Switched reluctance type self-sensing active pulse torque compensation

Abstract

A system (102) and method for torque compensation in a switched reluctance (SR) machine (104) disposed in a machine (100) are disclosed. The system (102) may include the SR machine (104), an inverter (122), and a controller (124). The controller (124) is in operative communication with the inverter (122) and is configured to determine a commanded primary current associated with energizing a first portion of the plurality of windings (130) with a primary current (138) for a controlled phase (132) and to determine a commanded parasitic current associated with energizing a second portion of the windings (130) with a parasitic current (140) in an uncontrolled phase (134). The controller (124) is further configured to determine an offset current (142) based on the commanded parasitic current, determine a target current (136) based on a first sum of the commanded main current and the offset current (142), and command the inverter (122) to operate the target current (136) in the first portion of the winding (130) during the control phase (132).

Description

[Technical Field]

[0001] The present disclosure relates generally to switched reluctance (SR) machines, and more particularly to a system for torque compensation. [Background technology]

[0002] SR machines are typically electric machines configured to convert electrical energy into rotational torque or rotational torque into electrical energy for any of a variety of applications including power generation, power backup, offshore drilling, machine tools, traction motors, industrial work machines, marine work machines, etc.

[0003] SR machines contain a rotor and a stator. Unlike typical brushed DC motor types, power is supplied to windings in the stator (case) rather than the rotor. Accurately determining the position of the rotor relative to the stator of an SR machine while stationary or at substantially lower machine speeds is critical to the machine's performance and efficiency. Traditionally, rotor position information for SR machines is obtained using direct position sensor(s) mounted on the shaft, but such hardware increases the cost and complexity of the overall drive system. Methods for obtaining or deriving position information without the use of traditional direct position sensors are helping to reduce the minimum package size and cost of SR machines.

[0004] Some SR machines may be equipped with a sensorless control system that estimates the rotor position and speed relative to the stator without using traditional direct position sensors. Such control systems may estimate the rotor position by injecting current pulses into one or more idle phases of the SR machine's stator. The stator currents flowing during the idle phases may then be estimated using an observer-based estimation approach. The estimated stator currents can then be compared with the actual stator currents to generate an error signal. The error signal can be used to calculate an estimated rotor position and an estimated rotor speed. However, when the rotor is at a substantially low machine speed or is stopped, the generated error signal may be very weak, making it very difficult to accurately determine the rotor's position relative to the stator. Furthermore, when the SR machine is operating in the motoring quadrant, the stator currents flowing during the idle phase(s) may generate an undesirable braking torque.

[0005] U.S. Patent No. 7,604,088 discloses an electric power steering system that provides a good steering feel without using compensation logic such as inertia compensation and friction compensation. This electric power steering system includes a road noise suppression control means that controls the steering assist motor to attenuate torque transmission in a high-frequency range representing road noise more than in a frequency range representing road information. The friction value of the steering mechanism is reduced to a level where the natural vibration of the steering mechanism appears. The rotor inertia of the steering assist motor is set to a small value so that the frequency of the natural vibration exists in the frequency range where torque transmission is attenuated by the road noise suppression control means. While this is beneficial, a better system is needed. Summary of the Invention

[0006] In one aspect of the present disclosure, a system for torque compensation in a switched reluctance (SR) machine disposed in a machine is disclosed. The system includes the SR machine, an inverter, and a controller. The SR machine includes a stator and a rotor rotatably disposed within the stator. The stator includes a plurality of windings. The SR machine is configured to rotate the rotor when one or more windings are energized. The inverter is operably connected to the plurality of windings. The inverter can be configured to generate a target current in a first portion of the plurality of windings. The controller is in operative communication with the inverter and is configured to: determine, by the controller, a commanded main current associated with energizing a first portion of the plurality of windings with a main current in a control phase; determine, by the controller, a commanded parasitic current associated with energizing a second portion of the windings with a parasitic current in a non-controlled phase; determine an offset current based on the commanded parasitic current; determine a target current based on a first sum of the commanded main current and the offset current; and command the inverter to operate the target current in the first portion of the windings during the control phase.

[0007] In another aspect of the present disclosure, a method for torque compensation in an SR machine is disclosed. The SR machine includes a stator and a rotor rotatably disposed within the stator. The stator includes a plurality of windings. The SR machine is configured to rotate the rotor when one or more of the windings are energized. The method includes determining, by a controller, a commanded main current associated with energizing a first portion of the plurality of windings with a main current in a control phase; determining, by the controller, a commanded parasitic current associated with energizing a second portion of the windings with a parasitic current in a non-control phase; determining an offset current based on the commanded parasitic current; determining a target current based on a first sum of the commanded main current and the offset current; and actuating the target current for the first portion of the windings during the control phase.

[0008] In yet another aspect of the present disclosure, a computer program product is disclosed. The computer program product includes a computer-usable medium having computer-readable program code embodied therein. The computer-readable program code is configured to be executed to implement a method for torque compensation in an SR machine including a stator including a plurality of windings and a rotor rotatably disposed within the stator, the SR machine configured to rotate the rotor when one or more windings are energized, the method including: determining, by a controller, a commanded main current associated with energizing a first portion of the plurality of windings with a main current in a control phase; determining, by the controller, a commanded parasitic current associated with energizing a second portion of the windings with a parasitic current in a non-controlled phase; determining an offset current based on the commanded parasitic current; determining a target current based on a first sum of the commanded main current and the offset current; and actuating the target current for the first portion of the windings during the control phase. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram of an exemplary machine including an SR machine. [Figure 2] 1 is a schematic diagram of an exemplary embodiment of an electric drive system according to the present disclosure. [Figure 3] 1 is a flow diagram of an exemplary method of torque compensation according to the present disclosure. [Figure 4] FIG. 2 is a schematic diagram of an exemplary parasitic pulse injected into a parasitic injection window. [Figure 5] FIG. 10 is a diagram comparing two exemplary target currents. DETAILED DESCRIPTION OF THE INVENTION

[0010] Reference will now be made in detail to specific embodiments or features, examples of which are illustrated in the accompanying drawings. Generally, corresponding reference numerals are used throughout the drawings to refer to the same or corresponding parts unless otherwise specified.

[0011] FIG. 1 is a diagram of an exemplary machine 100 incorporating features of the present disclosure, a wheel loader, or SR machine 104, and an electric drive system 102 including, for example, an SR motor or an SR generator. For purposes of illustration, the exemplary embodiment shows the SR machine 104 utilized as an SR motor, although in other embodiments, the SR machine 104 may be utilized as a generator (operably coupled to a power source 110 (e.g., an engine)). As shown, the machine 100 includes a frame 106, a traction system 108 supporting the frame 106, a power source 110 mounted on the frame 106, and an electric drive system 102 configured to transfer energy from the power source 110 to the traction system 108. The machine 100 may also include a cab 112. The power source 110 is configured to power the machine 100 and provide operating power to the electric drive system 102. In some embodiments, the power source 110 may be a direct current (DC) power source. Power supply 110 may be in operative communication with operator controls 114 in operator cab 112 and may be configured to receive control signals from operator controls 114. Additionally, power supply 110 may be operatively connected to other systems of machine 100.

[0012] Electric drive system 102 is operably coupled to power source 110 and may selectively propel machine 100 via control signals from operator controls 114. Electric drive system 102 may be operably connected to traction system 108, which may be operably connected to machine 100 via axles, drive shafts, transmissions, and / or other components, as shown. In some embodiments, traction system 108 may be provided in the form of a wheel drive system, a track drive system, or any other type of drive system configured to engage the ground and propel machine 100.

[0013] In some embodiments, the electric drive system 102 may additionally or alternatively be operably coupled to a power source 110 to selectively operate an implement 116, which may be movably mounted on the frame 106 and operably connected to the electric drive system 102. The illustrated implement 116 includes a lift arm assembly 118 and a bucket 120. Other embodiments may include any other implement suitable for various tasks, such as, for example, dozing, blades, brushing, compacting, grading, lifting, ripping, tilling, etc.

[0014] As indicated above, Figure 1 is provided as one example of a machine 100 that can utilize the electric drive system 102 of the present disclosure. Other examples are possible and may differ from those described in connection with Figure 1.

[0015] As shown in FIG. 2 , electric drive system 102 includes a switched reluctance (SR) machine 104, an inverter 122, and a controller 124. SR machine 104 includes a rotor 126 rotatably disposed within a (fixed) stator 128. In an exemplary embodiment, SR machine 104 may be configured to operate as an SR motor. Rotor 126 of SR machine 104 may be coupled to an output shaft (not shown), which may in turn be connected to drive a mechanical load (not shown). Each (phase) winding 130 of stator 128 of SR machine 104 may be electrically coupled to inverter 122. SR machine 104 may be configured to rotate rotor 126 in response to a current (e.g., a target current 136, a main current 138) supplied to stator 128 from inverter 122. The windings 130 that are energized with a target current 136 (see FIG. 5) or a main current 138 to rotate the rotor 126 (FIG. 2) in a commanded direction according to the machine command are said to be in the control phase 132. The remaining windings 130 that are not energized or are energized by a parasitic current 140 (FIG. 4), such as for diagnostic / positioning purposes, are said to be in the idle or non-control phase 134 (FIG. 2).

[0016] The inverter 122 may be electrically connected to the power source 110 (FIG. 1). In some embodiments, the inverter 122 (FIG. 2) may receive a DC current and supply an AC current to the stator 128 of the SR machine 104. More specifically, the inverter 122 is in operative communication with the controller 124 and is configured to supply (AC) current to selected windings 130 of the stator 128 of the SR machine 104 in response to control signals / commands received from the controller 124. The supplied current may be a target current 136 (FIG. 5), a main current 138 (see FIG. 5), a parasitic current 140 (FIG. 4), or other current.

[0017] Controller 124 (FIG. 2) is configured to control the operation of inverter 122. Controller 124 may be configured to send control signals to inverter 122 to selectively energize current through one or more windings 130 of SR machine 104. As mentioned above, when energized to drive a desired rotation of rotor 126, windings 130 are considered to be in a control phase 132, and as described later herein, the current supplied by inverter 122 may be referred to as a target current 136 (FIG. 5), or, in the absence of an offset current 142 (described later herein), the current supplied by inverter 122 (FIG. 2) in control phase 132 may be referred to as a main current 138 (FIG. 5).

[0018] The controller 124 ( FIG. 2 ) may be further configured to send commands to the inverter 122 to inject a parasitic current 140 ( FIG. 4 ) (e.g., a commanded parasitic current) into at least one idle or uncontrolled phase 134 ( FIG. 2 ) of the stator 128 of the SR machine 104 when the SR machine 104 is operating at zero revolutions per minute (rpm), near zero rpm, or other relatively low speeds. The parasitic current 140 ( FIG. 4 ) may be supplied by the inverter 122 ( FIG. 2 ) in the form of current pulses (“parasitic pulse(s)” 146) within an injection window (“parasitic injection window” 144) time frame. The beginning of the parasitic injection window is defined by an “on” rotation angle, and the end of the parasitic injection window is defined by an “off” rotation angle. The “on” rotation angle and the “off” rotation angle are each measured relative to a position θ of the rotor 126. As used herein, θ refers to a reference electrical cycle rotor position. FIG. 4 shows a schematic diagram of an exemplary parasitic pulse 146 injected by the inverter 122 into at least one idle or uncontrolled phase 134 of the stator 128 within a parasitic injection window 144 .

[0019] The controller 124 ( FIG. 2 ) may include a processor 148 and a memory component 150. The controller 124 is in operative communication with the SR machine 104 and the inverter 122. The controller 124 is configured to determine a commanded main current associated with energizing a first portion of the plurality of windings 130 with a main current 138 in a control phase 132. The controller 124 is further configured to determine a commanded parasitic current associated with energizing a second portion of the plurality of windings 130 with a parasitic current 140 in a non-control phase 134. The controller 124 is further configured to determine an offset current 142 based on the commanded parasitic current, and to determine a target current 136 based on the sum of the commanded main current and the offset current 142. The controller 124 is further configured to command the inverter 122 to energize the first portion of the windings 130 with the target current 136 during the control phase 132.

[0020] Processor 148 may be a microcontroller, a digital signal processor (DSP), an electronic control module (ECM), an electronic control unit (ECU), a field programmable gate array (FPGA), a microprocessor, or any other suitable processor 148 known in the art. Processor 148 may execute instructions to determine the commanded main current, the commanded parasitic current, the offset current 142, and the target current 136 and generate control signals to operate inverter 122. Such instructions may be loaded or embedded in a computer-readable medium, such as memory component 150, or may be provided external to processor 148. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions to implement the control methods.

[0021] As used herein, the term "computer-readable medium" refers to any non-transitory medium or combination of media that participates in providing instructions to processor 148 for execution. Such media may include all computer-readable media except for transitory propagating signals. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape or other magnetic media, CD-ROMs, other optical media, or other computer-readable media.

[0022] Controller 124 is not limited to one processor 148 and memory component 150. Controller 124 may include several processors 148 and memory components 150. In one embodiment, processor 148 may be a parallel processor that has access to shared memory component(s) 150. In another embodiment, processor 148 may be part of a distributed computing system in which processor 148 (and its associated memory component 150) may be located remotely from one or more other processors 148 (and associated memory component 150) or FPGAs that are part of the distributed computing system.

[0023] The controller 124 may also be configured to obtain from the memory component 150 formulas and other data required for the calculations described herein.

[0024] A method of torque compensation in an SR machine 104 is also disclosed. The method may include determining, by a controller 124, a commanded main current associated with energizing a first portion of a plurality of windings 130 in a control phase 132 with a main current 138, determining, by the controller 124, a commanded parasitic current associated with energizing a second portion of the windings 130 in a non-controlled phase 134 with a parasitic current 140, determining an offset current 142 based on the commanded parasitic current, determining a target current 136 based on a sum of the commanded main current and the offset current 142, and actuating the target current 136 for the first portion of the windings 130 during the control phase 132.

[0025] Also disclosed is a computer program product comprising a computer usable medium having computer readable program code embodied thereon that is configured to be executed to implement a method for torque compensation in a switched reluctance SR machine 104, the method including determining, by a controller 124, a commanded main current associated with energizing with a main current 138 a first portion of a plurality of windings 130 in a controlled phase 132; determining, by the controller 124, a commanded parasitic current associated with energizing with a parasitic current 140 a second portion of the windings 130 in a non-controlled phase 134; determining an offset current 142 based on the commanded parasitic current; determining a target current 136 based on a sum of the commanded main current and the offset current 142; and actuating the target current 136 for the first portion of the windings 130 during the control phase 132. Industrial Applicability

[0026] In operation, the controller 124 may be configured to operate according to a predetermined method 300, for example, as shown in Figure 3. Figure 3 is an exemplary flow chart illustrating the method 300 for torque compensation.

[0027] In block 310, the controller 124 determines a commanded main current associated with energizing a first portion of the plurality of windings 130 of the control phase 132 of the SR machine 104 with a main current 138 (see FIG. 5 ). The commanded main current is associated with generating an AC current provided by the inverter 122 to energize one or more windings 130 of the stator 128 to generate a rotational attraction force on the rotor 126 at a selected speed or torque. Such a current may be referred to as the main current 138. The energized winding 130 is considered to be in the control phase 132 for the duration of the main current 138. In some embodiments, in a particular speed and torque region, which may vary depending on the SR machine 104, the main current 138 may have an approximately trapezoidal waveform, as shown in FIG. 5 .

[0028] In one embodiment, the determining of block 310 may include controller 124 receiving a commanded main current from another controller, a user interface, or a mechanical system, or may include retrieving the commanded main current from memory component 150. In yet another embodiment, the determining may include controller 124 calculating the commanded main current based on operating parameters. Such operating parameters may include rotor speed, rotor position, DC link voltage of electric drive system 102, torque command, or a combination thereof. Controller 124 may also receive operating parameters including a target, actual, or estimated speed, rotor torque command, and / or a target, estimated, or actual DC link voltage associated with electric drive system 102.

[0029] In block 320, controller 124 determines a commanded parasitic current associated with the energization of a second portion of winding 130 by parasitic current 140 ( FIG. 4 ) in uncontrolled phase 134. The commanded parasitic current is associated with the generation of AC current provided by inverter 122 to energize one or more windings 130 (uncontrolled phase 134) of stator 128 to provide an amount of current that can be utilized to determine the position of rotor 126 within stator 128 without direct position sensing of rotor 126 by a position sensor attached to a shaft operatively coupled to rotor 126. Such current may be referred to as parasitic current 140.

[0030] While parasitic current 140 may be injected for diagnostic purposes, such injection of parasitic current 140 may also generate a braking torque in the opposite rotational direction to the desired torque generated by main current 138 in control phase 132 (e.g., when SR machine 104 is operating in the motoring quadrant). When rotor 126 is stationary, parasitic current 140 may generate a braking torque that may cause rotor 126 to rotate in an unintended direction and may increase the torque required for rotor 126 to begin rotating in the intended direction.

[0031] Typically, the amplitude of the parasitic current 140 will be relatively low (e.g., greater than 0 amperes (A) up to 150 amperes (A), 25-150 A, 45-53 A, or approximately 50 A), depending on the application, to provide sufficient current to determine the position of the rotor 126 while minimizing the generation of braking torque. The parasitic current 140 may include multiple current pulses ("parasitic pulses") 146 injected during a parasitic injection window 144. Each such parasitic pulse 146 has a pulse area 152 under the waveform curve, as is known in the art. In some embodiments, the parasitic pulses 146 may have an approximately trapezoidal waveform, as seen in FIG. 4 . In other embodiments, the parasitic current 140 may have other waveforms.

[0032] In block 330, the controller 124 determines a target current 136 (see FIG. 5 ) to be supplied by the inverter 122 to energize the windings 130 of one or more control phases 132 of the stator 128 during a parasitic injection window 144. The target current 136 is intended to compensate for the damping effect of the parasitic current 140 on torque (e.g., when operating in the motoring quadrant). As is known in the art, the SR machine 104 may operate in a damping quadrant and a motoring quadrant. The parasitic pulse 146 is considered to be in the damping quadrant when the SR machine 104 is motoring, and in the motoring quadrant when the SR machine 104 is braking. This applies whether the SR machine 104 is operating as a motor, a generator, or other applications of the SR machine 104. In one embodiment, when the speed of the rotor 126 is relatively low (e.g., in the range of approximately 0-500 rpm), the controller 124 may determine a target current 136 to be supplied by the inverter 122 to energize one or more control phases 132 of the stator 128 and compensate for the damping effect of the parasitic current 140. The target current 136 may be based on or equal to the sum of the commanded main current and the offset current 142.

[0033] As part of determining the target current 136, the controller 124 determines an offset current 142. The offset current 142 may be based on a commanded parasitic current (FIG. 4). In one embodiment, the offset current 142 may be set equal to the amplitude of the commanded parasitic current during a parasitic injection window 144. For example, in one embodiment, the offset current 142 may be set equal to the maximum or target amplitude of the parasitic current 140 (or parasitic pulse 146) within the parasitic injection window 144. In an exemplary embodiment, the parasitic current 140 may be equal to 50 A, and the offset current 142 may be set equal to 50 A. The commanded target current may then be equal to the commanded main current plus the offset current 142 of 50 A (the value of the amplitude of the parasitic current 140). The value of 50 A is an example. Other amplitudes associated with the parasitic current 140 can also be used to adjust the offset current 142 (e.g., greater than 0 amperes (A) up to 150 amperes (A), 25-150 A, 45-53 A, or approximately 50 A).

[0034] In some applications, the sum of the pulse areas 152 of each parasitic pulse 146 within the parasitic injection window 144 may not actually equal the area 154 under the target current 136 curve, so adding a constant value of the offset current 142 to the main current 138 may result in either over-compensation or under-compensation. In some cases, the target current 136 required to compensate for the effect of the braking torque is much higher than the target current 136 calculated by the controller 124 using a constant value (e.g., 50 A) of the amplitude of the parasitic current 140. To address this, the calculation of the offset current 142 may be refined. In the refinement, the controller 124 may determine / calculate the offset current 142 based on the sum of the commanded main current and the offset current 142, where the offset current 142 is based on the sum of the pulse areas 152 under each parasitic pulse 146 within the parasitic injection window 144.

[0035] 5 illustrates an exemplary scenario comparing a first target current 136a based on a commanded main current plus an offset current 142a equal to the parasitic current 140 (e.g., 50 A) with a second target current 136b based on the commanded main current plus the offset current 142b, where the offset current 142b is based on the sum of the pulse areas 152 under each parasitic pulse 146 within a parasitic injection window 144. In this exemplary scenario, the first target current 136a does not fully compensate for the braking torque of the parasitic current 140, while the second target current 136b fully compensates for such braking torque. The controller 124 may utilize a lookup table, hash table, map, or other structure (collectively “map”) to determine the pulse area 152 under each parasitic pulse 146 within the parasitic injection window 144. The pulse area 152 under each parasitic pulse 146 may be determined by retrieving an area value from a map based on the parasitic current 140 and the (estimated or actual) rotational speed of the rotor 126. In another embodiment, the pulse area 152 under each parasitic pulse 146 may be determined by retrieving an area value from a map based on the parasitic current 140, the (estimated or actual) rotational speed of the rotor 126, and the torque command for the rotor 126. In another embodiment, the pulse area 152 under each parasitic pulse 146 may be determined by retrieving an area value from a map based on the parasitic current 140, the (estimated or actual) rotational speed of the rotor 126, and the torque command for the rotor 126, and the (estimated or actual) DC link voltage associated with the electric drive system 102. The values ​​in the map of pulse area 152 may be the result of empirical evaluation, testing, known calculations, or a combination of the above.

[0036] In block 340, the controller 124 activates the target current 136 in the first portion of the winding 130 during the control phase 132. In some embodiments, the controller 124 also activates the parasitic current 140.

[0037] In general, the foregoing disclosure may prove useful in a variety of applications related to SR machines. More specifically, the disclosed electric drive system 102 and method may be used to compensate for the effect of parasitic currents 140 on rotor 126 (e.g., utilized to determine the position and velocity of rotor 126), i.e., to compensate for the braking torque generated by parasitic currents 140.

[0038] From the foregoing, it will be appreciated that, while only certain embodiments have been described for purposes of illustration, alternatives and modifications will be apparent to those skilled in the art in light of the foregoing description. These and other alternatives are considered equivalents and are included within the spirit and scope of this disclosure and the appended claims.

Claims

1. A system (102) for torque compensation in a switched reluctance (SR) machine (104) disposed in a machine (100), comprising: a switched reluctance (SR) machine (104) including a stator (128) including a plurality of windings (130) and a rotor (126) rotatably disposed within the stator (128), the SR machine configured to rotate the rotor (126) when one or more of the windings (130) are energized; an inverter (122) operably connected to the plurality of windings (130) and configured to generate a target current (136) in a first portion of the plurality of windings (130); a controller (124) in operative communication with the inverter (122), the controller (124) comprising: determining a commanded main current associated with energizing the first portion of the plurality of windings of the control phase with a main current; determining a commanded parasitic current associated with energization by the parasitic current (140) of the second portion of the winding (130) during the uncontrolled phase (134); determining an offset current (142) based on the commanded parasitic current; determining a target current (136) based on a first sum of the commanded main current and the offset current (142); A system (102) configured to command the inverter (122) to operate the target current (136) in the first portion of the winding (130) during the control phase (132).

2. The system of claim 1 , wherein the offset current (142) is equal to an amplitude of the commanded parasitic current during a parasitic injection window (144).

3. The system of claim 2 , wherein the amplitude is a maximum amplitude of the commanded parasitic current during the parasitic injection window (144).

4. the parasitic current (140) is a plurality of parasitic pulses (146) injected into a parasitic injection window (144), each parasitic pulse (146) having a pulse area (152); 2. The system of claim 1, wherein the offset current is equal to a second sum of the pulse areas under each parasitic pulse within the parasitic injection window.

5. The system of claim 1 , wherein the determination of the offset current (142) is based on the commanded parasitic current and a rotational speed of the rotor (126).

6. The system of claim 1 , wherein the determination of the offset current (142) is based on the commanded parasitic current, a rotational speed of the rotor (126), and a torque command for the rotor (126).

7. 2. The system of claim 1, wherein the determination of the offset current is based on the commanded parasitic current, a rotational speed of the rotor, a torque command for the rotor, and a DC link voltage.

8. 1. A method for torque compensation in an SR machine (104) including a stator (128) including a plurality of windings (130) and a rotor (126) rotatably disposed within the stator (128), wherein energizing one or more of the windings (130) causes the rotor (126) to rotate, the method comprising: determining, by the controller (124), a commanded main current associated with energizing a first portion of the plurality of windings (130) of the control phase (132) with a main current (138); determining, by the controller (124), a commanded parasitic current associated with energization by a parasitic current (140) of a second portion of the winding (130) during an uncontrolled phase (134); determining an offset current (142) based on the commanded parasitic current; determining a target current (136) based on a first sum of the commanded main current and the offset current (142); and actuating the target current (136) in the first portion of the winding (130) during the control phase (132).

9. The method of claim 8, wherein the offset current (142) is equal to the amplitude of the commanded parasitic current during a parasitic injection window (144).

10. 10. The method of claim 9, wherein the amplitude is the maximum amplitude of the commanded parasitic current during the parasitic injection window (144).

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