the permanent magnetic alternator type wherein the permanent
magnet material is preferably one of the newer rare earth magnet
materials. The family of rare earth magnets for example,
neodymium-iron-boron are preferred wherever operating temperatures will
allow such usage. Alternatively, the rare earth magnet, samarium cobalt,
for example, can be used over an extended range of temperatures. A further
feature of the present invention permits the designer a choice of motor
configurations based on the unique needs of the motor application. For
instance, the permanent magnets may be mounted on the rotor or the stator
and additionally the airgap may be oriented with either radial or axial
flux.
In choosing an electric motor, a highly desirable feature is to utilize a
magnetic carrier structure totally absent or devoid of salient
ferromagnetic features to substantially reduce any components of
reluctance torque. A motor design devoid of salient ferromagnetic elements
also reduces unstable magnetic attractive forces between the magnetic
carrier and the core. Magnetic attractive forces have been identified as a
source of noise, either directly as the rotor is pulled from side-to-side
or indirectly by causing an increase in bearing loading. It is further
preferred that the permanent magnet portion of the magnetic circuit of the
electric motor not contain ferromagnetic material.
One preferred motor embodiment which provides high torque at relatively low
top speed is a disc alternator type having axially magnetized permanent
magnets mounted on the rotor. The preferred motor embodiment is also known
as an axial-flux permanent magnet disc motor. The magnetic flux crosses
the airgap axially on both sides of the rotor leaving a stator on one side
of the rotor disc and entering a similar stator on the opposite side of
the rotor disc. In this motor type configuration, the magnet carrier is
made from non-ferromagnetic components and without salient ferromagnetic
elements which as discussed above provide a significant advantage.
Reference may be made to U.S. Pat. No. 4,443,906 for information relative
to the general construction and operation of an electric motor having a
rotor made of a non-ferromagnetic material and formed with radially
disposed permanent magnets and a stator formed with a radially disposed
armature winding wherein rotation is imparted to the rotor through
excitation by a 3-phase switching circuit. The coil segments comprising
the armature winding conduct current at right angles to the magnetic field
produced by the permanent magnets to effectively vary the electrical
current throughout the armature winding in order to maintain precise phase
timing between the electric fields of the armature winding and the
magnetic fields of the permanent magnets. Reference may be made to the
disclosure of U.S. Pat. No. 4,443,906 for further details and which
disclosure is hereby incorporated by reference.
U.S. Pat. No. 4,868,477 discloses a method and apparatus for controlling
torque and torque ripple in a variable reluctance motor. The present
invention utilizing an axial-flux permanent magnet disc motor rather than
the reluctance motor disclosed in the '477 patent overcomes a number of
problems and disadvantages associated with reluctance motors, particularly
in applications where noise, specifically noise due to torque ripple, is
of prime importance. It is known that the operation of a variable
reluctance motor requires the variation of stator inductance and that any
torque ripple compensation provided must be imposed based on the
fundamental angle dependence operation of the motor. For example, exciting
a reluctance motor with a square or sinusoidal current waveform causes the
motor to produce an output torque which is predominantly angle dependent
and the amplitude of the ripple current is on the same order of magnitude
as the net torque output of the motor. Accordingly, a reluctance motor
inherently has a high torque ripple even under ideal or optimized
operating conditions. While the method and apparatus of the '477 patent
reduces the torque ripple of the reluctance motor utilized, the degree of
compensation necessary to reduce or eliminate noise due to torque ripple
cannot be achieved.
The magnetics and motor geometry of the axial-flux permanent magnet disc
motor inherently provides a reasonably smooth torque versus angle
characteristic. In contrast to the reluctance motor, the axial-flux
permanent magnet disc motor has a relative weak variation of stator
inductance with rotor position. The rotor magnetic circuit which is
comprised substantially by the permanent magnets behave incrementally like
a linear magnetic material with a relative permeability of a approximately
1.09. As stated above, the remaining parts of the rotor apart from the
magnet are also preferably made of a non-ferromagnetic material causing
the resulting reluctance torque to be negligible compared to the normal
operating torque.
A motor built according to the present invention is distinguished from the
class of conventional brushless DC motors as described above specifically
differing in the connection among the armature windings and between the
armature windings and the driving inverters. As illustrated schematically
in FIG. 2, a representative brushless DC motor generally designated 10
includes three windings 12, 14, 16 connected in a wye configuration with
respective ends 18, 20 and 22 coupled to an associated excitation voltage
source, typically Phase A, Phase B and Phase C, respectively. The opposite
ends 24, 26, 28 of windings 12, 14 and 16 respectively are connected
together. As known to those skilled in the art, Kirchhoff's current law
imposes a relationship among the electrical phase currents in the windings
and therefore the current in one given winding is dependent upon and
related to the current in each of the remaining windings. In contrast, the
current in each motor phase winding in the motor of the present invention
is controlled without reference to or dependence on the other voltage
phases of the remaining windings. As illustrated in FIG. 3, a motor
generally designated 30 is schematically illustrated therein wherein motor
phase winding 32 has respective ends 34,36 available for connection to an
associated excitation voltage source, typically Phase A and its respective
neutral, N.sub.A. Likewise, motor phase winding 38 has its respective ends
40,42 available for independent connection to an associated excitation
voltage source, typically, Phase B and its respective neutral N.sub.B. A
third motor winding 44 likewise has its respective ends 46,48 available
for connection to third excitation voltage source, typically, Phase C and
its respective neutral N.sub.C. Each of the motor windings 32, 38, 44,
respectively may be excited or driven from the output of a full H-bridge
inverter.
The motor phase windings may also be connected in a star configuration
utilizing a low impedance connection to the neutral. The source of DC
power is two symmetric voltage sources connected in series through a low
impedance connection to the midpoint. A low impedance conductor is
connected between the midpoint of the DC source and the neutral of the
star connection of the motor phase windings. In such a star configuration,
each motor phase winding may be fed by a simple Halfwave-bridge inverter
circuit.
It is desirable to provide a high performance pulse width modulation (PWM)
inverter driving circuit at a high frequency to minimize PWM ripple
amplitude and to permit rapid response to the rotor current control
circuit. Normal considerations to minimize inductance and switching losses
need be taken to enhance overall performance as in any high frequency
circuit design. Applicants have also found that it is desirable to use
IGBT (insulated gate bipolar transistors) as the switching elements in the
inverters.
In addition to the sources contributing to torque ripple as stated above,
another dominant contributor to torque ripple in a permanent magnet motor
is the variation of the magnetic flux in the airgap as a function of shaft
position. The variation of the magnetic flux gives rise to cyclic
variation in the torque coefficient which is defined as the torque per
unit of current. For example, if the windings are driven with a
time-invariant current while the motor turns, the average torque is
proportional to the current but the instantaneous torque varies in
accordance with rotor position.
An additional contributor to torque ripple is due to cogging torque which
is developed if the motor has armature teeth and is due to the tendency of
the permanent magnets to align with the tooth structure in preferred
orientations. The cogging torque is generally independent of load current
in the absence of any non-linear effects. However, cogging torque is
dependent on shaft position.
The effect on motor torque includes other sources, for example, reluctance
effects among others. It should be noted that the majority of the total
variation in torque is a repeatable function of rotor position and
armature current. An additional feature of the present invention is to
eliminate the cyclic variation of motor torque by defining the electric
current in the motor as a function of rotor position without adding to the
complexity of the motor design. Typically, shaft position feedback is
already present in the motor system application and which feedback is
required for proper timing of switching elements in the brushless DC
drive. In addition, motor current feedback is also generally used in the
control of the inverter used to excite the motor windings. In order to
eliminate the cyclic variation of motor torque according to the present
invention, the appropriate functional dependence of the current command
input control to the motor must be properly defined and selected, and to
be practical, an economical, reliable method for obtaining the required
functional dependence in hardware implementation must be available.
In order to make a proper selection of an appropriate current driving
waveform accounting for current dependent factors while still achieving
commutation requires that the command current control for any given phase
be separated into two distinct or defined parts. One part can be
considered as a relative current versus amplitude function wherein the
independent value of the function is the rotor position. The second part
is the instantaneous global current command which at any given instant is
the same for all phases. The current control signal to each phase of the
motor is the product of the two component parts. The global command
current value also serves as the fundamental control input to the motor.
The global input command may be used as an open-loop torque control
because the motor produces a torque which is nearly proportional to
current.
An additional feedback loop may be utilized to provide speed control or
some other controlled function which acts, for example, to provide maximum
torque or to eliminate some element of the torque ripple. The fundamental
requirement to achieve commutation is met if the relative current versus
angle function passes through (zero) 0 at the locations where the phase
conductors pass from pole-to-pole. As long as the relative currents follow
the position dependent functions assigned to them respectively, the
interaction of the magnetic field and armature current will produce a
torque which is directly proportional to the amplitude of the current with
position dependent gain.
In the extreme limitation where interaction of the magnetic field and
armature current is the only contribution to torque, variation in the
current amplitude in an inverse proportion relationship to the gain
produces a constant torque versus angle behavior. The global current
command signal required to produce a constant torque will be generally
more complicated than a simple inverse proportion relationship to the
torque constant when other effects contribute to motor torque; however,
the global current command signal remains a function only of position in
the absence of non-linear behavior.
Referring now to FIG. 1, a schematic functional block diagram of the
control system and motor embodying the present invention is illustrated
therein and generally designated 50. A programmable read-only memory
(PROM) is utilized to store digital signals representative of the shaft
position dependent current characteristic information which in turn is
utilized to determine the current command for each phase. The global
current command signal is connected to an input 52 of a multiplier circuit
shown generally by the functional block diagram 54. The global current
command signal may be used as an open-loop control signal for torque
control directly as explained above, or in applications where the motor
has an external control loop regulating the speed or some other function,
the input at lead 52 is generally the error output signal of the external
control. A second input 56 to the multiplier 54 receives a signal which is
a function of the global current compensation characteristic stored in a
PROM table look-up designated generally by the function block 58. The
output 60 of the multiplier 54 is inputted to a separate current
controller associated with each phase and generally represented by the
dashedline box 62, 64 and 66, respectively in FIG. 1. The current
controllers 62, 64 and 66 include a multiplier represented by the
functional block 68, 70 and 72, respectively. The output 60 of the
multiplier 54 is connected to the input 130 of the multiplier 68, the
input 132 of the multiplier 70 and the input 134 of the multiplier 72.
Each current controller 62, 64, 66 is substantially identical to one
another apart from the associated phase winding of the motor that it
drives. Accordingly, the current controller 62 is described with the
understanding that its description applies also to current controllers 64
and 66. The output 74 of the multiplier 68 is coupled to a summing circuit
76. The output 78 of the summing circuit 76 is coupled to the input of a
PWM regulation control circuit shown generally by the function box 80. The
output 82 of the PWM control circuit 80 is coupled to the inverter 84
which generates at its output 86 the motor phase winding driving current
which has a magnitude and waveform in accordance with the desired
compensation at the given shaft position of the motor 88. The output of
the inverter 84 is also fed back to a second input 90 of the summing
circuit 76 through the feedback loop 92 and is compared to the desired
input signal at the output 74 of the multiplier 68 and in turn produces an
error difference signal at the output 78 to drive the PWM control circuit
80 to achieve the desired current output from the inverter 84.
The current controller 64 includes the output 94 of multiplier 70 coupled
to summing circuit 96 the output 98 of which is coupled to PWM regulation
control circuit 100. The output 102 of the PWM control circuit 100 is
coupled to the inverter 104 upon whose output 106, the motor phase winding
driving current excites the appropriate phase of the motor 88 and is fed
back to the input 108 of the summing circuit 96 via the feedback loop 110.
The current controller 66 includes the output 112 of multiplier 72 coupled
to the summing circuit 114 whose output 116 is the difference signal
between the input and the feedback signal at input 126 from the inverter
122 output 124 via the feedback loop 128.
A programmable read-only memory (PROM) 136 stores information in a digital
format and is representative of the relative current amplitude
characteristic as a function of rotor position. The rotor position of the
motor 88 may be sensed using well known techniques such as optical or
magnetic encoders which may be coupled directly to the shaft of the motor
or may detect sensors on the shaft. Suffice for purposes of this
disclosure that a signal representative of the angular shaft position of
the motor is determined and provided on the feedback loop 138 for each
angular shaft position for which it is desired to have an output. The
output shaft encoded signal is fed to an input 140 of the PROM 136 and
functions as an input address to the PROM to access information stored in
a corresponding location in memory for output to the multipliers. The PROM
136 has a first output 142 coupled to the input 144 of the multiplier 68.
A second output 146 of the PROM 136 is connected to an input 148 of the
multiplier 70 and a third output 150 of the PROM 136 is connected to an
input 152 of the multiplier 72. It is possible to utilize a single PROM as
illustrated in FIG. 1 due to the periodicity of the current amplitude
function and the symmetries common in an electric motor by generating one
relative current amplitude function characteristic and shifting the
look-up register storing the information by a predetermined factor for
each phase being controlled. The PROM 136 may also have sectionalized
memory wherein the relative current amplitude function characteristic for
each phase is stored for subsequent retrieval and may differ from the
other phases to compensate for any phase asymmetries or other factors.
In instances where computation is required from instant-to-instant to
determine the global current compensation function signal it is
preferable, to provide efficient operation, to store the position
dependent information in one place. The computation may be performed once
at each time increment and the command current may be determined by
multiplication at each time increment. As illustrated in the functional
block diagram of FIG. 1, the global current compensation characteristic
information is accessed, retrieved from memory and outputted to the
multiplier 54 input 56 in accordance with the output shaft encoded signal
supplied to the input 154 via the feedback loop 138. Additional inputs,
generally designated 156, may also be used in conjunction with the shaft
encoded signal to access a different current compensation characteristic
stored in the global current compensation PROM 58 to provide a
compensation to reduce noise and torque ripple attributable to other
sources and specifically identified operating conditions.
In very simple cases where the required global current compensation
characteristic is a function of rotor position only and not dependent on
the current, the relative current amplitude function value may be
pre-multiplied by the global current compensation value once and stored in
a relative amplitude array in a memory device for subsequent retrieval. In
this case, separate storage for the global compensation command signal is
not required. This alternate embodiment is readily apparent through
simplification of the functional block diagram illustrated in FIG. 1.
One method to determine the appropriate global current compensation value
when there is dependence on variables in addition to shaft position is to
interpolate from a multi-variable table stored in the PROM. For example,
if the required compensation is a function of position and speed only, a
compensation versus position function characteristic can be stored for a
different number of values of speed. For purposes of this disclosure, each
such single speed function characteristic is referred to as a "page" in
memory. As the motor speed varies, the controller may step discretely from
"page" to "page" generally with some computation hysteresis to preclude
hunting between "pages". Alternatively, the controller may interpolate
continuously between "pages". Similar methods may be also used to
determine variations of the global current compensation characteristic
with respect to other variables of interest.
The information to be stored in the PROM look-up tables defining the
necessary compensation function at each desired shaft angular position may
be determined either theoretically or empirically. The motor designer
knows the motor torque per ampere versus angle characteristic of the motor
in advance of the actual construction of the motor. The characteristic may
then be confirmed after the motor is constructed or may be refined upon
testing of the motor. The theoretical compensation values to be stored in
the PROM look-up tables is generally sufficient for many applications,
however the theoretical motor torque per ampere versus angle transfer
function may be modified as necessary in accordance with a given
application to generate different compensation values for storage in the
PROM look-up table.
Referring now to FIGS. 4-9 in which a number of representative waveforms
are illustrated and identified below, the method and apparatus of the
present invention are further illustrated and the waveforms are the result
of numerical simulations of the operation of the invention. FIG. 4
illustrates a representative waveform of the back electromagnetic force
(EMF) at a given motor speed. The back EMF waveform is used in tabular
form as input data to the process of determining the relative current
amplitude function. The table entries describing the back EMF waveform are
thus that of a given motor and is generally representative of the back EMF
in a permanent magnet motor where the design goal is to maximize the
magnet-to-armature mutual flux. The back EMF waveform is generally
designated 170 and as recognized by those skilled in the art, it cannot be
accurately approximated by a single frequency sinusoidal function.
FIG. 5 shows a sinusoidal command current waveform generally designated
172, which may be used to control the PWM inverter as described above. The
calculated output of the response of the inverter circuit is illustrated
by the waveform generally designated 174. It is seen that the
pulse-by-pulse response of the inverter circuit represented by the
waveform 174 tracks the sinusoidal command current characteristic very
closely and accordingly can be expected to accurately track the input
command current control waveform signal.
Referring to FIG. 6, a torque output waveform generally designated 176 is
illustrated and corresponds to the torque output that would be generated
in accordance with the sinusoidal command current control waveform signal
illustrated in FIG. 5. It should be noted that the torque and power output
waveform characteristic are identical apart from a scale factor. The
torque output waveform (and power output waveform) exhibit a significant
ripple when the command current control waveform signal is a sinusoidal
function.
Although there are a number of specific PWM logic circuits and controls for
inverter driver circuits, the exemplary illustration utilized in the
numerical simulation scheme above contemplates a switch transition
whenever the absolute value of the output current exceeds the absolute
value of the command current, which scheme produces a bias in the low
frequency current. The amplitude of the low frequency current is
approximately half the peak-to-peak value of the PWM ripple. The magnitude
of the PWM ripple is a function of the output current and the difference
between the back EMF and the DC bus voltage used in the PWM logic circuit.
The above factors, output current and back EMF, which determine the ripple
amplitude are predetermined functions of angular shaft position and
therefore the command current signal may be modified by a value which is
equal to the low frequency bias to produce an output current which more
nearly approximates the desired sinusoidal function without a bias. In the
typical case of a motor with a non-sinusoidal back EMF it can be seen that
a perfect single frequency sinusoidal current will not be the optimum
waveform to reduce the torque ripple.
The torque ripple and output power ripple can be reduced in accordance with
the present invention by modifying the command current waveform as
illustrated in FIG. 7. The modified command current waveform is generally
designated 178 and the output pulse-by-pulse response of the inverter
circuit is indicated generally by the response curve 180. The command
current waveform 178 is derived utilizing an algorithm such that the power
output of each phase varies as a sine-squared function of time. The table
entries for the reference command current control waveform in the
illustrated embodiment are computed utilizing the equation:
I.sub.com =P*sin.sup.2 (Theta)/V.sub.bemf
wherein P is the peak power required from one phase and which power is 2/3
of the 3-phase average power; Theta is a pointer variable and advances | | |
