The present invention relates to a motor system, a stepper motor, and a rotor therefor. More in particular, the present invention relates to detecting, in a motor system, an angular position of a rotor of an electric stepper motor.

Electric motors are commonly used to actuate machines, such as robotic systems. Permanent magnet stepper motors (PMSMs) are popular in many applications due to the high torque-to-volume ratio which allows for directly driving the joints of, for example, a 3-D printer without the need for a gearbox.

US2014/184030A1 discloses absolute multi-turn position sensing integrated within the structure of a hybrid stepper motor implemented by sharing the magnetic structure of the motor with the sensing means. An alternating magnetic field is obtained from a single magnet within the stepper motor rotor by use of alternating flux paths directed to large Barkhausen jump effect sensing elements. Pulses generated from the large Barkhausen sensing are decoded electronically and stored in a non-volatile memory to absolutely locate the motor position within a fraction of 1 electrical cycle of the motor over an arbitrary range. This coarse position sensing can optionally be extended by use of a higher resolution absolute within-electrical-cycle sensing means to provide integrated high resolution position sensing over an arbitrary number of revolutions.

WO2020/213265A1 discloses a monitoring device provided with: a current sensor for detecting two-phase current information for each of a plurality of drive motors; a motor information calculation unit for calculating the torque current or rotational speed of the corresponding drive motor from the current information; a feature quantity calculation unit for calculating feature quantities for the torque currents or rotational speeds of the plurality of drive motors; a state estimation unit for estimating a device state on the basis of the feature quantity of a drive motor having a correlation from among the plurality of drive motors; a data storage unit for storing reference value data; and an abnormality determination unit for determining an abnormality state on the basis of the estimated device state and the reference value data.

In many motor systems, it is of importance that a position of each joint is accurately known. To that end, there is a need for determining an angular position of a rotor of the electric motor that drives the joint. Typically, this is achieved by a combination of calibration (e.g., by measuring the position at a specific moment) and tracking (e.g., by recording all angular displacements from the moment of calibration). Known systems use dedicated components for calibration and tracking, and re-calibration may be required when the tracking phase is disrupted due to, for example, a power cycle or a stalled motor (i.e., skipping of steps).

A range of techniques for performing position detection are known. Most commonly, a concept of a uniquely identifiable reference position is utilized using a limit switch, photo- interrupter, Hall-effect sensor, or the like. For example, an optical sensor can be used to identify a marker placed on one or more angular positions of the rotor. On the other hand, tracking can for example be done by counting commanded angular displacements in feed-forward control, or by measuring incremental displacements using photo-interrupters or Hall-effect sensors, for example. Furthermore, certain sensors allow to directly measure the angular position such as potentiometer, electromagnetic resolver, magnetic absolute encoder.

The inclusion of physical sensors for position calibration, absolute measurement and/or tracking in the motor requires space and additional cabling, and therefore effectively reduces the torque-per-volume ratio of the motor assembly while also adding complexity and cost to the motor system.

It is an object of the present invention to provide a motor system, and a stepper motor and rotor therefor, in which the abovementioned problems do not occur or hardly so.

According to an aspect of the present invention, a motor system is provided, comprising a stepper motor, the stepper motor comprising a stator and a rotor, wherein the stator comprises a cavity in which the rotor is arranged, and a plurality of stator coils arranged around a circumference of the cavity, the plurality of stator coils being configured to drive the rotor to rotate in a rotational direction, and wherein the rotor comprises a rotor body having a plurality of rotor poles that are irregularly spaced along a circumference of the rotor body; a driving unit configured to drive each stator coil using a respective driving signal to thereby cause the rotor to rotate; and a position determining unit. The position determining unit is configured to, while the rotor is rotating, measure a current through one or more stator coils among the plurality of stator coils, each current comprising a superposition of at least a driving current as a result of driving a corresponding stator coil and an induced current resulting from a changing magnetic flux through said corresponding stator coil due to the rotating rotor, and determine an angular position of the rotor based on the measured current(s) and a known spacing between the plurality of rotor poles.

According to another aspect of the present invention, a motor system is provided, comprising a stepper motor, the stepper motor comprising a stator and a rotor, wherein the stator comprises a cavity in which the rotor is arranged, and a plurality of stator coils arranged around a circumference of the cavity, the plurality of stator coils being configured to drive the rotor to rotate in a rotational direction, and wherein the rotor comprises a plurality of mutually fixated rotor bodies arranged at axially different positions, each rotor body having a plurality of rotor poles that are substantially uniformly spaced along a circumference of the rotor body, wherein the number of rotor poles corresponding to each rotor body is different; a driving unit configured to drive each stator coil using a respective driving signal to thereby cause the rotor to rotate; and a position determining unit. The position determining unit is configured to, while the rotor is rotating, measure a current through one or more stator coils among the plurality of stator coils, each current comprising a superposition of at least a driving current as a result of driving a corresponding stator coil and an induced current resulting from a changing magnetic flux through said corresponding stator coil due to the rotating rotor, and determine an angular position of the rotor based on the measured current(s) and a known spacing between the plurality of rotor poles of each of the plurality of rotor bodies.

By using a rotor with irregularly spaced rotor pole pairs, or a combination of rotor bodies having regularly spaced rotor pole pairs that together form an irregular magnetic flux pattern, a unique magnetic flux pattern or back-emf pattern can be defined along a circumference of the rotor, which magnetic flux induces a current in the stator coils, based on which the angular position can be determined. As such, in the motor system according to the present invention, there is no need for additional sensors in the stepper motor to determine an angular position of the rotor, resulting in a higher torque-per-volume ratio and lower cost of the motor.

Here, it is noted that the above-described embodiments in relation to the aspect concerning a rotor body with irregularly spaced rotor poles similarly apply to the above aspect including a plurality of rotor bodies having a different number of regularly or uniformly spaced rotor poles.

The position determining unit may be configured to measure a current through each stator coil among the plurality of stator coils, calculate a discrete Fourier transform, DFT, of a vector comprising the measured current through each stator coil, and determine the angular position of the rotor using the calculated DFT.

The position determining unit may be configured to measure the current through each stator coil at a plurality of different time instances, determine, for each time instance, a respective angular position of the rotor, and calculate an average angular position of the rotor based on the determined angular positions.

The position determining unit may be configured to determine the angular position of the rotor by comparing the current(s) through the stator coil(s), measured at one or more respective time instances, with a reference model.

The control unit may be further configured to update a tracked or calibrated position of the rotor stored in the control unit or position determining unit based on said comparison.

The position determining unit may be comprised in a control unit, and the control unit may be further configured to control the driving unit to generate the driving signals and provide the driving signals to corresponding stator coils. Additionally or alternatively, the driving unit may comprise a plurality of driving circuits formed by half H-bridge switching circuits, each being configured to drive a respective stator coil. Additionally or alternatively, the driving signals may each comprise a sinusoidal signal.

The plurality of stator coils may be arranged in a plurality of groups of an equal number of stator coils, wherein the stator coils of the plurality of groups are arranged in an interleaved manner. In that case, the driving unit may be configured to drive stator coils in a same group with a same or corresponding driving signal. Furthermore, in this embodiment, a spacing pattern between rotor poles may repeat P times along the circumference of the rotor body, wherein P is the number of stator coils in each of the plurality of groups.

The stator may comprise a plurality of arms on which the stator coils are arranged, the arms being regularly arranged around a circumference of the cavity. Each arm may comprise a plurality of stator teeth arranged facing the rotor, and each stator coil may be configured to magnetize the stator teeth of a corresponding arm based on the corresponding driving signal. In a further embodiment, the stator teeth may each have an equal size.

According to an embodiment, the plurality of rotor poles of the or each rotor body may be arranged in rotor pole pairs comprising a respective magnetic north pole and a respective magnetic south pole, and a number of rotor pole pairs of the or each rotor body may preferably be greater than a total number of stator teeth.

The or each rotor body may be comprised of a first rotor half on which magnetic north poles among the plurality of rotor poles are arranged, and a second rotor half on which magnetic south poles among the plurality of rotor poles are arranged.

Each of the plurality of rotor poles may comprise magnetized rotor teeth arranged facing away from the or each rotor body. In a further embodiment, the rotor teeth may have a size corresponding to a size of the stator teeth.

A total number of rotor poles may be non-di visible by a total number of stator coils.

A variation in spacing between rotor poles of the rotor with irregularly spaced rotor poles may lie in a range between 0.25% and 10%, preferably between 0.5% and 5%, more preferably between 0.75% and 2%.

According to an embodiment, the rotor poles may be formed by a permanent magnet structure arranged in or forming part of the or each rotor body. Additionally or alternatively, the or each rotor body may be mounted on a rotor shaft.

According to yet another aspect of the present invention, a stepper motor for the motor systems described above is provided as described above. According to yet another aspect of the present invention, a rotor as defined above and suitable for the stepper motor and motor systems described above is provided.

Next, exemplifying embodiments will be described with reference to the appended drawings, wherein:

Figure 1 is a perspective view of a stepper motor according to an embodiment of the present invention;

Figure 2 is a perspective view of a stator of the stepper motor shown in Figure 1 ; Figures 3A and 3B are perspective views of a rotor according to embodiments of the present invention;

Figure 4 is a cross-sectional view of the stepper motor shown in Figure 1;

Figure 5 is a motor system including a cross-sectional view of a stepper motor and a schematic view of a control unit and a driving unit according to an embodiment of the present invention;

Figures 6A and 6B are signal diagrams corresponding to the embodiment in Figure 5 at relatively low revolutions per minute of the rotor;

Figures 7A and 7B are signal diagrams corresponding to the embodiment in Figure 5 at relatively high revolutions per minute of the rotor; and

Figure 8 is a signal diagram comprising a true angular position of the rotor and a tracked angular position of the rotor according to an embodiment of the present invention.

Hereinafter, reference will be made to the appended drawings. It should be noted that identical reference signs may be used to refer to identical or similar components.

In Figure 1, a perspective view of a stepper motor 1 according to an embodiment of the present invention is shown. Stepper motor 1 comprises a housing formed by a top lid 2a, a bottom lid 2b, and a side member 3. Side member 3 may form part of a stator frame of a stator (not shown) of stepper motor 1. Top lid 2a comprises a bore through which a shaft 4 of stepper motor 1 extends. Top lid 2a and bottom lid 2b may be physically connected to side member 3 and may enclose an interior portion of stepper motor 1, such as a rotor (not shown) of stepper motor 1.

Furthermore, stepper motor 1 comprises a plurality of driving pins 5 to which driving signals can be provided for controlling a magnetization of the stator. The rotor (not shown) can be mounted on shaft 4 such that the stator can actuate the rotor based on the driving signals, causing the rotor and rotate shaft 4 to rotate. Shaft 4 may be physically connected to an external element and may be configured to mechanically drive said element. As an example only, shaft 4 may be connected to a joint of, e.g., a 3-D printer and may be configured to mechanically drive said joint.

In Figure 2, a stator 10 according to an embodiment of the present invention is shown, comprising a stator frame 11 in which a cavity is arranged. The cavity is configured for receiving a rotor (not shown). For example, a side surface of stator frame 11 forms side member 3 of Figure 1.

Stator 10 further comprises a plurality of arms 12a-12g, each provided with a plurality of tooth-shaped stator elements 13 that are magnetizable by a corresponding stator coil (not shown) such that stator elements 13 can magnetically engage the rotor. As an example only, stator 10 may be formed of electrical steel plates, stack bonded with backlack. Stator 10 will be described in more detail with reference to Figures 4 and 5.

In Figure 3A, a rotor 20 according to an embodiment of the present invention is shown. Rotor 20 is comprised of a top rotor half 21a and a bottom rotor half 21b, each provided with an equal number of tooth-shaped rotor elements 22a, 22b. In particular, top rotor half 21a and bottom rotor half 21b of rotor 20 are formed such that rotor elements 22a corresponding to top rotor half 21a form magnetic north poles, and such that rotor elements 22b corresponding to bottom rotor half 21b form magnetic south poles.

A bore is provided in a center of each of top rotor half 21a and bottom rotor half 21b. The dimensions of the bore are such that shaft 4 can extend through said bore, and such that rotor 20 can be mounted to said shaft.

Top rotor half 21a and bottom rotor half 21b may be physically connected or integrally formed, so as to fixate an angular position relative to one another. Alternatively, top rotor half 21a and bottom rotor half 21b are fixated only through the shaft upon mounting said top rotor half 21a and bottom rotor half 21b to said shaft.

As an example only, rotor 20 may be formed from electrical steel plates, similarly to stator 10, and may be provided with a permanent ring magnet, such as a neodymium permanent ring magnet, arranged to magnetize rotor elements 22a, 22b.

Rotor elements 22a of top rotor half 21a and rotor elements 22b of bottom rotor half 21b are each irregularly (i.e., non-uniformly) spaced, such as to irregularly space the plurality of rotor poles or rotor pole pairs. As such, a magnetic flux associated with rotor 20 has non-uniformly spaced local maxima and minima. Based on the spacing between rotor elements 22a, 22b, the magnetic flux associated with rotor 20 may provide a uniquely identifiable angular position of rotor 20. For example, if a spacing sequence of rotor elements 22a, 22b does not repeat along an entire circumference of rotor 20, then an absolute angular position can be uniquely determined by measuring the magnetic flux pattern. This will be described below in further detail with reference to Figures 5-7B.

In Figure 3B, a rotor 25 according to another embodiment of the present invention is shown. Rotor 25 comprises a plurality of rotor bodies 26a-26c, each comprising a plurality of corresponding tooth-shaped rotor elements 27a-27c. Similarly to rotor 20 of Figure 3A, each rotor body 26a-26c may be formed of a top rotor half and a bottom rotor half that are physically or integrally connected, and rotor elements 27a-27c can be magnetized, for example using magnet, such as to form magnetic north poles in one of the top rotor half and bottom rotor half, and magnetic south poles in another of the top rotor half and bottom rotor half. Rotor elements 27a-27c of corresponding rotor bodies 26a-26c may each be uniformly spaced along a circumference of said corresponding rotor bodies 26a-26c. However, each rotor body 26a-26c has a different number of rotor elements 27a-27c to form a different number of rotor poles. Rotor bodies 26a- 26c are mutually fixated, for example by fixating each rotor body 26a-26c on shaft 4 extending through a bore in each of rotor bodies 26a- 26c, and/or by fixating the rotor bodies 26a-26c to one another. Even though each individual rotor body 26a-26c has uniformly spaced rotor elements 27a-27c, a combined magnetic flux associated with a combination of rotor bodies 26a-26c may effectively have non-uniformly spaced local maxima and minima, such that said magnetic flux effectively provides a uniquely identifiable angular position of rotor 20, similar to the above for rotor 20 in Figure 3A.

Hereinafter, for convenience, reference will be made to rotor 20 as described with reference to Figure 3A. However, it will be appreciated that the present invention similarly applies when rotor 20 is substituted for rotor 25.

In Figure 4, a cross-sectional top view of stepper motor 1 of Figure 1 is shown, in accordance with an embodiment of the present invention. Stepper motor 1 comprises stator 10 and rotor 20 mounted on shaft 4 and arranged in a cavity of stator frame 11. As described before, stator 10 comprises arms 12a-12g, each having corresponding tooth-shaped stator elements 13 arranged facing rotor 20. Stator 10 further comprises a plurality of stator coils 14a- 14g wound around a portion of respective arms 12a-12g. According to the embodiment of Figure 4, stator 10 comprises seven arms 12a-12g, each comprising seven stator elements 13, and rotor 20 comprises a total of 51 irregularly spaced pole pairs formed by 102 irregularly spaced rotor elements 22.

Stator coils 14a- 14g are electrically connected (not shown) to respective driving pins 5. An external driving unit (not shown) can drive stator coils 14a- 14g by providing a driving signal to corresponding driving pins 5. Upon being driven, stator coils 14a-14g are configured to magnetize corresponding stator elements 13 in accordance with a driving signal provided by the external driving unit. For example, stator elements 13 of respective arms 12a- 12g can be magnetized such that said stator elements 13 form magnetic north poles or magnetic south poles, and a magnitude of a corresponding magnetic field may be determined by the corresponding driving signal.

In stepper motor 1, upon being actuated by driving signals for stator coils 14a-14g, rotor 20 is configured to rotate based on the magnetization of stator elements 13. Due to the rotation of rotor 20, the magnetic flux, from the rotor poles of rotor 20, through each of stator coils 14a- 14g will change over time, resulting in a current being induced in each of stator coils 14a-14g. Therefore, a total current through each of stator coils 14a-14g is a sum of at least a driving current as a result of driving said stator coil 14a- 14g, and an induced current that is induced by the changing magnetic flux. Furthermore, due to the irregular spacing between rotor poles of rotor 20, the abovementioned induced current follows a pattern in accordance with the irregular spacing along the circumference of rotor 20, and said induced current, during a rotation of rotor 20, is thus indicative of an angular position of rotor 20.

More in particular, if a spacing pattern of rotor poles of rotor 20 does not repeat along the entire circumference of rotor 20, an absolute angular position of rotor 20 can be determined based on the induced current(s) and a known spacing between the plurality of rotor poles. For example, the induced current or total current through one or more of stator coils 14a-14g can be compared to a predetermined or generated reference model, representative of the known spacing between adjacent rotor poles, to determine an angular position of rotor 20 with respect to stator 10. In turn, a control system (not shown) of stepper motor 1 can use the determined angular position to correct, for example, a calibration value of the angular position of rotor 20, and to continue tracking the angular position based on the calibration value.

In some embodiments, the spacing pattern of rotor poles of rotor 20 repeats a number of times along the circumference of rotor 20. For example, rotor 20 comprises P substantially identical sections of irregularly spaced rotor poles along its circumference. In that case, the plurality of stator coils may be arranged in a plurality of groups of P stator coils, and the stator coils of the plurality of groups may be arranged in an interleaved manner. For example, the P stator coils in each group of stator coils may respectively be arranged uniformly along a circumference of rotor 20. The external driving unit may in that case be configured to drive stator coils in a same group with a same or corresponding driving signal.

In these embodiments, an induced current in stator coils 14a- 14g, due to a rotation of rotor 20, also follows a pattern in accordance with the irregular spacing along the circumference of rotor 20, though said pattern repeats P times throughout a full rotation of rotor 20. Due to this, there is an ambiguity in which section among the P sections rotor 20 is positioned. However, if an error or mismatch between an expected (e.g., tracked and/or stored) angular position and the determined angular position, based on the induced currents and the known spacing of the rotor poles, is sufficiently small, then absolute position detection may nevertheless be possible by comparing the determined angular position to the tracked or stored angular position. Furthermore, recalibration based on a determined angular position may be repeated periodically to avoid losing track of the absolute angular position of rotor 20.

In Figure 5, a motor system 50 according to an embodiment of the present invention is shown. Motor system 50 comprises stepper motor 1, a driving unit 30 and a control unit 40 comprising a position determining unit 41. Stepper motor 1 is described above, and a detailed description thereof with respect to Figure 5 is therefore omitted.

Driving unit 30 comprises a plurality of driving circuits 31 formed by half H-bridge switching circuits, each being configured to provide a driving voltage signal to a respective pair of stator coils 14a-14g. For convenience, driving circuits 31 are shown only for stator coils 14a-14c, though stator coils 14d-14g may also have a corresponding driving circuit.

Control unit 40 is configured to control driving unit 30 to generate the driving signals for stator coils 14a-14g. In addition, control unit 40 or position determining unit 41 of control unit 40 is configured to receive current measurements from current sensors 42, each configured to measure a current through a corresponding stator coil. For convenience, current sensors 42 are shown only for stator coils 14a-14c, though stator coils 14d-14g may also have a corresponding current sensor. When rotor 20 is rotating, each current comprises a superposition of at least a driving current as a result of driving a corresponding stator coil and an induced current resulting from a changing magnetic flux through said corresponding stator coil due to the rotating rotor. Position determining unit 41 is configured to determine an angular position based on the measured current(s) and a known spacing between the plurality of rotor poles.

In the following, a process of determining an angular position based on harmonic content in the measured currents is described using exemplifying embodiments. However, it will be appreciated by a person skilled in the art that the present invention is not limited to these exemplifying embodiments.

Referring to the configuration of Figures 4 and 5 and rotor 20 of Figure 3A, rotor elements 22a and rotor elements 22b may be positioned respectively at local maxima and local minima of the function [Equation 1]: (a) ⁼ 2r^l ^w r ^cos ( ⁿ _r ^a + Kr) wherein values of M, w _r , n _r and y _r are constants. More in particular, M represents the number of ‘rotor modes’, n _r corresponds to a particular ‘rotor mode’, and w _r is a weight of said particular ‘rotor mode’. Furthermore, y _r may be selected for each ‘rotor mode’ such that the magnetic flux pattern defined by (a) may be approximated by a rotor with rotor elements located at its extrema. For example, y _r may be selected such that a magnitude of the maxima and minima of (a) differ by less than 20% from the mean magnitude, preferably less than 10%, and more preferably within 5%, though the present invention is not limited to any such range.

The values in Table 1 provided below represent exemplifying options, in which NA represents a number of stator coils, and P represents a number of stator coils in each group of corresponding stator coils.

[Table 1]: Each value of n _r can effectively be seen as a ‘rotor mode’ representing a rotor with n _r uniformly spaced pole pairs (i.e., n _r uniformly spaced north poles and n _r uniformly spaced south poles). When combined in a weighted manner using weights w _r , a rotor is obtained with irregularly spaced rotor poles. Here, n _r can be written as n _r = P(7z + r) for some integer z. Table 1 similarly applies to rotor 25 of Figure 3B, for example by combining a plurality of rotor bodies r, each with one of n _r rotor pole pairs that are uniformly spaced, such that the combined magnetic flux from the rotor bodies effectively has minima and maxima identical or similar to that of Equation 1.

Taking a stepper motor configuration according to the first row of Table 1, a total magnetic flux from rotor 20 through each coil at a given rotor position will vary in accordance with rotor pole positions as defined in Equation 1.

The currents through the wire of each stator coil 14a-14g are denoted as lo- , respectively. Assuming a star configuration of stator coils 14a-14g, Kirchhoff’s law states that the sum of the currents must be zero, such that there are six independent degrees of freedom (DOFs). The Fourier transform of the currents through stator coils 14a-14g can therefore be represented by three complex variables, which are hereinafter referred to as the 50-plane, 51 -plane and 52 plane due to their correspondence with n _r in Table 1.

Two DOFs can be used for actuation of the rotor, called the 51 -phase and 51 -amplitude. Two other DOFs, the 50-phase and 52-phase, can be used for angular position determination.

Stepper motor 1 can be controlled by control unit 40 which drives rotor 20 as if it would have 51 regularly or uniformly spaced pole pairs, resulting in a 30% lower output torque based on the weight coefficient wz in Table 1 in this exemplifying embodiment. Alternatively, the lower output torque is compensated for by increasing a driving voltage signal of stator coils 14a-14g.

When rotor 20 is rotating, a voltage across each stator coil 14a-14g equals the sum of at least a resistor voltage due to the driving voltage signal, and a back-emf voltage due to a changing magnetic flux through the coil as a result of rotor 20 rotating.

Based on a measurement of current sensors 42, position determining unit 41 can apply a discrete Fourier transformation (DFT) to a vector comprising the measured current through each stator coil in an order in which they are arranged along a circumference of the cavity of stator 10, in accordance with [Equation 2]:

In doing so, coefficients of the calculated DFT are indicative of the driving current and induced current. In particular, the phase of the 50-plane and 52-plane described above, corresponding to coefficients A; and As, are indicative of a phase of rotor modes m and nj, and a difference between the phase of coefficients A; and /b may be indicative of the angular position of rotor 20. In other words, in this embodiment, the phase of coefficients Ai and As may represent information regarding the angular position of rotor 20 based on the known spacing between rotor poles of rotor 20, and can be used to determine said angular position of rotor 20.

Figure 6A shows a signal diagram of stator coil currents lo- at a relatively low rotation speed of rotor 20, based on the configuration shown in Figures 4 and 5 and the first row of Table 1. For example, the rotation speed of rotor 20 in this example is less than one revolution per minute (rpm), such as 0.5 rpm. Figure 6B shows an amplitude diagram of DFT coefficients Ai-A obtained from a DFT operation applied to currents 10-16 shown in Figure 6A. As seen in Figure 6A, each stator coil 14a-14g is driven with a sinusoidal signal having a respective phase.

As can be seen from Figures 6A and 6B, at relatively low rotational speeds of rotor 20, the Fourier transform is dominated by the sinusoid from the driving by driving unit 30, since most energy is concentrated in coefficients As and As (Aj being a complex conjugate of A2). Depending on the spacing between rotor poles of rotor 20, an induced current as a result of changing magnetic flux may not be prominent at low speeds of rotor 20. Since the magnitude of coefficients Ai and A is relatively small, the phases thereof may not be well-defined at relatively low rotational speeds of rotor 20. As an example only, a relatively low rotational speed may correspond to a rotational speed of 1 rpm or lower. However, it will be appreciated that such a rotation speed threshold may be dependent on the application and the physical implementation of stepper motor 1, and should not be seen as limiting to the present invention.

Figure 7A shows a signal diagram of stator coil currents 10-16 at a relatively high rotation speed of rotor 20, based on the configuration shown in Figures 4 and 5 and the first row of Table 1. For example, the rotation speed of rotor 20 in this example is greater than 5 rpm, such as 100 rpm, Figure 7B shows a phase diagram of DFT coefficients A1-A3 obtained from a DFT operation applied to currents 10-16 shown in Figure 7A.

As can be seen from Figures 7A, at higher rotational speeds, the amplitudes of the coil currents 10-16 are no longer (approximately) equal and a phase difference between coil currents JO- 16 changes as a result of an increased effect of the induced current due to the rotating rotor 20. The energy of the Fourier spectrum is no longer concentrated in coefficient As, but is now also present in coefficients A; and Aj. As a result, the phase of coefficients A; and /b is now well-defined. In this embodiment, the phase difference between coefficients As and A; changes based on the angular position of rotor 20 due to the known irregular spacing between rotor pole pairs. Therefore, this phase difference is indicative of the angular position of rotor 20 and can be used to determine said angular position of rotor 20.

In Figure 8, a signal diagram of a true angular position GT of rotor 20 and a tracked angular position <j> of rotor 20 is shown over time. In practical implementations of the present invention, the angular position of rotor 20 need not be measured and determined continuously. For example, the angular position of rotor 20 may be periodically determined as described above to recalibrate a tracking value of the angular position stored internally in position determining unit 41.

For example, the internally stored angular position may be a tracked value <j> of the angular position that is generally updated based on an expected rotation of rotor 20, for example based on the driving signals applied to the stator coils. Upon determining the angular position of rotor 20 based on the induced current(s) and the known spacing between rotor poles of rotor 20 in accordance with the present invention, there may be a deviation between the determined angular position and the tracked value <j> of the angular position. Control unit 40 may then be configured to update or recalibrate the tracked value <j> based on the determined angular position.

For example, in Figure 8, starting from time instance tl, there is a discrepancy between the true angular position of rotor 20, and the tracked value <j> that is internally stored and tracked. This may for example be because external forces physically adjusted the motor shaft, causing a change in angular position. Likewise, at time instance t3, a discrepancy occurs in an opposing direction with respect to the discrepancy at time instance tl. Upon determining the angular position of rotor 20 as described above, which determined angular position may be similar or substantially correspond to the true angular position GT, the tracked value <j> may be updated to correspond more to the determined angular position, for example in steps of predetermined size as shown in Figure 8. This may be performed periodically or iteratively until the deviation between the determined angular position and the tracked value <j> is zero or at least below a predetermined threshold, such as at time instance t2 and at time instance t4 in Figure 8. In a further embodiment, the predetermined size of the steps may be dependent on a magnitude of deviation between the determined angular position and the tracked value <j>. In another embodiment, the tracked value <j> is updated to correspond directly to the determined angular position, rather than incrementally approaching the determined angular positions using smaller steps.

In the above, the present disclosure has been explained using detailed embodiments thereof. However, it should be appreciated that the disclosure is not limited to these embodiments and that various modifications are possible without deviating from the scope of the present disclosure as defined by the appended claims.