Sensor device for determining the position of the rotor of an electrical machine and control device for an electric motor

Abstract

A sensor device for determining a position .sub.1 of a rotor of an electrical machine, for example an electric motor or electric generator. The sensor device comprises a number r of sensors, which detect the magnetic field generated by the rotor and/or a permanent magnet rotating with the rotor, and an electronic circuit which is configured to detect and digitalize the sensor signals a.sub.1 to a.sub.r and to form a signal vector {right arrow over (a)}=(a.sub.1, . . . , a.sub.r), to form a measurement vector {right arrow over (q)} according to a predetermined linear function g to {right arrow over (q)}=g({right arrow over (a)}), to calculate a vector {right arrow over (p)}=M.sub.rot1.Math.{right arrow over (q)}, wherein {right arrow over (p)} is a 2-component vector with the components p.sub.1 and p.sub.2 and M.sub.rot1 is a 2n matrix, and to determine the position .sub.1 of the rotor to .sub.1=a tan 2(p.sub.2, p.sub.1). The invention further concerns a control device for an electric motor with such a sensor device.

Claims

1. A sensor device configured to determine a first position .sub.1 of a rotor of an electrical machine, wherein the electrical machine comprises the rotor and a stator with stator coils, wherein the rotor is a permanent magnet with a predetermined number n.sub.rot1>1 of pole pairs or a passive rotor, wherein the magnetic field generated by the rotor and/or by the permanent magnet rotating with the rotor has a multiple character and the first position .sub.1 is therefore an incremental position, wherein the sensor device has a predetermined number r of magnetic sensors, which detect the magnetic field generated by the rotor and/or by the permanent magnet rotating with the rotor, and an electronic circuit, wherein the electronic circuit is configured to determine the first position .sub.1 of the rotor with only the four following steps of: first, detecting and digitizing the sensor signals a.sub.1 to a.sub.r and forming a signal vector {right arrow over (a)}=(a.sub.1, . . . , a.sub.r), second, after the first step, forming a measurement vector {right arrow over (q)} according to a predetermined linear function g such that {right arrow over (q)}=g({right arrow over (a)}), wherein the measurement vector {right arrow over (q)} comprises a number, n, of components, with 2nr, third, after the second step, calculating a vector {right arrow over (p)}=M.sub.rot1.Math.{right arrow over (q)}, wherein {right arrow over (p)} is a 2-component vector with the components p.sub.1 and p.sub.2 and M.sub.rot1 is a 2n matrix, and fourth, after the third step, determining the first position .sub.1 of the rotor such that .sub.1=a tan 2(p.sub.2, p.sub.1).

2. The sensor device according to claim 1, further configured to calculate a vector {right arrow over (x)}=M.sub.rot2.Math.{right arrow over (q)}, wherein {right arrow over (x)} is a 2-component vector with the components x.sub.1 and x.sub.2 and M.sub.rot2 is a 2n matrix, and to determine a second position .sub.2 of the rotor to .sub.2=a tan 2(x.sub.2, x.sub.1), wherein the second position .sub.2 is an absolute position.

3. The sensor device according to claim 2, wherein the sensor device is further configured to recalculate the second position .sub.2 from the positions .sub.1 and .sub.2 to obtain the absolute position .sub.2 with a higher accuracy.

4. The sensor device according to claim 2, wherein the function g({right arrow over (a)}) is one of the following functions:
g({right arrow over (a)})={right arrow over (a)},1)
g({right arrow over (a)})={right arrow over (a)}{right arrow over (a)}.sub.0,2)
g({right arrow over (a)})=P.Math.{right arrow over (a)}, or3)
g({right arrow over (a)})=P.Math.({right arrow over (a)}{right arrow over (a)}.sub.0),4) wherein {right arrow over (a)}.sub.0 designates an offset vector and P a projection matrix.

5. The sensor device according to claim 4, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein second position .sub.2 of the rotor of the electric motor determined by the sensor device is fed to the motor controller, the motor controller is configured to generate control signals dependent on the second position .sub.2 for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

6. The sensor device according to claim 2, further configured to determine a position of the stator rotational field of the electrical machine, for which it is configured to calculate a vector {right arrow over (y)}=M.sub.stat.Math.{right arrow over (q)}, wherein {right arrow over (y)} is a 2-component vector with the components y.sub.1 and y.sub.2 and M.sub.stat is a 2n matrix, and to determine the position of the stator rotational field to =a tan 2(y.sub.2, y.sub.1).

7. The sensor device according to claim 6, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein the second position .sub.2 of the rotor and the position of the stator rotational field of the electric motor determined by the sensor device are fed to the motor controller, the motor controller is configured to generate control signals dependent on the positions .sub.2 and for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

8. The sensor device according to claim 2, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein the second position .sub.2 of the rotor of the electric motor determined by the sensor device is fed to the motor controller, the motor controller is configured to generate control signals dependent on the second position .sub.2 for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

9. The sensor device according to claim 1, wherein the function g({right arrow over (a)}) is one of the following functions:
g({right arrow over (a)})={right arrow over (a)},1)
g({right arrow over (a)})={right arrow over (a)}{right arrow over (a)}.sub.0,2)
g({right arrow over (a)})=P.Math.{right arrow over (a)}, or3)
g({right arrow over (a)})=P.Math.({right arrow over (a)}{right arrow over (a)}.sub.0),4) wherein {right arrow over (a)}.sub.0 designates an offset vector and P a projection matrix.

10. The sensor device according to claim 9, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein the first position .sub.1 of the rotor of the electric motor determined by the sensor device is fed to the motor controller, the motor controller is configured to generate control signals dependent on the first position .sub.1 for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

11. The sensor device according to claim 1, wherein the electrical machine is a synchronous motor, asynchronous motor, alternating current motor, stepping motor or electric generator.

12. The sensor device according to claim 1, wherein the electrical machine is a flat motor.

13. The sensor device according to claim 1, wherein the magnetic sensors are Hall sensors or magnetoresistive sensors and arranged on a common substrate.

14. The sensor device according to claim 1, further configured to determine a position of the stator rotational field of the electrical machine, for which it is configured to calculate a vector {right arrow over (y)}=M.sub.stat.Math.{right arrow over (q)}, wherein {right arrow over (y)} is a 2-component vector with the components y.sub.1 and y.sub.2 and M.sub.stat is a 2n matrix, and to determine the position of the stator rotational field to =a tan 2(y.sub.2, y.sub.1).

15. The sensor device according to claim 14, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein the first position .sub.1 of the rotor and the position of the stator rotational field of the electric motor determined by the sensor device are fed to the motor controller, the motor controller is configured to generate control signals dependent on the positions 1i and W for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

16. The sensor device according to claim 1, further comprising: a control device for an electric motor which comprises a rotor and a stator, wherein the control device comprises, a motor controller, and a drive unit, wherein the first position .sub.1 of the rotor of the electric motor determined by the sensor device is fed to the motor controller, the motor controller is configured to generate control signals dependent on the first position .sub.1 for the drive unit, and the drive unit is configured to generate currents for the stator coils of the electric motor.

Description

BRIEF DESCRIPTION OF THE DRAWING FIGURES

(1) The accompanying drawings, which are incorporated into and constitute a part of this specification, illustrate one or more embodiments of the present invention and, together with the detailed description, serve to explain the principles and implementations of the invention. The figures are not to scale. In the drawings:

(2) FIGS. 1 and 2 show electric motors equipped with a sensor device according to the invention,

(3) FIG. 3 schematically shows an electric motor and a first control device, and

(4) FIG. 4 schematically shows an electric motor and a second control device.

DETAILED DESCRIPTION OF THE INVENTION

(5) FIGS. 1 and 2 show examples of electric motors equipped with a sensor device according to the invention. The electric motor comprises a rotor 1 rotatable about an axis 3 and a stator 2. The rotor 1 is mounted on a shaft which rotates about the axis 3. The sensor device comprises a predetermined number r of magnetic sensors, for example Hall elements or magnetoresistive sensors, e.g., AMR (Anisotropic MagnetoResistive), GMR (Giant MagnetoResistive) and TMR (Tunnel MagnetoResisitive) sensors. The number r of the sensors depends on the tasks which the sensor device has to fulfill. For the sake of clarity, only three sensors S1, S2 and S3 are shown, although the number r of the sensors can also be two or more than three.

(6) FIGS. 1 and 2 showon the left in cross-section and on the right in plan viewthe basic principle of a synchronous motor or an asynchronous motor. In the synchronous motor, the rotor 1 is a permanent magnet, in the asynchronous motor, the rotor 1 is a passive rotor, which is either short-circuited permanently or in a case-by-case manner, e.g., a cage runner. The two electric motors are supplied with a rotary current having a predetermined number, n.sub.ph, of phases. The number of the phases can be 2, 3 or more. The stator 2 of these electric motors has a predetermined number, n.sub.stat, of coil tuples. Each of the coil tuples comprises n.sub.ph coils for the n.sub.ph, phases of the rotary current, so that a coil of a coil tuple is assigned to each phase of the rotary current. The stator rotation field is invariant with respect to rotations about 360/n.sub.stat.

(7) The electric motor shown in FIGS. 1 and 2 are designed for operation with three-phase alternating current, the phases of which are designated as U, V and W. The stators 2 comprise six coils, all of which have the same winding sense. The six coils therefore form n.sub.stat=2 coil triples, i.e., the coil tuples are coil triples. Each of the two coil triples comprises three coils, namely a coil for the phase U, a coil for the phase V and a coil for the phase W. The stator rotational field thus corresponds to a rotating magnetic quadrupole.

(8) The six coils can alternatively have a different winding sense, namely U, V, W, U, V and W, the minus sign denoting the inverted winding sense. In this case, the six coils form a single coil tuple, i.e., it is n.sub.stat=1. In this case, the stator rotational field corresponds to a rotating magnetic dipole.

(9) The electric motors can also have a different number of coils and other wirings.

(10) The rotor 1 of the synchronous motor shown in FIG. 1 is a permanent magnet having a predetermined number n.sub.rot1, of pole pairs, in the example shown n.sub.rot1=4. In addition, a permanent magnet 4, in particular a dipole magnet, can be attached to the rotor shaft. A dipole magnet has n.sub.rot1=1. A multipole magnet has n.sub.rot1>1.

(11) In an asynchronous motor, at least one permanent magnet 4 is attached to the shaft. The permanent magnet 4 can be a dipole magnet (as shown in FIG. 2) or a multipole magnet. In particular, two permanent magnets 4 can be provided, namely one with n.sub.rot1=1 and one with n.sub.rot2>1.

(12) This results in the following: The rotor 1 and/or one or two permanent magnets rotating with the rotor 1 produce a magnetic field which has a dipole character, a multipole character or a dipole character and a multipole character. The magnetic field rotating with the rotor 1 is accordingly characterized by one or two values n.sub.rot1, n.sub.rot2, wherein n.sub.rot1 (or n.sub.rot2)=1 for the dipole field and n.sub.rot2 (or n.sub.rot1)>1 for the multipole field. The currents flowing through the stator coils of the stator 2 produce a stator rotational field, which also rotates about the axis 3. In principle, the magnetic field generated by the rotor 1 is invariant against rotations by 360/n.sub.rot1 (or 360/n.sub.rot2, respectively) and the magnetic field generated by the stator 2 is invariant against rotations about 360/n.sub.stat.

(13) A magnetic field rotating with the rotor 1 with n.sub.rot1=1 makes it possible to determine the absolute position of the rotor 1, i.e., its position within the full angular range of 0-360. A magnetic field rotating with the rotor 1 with n.sub.rot>1 makes it possible to determine an incremental position of the rotor 1, i.e., the corresponding position value in the interval 0-360 is repeated n.sub.rot times with a complete rotor rotation, so that position changes of the rotor 1 are detectable, but not its absolute position. If the magnetic field rotating with the rotor 1 has both dipole characteristics and multipole characteristics, the absolute position as well as the incremental position of the rotor 1 can be determined with the sensor device according to the invention.

(14) The sensors are intended to detectas useful fieldthe magnetic field generated by the rotor 1 and/or by the permanent magnet rotating with the rotor 1, but not the magnetic interference fields generated by the stator 2. The sensors are therefore preferably arranged on the front face of the electric motor of FIG. 1 on the side facing the axis 3, i.e., on the inside of the rotor 1, and in the electric motor of FIG. 2 preferably on the side of the permanent magnet 4 facing away from the stator 2 in order to minimize the signal component of the magnetic interference fields generated by the stator 2. The sensors are advantageously arranged on a common substrate, for example a printed circuit board.

(15) If the sensor arrangement is configured for controlling an electric motor which also uses the stator rotational field for control purposes, the sensors, or at least some of them, are also intended to detect the stator rotational field. In this case, the sensors are advantageously arranged in such a way that most of them detect both the magnetic field rotating with the rotor 1 as well as the magnetic field rotating with the stator 2.

(16) Sensor Device

(17) The sensor device additionally comprises an electronic circuit 5 (FIG. 3) with all necessary electronic components, in particular A/D converters and computing unit, which are required for operating the sensors and for evaluating the signals a.sub.1 to a.sub.r supplied by the r sensors. The determination of a position .sub.1 requires, and is subsequently explained, the multiplication of a matrix M.sub.rot1 with a measurement vector derived from the sensor signals a.sub.1 to a.sub.r. The matrix M.sub.rot1 is stored in a memory of the electronic circuit 5. If two positions, for example the absolute position and an incremental position, are to be determined, two different matrices M.sub.rot1 and M.sub.rot2 are accordingly stored in the memory.

(18) The sensor device is configured, to detect and digitalize the sensor signals a.sub.1 to a.sub.r and to form a signal vector {right arrow over (a)}=(a.sub.1, . . . , a.sub.r), to form a measurement vector {right arrow over (q)} according to a predetermined linear function g to {right arrow over (q)}=g({right arrow over (a)}), wherein the measurement vector {right arrow over (q)} comprises a number, n, of components, with 2nr, to calculate a vector {right arrow over (p)}=M.sub.rot1.Math.{right arrow over (q)}, wherein {right arrow over (p)} is a 2-component vector with the components p.sub.1 and p.sub.2 and M.sub.rot1 is a 2n matrix, and to determine a first position .sub.1 of the rotor to .sub.1=a tan 2(p.sub.2, p.sub.1).

(19) The sensor device may further be configured, to calculate a vector {right arrow over (x)}=M.sub.rot2.Math.{right arrow over (q)}, wherein {right arrow over (x)} is a 2-component vector with the components x.sub.1 and x.sub.2 and M.sub.rot2 is a 2n matrix, and to determine a second position .sub.2 of the rotor to 2=a tan 2(x.sub.2, x.sub.1).

(20) The function g({right arrow over (a)}) is in particular one of the following functions:
g({right arrow over (a)})={right arrow over (a)},1)
g({right arrow over (a)})={right arrow over (a)}{right arrow over (a)}.sub.0,2)
g({right arrow over (a)})=P.Math.{right arrow over (a)}, or3)
g({right arrow over (a)})=P.Math.({right arrow over (a)}{right arrow over (a)}.sub.0),4)
wherein {right arrow over (a)}.sub.0 designates an offset vector and P a projection matrix. The use of an offset vector allows correction of possible offsets of the sensors. The use of the projection matrix makes it possible to project signal components caused by interference fields out of the measured values. The function a tan 2(p.sub.2, p.sub.1) corresponds for example to the arctangent function known from the programming language C.

(21) The matrices M.sub.rot1 and M.sub.rot2 depend on the multipole character of the magnetic field rotating with the rotor 1, i.e., from the parameter nrot.sub.1 or n.sub.rot2, respectively. With a matrix M.sub.rot1, which has been calculated with n.sub.rot1=1, the first position .sub.1 is the absolute position in the angle range from 0-360. With a matrix M.sub.rot2, which has been calculated with n.sub.rot2>1, the second position .sub.2 this is in fact also a position in the angle range from 0-3600, but this does not correspond to the actual absolute position of the rotor 1, since the delivered position .sub.2 passes n.sub.rot2 times through the angular range of 0-360 during a complete rotor rotation. The second position .sub.2 is therefore an incremental position.

(22) The matrices M.sub.rot1 and M.sub.rot2 and given the case the projection matrix P can be determined for example with the COBROS method, which is described in the above-referenced and in this application incorporated related U.S. patent application Ser. No. 15/694,798. Where necessary, further explanations are given below.

(23) With n.sub.rot1=1 and n.sub.rot2>1 the first position .sub.1 is the absolute position and the second position .sub.2 is the incremental position, the accuracy of the incremental position being generally higher than the accuracy of the absolute position. The absolute position .sub.1 is therefore advantageously recalculated from the more accurate incremental position .sub.2 and the less exact absolute position .sub.1. The calculation depends on the angle range in which the incremental position .sub.2 is supplied. The a tan 2 ( ) function always provides angles in the range 0-360. The recalculation then takes place, for example, to .sub.1=.sub.2/n.sub.rot2+INT(.sub.1*n.sub.rot2/360)*360/n.sub.rot2, where the function INT (x) returns the integer portion of x.

(24) The influence of the stator rotational field on the measured position disappears if the rotational symmetry of the stator rotational field is different from the rotational symmetry of the rotor field. This is the case, if n.sub.stat< >n.sub.rot1 and, given the case, additionally also n.sub.stat< >n.sub.rot2. In order to determine the absolute position in this case, either it has to be n.sub.stat>1 or the sensors must be arranged in such a way that they do not detect the stator rotational field or are shielded as far as possible from the stator rotational field.

(25) The influence of the stator rotational field on the measured position can, on the other hand, be eliminated by means of a projection matrix P and a sufficient number r of sensors.

(26) These principles are explained in more detail below with reference to some exemplary embodiments.

Example 1

(27) The number r of the sensors is r=2. The number n.sub.stat of the coil tuples of the stator 2 is selected differently from the number n.sub.rot1 of the pole pairs of the rotor 1, so that the rotating field generated by the stator 2 does not influence the measuring result. With r=2 sensors, an offset correction and the suppression of the rotating field of the stator 2 is possible, but no suppression of external magnetic disturbing fields. The function g({right arrow over (a)}) is therefore either g({right arrow over (a)})={right arrow over (a)} or g({right arrow over (a)})={right arrow over (a)}{right arrow over (a)}.sub.0.

(28) The determination of the matrix M.sub.rot1 according to the method described in the above-referenced related U.S. patent application Ser. No. 15/694,798 requires the calculation of an auxiliary matrix W having the matrix elements W.sub.ij

(29) $W_{\mathrm{ij}}=\{\begin{array}{c}\sin \left(\mathrm{fe}.Math.\frac{\left({}_{\max }-{}_{\min }\right)\left(j-1\right)}{m}\right),i=1\\ \cos \left(\mathrm{fe}.Math.\frac{\left({}_{\max }-{}_{\min }\right)\left(j-1\right)}{m}\right),i=2\end{array},\mathrm{for}j=1\mathrm{to}m,$
wherein the number of pole pairs of the rotor 1 is to be used for the parameter e, i.e., it is e=n.sub.rot1. Since the angular range is 360, this simplifies to

(30) $W_{\mathrm{ij}}=\{\begin{array}{c}\sin \left({\mathrm{fn}}_{\mathrm{rot}1}.Math.\frac{2\left(j-1\right)}{m}\right),i=1\\ \cos \left({\mathrm{fn}}_{\mathrm{rot}1}.Math.\frac{2\left(j-1\right)}{m}\right),i=2\end{array},\mathrm{for}j=1\mathrm{to}m,$

(31) If the magnetic field has both dipole and multipole characteristics and if n.sub.rot1< >n.sub.stat as well as n.sub.rot2< >n.sub.stat, then both the absolute position and an incremental position can be determined. The determination of the matrix M.sub.rot2 takes place in the same way, with n.sub.rot1 replaced by n.sub.rot2 in the equation above. The position .sub.1 or .sub.2 of the rotor 1 calculated with the sensor device according to the invention achieves a higher measuring accuracy or smaller angular errors with only two sensors compared to the position calculated with the widespread sin-cos evaluation method.

Example 2

(32) An additional sensor allows the suppression of a magnetic field having an arbitrary spatial structure.

Example 3

(33) A number m of additional sensors enable for example the suppression of m mutually independent external magnetic fields, each of which has an arbitrary spatial structure.

Example 4

(34) Two additional sensors allow suppression of the stator rotational field during operation with a 3-phase rotating current as long as the relative phase position of the three currents is 120. This case is interesting when the number n.sub.stat of the coil tuples of the stator 2 equals the number n.sub.rot of the pole pairs of the rotor 1.

Example 5

(35) Three additional sensors allow for example the suppression of the stator rotational field during operation with a 3-phase rotating current, if the three phases are arbitrarily controlled, i.e., if they are not or only partially correlated.

(36) The suppression of the stator rotational field is performed automatically, if the number n.sub.stat of the coil tuples of the stator 2 and the number n.sub.rot1 and given the case n.sub.rot2 of the pole pairs of the motor 1 are different. However, the suppression of the stator rotational field can also be effected by means of a projection matrix P, which can be determined, for example, by means of the method described in the above-referenced related U.S. patent application Ser. No. 15/694,798. The application of the external field in the determination of the projection matrix P takes place in the case of the examples 4 and 5, in that in step 1.1 or 1.3.1 of the method described in the related U.S. patent application: a) first the stator coils associated with the first phase of the three-phase rotating current are supplied with a predetermined current, b) and then the stator coils associated with the second phase of the three-phase rotating current are supplied with a predetermined current, c) and then given the case the stator coils associated with the third phase of the three-phase rotating current are supplied with a predetermined current.

(37) When the amplitude of the currents flowing through the stator coils exceeds a certain limit, non-linear magnetic saturation effects occur in the magnetic material of the stator 2 and/or the rotor 1, which lead to harmonic waves in the sensor signals. The disturbing influence of the harmonic waves on the rotor position determination can be eliminated by using more than r=4 sensors.

(38) Control Device for an Electric Motor

(39) The sensor device may be supplemented with further electronic components to form a control device for an electric motor. Depending on the application, the control device can use an absolute position or an incremental position of the rotor for controlling the electric motor. In the following, the position used is designated by . The position is either the position .sub.1 or the position .sub.2.

(40) The control device can, for example, be configured to use the desired position .sub.soll and the measured actual position in order to control the currents flowing through the stator coils of the stator 2. However, the control device can also be configured to detect, in addition to the position of the rotor 1 also the position (=rotational position or rotation angle or rotary phase) of the magnetic field generated by the currents flowing through the stator coils, which in turn allows control of the stator currents corresponding to the actual positions and . This magnetic field will hereinafter be referred to as stator rotational field. This is possible with a number of at least four sensors, of which at least some are arranged in such a way that they also detect the stator rotational field. The control devices according to the invention are suitable for any electric motors, including stepping motors or speed-controlled electric motors. The positions and are usually dynamic, i.e., time-dependent signals. Subsequently, some examples are described.

Example 6

(41) FIG. 3 schematically shows an electric motor 8 and a control device 9. The control device 9 comprises a sensor device 10 of the type described above, and further a motor controller 6 and a drive unit 7. The position of the rotor 1 of the electric motor 8 determined by the sensor device 10 is fed to the motor controller 6 which therefrom generates control signals for the drive unit 7. The drive unit 7 generates the currents for the stator coils of the electric motor 8. The electric motor 8 is operated, for example as shown, with a 3-phase rotating current. The three currents are accordingly designated with U, V and W. The currents U, V and W depend on time.

Example 7

(42) FIG. 4 schematically shows the electric motor 8 and a control device 9. The control device 9 comprises again a sensor device 10 of the type described above, which is additionally configured to detect the position of the stator rotational field, with the steps: to calculate a vector {right arrow over (y)}=M.sub.stat.Math.{right arrow over (q)}, wherein {right arrow over (y)} is a 2-component vector with the components y.sub.1 and y.sub.2 and M.sub.stat is a 2n matrix, and to determine the position of the stator rotational field to =a tan 2(y.sub.2, y.sub.1).

(43) The matrix M.sub.stat can for example also be determined according to the COBROS method referred to above which is described in the above-referenced related U.S. patent application Ser. No. 15/694,798, wherein the number n.sub.stat of the coil tuples of the stator 2 is to be used for the parameter e in the calculation of the auxiliary matrix W. The elements of the auxiliary matrix W are thus given for the determination of the matrix M.sub.stat by

(44) $W_{\mathrm{ij}}=\{\begin{array}{c}\sin \left({\mathrm{fn}}_{\mathrm{stat}}.Math.\frac{2\left(j-1\right)}{m}\right),i=1\\ \cos \left({\mathrm{fn}}_{\mathrm{stat}}.Math.\frac{2\left(j-1\right)}{m}\right),i=2\end{array},\mathrm{for}j=1\mathrm{to}m,$

(45) At least one position of the rotor 1, i.e., .sub.1, .sub.2, or both positions .sub.1 and .sub.2, and the determined position t of the stator rotational field are supplied to the motor controller 6, which generates control signals for the drive unit 7 therefrom.

(46) The sensor device according to the invention for determining the position of the rotor and of the rotary phase of the stator offers several advantages, including: a high integration density, i.e., the construction of a space-saving sensor device; which also allows the construction of extremely compact flat motors, all necessary measuring signals are obtained from the same sensors, all measurement signals are used for the solution of all tasks (elimination of external fields, determination of the rotor position angle, determination of the rotary current angle), all processing steps are executed in the same architecture (FPGA, microprocessor or DSP), thus exhibiting the same delays or possibly distortions. This ensures that the measured value quality of the rotary current phase position and the rotor position is independent of the operating point at which the motor is operated. In addition, all measurement signals refer to exactly the same measuring time. This allows very robust motor systems to be implemented, for example, in order to operate the electric motor at the operating point with maximum torque.

(47) While embodiments and applications of this invention have been shown and described, it would be apparent to those skilled in the art having the benefit of this disclosure that many more modifications than mentioned above are possible without departing from the inventive concepts herein. The invention, therefore, is not to be restricted except in the spirit of the appended claims and their equivalents.