Thermal compensation of commutation coils in brushless direct current motors

Abstract

Systems and methods for thermal compensation in brushless direct current motors are disclosed. In some examples, a first stator coil is driven using a first control signal to initiate movement of a rotor comprising a permanent magnet. A perceived current through the first stator coil is measured and scaled using a resistive divider network comprising a thermistor. A difference between the perceived current through the first stator coil and an actual current through the first stator coil is then determined. A second stator coil is driven using a second control signal at a time determined based on the determined difference. In some examples, an induced back electromotive force (BEMF) signal is determined based on the determined difference. The time to drive the second stator coil in these examples can be generated based on a comparison between the first control signal and the induced BEMF signal.

Description

THERMAL COMPENSATION OF COMMUTATION COILS IN BRUSHLESS DIRECT CURRENT MOTORSCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 549,987, entitled “THERMAL COMPENSATION OF COMMUTATION COILS IN BRUSHLESS DIRECT CURRENT MOTORS” filed February 5, 2024, the disclosure of which is hereby incorporated by reference in its entirety for all purposes.FIELD

[0002] This technology generally relates to linear and rotary brushless direct current (BLDC) motors and. more particularly, to methods and devices for thermal compensation of commutation coils for more effectively and accurately controlling BLDC motors.BACKGROUND

[0003] Multiphase linear and rotary brushless direct current (BLDC) motors are used in a variety of different types of deployments and disciplines. For example, BLDC motors are employed in vehicles (e.g., trains), wind turbines, spacecraft, nuclear reactor centrifuges, commercial building system components (e.g., magnetic bearings, elevators, lifts, fans, compressors, chillers, and pumps), household appliance system components (e.g., lamps, chairs, sofas, beds, washing machines, rooms, and toys), and advertising system components (e g., objects inside or above various frames), and in automation track systems to move objects, among many other use-cases.

[0004] In one example, liquid handler systems use automation track systems to move pucks coupled to vessels containing patient bodily fluid samples (e.g., blood, urine, spinal fluid) to various laboratory instruments for analysis. Liquid handler systems that are designed to dispense and process selected quantities of reagents, samples, or other liquids, can be adapted to analyze samples using, for example, immunoassay and / or clinical chemistry techniques. Such liquid handlers could be referred to as “analyzers” or “analyzer systems,” and can include a number of modules and a transport system to move samples between the various modules. It is desirable for liquid handler transport systems to move sample containers (e.g., reaction cuvettes, tubes, or vessels) in a smooth manner, avoid causing the sample containers to collide with each other, and otherwise prevent liquids from spilling from their containers during transport. In particular, liquid spills waste reagents and / or samples, which could potentially impact the integrity of any tests being performed and can create obstructions that could impair the movement of subsequent sample containers.

[0005] Recently, there has been some development using coils embedded in the track surface to propel permanent magnet(s) in the base of a vessel mover. In particular, the coils in the track are selectively activated to apply a magnetic field to the magnet(s) in the vessel movers, synchronizing the fields to the movement of the magnet(s), causing movement along a plane. Conventionally, the coils are made of narrow-gauge wound copper wire. This approach is simple to construct, but is expensive, especially as the number of coils goes up to accommodate a large number of paths and the overall size of a laboratory automation or other type of track system. Further, drive circuits are needed for the coils and Hall effect sensors need to be placed near the track surface to detect the location and movement of the permanent magnet(s) of the vessel movers. The circuits can be constructed on printed circuit boards (PCBs), which may be separate from a substrate of the wire windings of the coils.

[0006] Synchronous activation of the coils creates a moving magnetic field that moves to / from adjacent planar coils along the row of coils. By synchronously activating groups of coils, a magnet in the base of a vessel mover / carrier can be selectively propelled along a chosen path. Accordingly, the coils can be periodically spaced along the longitudinal axis of a track and individually commutated in a multiphase manner to adequately propel a vessel mover in a desired direction in a safe, predictable, quiet, and efficient manner. Thus, the planar coils can be incorporated into PCBs such that they are spaced to efficiently impart force to move the vessel mover when commutated. The primary benefits of using a linear coil drive include realization of high-fidelity analog current waveforms, lower force (torque) ripple, lower system electrical noise, reduced electromagnetic emissions, lower acoustic noise, greater control resolution for position and velocity, lower cost components, reduced difficulty' to source components, reduced maintenance costs, and increase to useful life of the system.

[0007] However, a voltage occurs in BLDC motors due to relative motion between the moving magnetic components (i.e., the rotor) of the vessel movers and the BLDC motor's coils (i.e., the stator windings), which is referred to as back electromotive force (BEMF) and causes a BLDC motor to act as a generator while operating as a motor. The BEMF is due to inductance and Faraday's law, occurs even when the motor current is not changing, and arises from the geometric considerations of the magnetic components of a vessel mover moving linearly or rotationally in proximity to a conductor or coil. When the speed varies in a BLDC motor, the winding characteristics may fluctuate, resulting in variation of BEMF. At high speeds, the motor rotors are rotating rapidly and have a high BEMF, and the same phenomenon exists in linear BLDC motors.

[0008] As a result of BEMF voltage induced into the coils by the permanent magnet of the moving vessel mover, the characteristics of the movement of the vessel mover can vary, which can introduce significant wear patterns, acoustic noise, and / or force ripple, for example, as well as cause spillage of fluids in an exemplary liquid handler robotic system deployment. Accordingly, current automation track systems employing BLDC motors attempt to compensate for the BEMF voltage in the commutation cycle. To facilitate the compensation, the BEMF voltage is generally obtained using observer software, which calculates the BEMF voltage based on known BLDC motor parameters. However, observer software algorithms are only capable of approximating the BEMF voltage, and therefore yield inaccurate and inefficient compensation in commutation cycles that negatively impact the efficiency and other characteristics of automation track and other systems employing BLDC motors.

[0009] Current BLDC motors also fail to compensate for temperature changes due to environmental temperature variation or heat dissipation resulting from operation of the BLDC motor and associated system. Stator coils in BLDC motors, whether wire-wound or planar, are typically constructed of copper, which has a positive linear temperature coefficient (TC) of approximately 0.393 percent per degree centigrade. The TC of copper translates to almost a 40 percent increase in resistance with a corresponding 100-degree centigrade rise in temperature due to the ambient environment, self-heating, or both. Other stator coil materials will likewise have a TC that will impact resistance.

[0010] This variation in resistance will impact the commutation cycle of the stator coils, resulting in a reduction in peak current, wear patterns, acoustic noise, and / or force ripple, for example. Thus, BLDC motors that operate over a range of temperatures currently may exhibit undesirable movement characteristics, which are exacerbated proportional to the increase or decrease in temperature. Since force in a linear BLDC motor and torque in a rotary BLDC motor are directly proportional to stator current, and stator current is proportional to the applied motor voltage divided by the stator coils’ resistances, higher temperatures can result in higher stator resistances and consequently lower forces or torques output by the BLDC motor.SUMMARY

[0011] Described herein are systems and methods for thermal compensation of commutation coils in brushless direct current (BLDC) motors.

[0012] In one embodiment, the present disclosure is directed to a method for thermal compensation in brushless direct current motors, comprising driving a first stator coil using a first control signal to initiate movement of a rotor comprising a permanent magnet. A perceivedcurrent through the first stator coil is measured using a resistive divider network comprising a thermistor. A difference between the perceived current through the first stator coil and an actual current through the first stator coil is then determined. A second stator coil is driven using a second control signal at a time determined based on the determined difference.

[0013] In some examples, the method can further include determining an induced back electromotive force (BEMF) signal based on the determined difference between the perceived current through the first stator coil and an actual current through the first stator coil. The induced BEMF signal is generated by the movement of the rotor relative to the first stator coil. The first control signal and the induced BEMF signal are then compared. The time to drive the second stator coil is then generated based on the comparison between the first control signal and the induced BEMF signal.

[0014] In some examples, the first stator coil and the compensating thermistor network are made of substantially the same conductive material or comprise substantially the same temperature coefficient. In other examples, the resistive divider network further comprises an upper leg comprising the thermistor and a lower leg comprising a fixed-value resistor. In these examples, the thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first stator coil. In yet other examples, a first resistance of the thermistor increases or decreases proportionally to a second resistance of the first stator coil. Additionally, the resistive divider network can comprise one or more fixed- value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first stator coil over the temperature range.

[0015] In some examples, the method can further include measuring a voltage across the first stator coil while a known current is injected into the first stator coil. A resistance of the first stator coil is then determined by dividing the measured voltage by the known current. The resistive divider network in these examples is then configured to yield a divisor substantially the same as the determined resistance.

[0016] In one embodiment, the present disclosure is directed to a transport system comprising a control system comprising one or more of a hybridized movement control architecture or a processor. The control system is configured to measure a perceived current through a first one of a plurality of conductive coils using a resistive divider network comprising a thermistor. The first one of the plurality of conductive coils is driven using a first control signal to provide a selective magnetic field to propel a magnetic base of a vessel mover. A second one of the plurality of conductive coils is then driven using a second control signalat a time determined based on a difference between the perceived current and an actual current through the first one of the plurality of conductive coils independent of temperature variation.

[0017] In some examples, the transport system further comprises a circuit configured to determine an induced BEMF signal based on the difference between the perceived current and the actual current. The induced BEMF signal is generated by the movement of the magnetic base of the vessel mover relative to the first one of the plurality of conductive coils. In these examples, the control system is further configured to compare the first control signal and the induced BEMF signal and generate the time to drive the second one of the plurality of conductive coils based on the comparison. In some examples, the transport system includes a track comprising a plurality of multilayer printed circuit boards (PCBs) arranged along a transport path, each PCB having one or more of the plurality of conductive coils.

[0018] The circuit can comprise a digital circuit or an analog circuit. In examples using an analog circuit, the transport system further comprises an analog-to-digital converter configured to convert an analog input into the BEMF signal, and the control system is further configured to obtain the BEMF signal from the analog-to-digital converter.

[0019] In some examples, the first one of the plurality of conductive coils and the thermistor are made of substantially the same conductive material or comprise substantially the same temperature coefficient. Additionally, the resistive divider network can further comprise an upper leg comprising the thermistor and a lower leg comprising a fixed- value resistor. The thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first one of the plurality of conductive coils over a desired operating temperature range of the transport system. A first resistance of the thermistor can also increase or decrease proportionally to a second resistance of the first one of the plurality' of conductive coils in some examples. Further, the resistive divider network can comprise one or more fixed- value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first one of the plurality of conductive coils over the temperature range.BRIEF DESCRIPTION OF THE FIGURES

[0020] The accompanying drawings, which are incorporated in and form a part of the specification, illustrate the embodiments of the invention and together with the written description serve to explain the principles, characteristics, and features of the invention. In the drawings:

[0021] FIG. 1 is a diagram of a track segment of a liquid handler system, in accordance with at least one aspect of the present disclosure;

[0022] FIG. 2 is a diagram of a vessel mover actuator, in accordance with at least one aspect of the present disclosure;

[0023] FIG. 3 is a top-view of a PCB coil in accordance with at least one aspect of the present disclosure;

[0024] FIG 4 is a cross sectional view of a printed circuit board (PCB) coil in accordance with at least one aspect of the present disclosure;

[0025] FIG. 5 is a top-view of a PCB coil track in accordance with at least one aspect of the present disclosure;

[0026] FIG. 6A is a top-view of a PCB coil track intersection in accordance with at least one aspect of the present disclosure;

[0027] FIG 6B is a cross sectional view of a PCB coil intersection in accordance with at least one aspect of the present disclosure;

[0028] FIG 6C is a cross sectional view of a PCB coil intersection in accordance with at least one aspect of the present disclosure;

[0029] FIG. 6D is a top-down x-ray view of a PCB coil track intersection in accordance with at least one aspect of the present disclosure;

[0030] FIG. 6E is a top-down x-ray view of another PCB coil track intersection in accordance with at least one aspect of the present disclosure;

[0031] FIG. 7 is a diagram of a liquid handler system including a vessel tracking system, in accordance with at least one aspect of the present disclosure;

[0032] FIG. 8 is a diagram of an exemplary driver circuit with BEMF signal extraction in the analog domain in accordance with at least one aspect of the present disclosure;

[0033] FIGS. 9A-C are plots of voltage versus time for control and BEMF signals for an exemplary conductive stator coil;

[0034] FIG. 10 is a flowchart of an exemplary method for BLDC motor control; and

[0035] FIG. 11 is a diagram of an exemplary driver circuit ith thermal compensation in the analog domain in accordance with at least one aspect of the present disclosure.DETAILED DESCRIPTION

[0036] Independent of the grammatical term usage, individuals with male, female or other gender identities are included within the term.

[0037] This disclosure is not limited to the particular systems, devices and methods described, as these may vary. The terminology used in the description is for the purpose of describing the particular versions or embodiments only and is not intended to limit the scope.

[0038] As used herein, the terms “algorithm,” “system,” “module,” “engine,” or “architecture,” if used herein, are not intended to be limiting of any particular implementation for accomplishing and / or performing the actions, steps, processes, etc., attributable to and / or performed thereby. An algorithm, system, module, engine, and / or architecture may be, but is not limited to, software, hardware and / or firmware or any combination thereof that performs the specified functions including, but not limited to, any use of a general and / or specialized processor in combination with appropriate software loaded or stored in a machine-readable memory and executed by the processor. Further, any name associated with a particular algorithm, system, module, and / or engine is, unless otherwise specified, for purposes of convenience of reference and not intended to be limiting to a specific implementation. Additionally, any functionality7attributed to an algorithm, system, module, engine, and / or architecture may be equally performed by multiple algorithms, systems, modules, engines, and / or architectures incorporated into and / or combined with the functionality of another algorithm, system, module, engine, and / or architecture of the same or different type, or distributed across one or more algorithms, systems, modules, engines, and / or architectures of various configurations.PCB-Based Automation Track Configurations

[0039] While examples of this technology are described and illustrated herein with reference to linear brushless direct current (BLDC) motors employed in automation track systems configured to transport vessel movers (e.g., pucks or sample carriers), the disclosed technology7is equally applicable to linear BLDC motors in other types of deployments, as well as rotary BLDC motors, as will be explained in more detail below. Accordingly, the linear BLDC motor of the automation track system disclosed herein is for exemplary purposes only, and other types of linear and rotary BLDC motors can advantageously be controlled using the back electromotive force (BEMF) signal extraction systems and methods of the disclosed technology7.

[0040] Automation track systems can include a variety of different types of transport systems, including electro-magnetic drive systems, friction-based track systems, or conveyor belts. In one example, automation track systems can include a track having a plurality7of synchronously controlled electro-magnetic coils. The automation track can be configured totransport a vessel mover or other object, which ty pically consists of permanent magnet(s) whose field interacts with that generated by an electro-magnet coil array on the track. In these systems, the automation track is configured to move the vessel movers via synchronously controlled electro-magnetic coils that propel the vessel movers along the system’s track sections. Conventional electro-magnetically driven transport systems use metallic substrates for the automation track. Metallic substrates have several disadvantages, including cost and weight. Accordingly, exemplary’ automation track systems described herein include printed circuit board (PCB)-based substrates for the automation track. In these examples, each track segment can include one or more PCBs having coil arrays that are configured to electromagnetically actuate the vessel mover to transport the vessel mover.

[0041] In some embodiments, track sections are divided up into several coil boards. The coils can be formed in the copper layers of the PCB itself. In some embodiments coil boards are controlled by master boards and node controllers (also referred to herein as a traffic control unit). In some embodiments, each master board can control up to eight different coil boards. Meanwhile, a node controller is centralized. A single node controller can control the entire vessel mover track. In some embodiments, multiple distributed node controllers can be used for scalability. For example, in larger systems, multiple node controllers may be used, and control of vessel movers can be handed off as they traverse different regions of the track. In some embodiments the components of the master boards can be integrated directly into the coil boards, allowing inclusion of drivers and magnetic coils on the same circuit board.

[0042] An automation track system can utilize a modular design whereby track components reside yvithin modules and each module can easily be linked together to join the track segments by placing adjacent modules in proximity and linking them. Lids above track can be removed during installation or service to facilitate linking of tracks. In some embodiments, track sections are expanded by placing modules adjacent to one another and bolting the track sections of each module together forming a single multi-branching track system. Signaling cables can be daisy- chained together for ease of expanding control, although other methods for communicably coupling modules and / or track sections together can also be used in other examples.

[0043] In some examples, vessel movers ride between rails on a track surface. The rails can be aluminum or stainless-steel extrusions that also include vertical sides on the exterior of the track components underneath track surface. These extrusions can include brackets to easily bolt internal components to these side pieces to form a track unit. In some embodiments described herein, the track surface is a PCB and the PCB track surface can include one or more coatings or other components. At the bottom of the side components of rails resides a baseplate.The baseplate can be mounted to the modules containing track sections and provide support for the track system.

[0044] Beneath the track surface resides a series of coils in some examples. In some embodiments, coil boards are PCBs that include several coils, transverse to the direction of the track, and repeated in a longitudinal direction. In some embodiments, the coils are printed in a multi-layer PCB. Furthermore, in some embodiments, the coils can be printed directly in the layers of the coil boards, making the coil boards and coils one monolithic entity, and resulting in a relatively thin combination. In some embodiments, the coil boards receive a control signal to indicate the trajectory to apply to a vessel mover traveling along that coil board and a power source of 24 VDC. In some embodiments the PCB coil board itself forms the track (i.e., riding) surface. The coil boards include coils, motor drivers to drive those coils, and, optionally, one or more sensors to detect the presence of carriers traversing the track surface above the coil board by detecting the magnets of the vessel movers.

[0045] Thus, each of the segments that collectively comprise an automation track includes a plurality of coils that are activated, in sequence, to provide a linear motor in conjunction with magnets in the bottoms of vessel movers. Each coil is activated to provide a push or pull force on magnet(s) placed in the bottom of each vessel mover. The speed at which coils are activated in sequence determines the speed of the vessel mover on that section of track. Furthermore, vessel movers may be moved into a position and stopped at a predetermined location with high resolution by precisely modulating current within the coils and carefully controlling the commutation frequency of coils at that location.

[0046] FIG. 1 shows an illustrative embodiment of a track segment 201 of an automation track system. As generally described above, the automation track system is configured to support one or more vessel movers 202 (also referred to as a “carrier” or “sample earner”), which are configured to receive a vessel 204 (e.g., test tube) therein. The track segment 201 can include a riding surface 206, which is the upper surface of the track segment 201 that supports the vessel mover 202 thereon and along which the vessel mover 202 is transported between the modules or components (e.g., clinical analyzers) of the automation track system 200.

[0047] In some embodiments, the riding surface 206 can include an active region 207 that the vessel mover 202 is intended to move along. As shown, the active region 207 is the area corresponding to coils embedded in or below' surface 206. The active region 207 can generally correspond to the medial portion of the riding surface 206, and the relative width of the region 207 (as defined by the coils) is a design choice affected by the placement of magnets in thevessel mover 202. If any liquid contaminants are present on the active region 207, they could negatively impact or otherwise impair the movement of the vessel mover 202, as noted above. In some embodiments, the track segment 201 could include a PCB substrate, as generally described herein. Optionally, guide rails 211 can be used to help limit the lateral placement of vessel mover 202 relative to the track and active region 207.

[0048] Further, as shown in FIG. 2, the track system can include one or more coil arrays 208 associated with each track segment 201. The coil arrays 208 can be configured to generate a magnetic field that interacts with a magnet 203 positioned within the base of the vessel mover 202. The coil arrays 208 and the vessel mover magnet 203 can collectively define a linear electromechanical actuator. By synchronously controlling the coil arrays 208, the track system can propel the vessel movers 202 (and, thus, the vessels 204) across the track segments 201 to the desired module or other component of the system.PCB Printed Coils

[0049] Existing electromagnetic actuator topologies include a combination of conductive wire wound around a bobbin in curved shapes which are then augmented by mechanical diverter mechanisms comprising engagement arms and associated motors to guide vessel movers off linear paths. These solutions are cumbersome to manufacture and suffer part to part inefficiencies due to the coil winding process and ability to assemble and align separate motor segments.

[0050] Some embodiments described herein instead utilize PCB manufacturing techniques in conjunction with movable vessel movers with bodies containing permanent magnets. A coupled electromagnetic device is created that is only possible due to the specific physics achievable within a PCB fabrication combined with mover and load constraints required by the application. A particular arrangement of artwork used to retain copper within the layer stack is prescribed which creates an exact relationship of resistance, inductance, and parasitic (floating) capacitance, which by design creates a specific relationship between factors optimized for the particular motion characteristics required by automation entities.

[0051] Spirals are formed on many PCB layers which are interconnected by vias through the substrate layer stack to create a coil with electrical properties that balance the thermal dissipation of copper losses with nominal and peak thrust forces required by the system. These interconnections are in some cases through the entire substrate stack and in others only connecting specific layers. The arrangement of spirals including but not limited to the width of copper, the separation from adjacent current carrying conductors, the exact shift of spiralsbetween layers, the length of copper between end caps, the gap at the center of a spiral stack and the gap between adjacent spirals, as well as other design artifacts are all interdependent and optimized as a multi-objective solution.

[0052] The arrangement of spirals on each layer within the PCB layer stack creates sets of coils that enable electromagnetic forces to be produced in different directional axes. With coordinated switching of the coil layers, a coupled magnetic vessel mover 202 can then be motivated in different axes of motion with respect to the physical PCB. Motion may be along, across or a combination of more than one axis of the PCB substrate. Moreover, higher level routing between paths of travel may be achieved by designated motions such as performing 90 degree turns at the end of linear travel, a four- way diversion onto a perpendicular lane of travel, or continuation of a linear path without any mechanical assistance devices.

[0053] Some embodiments presented herein rely on physical contact between the static portion of the motor and the movable entities. Unlike typical linear motor designs there are no constraints on the motion of the moving parts relative to the stationary parts. In some embodiments, there are no contact guides, mechanical devices or bearings employed other than the normal faction that results from entities resting on the stationary PCB substrate. The friction resulting from the normal contacts are managed by material choices to minimize the friction, whilst at the same time ensuring the life of the surfaces is sufficient for the intended system lifespan. Coating can be applied to the PCB substrate and / or the entity base (magnet and / or entity structure) to perform in concert as a pair achieving a specific regime of slip-stick friction that the automation track system uses for positioning of entities relative to the PCB substrate.

[0054] Furthermore, the manufacturing processes of PCB design yield extremely high- quality surfaces and tight geometric tolerances (variation typically <2% unit-to-unit) that enable a novel segment- to-segment alignment scheme to be achieved. Features and flexible material selections in the supporting structure align the separate PCB motor segments, which ensure seamless transfer of entities from one segment to another. The designs of the electromagnetic system, mechanical system, thermal systems, and controller architecture described above are tightly coupled, each providing features and functionality to the other as part of the optimization that manifests the complete automation solution.

[0055] By using a PCB arrangement rather than winding insulated copper wire mechanically, any specific profile of the individual traces making up a coil can be created in design software. Coils can have a thickness dictated by the specific PCB manufacturing process selected, which may allow coils of any reasonable thickness to be used for each layer. Tracewidths are dictated by the computationally created photoresist masks that are used during the printing process. Thus, a total cross-section for each coil trace can be selected as part of the design process without complicating the manufacturing process. Similarly, the gaps between individual layers of spiral coil traces are dictated by the properties of the layers selected, including the thickness of core or prepreg layers and their dielectric properties. Within each layer, the gap between adjacent traces in a spiral can be selected in the printing mask. In contrast, traditional wound coils are limited to a single round profile of copper wire and the dielectric thickness for the wire that is w ound around a bobbin.

[0056] Similarly, the exact shape of each coil spiral can be selected during the design process, resulting in a photoresist mask and resulting coil traces having the desired shape. Because a lithographic fabrication process is used, there is generally no substantial penalty incurred by choosing one shape or another during the manufacturing process. This means that the outer profile of the windings can appear more rectangular to maximize the amount of copper used in the coils and the uniformity of the field. Any other design considerations can also influence the exact shape of the PCB spiral layers. Furthermore, individual spiral layers can have slightly different profiles and individual traces within each spiral can have different shapes with, etc. This allows coil design to be optimized to field parameters. Finally, because the PCB manufacturing process is controlled by a precise masking and etching process, repeatability between the different PCB boards can be easily achieved with high quality results.

[0057] FIG. 3 is a top view of a PCB coil 310. which can be one of the coils of the coil array 208 of FIG. 2, for example. The primary component of PCB coil 310 is a stack of spiral traces 314 in a multi-layer PCB. Spiral traces 314 can be printed on multiple layers of the PCB during the PCB fabrication process to allow a greater number of turns of PCB coil 310. Spiral traces 314 can be printed in a clockwise or counterclockwise direction depending on the application. Each layer of spiral traces 314 can spiral inward or outward along a conductive path, which can differ between layers. Layers of spiral traces 314 can be interconnected to one another by vias 312 and 316. Vias include what will be referred to as intra-coil vias 316 that connect one end of a single layer of coil trace to one end of a coil trace in an adjacent layer, allowing one large stack of traces to form a single conductive coil. Vias also include what will be referred to as terminal vias that provide a conducting path to the top layer and bottom layer of a coil stack, allowing electrical connection to the terminals of stacked coil.

[0058] Multi-layer PCBs can be constructed using any applicable technique including by laminating alternating insulating layers with etched layers of copper (e.g., etched by masking and activating a photoresist layer that then allows the selective masking of copper when thecopper layer is chemically etched). Vias are drilled and filled with a conductor (copper) to provide electrical paths between the etched copper layers. In general, coil 310 is an elongated coil having a long axis and a short axis. Adjacent coils are placed along a track such that an edge (right or left) of each coil intersected by the short axis is substantially parallel with an edge of each adjacent coil (such as shown in FIG. 6A). By arranging coils in this manner, within each PCB and by placing PCBs together, continuous groups of coils creating one or more continuous path for the magnetic vessel movers to move along are formed. That is. the coils are placed adjacent to one another in a horizontal plane defined by the PCB track surface, such that their longer sides are adjacent.

[0059] FIG. 4 is a conceptual illustration of the cross section of PCB coil 310, without the specific details of the insulator materials. Coil 310 is created by laminating layers 318, which are made up of etched copper layers and an insulating dielectric material such as fiberglass and resin core or prepreg sheets that are laminated in the presence of heat and vacuum. Any number of layers 318 can be used, allowing any number of turns in printed coil to be created (the number of turns in each spiral times the number of layers of spirals gives the total turns for the printed coil 310). For example, a few hundred turns can be achieved by a dozen turns per spiral layer and twenty layers. The exact arrangement of traces within each spiral and how those traces are spaced relative to adjacent layers can be chosen to meet EMI or other specifications. In some embodiments, each conductive coil comprises at least twelve single-layer spirals, and each spiral comprises at least twelve turns.

[0060] In the single-coil example shown in FIG. 4, the traces forming the spirals are shown in black, while the copper traces 320 that run from the spirals to vias 312 and 316 are illustrated separately for clarity. While vias are illustrated as overlapping in the two-dimensional cross section, the vias do not actually overlap, instead being formed in separate holes in the PCB. A top surface of the PCB provides a track surface for vessel movers 202. In some embodiments, a low friction surface, such as s high density polymer (HDPE, UHMWPE, or UHMW adhesive films), liquid photo-imageable solder mask (such as LP-40), or PTFE, is applied to the top surface after PCB manufacturing to facilitate smooth movement of a vessel mover 202.

[0061] FIG. 5 shows a series of parallel PCB printed coils 310. By printing these coils in parallel, they can be synchronously activated to create a moving magnetic field to drive the magnet 203 in the base of the vessel mover 202 in either direction along direction 322. Depending on design requirements, any suitable number of coils 310 can be printed on a single PCB board (also referred to herein as a coil board) and additional PCB boards can be placedadjacent to one another to create a track of any length. In this example, the demarcation between separate PCB boards is not shown. In some embodiments, six coils are printed per PCB board.

[0062] The example shown in FIG. 5 is a straightaway where symmetrically oval coils 310 are oriented in parallel. As explained below, different arrangements can be created for curves and junctions, such as adding a trapezoidal component to the shape of the oval coils 310 and aligning adjacent coils 310 to have parallel edges. The specific aspect ratio of the coils 310, width and length, center size, overall shape, and spacing between coils 310 can be selected to create a linear synchronous motor (LSM) with desired physical properties.

[0063] FIG. 6A illustrates how an intersection that can be created using PCB printed coils 310. Unlike traditional bobbin-wound coils, PCB coils 310 are substantially thinner for the same number of turns. This means that two coils 310 can be stacked upon one another without moving the track surface substantially away from the edge surface of the coil 310. When a magnet 203 is spaced away from the surface of a spiral coil 310, the magnetic field diverges, and the field is less uniform and strong due to fringing effects. Therefore, it is desirable to keep the surface of the track as near to the top edges of the horizontally -laying coils 310 as possible. This is unachievable with traditional mechanical windings.

[0064] In the example illustrated in FIG. 6A, coils 310 are laid out in two intersecting directions, direction 322 as shown in FIG. 5 and perpendicular direction 324. Note that directions 324 and 322 need not be perpendicular, in some embodiments, as any intersection layout can be achieved using stacked coils 310. The arrangement shown in FIG. 6A can be logically grouped into two directional arrays or groups of coils 310. Coil group 328 is arranged horizontally along direction 322. Coil group 326 is arranged vertically in the page along direction 324. An intersecting group of coils 330 contains coils 310 of both sets, stacked on one another or interleaved with one another.

[0065] PCB coils 310A in group 326 can have substantially the same as or different characteristics from coils 310, depending on design requirements. To move the vessel mover 202, for example, from path 322 to path 324, the vessel mover 202 can be moved to the intersection at coils 330 by selectively and synchronously activating coils in set 328 to move the magnet 203 in the vessel mover 202 to the intersection. Once the magnet 203 has been moved to the intersecting group of coils 330, the coils within set 326 can be synchronously activated to move the magnet 203 along path 324. Alternatively, if the vessel mover 202 is not to turn at the intersection, the coils in group 328 will continue to synchronously activate. The specific direction in which the vessel mover 202 moves along path 322 or 324 is dictated by the order of synchronous activation of the coils 310.

[0066] Coil groups 326 and 328 form two paths of horizontally (in the plane of the PCB) adjacent coils 310. Each group provides a different direction of possible motion for vessel movers 202 propelled by the selective creation of a magnetic field within each direction group of coils 326 and 328. By overlapping parts of each coil group 326 and 328 below the PCB track surface, an intersection is formed, allowing the vessel mover 202 to selectively move between each directional group or continue the same path as the directional group of coils that propelled the vessel mover 202 to the intersection.

[0067] FIG. 6B shows a cross-section of the PCB layers used to create the stacked coils 310 and 310A in section 330. It should be appreciated that only six layers are shown for illustration purposes, but in practice many more layers would likely be used depending on the application. In this example, solid black windings 314A illustrate the topmost coil, while white windings 314B illustrate the windings in the bottom coil. Each coil 310 is created by stacking spirals that are electrically coupled through intra-coil vias 316, linked by copper traces 320. Terminal vias 312 provide terminal leads for a circuit to provide a current to each individual coil. It should also be appreciated that while FIG. 6B shows individual windings of the two stacked coils 310 directly on top one another, the individual traces of the windings for each stacked coil 310 go in different directions and only have this stacked arrangement at the intersection of the individual traces. That is, there will be portions of each stacked coil 310 where the windings from the top-most coil are not directly atop the windings of the bottommost coil, as can be seen in FIG. 6D.

[0068] In some embodiments, the stacked coils of windings 314A-B are laminated into a single monolithic PCB board having several layers that is at least twice the number of layers of each coil 310. In some embodiments, stacked coils 310 can be created by creating two separate PCBs for each coil group and then stacking those PCBs. These stacked PCBs can be affixed to one another using any suitable fixation technique, such as epoxy or screws.

[0069] When stacked coils 310 are created using a single laminated PCB, it is also possible to interleave the windings of each coil 310 such that the top-most surface of each coil 310 is roughly adjacent to the surface of the PCB. Such an example is shown in FIG. 6C. where layers of windings 314A-B are printed on interleaved laminated layers of the PCB. This requires slightly longer vias to connect the non-adjacent layers to form a single coil 310.

[0070] FIG. 6D is an x-ray view showing an exemplary' arrangement of stacked coils 310 to illustrate the individual traces and show' how they intersect in the adjacent PCB layers. The arrangement of vias is merely conceptually illustrative. The specific arrangement of vias forstacked coils 310 in a monolithic multi-layer PCB would be carefully selected to avoid interfering with individual traces of the stacked spirals.

[0071] FIG. 6E is an x-ray view showing another exemplary arrangement of stacked coils 310 in which all of the coils 310 are in the same orientation when stacked (i.e., not alternately flipped as illustrated in FIG. 6C) and interconnected in a continuous outside-to-inside manner. The coil 310 configuration illustrated in FIG. 6D allows an alternate means to control interleaving via geometry and PCB trace routing as compared to that described and illustrated in more detail above. However, other methods for stacking, interleaving, interconnecting, and otherwise arranging coils 310 can also be used in other examples.Automation Track Apparatus

[0072] The synchronous activation of coils 310 can be selected according to a predetermined motion profile that sets maximum acceleration and / or maximum velocity constraints to limit vessel spilling, for example. That is, the exact location of the magnetic field created by the selection and activation of coils 310 can move according to a motion profile that accounts for acceleration and maximum velocity for the application. For example, the motion profile can slowly accelerate a vessel mover 202 to avoid spillage, moving the vessel mover 202 faster as it continues to accelerate. Similarly, as a vessel mover 202 approaches an intersection, such as a perpendicular intersection, the vessel mover 202 can slow down by applying a decelerating motion profile to a magnetic field, activating adjacent coils 310 in a decelerating manner. Motion profiles are ty pically achieved by sending controller signals to driver amplifiers under software control. Software modules monitor the motion of each vessel mover 202 and control the application of synchronous motor signals to the coils 310 to achieve a desired trajectory.

[0073] Electrical components (e.g., sensors, driver circuits, etc.) to assist the control and operation of the automation track can also be incorporated into PCB(s) and / or motor controller circuits can be placed on board(s). These can include FPGA or processors that control amplifiers mounted to PCB(s) that provide a precise current to each individual coil 310. This allows the coils 310 to be activated synchronously according to a motion profile. In some embodiments, the motor control and drivers are mounted on a separate PCB, electrically coupled to coils 310. In some embodiments, motor control components can be mounted on the underside of the PCB. This can present EMI challenges, so in some embodiments, motor control components are mounted on a separate board for intersection PCB boards, and other deployments for one or more of the electrical components can also be used in other examples.

[0074] As generally described above and shown in FIG. 7, automation track apparatus 250 can include one or more modules 252 (e.g.. modules configured to process liquid samples in an exemplar}- deployment of the automation track apparatus 250 as a liquid handling system), a track system 200 interconnecting the various modules 252, vessel movers 202 that transport objects (e.g., liquid samples) between the various modules 252 along the track system 200, and coil array(s) 208 (e.g., of coils 310) associated with the track system 200 that is configured to drive the vessel movers 202. To drive the vessel movers 202. the coil array 208 is communicably coupled to a hybridized movements control architecture 300 of a control system 254 that also includes at least one processor 260 and memory 262, which can be communicably coupled together via a system bus. for example. Thus, the control system 254 is configured to control the coil array 208 to control the movement and routing of the vessel movers 202 along the track system 200, which in turn allows the vessel movers 202 to transport objects between the modules 252 in particular sequences and with particular timings according to the system requirements.

[0075] The control system 254 can include hardware, software, firmware, or any combination thereof that is able to execute the described functions. In the illustrated example, the control system 254 includes the processor 260 coupled to a memory 262 storing instructions that, when executed by the processor 260, cause the control system 254 to execute one or more of the described processes, steps, and / or functions described and illustrated herein. Thus, the processor 260 can be a central processing unit (CPU) or microprocessor, for example, and the memory can include any combination of random-access memory (RAM), read-only memory (ROM), and / or flash memory. for example, and other types of processors and / or memory can also be used in the control system 254 in other examples.

[0076] The hybridized movement control architecture 300, which is a circuit and / or related control software, can be configured to monitor the activity of vessel movers 202 and / or control the selective application of synchronous currents to relevant coils 310 in the coil array 208. This creates a magnetic field to propel the magnetic vessel movers 202 along the track system 200. The application of these currents can be done in accordance with a software-defined desired motion profile for the vessel mover 202 and can be adapted based on real-time feedback from the BEMF device 256 to move the vessel movers 202 in accordance with a desired control scheme.

[0077] Due to relative motion between the moving permanent magnet 203 of the vessel movers 202 and the magnetic field produced by the coil array 208. a voltage occurs, which is referred to as a BEMF voltage. As a result of the BEMF voltage induced into the coil array 208by the permanent magnet 203 of the moving vessel mover 202, the characteristics of the movement of the vessel mover 202 can vary, which can introduce significant wear patterns, acoustic noise, and / or force ripple, for example, as well as cause spillage of fluids in an exemplary liquid handler system deployment. With this technology, the control system 254 advantageously uses a BEMF signal directly measured and provided by a BEMF device 256 to more effectively and accurately compensate for the BEMF voltage in the commutation cycle, as explained in more detail below.

[0078] The automation track apparatus 250 can include any number of coil arrays 208, vessel movers 202, control systems 254, and / or BEMF devices 256 in other examples. For example, each of a plurality of control systems 254 can be communicably coupled to one of a plurality of BEMF devices 256 and a plurality of coil arrays 208. with those components collectively associated with one of a plurality of track segments that collectively comprise the track system 200, and other permutations and topologies can also be used.

[0079] Any number of the control systems 254 of the automation track apparatus 250 can be communicably coupled to a traffic control unit 264 that is configured to monitor the locations of the vessel movers 202 along the track system 200 and control the movement and / or routing of the vessel movers 202 accordingly by communicating with the various control systems 254 to cause the control systems 254 to selective energize or commutate coils 310 of the coil array 208.

[0080] In some examples, the control system includes a communication interface (not shown), which is communicably coupled to the traffic control unit 264 as well as, via a system bus for example, the processor 260, memory 262, and / or hybridized movement control architecture.300 of the control system 254. In some examples, the traffic control unit 264 is configured to communicate with the communication interface via a communication network (not shown), which can be a wired or wireless network that uses any communication protocol (e.g., Internet protocol (IP) or point-to-point over Ethernet), although other methods of communication between the traffic control unit 264 and one or more control systems 254 can also be used in other examples.Driver Circuit and BEMF Extraction

[0081] The BEMF signal extraction performed by the BEMF device 256 can be implemented in the analog domain, as illustrated in FIG. 8, for example, in the digital domain, or in a combination of both domains (e.g., filtering done in the analog domain with computation done in the digital domain). Thus, the BEMF device 256 includes a BEMF extraction circuit,which can be analog, digital, or both. In the examples described and illustrated herein, the BEMF signal is extracted based on obtaining the difference between the perceived current in the stator coil and the actual current in the stator coil through direct measurement of actual coil voltage and actual drive current. The difference between the perceived current minus the actual current directly corresponds to the contribution of the induced BEMF voltage at any point in time.

[0082] Determination of the perceived coil current is derived by dividing the voltage across a coil of the coil array 208 by the impedance of the coil. Dividing the coil voltage by the coil impedance with no BEMF present will result in a perceived current i(t), wherein i is the current and t is time. As a BEMF voltage is induced into the coil by amoving magnet 203, the perceived current will increase proportional to the strength and speed of the magnet 203. This increase in the perceived current minus the actual current results in a signal or value that is equivalent to the induced BEMF.

[0083] Referring now to FIG. 8, an exemplary' linear current driver circuit 350 with a Darlington pair and BEMF extraction via a BEMF device 256 is disclosed. In this example, a linear analog driver circuit 350 is disclosed but in other examples the driver circuit 350, and / or the BEMF device 256, can be implemented in software, and other permutations can also be used. Additionally, while a Darlington pair is disclosed in this example as the currentcontrolling element, a Bipolar Junction Transistor (BJT), Metal Oxide Semiconductor Field Effect Transistor (MOSFET), or another type of transistor can also be used in other examples. For example, a BJT may be used and operated in its current mode for greater linearity and may require a lower operating voltage range than an utilizing a MOSFET requiring higher Vgs (gate-source) voltage. In this example, a relatively low voltage operational amplifier(s) may be used since the BJT's voltage drive requirements are relatively low. Other considerations can also be used to select the current-controlling element for a particular deployment.

[0084] The coil 310 in this example is represented by a resistor, capacitor, and an inductor, each of which has a value determined based on actual geometry of the coil 310, and can be determined empirically, computationally, or via a finite element analysis, for example. The coil 310 is also represented by a resistor having an effective divisor value of 55, which is the known resistance at room temperature of the copper material used to manufacture the coil 310 in this particular example but could be a different value for a different material and / or temperature in other examples.

[0085] In this example, the preset or source voltage at V 1 352 is delivered from the control system 254 and used to drive or excite the coil 310 for the intended motion profile includingacceleration, speed, and / or deceleration. The voltage at Vsense 354 is a function of the measured or actual current through the coil 310 and the one Ohm resistor R2 356. The voltages at VI 352 and Vsense 354 are delivered to a relatively high gain operational amplifier 355 with the output representing the difference between the voltages at VI 352 and Vsense 354 multiplied by the gain of the operational amplifier 355. The output of the operational amplifier 355 modulates the input to the transistor QI 358 to facilitate an increase or decrease of the current flowing through the transistor QI 358 such that the current through the resistor R2 356 is equivalent to the voltage as a function of current at V 1 352.

[0086] Additionally, the input to the resistor R6 360 is the voltage at the high side of the coil 310 and the input to the resistor R8 362 is the voltage at the low side of the coil 310. Thus, the output of the operational amplifier 364 represents the difference between the voltage at the lower and higher sides of the coil 310 or, in other words, the voltage across the coil 310. The operational amplifier 364 is configured as a differential amplifier with unity gain in this example. Accordingly, the voltage at deltaV 366 represents the voltage across the coil divided by 55, which is the resistance of the coil 310 at room temperature (55 Ohm) and is represented by the combination of the resistor R9 368 and the resistor R10 370, which together form a resistive divider network. Accordingly, the voltage at Vsense 354 represents the actual current through the coil 310 as a function of voltage and impedance (i.e., resistance in this example) and the voltage at deltaV 366 is the perceived current as a function of voltage and impedance (i.e., resistance in this example).

[0087] The output of the operational amplifier 372 is then the difference in voltage between the voltage at Vsense 354 through the resistor R12 374 and the voltage at deltaV 366 through the resistor R13 376 or, in other words, the BEMF voltage or signal 378. In this example, the operational amplifier 372 also is configured as a differential amplifier with unity gain. Thus, there is an induced BEMF voltage at V4 380, which represents the induction of a voltage into the coil 310 by a moving magnet 203. In operation, the voltage at V4 380 is induced by the moving magnet 203 across the coil 310 as a function of the speed of the magnet 203. The BEMF voltage V4 380 is artificially induced in FIG. 8 to represent and illustrate the BEMF voltage induced by the moving magnet 203 in an actual deployment of this technology.

[0088] Thus, if in an actual deployment of this technology there is no BEMF signal 378, there is no moving magnet 203 across the coil 310. To illustrate that state of the system, there would be no induced BEMF voltage at V4 380 in the circuit of FIG. 8. Accordingly, in an actual deployment of this technology, the induced BEMF voltage at V4 380 would vary based on the speed of the magnet 203 or vessel mover 202 across the coil 310. In other words, a staticinduced BEMF voltage at V4 380 is shown in FIG. 8 to represent an induced BEMF voltage that would be variable, would result from the movement of the magnet 203, and would not be an explicit voltage input from any other external voltage source.

[0089] Accordingly, the circuit of FIG. 8 effectively measures the difference between a perceived current through the coil 310 and an actual current through the coil 310 as a result of the voltage delivered by the control system 254 to extract a BEMF signal 378 representing the BEMF voltage induced and generated by the movement of the rotor (i.e., the magnet 203) relative to the stator (i.e., the coil 310). If the extracted BEMF signal 378 is equal to zero, then there is no vessel mover 202 with magnet 203 moving across the coil 310 or induced BEMF voltage as a result of such movement. In some examples, the analog BEMF signal 378 can be input to an analog-to-digital converted (ADC) 382 and the digital output of the ADC 382 can then be provided to the control system 254.

[0090] The control system 254 (e.g., the hybridized movement control architecture 300) can compare the received BEMF signal 378, or a digital representation thereof, to the control signal previously used to drive the coil 310 (e.g., the voltage supplied at VI 352) to determine whether the BEMF signal 378 and the control signal are in phase. If the BEMF signal 378 and the control signal are out of phase, then the vessel mover 202 with the magnet 203 arrived over the coil 310 too early or too late as compared to when the coil 310 was driven by the control signal. Since the extracted BEMF signal 378 is induced by the moving magnet 203 over the coil 310, the presence of the BEMF signal 378 before the coil 310 was driven indicates that the vessel mover 202 arrived at the coil 310 early and its movement should be retarded. Conversely, if the coil 310 was driven before the BEMF signal 378 was detected, then the vessel mover 202 arrived at the coil 310 late and its movement should be accelerated. This is similar to the instantaneous magnet position in a rotor with respect to a stationary stator coil and used to advance or retard the rotor’s speed accordingly.

[0091] To facilitate the commutation adjustment, the control system 254 can drive another coil (e.g., a subsequent or adjacent coil to coil 310 in a same coil array 208) using another control signal that is initiated at a time determined based on the comparison of the BEMF signal 378 and the control signal previously used to drive the initial coil 310. Thus, the timing of the commutation cycle of the BLDC motor can be controlled or compensated based on the induced and measured BEMF signal 378.

[0092] Referring to FIG. 9A, an exemplary plot of voltage versus time for an exemplary coil 310 is illustrated. In this example, the plot includes a voltage of an exemplary control signal 384A and another voltage of an exemplary BEMF signal 386A. The control signal 384Aand the BEMF signal 386 A are out of phase because the control signal 384 A is initiated before the BEMF signal 386 A is detected. Additionally, when the control signal 384 A has completed, the BEMF signal 386A is still detected. Thus, in this example, the vessel mover 202 arrived too late with respect to the commutation cycle corresponding to the control signal 384A and the vessel mover 202 therefore should be retarded by controlling the timing at which subsequent coil(s) 310 are driven.

[0093] Referring to FIG. 9B another exemplary plot of voltage versus time for an exemplary coil 310 is illustrated. In this example, the plot includes a voltage of an exemplary control signal 384B and another voltage of an exemplary7BEMF signal 386B. The control signal 384B and the BEMF signal 386B are out of phase because the control signal 384B is initiated after the BEMF signal 386B is detected. Additionally, the BEMF signal 386B is no longer detected before the control signal 384B has completed. Thus, in this example, the vessel mover 202 arrived too early with respect to the commutation cycle corresponding to the control signal 384B and the vessel mover 202 therefore should be accelerated by controlling the timing at which subsequent coil(s) 310 are driven.

[0094] Referring to FIG. 9C, another exemplary plot of voltage versus time for an exemplary coil 310 is illustrated. In this example, the plot includes a voltage of an exemplary control signal 384C and another voltage of an exemplary7BEMF signal 386C. The control signal 384C and the BEMF signal 386C are substantially in phase because the control signal 384B is initiated at substantially the same time as the BEMF signal 386C is detected. Additionally, the BEMF signal 386C is detected up to substantially the same time as the control signal 384C has completed. Thus, in this example, the vessel mover 202 arrived as substantially the desired time and in phase with respect to the commutation cycle corresponding to the control signal 384C and the speed of the vessel mover 202 therefore does not require adjustment via controlling the timing at which subsequent coil(s) 310 are driven.

[0095] Thus, with the BEMF signal 378 from the BEMF device 256, the hybridized movement control architecture 300, for example, can compare the BEMF signal 378 to a first control signal used to drive the corresponding coil 310 of the coil array 208 to initiate movement of the rotor (i.e., the permanent magnet 203) to determine whether those signals are in phase. The comparison of the BEMF signal 378 to the first control signal will indicate whether the actual position of the vessel mover 202 is ahead or behind the first control signal such that the commutation of subsequent coil(s) of the coil array 208, or another coil array 208 in the system, should be adjusted in order to retard or accelerate the vessel mover 202, respectively. Thus, with this technology, subsequent stator coils are driven using an additionalcontrol signal at a time advantageously determined based on the comparison of the first control signal and the extracted BEMF signal 378 representing the BEMF induced by the vessel mover 202 with respect to a prior coil 310.

[0096] Referring to FIG. 10, a flowchart of an exemplary method for BLDC motor control is illustrated. One or more of the steps of FIG. 10 described and illustrated in detail below can be performed by the control system 254 in some examples, although other components described herein can also perform one or more steps of the described method. In step 1000 in this example, a first stator coil 310 of a coil array 208 is driven using a first control signal to initiate movement of a rotor including a permanent magnet 203. The first stator coil 310 can be driven using drive circuit 350 that supplies a voltage at VI 352, for example, although other methods for driving the first stator coil 310 can be used in other examples. Control current values are used together with the commutation frequency to precisely move the rotor based on mass, friction, payload, desired acceleration, speed, and / or deceleration profiles, for example.

[0097] In step 1002, a difference between a perceived current through the first stator coil 310 and an actual current through the first stator coil 310 is measured to obtain an induced BEMF signal generated by the movement of the rotor (i.e., the permanent magnet 203) relative to the first stator coil 310. To measure the difference in some examples, a first voltage across the first stator coil 310 is directly measured using a first operational amplifier configured as a differential amplifier with unity gain. A second voltage proportional to the perceived current through the first stator coil 310 is then determined by dividing the first voltage by a divisor equal to a resistance of the first stator coil 310. The second voltage can be generated using a resistive divider network that includes at least first and second resistors having respective first and second resistance values that combined comprise a particular temperature (e g., room temperature) resistance value of the first stator coil 310, which can be based on the material used to form the first stator coil 310.

[0098] In this example, the BEMF signal is then extracted based on a third voltage proportional to the BEMF signal and determined by subtracting a fourth voltage proportional to another current through a fixed current sense resistor from the second voltage. A second operational amplifier configured as a differential amplifier with unity gain can be used to generate a difference between the second voltage and the fourth voltage from which the BEMF signal is extracted.

[0099] In step 1004, the first control signal and the BEMF signal are compared. For example, the time at which the first control signal and the BEMF signal are initiated and / ordrop to zero can be compared to determine whether the first control signal and the BEMF signal are in phase or out of phase.

[0100] In step 1006, a determination is made as to whether the first control signal and the BEMF signal are out of phase based on the comparison in step 1004. If the first control signal and the BEMF signal are in phase, then the No branch is taken back to step 1000 and a subsequent stator coil is driven without compensation for the induced BEMF voltage. However, if the first control signal and the BEMF signal are out of phase, then the Yes branch is taken to step 1008.

[0101] In step 1008, a second stator coil is driven using a second control signal at a time determined based on the comparison in step 1004. In some examples, the time at which the second control signal is initiated to drive the second stator coil is determined based on an amount by which the first control signal and the BEMF signal are out of phase, as determined based on the comparison in step 1004. Accordingly, the commutation cycle of the BLDC motor is controlled and compensated based on the feedback from the directly measured induced BEMF signal in this example. Subsequent to driving the second stator coil in this example, the system proceeds back to step 1002. and steps 1002-1008 are repeated in a subsequent commutation cycle of the BLDC motor.

[0102] The technology' described and illustrated by way of the examples herein may be used in conjunction with linear voltage-controlled current source(s) as well as other types of stator / coil driver topologies including chopper integrated circuits, pulse width modulation (PWM), pulse density modulation (PDM), and similar with adequate filtering of the current signal. The driver circuit, BEMF device 256, and related technology' disclosed herein eliminate the need for using a software observer or the opening of a time window within the commutation cycle, provides a real-time voltage output proportional to an induced BEMF, exhibits improved power supply rejection due to the ratiometric relationship between coil voltage and coil current, and features operation over a wide bandwidth. By compensating the commutation cycle in a BLDC motor based on a more accurate, real-time BEMF signal 378 as disclosed herein, the rotor (e.g., vessel mover 202) can operate more smoothly and precisely, thereby reducing wear, acoustic noise, and / or force ripple, among other advantages.Thermal Compensation

[0103] Referring back to FIG. 8, in the BEMF signal extraction and motor control examples described above, a resistive divider network is included in the BEMF device 256. which includes a 54k resistor R9 368 and a Ik resistor R10 370. As explained above, the voltage atdeltaV 366 represents the voltage across the coil 310 divided by 55, which is the resistance of the copper coil 310 at room temperature and is represented by the combination of the resistor R9 368 and the resistor RIO 370, which together form a resistive divider network. The 55 Ohm resistance of the coil 310 at room temperature is simulated by the 55 Ohm resistor R1 388 in the analog circuit diagram of FIG. 8, and thus the resistance of the coil 310 is equivalent to the resulting benefit of the resistive divider network, which effectively provides a divisor such that the current at deltaV 366 is proportional to and reflects any voltage associated with an induced BEMF.

[0104] However, the resistive divider network of the circuit illustrated in FIG. 8 includes fixed-value resistors R9 368 and R10 370 and is therefore static and temperature-agnostic. In other words, as the temperature changes, the resistance of the coil 310 will change, but the divisor yielded by the resistive divider network that includes resistor R9 368 and resistor R10 370 will remain the same and will be disproportionate to the actual resistance exhibited by the coil 310.

[0105] As a result, the inaccuracy of the voltage at deltaV 366 will increase proportional to the magnitude of the temperature change, the resulting amplitude of the BEMF signal 378 will likewise be inaccurate, the control signal for a subsequent coil, which is dependent on the BEMF signal 378 as explained above with reference to steps 1004-1008 of FIG. 10, may be initiated at an inaccurate time if the control system 254 utilizes amplitude threshold detection, and the vessel mover may exhibit undesirable characteristics. So, the circuit of FIG. 8 works well to control the BLDC motor at a constant temperature (e.g., room temperature), or with a resistive divider network having a temperature coefficient substantially matching the resistance of the coil 310 at the constant temperature but may become less effective at controlling coil commutation as the temperature increases or decreases.

[0106] Referring now to FIG. 11 is a diagram of the exemplary circuit of FIG. 8 with thermal compensation in the analog domain in accordance with at least one aspect of the present disclosure. As explained above with reference to FIG. 8, the exemplary linear current driver circuit 350 of the analog circuit of FIG. 11 is implemented with a Darlington pair and BEMF extraction via a BEMF device 256. While a linear analog driver circuit 350 is disclosed, in other examples the driver circuit 350, and / or the BEMF device 256, can be implemented in software, and other permutations can also be used. Additionally, while a Darlington pair is disclosed in this example as the current-controlling element, a BJT, MOSFET, or another type of transistor can also be used in other examples.

[0107] The coil 310 in this example is represented or simulated by a resistor, capacitor and an inductor, each of which has a value determined based on actual geometry of the coil 310 and can be determined empirically, computationally, or via a finite element analysis, for example. The coil 310 is also represented by a first thermistor 390, which changes resistance based on temperature, as would be the case for the coil 310 in an actual deployment. Additionally, the BEMF device 256 in this example is modified to replace the resistors R9 368 and R10 370 with a resistive divider network 392 that includes a second thermistor 394, and optionally one or more fixed-value resistors (not shown), as explained in more detail below.

[0108] As with the capacitance and inductance, the resistance of the coil 310 can be determined empirically or mathematically based on the materials from which the coil 310 is made (e.g.. copper). The resistance of the coil 310 is then used to inform the device(s) used for the resistive divider network 392, as explained in more detail below. For example, the voltage across one or more coils 310 in the BLDC motor can be measured while a known current is injected into the coil 310. The resistance of the coil 310 can then be determined by dividing the measured voltage by the known current. In this way. the system can compensate for any production variations in coil resistance from coil to coil. In particular, the resistive divider network 392 can be configured to yield a divisor substantially the same as the determined resistance. In other words, the process of injecting a current and measuring a voltage facilitates measurement and calculation of the ratio of voltage and current, which is the resistance of the coil 310. The ratio or resistance can then be used to scale the BEMF signal. By periodically performing this process (i.e., injecting a current, measuring the voltage, and calculating the resistance), temperature is negated without even needing to directly measure for temperature as the divisor (e g., voltage / actual current) encompasses the temperature dependency of the material of the coil 310.

[0109] With the measured or otherwise determined resistance of the coil 310 at one or more known temperatures, the resistive divider network 392 can be established to compensate for thermal variation. More specifically, the second thermistor 394 can be selected that best matches the temperature coefficient of the coil 310 to ensure that the divisor value increases and decreases in a substantially similar manner to that of the coil 310.

[0110] Thus, in some examples, the second thermistor 394 can be made of substantially the same conductive material (e.g., copper) and / or comprise substantially the same temperature coefficient as the coil 310 so that the resistive network 392 reflects the resistance across the coil 310. In other words, a first resistance of the second thermistor 394 increases or decreases proportionally to a second resistance of the coil 310 as the temperature varies.[OHl] In some examples, the resistive divider network 392 includes an upper leg including the second thermistor 394 and a lower leg including a fixed-value resistor (not shown). Accordingly, in these examples, the second thermistor 394 and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the coil 310.

[0112] In one particular example, the upper leg of the resistive divider network 392 can include a 10 kOhm positive temperature coefficient (PTC) linear thermistor, such as the TFPT1206L1002F thermistor available from Vishay Intertechnology. Inc of Malvern. Pennsylvania, and a 185 Ohm resistor in the lower leg. In this example, the resistive divider network 392 yields a divisor of 55, which may be equal to the room temperature resistance of the coil 310 and has a resistance value that will increase proportionally to the coil resistance. In this example, the uncompensated coil 310 winding effects were advantageously reduced from +17.5 percent over an operating temperature range of 25 degrees centigrade to 70 degrees centigrade to -1.5 percent over the same temperature range.

[0113] In some examples, the resistive divider network 392 can include one or more fixed- value resistors configured to scale a first resistance of the second thermistor 394 over a temperature range to a second resistance of the coil 310 over the temperature range. For example, a fixed-value resistor of 939 Ohm can be placed in the upper leg of the resistive divider network 392 coupled to a 10 kOhm thermistor, such as used in the example described above, further coupled to a 203 Ohm fixed- value resistor in the lower leg of the resistive divider network 392. In this example, the uncompensated coil 310 winding effects were advantageously reduced from +17.5 percent over an operating temperature range of 25 degrees centigrade to 70 degrees centigrade to +0.4 percent over the same temperature range.

[0114] With the thermal compensation of the disclosed technology, no temperature measurements are required and the BEMF signal 378 will more accurately reflect the resistance across the coil 310 across a temperature range and the resulting control signal for commutating a subsequent coil, which is generated as explained above with reference to FIG. 10, for example, will be more accurate. With more accurate commutation of the coils in a BLDC motor, the undesirable movement characteristics, such as a wear patterns, acoustic noise, and / or force ripple, for example, can advantageously be reduced.

[0115] While various illustrative embodiments incorporating the principles of the present teachings have been disclosed, the present teachings are not limited to the disclosed embodiments. Instead, this application is intended to cover any variations, uses, or adaptations of the present teachings and use its general principles. Further, this application is intended tocover such departures from the present disclosure that are within known or customary' practice in the art to which these teachings pertain.

[0116] In the above detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols ty pically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the present disclosure are not meant to be limiting. Other embodiments may be used, and other changes may be made, without departing from the spirit or scope of the subj ect matter presented herein. It will be readily understood that various features of the present disclosure, as generally described herein, and illustrated in the Figures, can be arranged, substituted, combined, separated, and designed in a wide variety' of different configurations, all of which are explicitly contemplated herein.

[0117] Aspects of the present technical solutions are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the technical solutions. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0118] These computer readable program instructions can be provided to a processor of a special purpose computer or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0119] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0120] The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present technical solutions. In this regard, each block in the flowchart or block diagrams can represent a module, segment, or portion of instructions, which includes one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession can, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0121] A second action can be said to be “in response to'’ a first action independent of whether the second action results directly or indirectly from the first action. The second action can occur at a substantially later time than the first action and still be in response to the first action. Similarly, the second action can be said to be in response to the first action even if intervening actions take place between the first action and the second action, and even if one or more of the intervening actions directly cause the second action to be performed. For example, a second action can be in response to a first action if the first action sets a flag and a third action later initiates the second action whenever the flag is set.

[0122] The present disclosure is not to be limited in terms of the particular embodiments described in this application, which are intended as illustrations of various features. Many modifications and variations can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. Functionally equivalent methods and apparatuses within the scope of the disclosure, in addition to those enumerated herein, will be apparent to those skilled in the art from the foregoing descriptions. It is to be understood that this disclosure is not limited to particular methods, reagents, compounds, compositions or biological systems, which can. of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0123] With respect to the use of substantially any plural and / or singular terms herein, those having skill in the art can translate from the plural to the singular and / or from the singular to the plural as is appropriate to the context and / or application. The various singular / plural permutations may be expressly set forth herein for sake of clarity.

[0124] It will be understood by those within the art that, in general, terms used herein are generally intended as "open" terms (for example, the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” et cetera). While various compositions, methods, and devices are described in terms of “comprising” various components or steps (interpreted as meaning “including, but not limited to”), the compositions, methods, and devices can also “consist essentially of’ or “consist of’ the various components and steps, and such terminology should be interpreted as defining essentially closed-member groups.

[0125] As used in this document, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art. Nothing in this disclosure is to be construed as an admission that the embodiments described in this disclosure are not entitled to antedate such disclosure by virtue of prior invention.

[0126] In addition, even if a specific number is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (for example, the bare recitation of “two recitations,” without other modifiers, means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C. et cetera” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (for example, “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together. A and C together, B and C together, and / or A, B. and C together, et cetera). In those instances where a convention analogous to “at least one of A, B, or C, et cetera” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (for example, “a system having at least one of A, B, or C” would include but not be limited to sy stems that have A alone, B alone, C alone, A and B together. A and C together, B and C together, and / or A, B, and C together, et cetera). It will be further understood by those within the art that virtually any disjunctive word and / or phrase presenting two or more alternative terms, whether in the description, sample embodiments, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”

[0127] In addition, where features of the disclosure are described in terms of Markush groups, those skilled in the art will recognize that the disclosure is also thereby described in terms of any individual member or subgroup of members of the Markush group.

[0128] As will be understood by one skilled in the art, for any and all purposes, such as in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, et cetera. As a non-limiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, et cetera. As will also be understood by one skilled in the art all language such as “up to,” “at least,” and the like include the number recited and refer to ranges that can be subsequently broken down into subranges as discussed above. Finally, as will be understood by one skilled in the art, a range includes each individual member. Thus, for example, a group having 1-3 components refers to groups having 1, 2, or 3 components. Similarly, a group having 1-5 components refers to groups having 1. 2, 3, 4, or 5 components, and so forth.NON-LIMITING ILLUSTRATIVE EMBODIMENTS

[0129] The following is a list of non-limiting illustrative embodiments disclosed herein.

[0130] Illustrative embodiment 1. A method for thermal compensation in brushless direct current motors, comprising: driving a first stator coil using a first control signal to initiate movement of a rotor comprising a permanent magnet; measuring a perceived current through the first stator coil and scaling the perceived current using a resistive divider network comprising a thermistor; determining a difference between the perceived current through the first stator coil and an actual current through the first stator coil; and driving a second stator coil using a second control signal at a time determined based on the determined difference.

[0131] Illustrative embodiment 2. The method according to the preceding embodiment, further comprising: determining an induced back electromotive force (BEMF) signal based on the determined difference, wherein the induced BEMF signal is generated by the movement of the rotor relative to the first stator coil; comparing the first control signal and the induced BEMF signal; and generating the time to drive the second stator coil based on the comparison.

[0132] Illustrative embodiment 3. The method according to one of the preceding embodiments, wherein the first stator coil and the thermistor are made of substantially the same conductive material or comprise substantially the same temperature coefficient.

[0133] Illustrative embodiment 4. The method according to one of the preceding embodiments, wherein: the resistive divider network further comprises an upper leg comprising the thermistor and a lower leg comprising a fixed-value resistor; and the thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first stator coil.

[0134] Illustrative embodiment 5. The method according to one of the preceding embodiments, wherein a first resistance of the thermistor increases or decreases proportionally to a second resistance of the first stator coil.

[0135] Illustrative embodiment 6. The method according to one of the preceding embodiments, wherein the resistive divider network comprises one or more fixed-value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first stator coil over the temperature range.

[0136] Illustrative embodiment 7. The method according to one of the preceding embodiments, further comprising: measuring a voltage across the first stator coil while a known current is injected into the first stator coil; and determining a resistance of the first stator coil by dividing the measured voltage by the known current, wherein the resistive divider network is configured to yield a divisor substantially the same as the determined resistance.

[0137] Illustrative embodiment 8. A transport system, comprising a control system comprising one or more of a hybridized movement control architecture or a processor and configured to: measure a perceived current through a first one of a plurality of conductive coils using a resistive divider network comprising a thermistor, wherein the first one of the plurality of conductive coils is driven using a first control signal to provide a selective magnetic field to propel a magnetic base of a vessel mover; and drive a second one of the plurality of conductive coils using a second control signal at a time determined based on a difference between the perceived current and an actual current through the first one of the plurality7of conductive coils.

[0138] Illustrative embodiment 9. The transport system according to the preceding embodiment, comprising a circuit configured to determine an induced BEMF signal based on the difference between the perceived current and the actual current, wherein the induced BEMF signal is generated by the movement of the magnetic base of the vessel mover relative to the first one of the plurality of conductive coils, wherein the control system is further configured to: compare the first control signal and the induced BEMF signal; and generate the time to drive the second one of the plurality of conductive coils based on the comparison.

[0139] Illustrative embodiment 10. The transport system according to one of the preceding embodiments, further comprising a track comprising a plurality of multilayer printed circuit boards (PCBs) arranged along a transport path, each PCB having one or more of the plurality of conductive coils.

[0140] Illustrative embodiment 11. The transport system according to one of the preceding embodiments, wherein the circuit comprises: a digital circuit; or an analog circuit and the transport system further comprises an analog-to-digital converter configured to convert an analog input into the BEMF signal, and the control system is further configured to obtain the BEMF signal from the analog-to-digital converter.

[0141] Illustrative embodiment 12. The transport system according to one of the preceding embodiments, wherein the first one of the plurality of conductive coils and the thermistor are made of substantially the same conductive material or comprise substantially the same temperature coefficient.

[0142] Illustrative embodiment 13. The transport system according to one of the preceding embodiments, wherein: the resistive divider network further comprises an upper leg comprising the thermistor and a lower leg comprising a fixed-value resistor; and the thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first one of the plurality of conductive coils over a desired operating temperature range of the transport system.

[0143] Illustrative embodiment 14. The transport system according to one of the preceding embodiments, wherein a first resistance of the thermistor increases or decreases proportionally to a second resistance of the first one of the plurality of conductive coils.

[0144] Illustrative embodiment 15. The transport system according to one of the preceding embodiments, wherein the resistive divider network comprises one or more fixed- value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first one of the plurality of conductive coils over the temperature range.

[0145] Various of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art, each of which is also intended to be encompassed by the disclosed embodiments.

Claims

CLAIMSWhat is claimed is:1 . A method for thermal compensation in brushless direct current motors, comprising: driving a first stator coil using a first control signal to initiate movement of a rotor comprising a permanent magnet; measuring a perceived current through the first stator coil and scaling the perceived current using a resistive divider network comprising a thermistor; determining a difference between the perceived current through the first stator coil and an actual current through the first stator coil; and driving a second stator coil using a second control signal at a time determined based on the determined difference.

2. The method of claim 1, further comprising: determining an induced back electromotive force (BEMF) signal based on the determined difference, wherein the induced BEMF signal is generated by the movement of the rotor relative to the first stator coil; comparing the first control signal and the induced BEMF signal; and generating the time to drive the second stator coil based on the comparison.

3. The method of claim 1, wherein the first stator coil and the thermistor are made of substantially the same conductive material or comprise substantially the same temperature coefficient.

4. The method of claim 1, wherein: the resistive divider network further comprises an upper leg comprising the thermistor and a lower leg comprising a fixed-value resistor; and the thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first stator coil.

5. The method of claim 1 , wherein a first resistance of the thermistor increases or decreases proportionally to a second resistance of the first stator coil.

6. The method of claim 1, wherein the resistive divider network comprises one or more fixed-value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first stator coil over the temperature range.

7. The method of claim 1, further comprising: measuring a voltage across the first stator coil while a known current is injected into the first stator coil; and determining a resistance of the first stator coil by dividing the measured voltage by the known current, wherein the resistive divider network is configured to yield a divisor substantially the same as the determined resistance.

8. A transport system, comprising a control system comprising one or more of a hybridized movement control architecture or a processor and configured to: measure a perceived current through a first one of a plurality' of conductive coils using a resistive divider network comprising a thermistor, wherein the first one of the plurality of conductive coils is driven using a first control signal to provide a selective magnetic field to propel a magnetic base of a vessel mover; and drive a second one of the plurality of conductive coils using a second control signal at a time determined based on a difference between the perceived current and an actual current through the first one of the plurality of conductive coils.

9. The transport system of claim 8, comprising a circuit configured to determine an induced BEMF signal based on the difference between the perceived current and the actual current, wherein the induced BEMF signal is generated by the movement of the magnetic base of the vessel mover relative to the first one of the plurality of conductive coils, wherein the control system is further configured to: compare the first control signal and the induced BEMF signal; and generate the time to drive the second one of the plurality’ of conductive coils based on the comparison.

10. The transport system of claim 9, further comprising a track comprising a plurality of multilayer printed circuit boards (PCBs) arranged along a transport path, each PCB having one or more of the plurality of conductive coils.

11. The transport system of claim 9, wherein the circuit comprises: a digital circuit; or an analog circuit and the transport system further comprises an analog-to-digital converter configured to convert an analog input into the BEMF signal, and the control system is further configured to obtain the BEMF signal from the analog-to-digital converter.

12. The transport system of claim 8. wherein the first one of the plurality of conductive coils and the thermistor are made of substantially the same conductive material or comprise substantially the same temperature coefficient.

13. The transport system of claim 8, wherein: the resistive divider network further comprises an upper leg comprising the thermistor and a lower leg comprising a fixed-value resistor; and the thermistor and the fixed-value resistor collectively yield a divisor substantially the same as a resistance of the first one of the plurality of conductive coils over a desired operating temperature range of the transport system.

14. The transport system of claim 8, wherein a first resistance of the thermistor increases or decreases proportionally to a second resistance of the first one of the plurality of conductive coils.

15. The transport system of claim 8, wherein the resistive divider network comprises one or more fixed-value resistors configured to scale a first resistance of the thermistor over a temperature range to a second resistance of the first one of the plurality of conductive coils over the temperature range.-se

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