Method and apparatus for establishing a reference current for use in operating a synchronous motor

A method of establishing a reference current for use in operating a synchronous motor. A torque-angle profile of the motor is obtained, an excitation component and a reluctance component of the torque-angle profile are obtained, and the reference current is obtained from the excitation component and the reluctance component of the torque-angle profile.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to the operation of synchronous motors. More 
particularly, the present invention relates to a method and apparatus for 
establishing one or more reference currents for use in operating a 
synchronous motor. 
2. Description of Related Art 
The torque produced by a synchronous motor usually contains pulsations of 
rich harmonics. These harmonics are generally due to imperfect 
interactions between the magnetic flux of the rotor and stator currents. 
In many cases, the pulsating torque causes deterioration of machine 
performance and may produce noise and vibration that can be detrimental to 
the motor. Much effort has been expended in attempts to solve this torque 
pulsation problem. 
In one approach, the problem is addressed with appropriate motor designs. 
In particular, the structure of the motor is optimized to reduce the 
sources of harmonics. For example, the reluctance torque is suppressed by 
surface mounting of the rotor magnets and skewing of the stator slots. 
In another approach, the problem is addressed with innovative control 
strategies. For example, current inputs to the motor are controlled so 
that no harmonic torque is produced. This approach has more flexibility 
than the first approach because a general control methodology, once found, 
can be applied to motors with various designs. Recently, this second 
approach has become attractive due to the development and availability of 
fast power electronics and digital electronics with which more 
sophisticated control can be realized. 
SUMMARY OF THE INVENTION 
Features and advantages of the invention will be set forth in the 
description which follows, and in part will be apparent from the 
description or may be learned by practice of the invention. The objectives 
and other advantages of the invention will be realized and attained by the 
methods and apparatuses particularly pointed out in the written 
description and claims hereof as well as the appended drawings. 
To achieve these and other advantages and in accordance with the purpose of 
the invention, as embodied and broadly described, the invention provides 
for a method of and apparatus for establishing a reference current for use 
in operating a synchronous motor, wherein the reference current is 
established from an excitation component and a reluctance component of a 
torque-angle profile of the motor. 
In another aspect, the invention provides for a method of and apparatus for 
operating a synchronous motor in accordance with a torque command and an 
excitation component and reluctance component of a torque-angle profile of 
the motor. A reference current is established from the torque command and 
the excitation component and reluctance component of the torque-angle 
profile and the reference current is compared with a feedback current to 
generate a switching signal. A drive signal is generated in accordance 
with the switching signal and the drive signal is supplied to the motor. 
It is to be understood that both the foregoing general description and the 
following detailed description are exemplary and explanatory and are 
intended to provide further explanation of the invention as claimed.

DETAILED DESCRIPTION OF THE INVENTION 
Reference will now be made in detail to the present preferred embodiments 
of the invention, examples of which are illustrated in the accompanying 
drawings. Wherever possible, the same reference numbers will be used 
throughout the drawings to refer to the same or like parts. Although the 
present invention is applicable to synchronous motors having any number of 
phase windings, the invention will be described in connection with 
synchronous motors having three phase windings, i.e., an A-phase winding, 
a B-phase winding, and a C-phase winding. 
As described above, the present invention provides for a method of and 
apparatus for establishing one or more reference currents for use in 
operating a synchronous motor, wherein the reference currents are 
established from an excitation component and reluctance component of a 
torque-angle profile of the motor. For the purposes of this invention, the 
torque-angle profile of a synchronous motor is a trace or profile of the 
torque produced by one or more of the phase windings of the motor, i.e., 
the per-phase torques, with respect to an angular position of the motor's 
rotor. As will be explained in more detail below, it is contemplated that 
for symmetrical synchronous motors, i.e., motors where the windings are 
identical and evenly spaced, the reference currents can be established 
merely by obtaining the excitation component and reluctance component of 
the torque-angle profile of one phase winding of the motor. As will be 
also explained in more detail below, the reference currents established in 
accordance with the teachings of the invention can be used to control the 
supply of one or more drive signals to the phase windings of the 
synchronous motor in such a manner that the motor produces a desired 
output torque. 
Generally, the total output or composite torque T.sub.s produced by a 
three-phase synchronous motor can be expressed as follows: 
EQU T.sub.s =T.sub.a (.theta.,i.sub.a)+T.sub.b (.theta.,i.sub.b)+T.sub.c 
(.theta.,i.sub.c) Eqn. 1.0 
where .theta. is the angular position of the motor's rotor with respect to 
a reference position, i.sub.a, i.sub.b, and i.sub.c are the input phase 
currents for the motor's A-phase, B-phase, and C-phase windings, 
respectively, and T.sub.a, T.sub.b, and T.sub.c are the per-phase torques 
produced by the phase currents i.sub.a, i.sub.b, and i.sub.c, 
respectively. To establish a reference current for use in operating a 
synchronous motor in accordance with the teachings of the present 
invention, the torque-angle profile for the synchronous motor must first 
be obtained, for example, by use of the arrangement shown in FIG. 1. 
As shown in FIG. 1, a DC motor 12, a torque transducer 14, and a position 
transducer 16 are coupled to the rotor (not shown) of a synchronous motor 
10 having an A-phase winding, a B-phase winding, and a C-phase winding. 
The outputs of the torque transducer 14 and the position transducer 16 are 
coupled to a processor 18. 
To obtain, for example, the A-phase torque-angle profile of the synchronous 
motor 10, the synchronous motor 10 is mechanically driven by the DC motor 
12 while the A-phase winding of the synchronous motor 10 is supplied with 
a current of one ampere and the B-phase and C-phase windings of the 
synchronous motor 10 are left open. As the synchronous motor 10 is 
mechanically driven, the angular position r(.theta.) of the rotor (not 
shown) of the synchronous motor 10 is detected with respect to a reference 
position by the position transducer 16 and provided to the processor 18. 
Concurrently, the A-phase torque T.sub.a of the synchronous motor 10 is 
measured by the torque transducer 14 and provided to the processor 18. 
Preferably, the synchronous motor 10 is driven by the DC motor 12 slowly 
enough such that the dynamics of the torque transducer 14 are negligible. 
As the processor 18 receives the torque and position measurements from the 
torque transducer 14 and the position transducer 16, respectively, the 
processor 18 records and compiles the measurements to obtain the A-phase 
torque-angle profile of the synchronous motor 10. An example of such an 
A-phase torque-angle profile is illustrated in FIG. 2. 
To obtain the B-phase torque-angle profile of the synchronous motor 10, the 
foregoing procedure is performed only the B-phase winding of the 
synchronous motor 10 is supplied with a current of one ampere and the 
A-phase and C-phase windings of the synchronous motor 10 are left open. 
Similarly, to obtain the C-phase torque-angle profile of the synchronous 
motor 10, the same procedure is performed, only the C-phase winding of the 
synchronous motor 10 is supplied with a current of one ampere and the 
A-phase and B-phase windings of the synchronous motor 10 are left open. It 
should be appreciated that if the synchronous motor 10 has a symmetrical 
structure, only the A-phase torque-angle profile need be obtained since 
the B-phase and C-phase torque-angle profiles can be deduced from the 
A-phase torque-angle profile by simply shifting the A-phase torque-angle 
profile by 120.degree. and 240.degree., respectively. If the synchronous 
motor 10 is not symmetrical, however, all three torque-angle profiles 
should be obtained independently. 
Once the torque-angle profile of the motor has been obtained, an excitation 
component and a reluctance component of the torque-angle profile are 
obtained. In particular, the torque-angle profile of the motor is broken 
down into an excitation component Te and a reluctance component Tr as 
follows: 
EQU T.sub.a,b,c =Te+Tr Eqn. 2.0 
where the excitation component Te and the reluctance component Tr can be 
expressed as the following Fourier series: 
##EQU1## 
Again, if the motor is symmetrical, only the excitation component and 
reluctance component of the torque-angle profile of one phase winding of 
the motor need be obtained. Further, it is contemplated that the 
excitation and reluctance components of the torque-angle profile can be 
obtained by any number of spectral analysis tools known to those skilled 
in the art such as, for example, Fourier Analysis. 
It should be noted that the excitation component Te is generally produced 
as a result of the interaction of the stator currents with the air gap 
flux of the motor and contains only odd order harmonics of the per-phase 
torque. The reluctance component Tr, on the other hand, is produced as a 
result of reluctance variation due to the motor saliencies and contains 
only even order harmonics of the per-phase torque. Further, the reluctance 
component Tr can be further broken down into a cogging component and a 
ripple component. The cogging component is due to a mutual-reluctance 
effect and is that portion of the reluctance component Tr that depends on 
the rotor position. The cogging component exists in the absence of any 
armature current and is normally minimized in motor designs to be 
relatively negligible, e.g., about 1-2 percent of the total motor torque. 
The ripple component is due to a self-reluctance effect and is a 
consequence of armature current commutation and harmonics that do not 
produce constant and smooth torque. 
Once the excitation and reluctance components of the torque-angle profile 
of the motor have been obtained, one or more reference currents for use in 
operating the motor can be established. For example, by taking into 
account the fact that if a motor is to produce a smooth and constant 
output torque the triplen, i.e., the third, sixth, ninth, etc., harmonics 
should not exist in the motor's per-phase torques, reference currents for 
use in operating the motor can be established such that the motor produces 
the desired smooth and constant output torque. Likewise, by further taking 
into account the power loss characteristics of the motor, reference 
currents can be established for use in operating the motor such that the 
motor produces not only a smooth and constant output torque but also a 
maximum output torque. 
For example, to establish a reference current that will result in a smooth, 
constant, and maximum output torque, a phase current Ia.sub.1 is first 
established from the excitation component Te and the reluctance component 
Tr of the A-phase torque T.sub.a of the motor. More specifically, the 
phase current Ia.sub.1 is established in accordance with the following 
relationship: 
##EQU2## 
If the motor is not symmetrical, phase currents Ib.sub.1 and Ic.sub.1 for 
the B-phase and C-phase windings, respectively, should also be established 
in accordance with the following relationships: 
Once the phase current Ia.sub.1 has been established, a delay angle of the 
phase current Ia.sub.1 is established. Using the minimum power loss 
theory, the phase current Ia.sub.1 will result in minimal loss of power if 
it has a delay angle .xi.a.sub.1 as follows: 
##EQU3## 
Having established the delay angle .xi.a.sub.1, a reference torque 
T.sub.aREF for the A-phase winding of the motor is established as follows: 
##EQU4## 
It should be noted that the reference torques T.sub.aREF, T.sub.bREF, and 
T.sub.cREF are the desired per-phase torques that the motor should produce 
during operation. It should also be noted that these reference torques do 
not contain any triplen harmonics. 
Finally, a reference current i.sub.aREF for the A-phase winding of the 
motor is established from the reference torque T.sub.aREF as follows: 
##EQU5## 
Assuming that the motor is symmetrical, reference currents i.sub.bREF and 
i.sub.cREF for the B-phase winding and C-phase winding of the motor, 
respectively, can be established as follows: 
EQU i.sub.bREF =i.sub.aREF (.theta.-120.degree.) Eqn. 9.0 
EQU .sub.cREF =i.sub.aREF (.theta.-240.degree.) Eqn. 10.0 
Although one technique for establishing one or more reference currents from 
the excitation component and reluctance component of a synchronous motor's 
torque-angle profile has been described thus far, it is contemplated that 
any number of techniques can be used, each technique being tailored for 
achieving a desired output torque. Thus, the foregoing technique for 
establishing the reference currents is not meant to be limiting and is 
shown only as an example. 
As mentioned above, the reference currents established by the present 
invention can be used in operating a synchronous motor. In particular, it 
is contemplated that these reference currents are applicable to 
synchronous motor circuits such as the synchronous motor circuit 20 
illustrated in FIG. 3. As shown in FIG. 3, the synchronous motor circuit 
20 comprises a controller 30, a current regulator 40, an inverter 50, a 
synchronous motor 60, and a position transducer 70. 
Preferably, the controller 30 includes a digital processor, such as a 
digital signal processor capable of performing high-speed computations. 
The controller 30 preferably also includes a memory for storing a model of 
the motor 60, whereby the motor 60 is characterized by the excitation 
component and reluctance component of the torque-angle profile of the 
motor 60. 
The current regulator 40 preferably includes a comparator circuit such as 
that shown in FIG. 4. Alternatively, the current regulator 40 can be 
implemented in software stored in an executed by the controller 30 or 
other processor (not shown). 
The inverter 50 includes a DC power source 80, a coupling capacitor 90, and 
plurality of switching devices 100a.sub.1-4, 100b.sub.1-4, and 
100c.sub.1-4. The DC power source 80 is preferably a battery or rectified 
AC power source, and the capacitor 90 absorbs transients or spikes 
generated during operation of the switching devices 100a.sub.1-4, 
100b.sub.1-4, and 100c.sub.1-4. Although the switching devices 
100a.sub.1-4, 100b.sub.1-4, and 100c.sub.1-4 are depicted in FIG. 3 as 
insulated gate bipolar transistors (IGBETs), it is contemplated that the 
switching devices 100a.sub.1-4, 100b.sub.1-4, and 100c.sub.1-4 can be 
other suitable switching devices, such as, for example, field-effect 
transistors (FETs), bipolar junction transistors (BJTs), or the like. 
The synchronous motor 60 preferably comprises an A-phase winding, a B-phase 
winding, and a C-phase winding, although the synchronous motor 60 can 
comprise any number of phase windings as is known to those skilled in the 
art. The synchronous motor 60 further has associated therewith a position 
transducer 70 coupled to the rotor (not shown) of the synchronous motor 
60. The position transducer 70, like the position transducer 16 of FIG. 1, 
detects the angular position r(.theta.) of the rotor (not shown) of the 
synchronous motor 60 with respect to a reference position. This feedback 
position signal r(.theta.) is supplied by the position transducer 70 to 
the controller 30. While the synchronous motor 60 can be any type of 
synchronous motor, e.g., a permanent magnet synchronous motor, a 
reluctance synchronous motor, a field-excited synchronous motor, or the 
like, the synchronous motor 60 is preferably of the permanent-magnet type. 
The reason for this is that permanent-magnet synchronous motors generally 
have relatively accurate position transducers coupled thereto, thereby 
making permanent-magnet synchronous motors especially suited for the 
purposes of the invention. To the contrary, other types of synchronous 
motors generally have either very low accuracy position transducers, e.g., 
reluctance synchronous motors, or no position transducers at all, e.g., 
field-excited synchronous motors, coupled thereto and are, therefore, not 
as well suited for the purposes of the invention. 
Operation of the synchronous motor circuit 20 of FIG. 3 will now be 
described. 
Assuming the excitation and reluctance components of the torque-angle 
profile of the motor 60 are known, operation of the synchronous motor 
circuit 20 generally begins with the issuance of a-torque command by an 
operator to the controller 30. For the purposes of this invention, the 
torque command represents a desired output torque of the synchronous motor 
60 and is generally represented by an output torque T.sub.s. 
Upon receipt of the torque command and the position feedback signal 
r(.theta.), the controller establishes reference currents i.sub.aREF, 
i.sub.bREF, and i.sub.cREF for the A-phase winding, B-phase winding, and 
C-phase winding, respectively, of the motor 60. Preferably, the controller 
30 establishes the reference currents i.sub.aREF, i.sub.bREF, and 
i.sub.cREF from the excitation component and reluctance component of the 
torque-angle profile of the motor 60 in the manner described above. 
The controller 14 supplies the reference currents i.sub.aREF, i.sub.bREF, 
and i.sub.cREF to the current regulator 40 where they are compared with 
feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB, respectively. As 
illustrated in FIG. 3, the feedback currents i.sub.aFB, i.sub.cFB, and 
i.sub.cFB are detected at the outputs of the switching devices 
100a.sub.1-4, 100b.sub.1-4, and 100c.sub.1-4, respectively, of the 
inverter 50 by current sensors (not shown), such as, for example, Hall 
sensors, sensing transformers, current sensing transistors, or the like. 
Upon comparing the reference currents i.sub.aREF, i.sub.bREF, and 
i.sub.cREF with the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB, 
respectively, the current regulator 40 generates switching signals in the 
form of pulses for turning the switching devices 100a.sub.1-4, 
100b.sub.1-4, and 100c.sub.1-4 of the inverter 50 on and off. Preferably, 
the current regulator generates these switching signals in such a manner 
that the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB track the 
reference currents i.sub.aREF, i.sub.bREF, and i.sub.cREF, respectively. 
To accomplish this tracking, the current regulator 40 can perform any 
number of known tracking or pulse-width modulation switching techniques 
including the "Bang-Bang" control method and the "Pulse-Width Modulation" 
control method, both of which are well-known in the art. Thus, the current 
regulator 40 can comprise, for example, the comparator circuit illustrated 
in FIG. 4. 
In the circuit of FIG. 4, the comparator 110a compares the reference 
current i.sub.aREF with the feedback current i.sub.aFB to generate a 
switching signal SW.sub.a. The switching signal SW.sub.a is applied to the 
switching devices 100a.sub.1 and 100a.sub.3. The switching signal SW.sub.a 
is also inverted by an inverter 120a and thereafter applied to the 
switching devices 100a.sub.2 and 100a.sub.4. When the reference current 
i.sub.aREF is less than the feedback current i.sub.aFB, the switching 
signal SW.sub.a operates to turn the switching devices 100a.sub.1 and 
100a.sub.3 on and to turn the switching devices 100a.sub.2 and 100a.sub.4 
off. Similarly, when the reference current i.sub.aREF is greater than the 
feedback current i.sub.aFB, the switching signal SW.sub.a operates to turn 
the switching devices 100a.sub.1 and 100a.sub.3 off and to turn the 
switching devices 100a.sub.2 and 100a.sub.4 on. 
Like the comparator 110a, the comparator 110b compares the reference 
current i.sub.bREF with the feedback current i.sub.bFB to generate a 
switching signal SW.sub.b. The switching signal SW.sub.b is applied to the 
switching devices 100b.sub.1 and 1004b.sub.3. Similarly, the comparator 
110c compares the reference current i.sub.cREF with the feedback current 
i.sub.cFB to generate a switching signal SW.sub.c which is applied to the 
switching devices 100c.sub.1 and 100c.sub.3. The switching signals 
SW.sub.b and SW.sub.c are also inverted by inverters 120b and 120c, 
respectively, and thereafter applied to the switching devices 100b.sub.2 
and 100b.sub.4 and to the switching devices 100c.sub.2 and 100c.sub.4, 
respectively. 
When the reference current i.sub.bREF is less than the feedback current 
i.sub.bFB, the switching signal SW.sub.b operates to turn the switching 
devices 100b.sub.1 and 100b.sub.3 on and to turn the switching devices 
100b.sub.2 and 100b.sub.4 off. And when the reference current i.sub.bREF 
is greater than the feedback current i.sub.bFB, the switching signal 
SW.sub.b operates to turn the switching devices 100b.sub.1 and 100b.sub.3 
off and to turn the switching devices 100b.sub.2 and 100b.sub.4 on. 
Similarly, when the reference current i.sub.cREF is less than the feedback 
current i.sub.cFB, the switching signal SW.sub.c operates to turn the 
switching devices 100c.sub.1 and 100c.sub.3 on and to turn the switching 
devices 100c.sub.2 and 100c.sub.4 off. And when the reference current 
i.sub.cREF is greater than the feedback current i.sub.cFB, the switching 
signal SW.sub.c operates to turn the switching devices 100c.sub.1 and 
100c.sub.3 off and to turn the switching devices 100c.sub.2 and 100c.sub.4 
on. 
In this manner, the current regulator 40 controls the inverter 50 such that 
the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB track the 
reference currents i.sub.aREF, i.sub.bREF, and i.sub.cREF. Thus, the phase 
windings of the synchronous motor 60 are energized by the inverter 50 in a 
sequence such that the motor 60 produces an output torque in accordance 
with the torque command. 
FIG. 5 illustrates a synchronous motor circuit 200 as an alternative to 
that illustrated in FIG. 3. As shown in FIG. 5, the synchronous motor 
circuit 200 comprises a controller 210, a current regulator 220, an 
inverter 230, a synchronous motor 240, and a position transducer 250. 
Preferably, the controller 210 is the same as the controller 30 of FIG. 3, 
and the regulator 220 preferably includes a comparator circuit such as 
that shown in FIG. 6. Alternatively, the current regulator 220 can be 
implemented in software stored in an executed by the controller 210 or 
other processor (not shown). 
The inverter 230 includes two DC power sources 260 and 270, a coupling 
capacitor 280, and a plurality of switching devices 290a.sub.1-2, 
290b.sub.1-2, and 290c.sub.1-2. The DC power sources 260 and 270 are 
preferably batteries or rectified AC power sources, and the capacitor 280 
absorbs transients or spikes generated during operation of the switching 
devices 290a.sub.1-2, 290b.sub.1-2, and 290c.sub.1-2. Although the 
switching devices 290a.sub.1-2, 290b.sub.1-2, and 290c.sub.1-2 are 
depicted in FIG. 5 as insulated gate bipolar transistors (IGBETs), it is 
contemplated that the switching devices 290a.sub.1-2, 290b.sub.1-2, and 
290c.sub.1-2 can be other suitable switching devices, such as, for 
example, field-effect transistors (FETs), bipolar junction transistors 
(BJTs), or the like. 
The synchronous motor 240 preferably comprises an A-phase winding, a 
B-phase winding, and a C-phase winding, although the synchronous motor 240 
can comprise any number of phase windings as is known to those skilled in 
the art. The synchronous motor 240 further has associated therewith a 
position transducer 250 coupled to the rotor (not shown) of the 
synchronous motor 240 for detecting the angular position r(.theta.) of the 
rotor (not shown) with respect to a reference position. The feedback 
position signal r(.theta.) is supplied by the position transducer 250 to 
the controller 210. While the synchronous motor 240 can be any type of 
synchronous motor, the synchronous motor 240 is preferably of the 
permanent-magnet type. Again, the reason for this preference is that 
permanent-magnet synchronous motors generally have relatively accurate 
position transducers coupled thereto making them especially suited for the 
purposes of the invention. 
Operation of the synchronous motor circuit 200 of FIG. 5 will now be 
described. 
Assuming the excitation and reluctance components of the torque-angle 
profile of the motor 240 are known, operation of the synchronous motor 
circuit 200 generally begins with the issuance of a torque command by an 
operator to the controller 210. Again, the torque command represents a 
desired output torque of the synchronous motor 240 and is generally 
represented by an output torque T.sub.s. 
Upon receipt of the torque command T.sub.s and the position feedback signal 
r(.theta.), the controller 210 establishes reference currents i.sub.aREF, 
i.sub.bREF, and i.sub.cREF for the A-phase winding, B-phase winding, and 
C-phase winding, respectively, of the motor 240. Preferably, the 
controller 210 establishes the reference currents i.sub.aREF, i.sub.bREF, 
and i.sub.cREF from the excitation component and reluctance component of 
the torque-angle profile of the motor 240 in the manner described above. 
The controller 210 supplies the reference currents i.sub.aREF, i.sub.bREF, 
and i.sub.cREF to the current regulator 220 where they are compared with 
feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB, respectively. As 
illustrated in FIG. 6, the feedback currents i.sub.aFB, i.sub.bFB, and 
i.sub.cFB are detected at the outputs of the switching devices 
290a.sub.1-2, 290b.sub.1-2, and 290c.sub.1-2, respectively, of the 
inverter 230 by current sensors (not shown), such as, for example, Hall 
sensors, sensing transformers, current sensing transistors, or the like. 
Upon comparing the reference currents i.sub.aREF, i.sub.bREF, and 
i.sub.cREF with the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB, 
respectively, the current regulator 220 generates switching signals in the 
form of pulses for turning the switching devices 290a.sub.1-2, 
290b.sub.1-2, and 290c.sub.1-2 of the inverter 230 on and off. Preferably, 
the current regulator 220 generates these switching signals in such a 
manner that the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB 
track the reference currents i.sub.aREF, i.sub.bREF, and i.sub.cREF, 
respectively. To accomplish this tracking, the current regulator 220 can 
perform any number of known tracking or pulse-width modulation switching 
techniques including the "Bang-Bang" control method and the "Pulse-Width 
Modulation" control method, both of which are well-known in the art. Thus, 
the current regulator 220 can comprise, for example, the comparator 
circuit illustrated in FIG. 6. 
In the circuit of FIG. 6, the comparator 300a compares the reference 
current i.sub.aREF with the feedback current i.sub.aFB to generate a 
switching signal SW.sub.a. The switching signal SW.sub.a is applied to the 
switching device 290a.sub.1. The switching signal SW.sub.a is also 
inverted by an inverter 310a and thereafter applied to the switching 
device 290a.sub.2. When the reference current i.sub.aREF is less than the 
feedback current i.sub.aFB, the switching signal SW.sub.a operates to turn 
the switching device 290a.sub.1 on and to turn the switching device 
290a.sub.2 off. Similarly, when the reference current i.sub.aREF is 
greater than the feedback current i.sub.aFB, the switching signal SW.sub.a 
operates to turn the switching device 290a.sub.1 off and to turn the 
switching devices 290a.sub.2 on. 
Like the comparator 300a, the comparator 300b compares the reference 
current i.sub.bREF with the feedback current i.sub.bFB to generate a 
switching signal SW.sub.b. The switching signal SW.sub.b is applied to the 
switching device 290b.sub.1. Similarly, the comparator 300c compares the 
reference current i.sub.cREF with the feedback current i.sub.cFB to 
generate a switching signal SW.sub.c which is applied to the switching 
device 290c.sub.1. The switching signals SW.sub.b and SW.sub.c are also 
inverted by inverters 310b and 310c, respectively, and thereafter applied 
to the switching devices 290b.sub.2 and 290c.sub.2, respectively. 
When the reference current i.sub.bREF is less than the feedback current 
i.sub.bFB, the switching signal SW.sub.b operates to turn the switching 
device 290b.sub.1 on and to turn the switching device 290b.sub.2 off. And 
when the reference current i.sub.bREF is greater than the feedback current 
i.sub.bFB, the switching signal SW.sub.b operates to turn the switching 
device 290b.sub.1 off and to turn the switching device 290b.sub.2 on. 
Similarly, when the reference current i.sub.cREF is less than the feedback 
current i.sub.cFB, the switching signal SW.sub.c operates to turn the 
switching device 290c.sub.1 on and to turn the switching device 290c.sub.2 
off. And when the reference current i.sub.cREF is greater than the 
feedback current i.sub.cFB, the switching signal SW.sub.c operates to turn 
the switching device 290c.sub.1 off and to turn the switching device 
290c.sub.2 on. 
In this manner, the current regulator 220 controls the inverter 230 such 
that the feedback currents i.sub.aFB, i.sub.bFB, and i.sub.cFB track the 
reference currents i.sub.aREF, i.sub.bREF, and i.sub.cREF. Thus, the phase 
windings of the synchronous motor 240 are energized by the inverter 230 in 
a sequence such that the motor 240 produces an output torque in accordance 
with the torque command. 
It should be appreciated that the motor circuit 200 of FIG. 5 differs from 
the motor circuit 20 of FIG. 3 in, among other things, the handling of 
nonzero return currents. In particular, each phase winding of the 
synchronous motor 60 of FIG. 3 has an independent current path for 
returning to ground nonzero return neutral currents which result from 
triplen harmonics in the reference currents i.sub.aREF, i.sub.bREF, and 
i.sub.cREF. The synchronous motor 240 Of FIG. 200, on the other hand, has 
but a single nonzero return neutral current path 320. Thus, the motor 
circuit 200 of FIG. 5 has a simpler structure than the motor circuit 20 of 
FIG. 3. It should also be appreciated that both the motor circuit 20 of 
FIG. 3 and the motor circuit 200 of FIG. 5 are preferred over conventional 
star or delta type inverters because nonzero return neutral currents 
generally cannot flow freely through those types of conventional 
inverters. 
It will be apparent to those skilled in the art that various modifications 
and variations can be made in the present invention without departing from 
the spirit or scope of the invention. Thus, it is intended that the 
present invention cover the modifications and variations of the invention 
provided they come within the scope of the appended claims and their 
equivalents.