Sensorless position detection of an electric motor

Abstract

An apparatus includes an electric motor including a stator and a rotor; a three-phase inverter electrically coupled to the electric motor; a power source electrically coupled to the three-phase inverter; and a controller communicatively coupled to the three-phase inverter. The controller is programmed to determine at least three measurements of a magnetic flux linkage from the electric motor at different times, express the measurements in Clarke coordinates, determine Clarke coordinates of a center of a circle defined by the Clarke coordinates of the measurements, and determine a position of the rotor relative to the stator based on the Clarke coordinates of the center of the circle.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This patent application claims priority to and all the benefits of U.S. patent application No. 16 / 739,704, filed on January 10, 2020, which is hereby incorporated by reference in its entirety. Background Art

[0003] A vehicle typically includes a suspension system. A vehicle's suspension system is coupled to the vehicle frame and each wheel assembly. The suspension system absorbs and attenuates shock and vibration transmitted from the wheel assembly to the vehicle frame. For each wheel assembly, the suspension system includes an upper control arm, a lower control arm, a coil spring, and a shock absorber. The shock absorber extends through the coil spring. One end of the shock absorber and coil spring may be connected to the lower control arm, and the other end of the shock absorber and coil spring may be connected to the upper control arm or the vehicle frame. Shock absorbers are typically hydraulic or pneumatic, but may alternatively be electromagnetic, where an electric motor is used to absorb and attenuate shock and vibration transmitted from the road surface to the wheel. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Figure 1 is a perspective view of an exemplary suspension system.

[0005] Figure 2 is a diagram of an exemplary electric motor.

[0006] Figure 3 is a circuit diagram of a device including an electric motor.

[0007] Figure 4 is a feedback block diagram for determining the flux linkage of an electric motor.

[0008] Figure 5 is a process flow diagram of an exemplary process for determining the center of a flux linkage circle in Clarke coordinates.

[0009] Figure 6 is a diagram of the flux linkage of an electric motor in Clarke coordinates.

[0010] Figure 7A is a graph showing the relationship between the magnetic flux linkage of the electric motor and time in the α dimension.

[0011] Figure 7B is a graph showing the relationship between the magnetic flux linkage of the electric motor and time in the β dimension.

[0012] Figure 7C It is a curve diagram of the relationship between the weighting factor of magnetic flux linkage and time.

[0013] Figure 7D is a graph of the flux linkage in Clarke coordinates during the first time span.

[0014] Figure 7E is a plot of the flux linkage in Clarke coordinates over a second time span.

[0015] Figure 8 is a process flow diagram of an exemplary process for controlling a device. DETAILED DESCRIPTION

[0016] Referring to the drawings, a device 30 includes an electric motor 32 including a stator 34 and a rotor 36; a three-phase inverter 38 electrically coupled to the electric motor 32; a power source 40 electrically coupled to the three-phase inverter 38; and a controller 42 communicatively coupled to the three-phase inverter 38. The controller 42 is programmed to determine at least three measurements of a flux linkage from the electric motor 32 at different times, express the measurements in Clarke coordinates, determine Clarke coordinates of a center of a circle 600 defined by the Clarke coordinates of the measurements, and determine a position of the rotor 36 relative to the stator 34 based on the Clarke coordinates of the center of the circle 600.

[0017] The electric motor 32 can be used as a component of a suspension system 18 of a vehicle 16, particularly as a shock absorber. The electric motor 32 following the method described below has advantages over different types of shock absorbers in that position sensors can be eliminated or checked. The device 30 can be used for regenerative shock absorption, i.e., for charging the power source 40 using road vibrations. The device 30 and method described herein provide for sensorless control of the electric motor 32, whether or not the device 30 is part of the suspension system 18. Omitting the position sensor 56 simplifies the design of the electric motor 32 and provides for a substantial cost reduction. Alternatively, the method can provide for a check of the functionality of the position sensor 56, if present. The method provides an efficient way to compensate for errors in measuring the flux linkage through the electric motor 32. The method avoids the use of filters, and the method can provide reliable information about the position of the electric motor 32, the movement of the rotor 36 relative to the stator 34, across a wide frequency range, even at low frequencies.

[0018] Reference Figure 1, the vehicle 16 includes a vehicle frame 20, a suspension system 18 coupled to the vehicle frame 20, and a wheel assembly 22 coupled to the suspension system 18. The wheel assembly 22 is movable vertically relative to the vehicle frame 20, e.g., via the suspension system 18. For each wheel assembly 22 of the vehicle 16, the suspension system 18 includes an upper control arm 24, a lower control arm 26, a coil spring 28, and an electric motor 32. In the context of the suspension system 18, the electric motor 32 is an electromagnetic shock absorber. The electric motor 32 functions as a shock absorber and can replace a traditional hydraulic or pneumatic shock absorber. The electric motor 32 can supplement the coil spring 28, or the electric motor 32 can replace the coil spring 28. If both are present, the electric motor 32 can extend through the coil spring 28, as shown in Figure 1 Figure 1 The electric motor 32 is coupled directly or indirectly to the vehicle frame 20 and the wheel assembly 22 such that when the wheel assembly 22 moves relative to the vehicle frame 20, the translator 36 moves relative to the stator 34, i.e., such that the translator 36 moves with one of the vehicle frame 20 and the wheel assembly 22, and the stator 34 moves with the other of the vehicle frame 20 and the wheel assembly 22. For example, the electric motor 32 and one end of the coil spring 28 can be connected to the lower control arm 26, and the other end of the electric motor 32 and the coil spring 28 can be connected to the upper control arm 24 or the vehicle frame 20. In particular, one of the stator 34 and the translator 36 is fixed to the upper control arm 24 or the vehicle frame 20, and the other of the stator 34 and the translator 36 is fixed to the wheel assembly 22. In other arrangements of the suspension system, the electric motor 32 can function as a shock absorber, in addition to that shown in Figure 1

[0019] Referring to Figure 2 , the electric motor 32 acts as a motor while also acting as a generator. The electric motor 32 converts electrical energy to mechanical energy, and vice versa. The mechanical energy takes the form of movement of the translator 36 relative to the stator 34. In the context of the electric motor 32 functioning as a shock absorber, the translator 36 can move relative to the stator 34 due to road irregularities, and the electric motor 32 can resist and / or cause movement of the translator 36 in response to the motion caused by the road.

[0020] As shown in Figure 2 , the electric motor 32 is a permanent magnet synchronous motor, and is a linear electric motor. The electric motor 32 includes a stator 34 and a translator 36 that moves relative to the stator 34 along an axis X. Alternatively, the electric motor 32 can be a rotary electric motor, with the translator 36 being a rotor that rotates relative to the stator 34 about the axis X.

[0021] The stator 34 includes a core 44 of magnetic material and electrical coils 46, 48, 50 wound around the core 44. The stator 34 receives three-phase electrical power through the electrical coils 46, 48, 50, which include a first coil 46, a second coil 48, and a third coil 50. Alternating current power supplied to the coils 46, 48, 50 creates a magnetic field that combines with the magnetic fields of the permanent magnets 52, 54 of the converter 36 to produce a force on the converter 36 parallel to the axis X (or a torque about the axis X if the electric motor 32 is rotating).

[0022] The converter 36 includes a series of permanent magnets 52, 54, specifically, a plurality of first permanent magnets 52 and second permanent magnets 54 alternating along the axis X (or around the axis X if the electric motor 32 is rotating and the converter 36 is a rotor). The first permanent magnets 52 have an opposite magnetic orientation to the second permanent magnets 54.

[0023] Referring to Figure 3 The three-phase inverter 38 is electrically coupled to the electric motor 32. The three-phase inverter 38 converts direct current from the power source 40 to alternating current delivered to the coils 46, 48, 50. The three-phase inverter 38 includes three inverter switch legs, each leg connected to one of the coils 46, 48, 50.

[0024] The power source 40 is electrically coupled to the three-phase inverter 38. The power source 40 supplies direct current power to the three-phase inverter 38. The power source 40 can be one or more batteries, such as lithium-ion batteries, nickel-metal hydride batteries, lead-acid batteries, etc.; or one or more capacitors, such as supercapacitors. In particular, the power source 40 can be a supercapacitor because supercapacitors recharge and discharge faster than batteries and can withstand more charge-discharge cycles than batteries.

[0025] The controller 42 is communicatively coupled to the three-phase inverter 38 to provide control signals to the three-phase inverter 38. The controller 42 can be a microprocessor-based computing device (e.g., an electronic controller, etc.), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), etc. The controller 42 includes a processor, memory, etc. The memory of the controller 42 includes media for storing instructions executable by the processor as well as for electronically storing data and / or databases. The controller 42 can be multiple controllers coupled together.

[0026] The device 30 may include a position sensor 56 coupled to the electric motor 32 to detect the position of the converter 36 relative to the stator 34. The position sensor 56 may be any sensor that provides an output mapped to the linear (or rotational) position of the converter 36 relative to the stator 34, such as a capacitive transducer, a capacitive displacement sensor, an eddy current sensor, an ultrasonic sensor, a Hall effect sensor, an inductive non-contact position sensor, a linear variable differential transformer, a piezoelectric transducer, a potentiometer, a proximity sensor, a linear encoder, a string potentiometer, etc. As described below with respect to Figure 8 As described above, the controller 42 can determine the position of the converter 36 relative to the stator 34 without the use of the position sensor 56 and can compare the result with the position reported by the position sensor 56. Alternatively, the electric motor 32 can lack the position sensor 56, and the controller 42 can determine the position of the converter 36 relative to the stator 34 in a sensorless manner.

[0027] refer to Figure 4 , shows a feedback loop 400 for compensating for an offset in the measured back EMF of the electric motor 32 to control the electric motor 32. The feedback loop 400 is executed by the controller 42. The memory of the controller 42 may store executable instructions for executing the steps of the feedback loop 400, or the controller 42 may include multiple controllers, each of which is programmed to execute the steps of the feedback loop 400. Figure 4 Some of the steps shown, and these controllers are connected together to transmit data, such as Figure 4 As a general overview of the feedback loop 400, an uncompensated back EMF measurement EMF is received from the electric motor 32. αβ,i *, the offset in this measurement is compensated by subtracting the output of the proportional integral (PI) controller 410, resulting in a compensated back EMF measurement EMF αβ,i The integrator 415 integrates the flux linkage measurement result Ψ αβ,i , using at least three flux linkage measurements Ψ in the center estimator 420 αβ,i To determine the flux linkage measurement result Ψ αβ,i The center of the circle 600 is defined as Ψ c , determine the weighting factor K R , in multiplication block 425 the center Ψ c and weighting factor K R The weighting factor K is multiplied and the PI controller 410 generates a compensation based on the resulting product to feed to the summing block 405. R It is used to determine the center of the circle Ψ c The flux linkage measurement results Ψ αβ,i The current flux linkage Ψ compensated by the feedback loop 400 αβfor actuating the electric motor 32 based on the position of the transducer 36 relative to the stator 34.

[0028] The un-compensated back EMF measurement EMF αβ,i * is received by the summation block 405, which can be determined from the measured three-phase current i abc and the measured stator 34 voltage u abc . First, the three-phase current i abc and the measured stator voltage u abc are converted to Clarke coordinates by using a simplified Clarke transformation (also known as a a- b transformation):

[0029]

[0030]

[0031] where i is current, u is voltage, T is the Clarke transformation, t is time, and a, b, and c represent the first coil 46, the second coil 48, and the third coil 50, respectively. The Clarke transformation T is geometrically interpreted as projecting the three-part quantities associated with the electrical coils 46, 48, 50 onto two fixed axes: the a-axis and the b-axis, i.e., the Clarke coordinates. Thus, all quantities in the Clarke coordinates are two-dimensional vectors. The un-compensated back EMF measurement EMF αβ,i * in the Clarke coordinates can be determined from the three-phase current i αβ and the stator voltage u αβ in the Clarke coordinates:

[0032]

[0033] where R s is the winding resistance of the stator 34, L sα is the synchronous inductance in the a-dimension, L sβ is the synchronous inductance in the b-dimension, and L sαβ is the mutual coupling. In many cases, the contributions of the synchronous inductance terms and the mutual coupling term are insignificant and can be neglected. The un-compensated back EMF measurement EMF αβ,i * is then fed into the summation block 405.

[0034] The summation block 405 subtracts compensation from the PI controller 410 from the un-compensated back EMF measurement EMF αβ,i * to obtain a compensated back EMF measurement EMF αβ,i . The compensation is initially (0, 0) and remains (0, 0) until the center estimator 420 has collected a minimum number of measurements, as described below.

[0035] The integrator 415 integrates the compensated back electromotive force measurement EMF αβ,i over time from the compensated back electromotive force measurement EMF αβ,i determines a flux linkage measurement Ψ αβ,i :

[0036]

[0037] where Ψ αβ (t0) is an initial flux linkage. The flux linkage measurement Ψ αβ is expressed in Clarke coordinates. The integrator 415 can include two scalar calculations, one for the a term and one for the β term.

[0038] The center estimator 420 requires at least three flux linkage measurements Ψ αβ,i at different times to determine the center of the circle 600 Ψ c as shown in Figure 6 . Figure 6 The circle 600 is shown, where the center is Ψ c = (Ψ α,c , Ψ β,c ). The circle 600 and thus the center of the circle Ψ c is defined by three flux linkage measurements Ψ αβ,i at different points in time, i.e., Ψ αβ,1 = (Ψ α,1 , Ψ β,1 ), Ψ αβ,2 = (Ψ α,2 , Ψ β,2 ), and Ψ αβ,3 = (Ψ α,3 , Ψ β,3 ). By collecting at least four flux linkage measurements Ψ αβ,i , the center of the circle Ψ c is overdetermined, and the center estimator 420 can use a least squares estimation to determine the center of the circle Ψ c . In the process 500, the center estimator 420 determines the center of the circle 600 Ψ c and a weighting factor K R , which is described below. The center of the circle Ψ c and the weighting factor K R are multiplied in the multiplication block 425, and the resulting weighted center of the circle K R Ψ c is fed to the PI controller 410.

[0039] The PI controller 410 provides proportional compensation and integral compensation to the center of the circle Ψ c , specifically the weighted center of the circle K R Ψ c. Weighted circle center K R Ψ c The error function of proportional compensation and integral compensation is provided, and (0,0) is the set value. By outputting to the summing block 405, the PI controller 410 forms a feedback loop 400, in which the magnetic flux linkage Ψ αβ is subjected to proportional compensation and integral compensation, and then becomes the circle center Ψ used to determine the circle 600 c The flux linkage measurement results Ψ αβ,i The proportional compensation and the integral compensation each correct the center Ψ c The initial magnetic flux linkage Ψ is corrected proportionally αβ (t0). Integral compensation corrects the offset voltage. The PI controller 410 may include two scalar calculations, one for the α term and one for the β term.

[0040] The output of the feedback loop 400 is the current flux linkage Ψ αβ , which is compensated so that the center Ψ c Equal to (0,0). When the center of the circle Ψ c When the correction is (0,0), the current flux linkage Ψ αβ =(Ψ α ,Ψ β ) provides the position of the converter 36 relative to the stator 34. Specifically, the current flux linkage Ψ αβ Angle θ e will map one-to-one to the linear position of the converter 36 relative to the stator 34 along the axis X, so the angle θ can be e is considered as the position of the converter 36 relative to the stator 34. If the electric motor 32 rotates, the angle θ e directly describes the rotational position of the converter 36 about the axis X relative to a fixed reference point on the stator 34. Position θ e It can be obtained from the equation θ e =arctan(Ψ β / Ψ α ) is given. The controller 42 is based on the position θ of the converter 36 relative to the stator 34 e To activate the electric motor 32. For example, the controller 42 instructs the three-phase inverter 38 to adjust the position of the converter 36 based on the actual position θ e The switch 36 is moved to a target position. The target position may be, for example, a fixed position to which the switch 36 returns after absorbing an impact from the road.

[0041] Figure 5 is a process flow diagram illustrating an exemplary process 500 for determining the center Ψ of a circle 600. c and weighting factor K Ri.e., the step performed by the circle center estimator 420 in the feedback loop 400. The memory of the controller 42 stores executable instructions for performing the steps of the process 500. As a general overview of the process 500, the controller 42 collects flux linkage measurements Ψ αβ,i , determines the circle center Ψ c of the circle 600, and determines the weighting factor K R .

[0042] The process 500 begins at block 505, where the controller 42 collects flux linkage measurements Ψ αβ,i . To determine the circle center Ψ c of the circle 600, the controller 42 needs at least three flux linkage measurements Ψ αβ,i . By collecting at least four flux linkage measurements Ψ αβ,i , the circle center Ψ c is overdetermined, and the controller 42 can use a least squares estimation to determine the circle center Ψ c .

[0043] Next, at block 510, the controller 42 determines the circle center Ψ c of the circle 600. Specifically, the controller 42 computes the circle center Ψ c by applying a least squares estimation by applying the equation (where the dagger superscript denotes the pseudo-inverse of a matrix (also known as the Moore-Penrose inverse matrix)), and A and B are given by

[0044]

[0045]

[0046] where Ψ α,i is the i-th flux linkage measurement in the alpha dimension in Clarke coordinates, Ψ β,i is the i-th flux linkage measurement in the beta dimension in Clarke coordinates, and N is the number of flux linkage measurements. The pseudo-inverse of A is given by: where T is the transpose operator. The circle center Ψ c can be computed using the following equation, which is equivalent to

[0047]

[0048] where a i1 is the element in the first column of the i-th row of the matrix A, i.e., a i1 = Ψ α,i - Ψ α,i+1 ; a i2is the element in the second column of the i-th row of matrix A, i.e., a i2 β,i β,i+1 ; and b i is the element in the i-th row of matrix B, i.e., b i α,i 2 α,i+1 2 β,i 2 β,i+1 2 . If the controller 42 has determined the circle center Ψ c at least once, the controller 42 only needs to update the bottom row in each of the matrices A and B, and move the remaining rows up, i.e., make the i-th row the i-1-th row. Thus, for each summation term in the above equations, the new summation term can be calculated by the following procedure: starting from the previous summation term result, subtract the term for argument i = 1, and add the term for argument i = N; for example, for the summation term the new result is the previous result minus a 11 b1plus a N1 b N This iterative update allows efficient use of computational resources.

[0049] Next, in block 515, the controller 42 determines a weighting factor K R . The weighting factor K R is indicative of the quality of the flux linkage measurements, e.g., the signal-to-noise ratio. For example, the weighting factor K R is negatively correlated with the condition number κ(.) of the matrix of flux linkage measurements Ψ αβ,i . The condition number κ(.) of a matrix is the ratio of the largest singular value of the matrix to the smallest singular value of the matrix, i.e., κ(M) = σ max (M) / σ min (M), where M is an arbitrary matrix. The condition number ranges from 1 to infinity, where a value close to 1 indicates that computations involving the matrix M will amplify noise by a relatively small factor, and a large value indicates that computations involving the matrix M will amplify noise by a relatively large factor. In particular, the weighting factor K R is given by an equation of the form:

[0050]

[0051] where x is a positive number. In particular, x can be equal to 2. The weighting factor K R ranges from 0 to 1, where a value close to 0 indicates that there is a large amount of noise in the computation of the circle center Ψ c , and a value close to 1 indicates that there is a small amount of noise in the computation of the circle center Ψ c ​​​​​​There is a small amount of noise present. After block 515, the process 500 ends. In running the feedback loop 400, the controller 42 can perform the process 500 several times, for example, once per time step of the controller 42.

[0052] Figures 7A to 7E is a plot showing convergence of the center of the circle Ψ c during the process of running the feedback loop 400. Figure 7A and Figure 7B show the element of the flux linkage Ψ αβ = (Ψ α , Ψ β ) as a function of time, where the dashed line represents the true value of the flux linkage Ψ αβ and the solid line represents the value of the flux linkage Ψ αβ output by the feedback loop 400. Figure 7C shows the weighting factor K R as a function of time. When the weighting factor K R is close to 0, the PI controller 410 provides relatively less compensation, and when the weighting factor K R is close to 1, the PI controller 410 provides relatively more compensation. Figure 7D shows the trajectory of the flux linkage Ψ αβ in Clarke coordinates, starting from the initial position (0, 0) at t = 0 and converging to the circle 600 centered at (0, 0) before t = 1. Figure 7E also shows the trajectory of the flux linkage Ψ αβ in Clarke coordinates, but only for the segment from t = 0.8 to t = 1, before which the flux linkage Ψ αβ has already converged to the circle 600 centered at (0, 0).

[0053] Figure 8 is a process flow chart showing an exemplary process 800 for controlling the device 30. The memory of the controller 42 stores executable instructions for performing the steps of the process 800. As a general overview of the process 800, in block 805 the controller 42 continuously performs flux linkage regulation according to the feedback loop 400; in block 810 continuously actuates the electric motor 32 based on the position of the converter 36 relative to the stator 34; in block 815 optionally operates the electric motor 32 as a generator to charge the power source 40; in block 820 waits for the measured flux linkage to stabilize, then (in decision block 830) continuously compares the position according to the feedback loop 400 to the position received from the position sensor 56 in block 825; and in block 835 provides a warning if the difference between the reported positions is greater than a threshold value. “Continuously” performing a step means that the controller 42 continues to perform the step while the process 800 moves to the next step. Thus, Figure 8The order of step initialization is shown, and once initialized, execution continues while the remaining blocks are executed, blocks 805, 810, and 815. As described above, the electric motor 32 may be configured without the position sensor 56, in which case the steps of comparing position and providing a warning are not performed.

[0054] In block 805, the controller 42 performs the flux linkage regulation described above with respect to the feedback loop 400 and process 500. The feedback loop 400 outputs the current flux linkage Ψ αβ =(Ψ α ,Ψ β ), the controller 42 uses the equation θ e =arctan(Ψ β / Ψ α ) Calculate the position θ of the converter 36 relative to the stator 34 from the current flux linkage e .

[0055] In block 810 , the controller 42 determines the position of the converter 36 relative to the stator 34 based on the position θ e Specifically, the controller 42 instructs the three-phase inverter 38 to actuate the electric motor 32 based on the actual position θ of the converter 36. e The switch 36 is moved to a target position. For example, the target position may be a fixed position to which the switch 36 returns after absorbing an impact from the road.

[0056] In block 815, the controller 42 charges the power source 40 with the electricity generated by the movement of the electric motor 32 (i.e., as the converter 36 moves relative to the stator 34). The electric motor 32 acts as a generator. In effect, the electric motor 32 provides regenerative damping. For example, if the controller 42 is programmed to operate the electric motor 32 to simulate a conventional oil-based shock absorber, the electric motor 32 will recapture some of the energy that would be expended heating the oil in a conventional oil-based shock absorber.

[0057] Next, in block 820, the controller 42 waits for the center of the circle 600 to c Stable to (0,0), that is, for the flux linkage Ψ αβ As far as stability is concerned, it is a circle centered at (0,0) 600, such as Figure 7E For example, the controller 42 may wait for a preset time after the process 800 is started. The preset time may be experimentally based on the flux linkage Ψ αβ It is usually selected how long it takes to stabilize to circle 600. For example, the controller 42 can wait until the center of the circle Ψ c Within a preset distance from (0,0) for a preset time. The preset distance may be chosen to be negligibly small, and the preset time may be chosen to be long enough to indicate the center of the circle Ψ cWhile waiting, the controller 42 continues to perform flux linkage regulation, activate the electric motor 32, and charge the power source 40 as described in blocks 805 to 815.

[0058] Next, in block 825 , the controller 42 receives a signal from the position sensor 56 indicating the position θ of the converter 36 relative to the stator 34 . p data.

[0059] Next, in decision block 830, the controller 42 determines the position θ of the transducer 36 from the sensor. p and the center Ψ based on circle 600 c The position θ of the converter 36 e Whether the difference between exceeds the threshold Δθ*, that is, whether Δθ=|θ p -θ e |>Δθ*. The threshold Δθ* can be selected based on the known resolution or noisiness of the position sensor 56. If the difference is greater than the threshold, i.e., Δθ>Δθ*, process 800 proceeds to block 835. If the difference is less than the threshold, i.e., Δθ<Δθ*, process 800 ends or restarts.

[0060] In box 835, the controller 42 provides a warning. For example, the controller 42 may transmit a diagnostic trouble code (DTC) indicating the fault and containing an appropriate code to the onboard fault diagnostic system of the vehicle 16. After box 835, the process 800 ends.

[0061] The present disclosure has been described in an illustrative manner, and it should be understood that the terminology used is intended to be descriptive rather than limiting. The adjectives "first" and "second" are used throughout this document as identifiers and are not intended to denote importance, order, or quantity. In light of the above teachings, many modifications and variations of the present disclosure are possible, and the present disclosure may be practiced in a manner other than that specifically described.

Claims

1. A device comprising: an electric motor comprising a stator and a converter; a three-phase inverter electrically coupled to the electric motor; a power supply electrically coupled to the three-phase inverter; and a controller communicatively coupled to the three-phase inverter and programmed to: determining at least three measurements of flux linkage from the electric motor at different times; Expressing the measurement results in Clarke coordinates; determining the Clarke coordinates of a center point of a circle defined by the Clarke coordinates of the measurements; and An angle of flux linkage is determined based on the Clarke coordinates of the center of the circle, and the angle of flux linkage is regarded as the position of the converter relative to the stator.

2. The apparatus of claim 1, wherein the electric motor is a linear electric motor.

3. The apparatus of claim 1, wherein the power source is a supercapacitor.

4. The apparatus of claim 1 , wherein the electric motor lacks a position sensor.

5. The apparatus of any one of claims 1 to 3, further comprising a position sensor coupled to the electric motor to detect a position of the converter relative to the stator, wherein the controller is further programmed to receive data indicative of the position of the converter relative to the stator from the position sensor, and to provide a warning in response to a difference between the position of the converter from the position sensor and the position of the converter based on the center of the circle exceeding a threshold.

6. The apparatus of any one of claims 1 to 4, wherein the controller is further programmed to charge the power source with electricity generated by movement of the electric motor.

7. The apparatus of any one of claims 1 to 4, further comprising a vehicle frame and a wheel assembly movable relative to the vehicle frame, wherein the electric motor is coupled to the vehicle frame and the wheel assembly such that the converter moves relative to the stator when the wheel assembly moves relative to the vehicle frame.

8. A method for controlling an electric motor comprising a stator and a converter, the method comprising: determining at least three flux linkage measurements from the electric motor at different times; Expressing the flux linkage measurement results in Clarke coordinates; determining the Clarke coordinates of the center of a circle defined by the Clarke coordinates of the flux linkage measurements; as well as An angle of flux linkage is determined based on the Clarke coordinates of the center of the circle, and the angle of flux linkage is regarded as the position of the converter relative to the stator.

9. The method of claim 8, further comprising providing a proportional offset to the center of the circle.

10. The method of claim 9, further comprising providing an integral offset to the center of the circle.

11. The method of claim 9, wherein the proportional compensation is further based on a weighting factor, wherein the weighting factor is inversely related to a condition number of the matrix of flux linkage measurements.

12. The method of claim 11 , wherein the weighting factor is given by an equation of the form: ;in, K R is the weighting factor, k(.) is the condition number of the matrix, x is a positive number, and the matrix A is given by the following equation: ; Among them, Ψ α,i is the measurement result of the i-th magnetic flux linkage in the α dimension in Clarke coordinates, Ψ β,i is the i-th flux linkage measurement in the β dimension in Clarke coordinates, and N is the number of flux linkage measurements.

13. The method of claim 9 , wherein the proportional compensation forms a feedback loop in which the measured back EMF is proportionally compensated and then integrated into one of the flux linkage measurements used to determine the Clarke coordinates of the center of the circle.

14. The method of any one of claims 8 to 13, further comprising actuating the electric motor based on the position of the converter relative to the stator.

15. The method of any one of claims 8 to 13, wherein collecting at least three flux linkage measurements comprises determining at least four flux linkage measurements, and determining the Clarke coordinates of the center of the circle comprises applying a least squares estimate to the Clarke coordinates of the flux linkage measurements.

16. The method of claim 15, wherein applying the least squares estimate comprises applying the following equation: ;in, Ψc is the center of the circle in Clarke coordinates, A and B are matrices given by the following equations, and the dagger notation represents the pseudo-inverse of the matrix: ; Among them, Ψ α,i is the measurement result of the i-th magnetic flux linkage in the α dimension in Clarke coordinates, Ψ β,i is the i-th flux linkage measurement in the β dimension in Clarke coordinates, and N is the number of flux linkage measurements.

17. The method of any one of claims 8 to 13, further comprising charging a power source with electricity generated by movement of the electric motor.

18. A controller comprising a processor and a memory storing instructions executable by the processor: determining at least three flux linkage measurements from an electric motor at different times, the electric motor comprising a converter and a stator; Expressing the flux linkage measurement results in Clarke coordinates; determining the Clarke coordinates of the center of a circle defined by the Clarke coordinates of the flux linkage measurements; and An angle of flux linkage is determined based on the Clarke coordinates of the center of the circle, and the angle of flux linkage is regarded as the position of the converter relative to the stator.

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