Method for estimating the position and speed of the rotor of a permanent magnet synchronous motor

Description

[0001] The invention relates to the field of permanent magnet synchronous electrical machines.

[0002] More particularly, the invention relates to a method for estimating the position and speed of the rotor of a synchronous electric machine with a permanent magnet rotor.

[0003] For environmental and cost reasons, electric machines are increasingly taking up space in the propulsion systems of electric vehicles. The permanent magnet synchronous machine is a particularly common machine in electric motor vehicles.

[0004] However, it is known that all types of closed-loop controls of this type of synchronous machine require precise knowledge of the rotation speed and position of the rotor.

[0005] This information can typically be obtained directly by a position sensor placed on the end of the machine shaft.

[0006] However, the presence of this element in the control system has several disadvantages such as the volume and the overall cost of the system. Therefore, it is preferable to replace the hardware sensor with a software sensor that can provide information on the rotation speed and position of the rotor based on other sensors already existing in the control system.

[0007] Many solutions are proposed today in the prior art to meet this need, such as for example in document US 2018 / 131305 A1.

[0008] These solutions can be grouped into two main categories: machine model-based techniques; and machine model-free techniques.

[0009] The first category uses observers who are able to reconstruct unmeasured quantities.

[0010] These techniques suffer from several problems. In particular, the proposed models are not always observable, especially at low speeds, and furthermore, variations in machine parameters greatly affect the estimation.

[0011] To address these issues, a second category called model-free is proposed. These techniques use high-frequency signal injection (voltage and / or current) to estimate velocity and position after signal processing steps.

[0012] Despite their low-speed performance, model-free techniques still suffer from the variation of some parameters. In addition, signal injection requires the integration of an additional device, which increases the implementation cost.

[0013] Thus, there is a need for a method for estimating the position and speed of synchronous machines that can solve the problems mentioned above.

[0014] For this purpose, a method is proposed for estimating the position and speed of the rotor of a synchronous electric machine with a permanent magnet rotor comprising: A step of measuring the three-phase currents of said electrical machine; A step of transforming said three-phase currents measured in a two-phase rotating reference frame, comprising a direct component and a quadrature component; A step of defining two intermediate variables of the estimation error of the rotor position as a function of the values ​​of the transformed current in said two-phase reference frame; A step of defining an observer to determine said position and speed of the rotor as a function of the two intermediate variables of the estimation error and the value of the transformed currents, and of the sign of the quadrature component of the two-phase current.

[0015] Thus, an estimation method can be obtained, which on the one hand reduces the implementation cost associated with the use of high-frequency signal injection devices. This method also makes it possible to estimate the position and / or speed by a single method independently of all the machine parameters.

[0016] This process avoids observability problems related to machine models.

[0017] Finally, this method also makes it possible to avoid delays due to the use of filters from high-frequency injection methods to extract the position estimation error.

[0018] In particular, said transformation step implements a Park transform, which is an efficient transform for this type of change of reference frame. The invention is however not limited to this specific transform.

[0019] In particular, the said observer is a sliding mode observer. This allows for a reliable and robust estimation.

[0020] In particular, the said observer also allows an estimation of the acceleration of the electric machine. This makes it possible in particular to reduce estimation deviations in transient phases.

[0021] In particular, the observer calculates the rotor position and speed as a function of the first or second intermediate variable, selected according to the sign of the quadrature component of the two-phase current. Thus, the intermediate variables can be easily implemented in the observer with few calculations.

[0022] The invention also relates to a device for estimating the position and speed of the rotor of a synchronous electric machine with a permanent magnet rotor comprising: Means for measuring the three-phase currents of said electrical machine; Means for transforming said three-phase currents measured in a two-phase rotating reference frame, comprising a direct component and a quadrature component; Means for defining two intermediate variables of the estimation error of the rotor position as a function of the values ​​of the transformed current in said two-phase reference frame; Means for defining an observer to determine said position and speed of the rotor as a function of the two intermediate variables of the estimation error and the value of the transformed currents, and of the sign of the quadrature component of the two-phase current.

[0023] In particular, all the means of this device may consist of a computer, in particular a computer embedded in a motor vehicle, but in an equivalent manner a processor, a DSP, a programmable logic circuit of the FPGA type, or any other digital calculation device. The different means of the device may be grouped in the same computer or separated into different computers depending on the technical constraints of integration of the device.

[0024] The invention also relates to an electrical assembly comprising a synchronous electric machine with a permanent magnet rotor and an estimation device as described previously.

[0025] The invention also relates to a motor vehicle comprising an electrical assembly as described previously.

[0026] Other features and advantages of the invention will emerge from reading the description given below of a particular embodiment of the invention, given for informational purposes but not as a limitation, with reference to the appended drawings in which: there figure 1 is a flowchart of a method according to the main embodiment of the invention; the figure 2 represents the speed and load torque profiles implemented in the context of the experimentation of the method according to the invention; the figure 3 is a representation of the dynamic parameters implemented within the framework of the experimentation of the method according to the invention; the figure 4 is a representation of the estimated and measured speeds (upper part) and the speed estimation error (lower part); the figure 5 is a representation of the estimated and measured positions (upper part) and the position estimation error (lower part); and the figure 6is a representation of the same experiment carried out using a method based on the injection of high-frequency signals.

[0027] In reference to the figure 1 , the invention proposes a method 1 for estimating the speed and position of the rotor of a permanent magnet synchronous electric machine comprising first of all a step 10 of measuring the three-phase currents of the electric machine ia, ib, ic.

[0028] It is understood within the scope of the present invention that the position of the rotor corresponds to its angular position in the stator.

[0029] We then proceed to a transformation step 11 of the three-phase currents into a two-phase reference frame ( i a , i b ). Here we transform these three-phase currents into a rotating two-phase reference frame.

[0030] We transform 11 the measured phase-shifted currents ( i a , i b ) from the measured currents ( ia , ib , ic) via (1), here with a Park transformation: i α i β = 2 3 1 − 1 2 − 1 2 0 3 2 − 3 2 i a i b i c

[0031] Considering the Park transformation for currents ( i a , i b ), we obtain: i α = cos θ i d − sin θ i q i β = sin θ i d + cos θ i q

[0032] Equation (2) can be rewritten in this form: i α i β = cos θ − sin θ sin θ cos θ i d i q

[0033] From system (3), we note that the currents linked to the stator ( i a , i b ) contain the rotor position information.

[0034] We then proceed to the definition of a transformation matrix Tm next: T m = cos θ ^ + π 4 sin θ ^ + π 4 − sin θ ^ + π 4 cos θ ^ + π 4

[0035] With θ̂ is the estimated position shifted by an angle of π 4 radians.

[0036] We then proceed to the transformation (4) of the two stator currents ( i a , i b ) by the transformation matrix Tm and we obtain the following new system of equations: i dm i qm = cos θ + π 4 sin θ + π 4 − sin θ + π 4 cos θ + π 4 i α i β

[0037] Or : i dm = i α cos θ ^ + π 4 + i β sin θ ^ + π 4 = cos θ − θ ^ − π 4 i d − sin θ − θ ^ − π 4 i q i qm = − i α sin θ ^ + π 4 + i β cos θ ^ + π 4 = sin θ − θ ^ − π 4 i d + cos θ − θ ^ − π 4 i q

[0038] These two out-of-phase currents are rewritten as a function only of the position estimation error ( i - θ̂ ), which explains the subsequent need to use tracking algorithms to minimize this sequence in order to recover the position i of the rotor.

[0039] We then proceed to a calculation step 13 of the rotor position estimation error.

[0040] To obtain the rotor position estimation error e i , we calculate the two differences ( I am - I am ) And ( I am - I am ) of the two equations (6) and (7) as shown by the following system of equations: E θ 1 = i qm − i dm + i d ∗ 2 E θ 2 = i dm − i qm − i d ∗ 2

[0041] Or i d ∗ is the d-axis reference current.

[0042] Thus we determine two new position estimation error terms, which we will subsequently call intermediate estimation error variables. I will, or more simply intermediate variables I will , depending on the difference between the two currents of the rotating reference frame and the reference current i*d.

[0043] Then we write I will , for i = [1,2]; depending on the currents in the Park frame id , iq and the position estimation error e θ , as follows: E θ 1 = i q 2 sin e θ − i d 2 cos e θ + i d ∗ 2 E θ 2 = − i q 2 sin e θ + i d 2 cos e θ − i d ∗ 2

[0044] As intermediate variables I will can be calculated from the measured currents, and assuming that the control monitors the current id towards its reference i d ∗ , we obtain: E θ 1 = i q 2 sin e θ + i d ∗ 2 1 − cos e θ E θ 2 = − i q 2 sin e θ − i d ∗ 2 1 − cos e θ

[0045] And by using trigonometric rules, equation (10) can be rewritten in the following form: E θ 1 = i q 2 sin e θ + i d ∗ 2 2 sin e θ 2 2 E θ 2 = − i q 2 sin e θ − i d ∗ 2 2 sin e θ 2 2

[0046] So, the intermediate variables I will can be approximated based on the position estimation error, as follows: E θ 1 ≈ i q 2 e θ + i d ∗ 2 e θ 2 E θ 2 ≈ − i q 2 e θ − i d ∗ 2 e θ 2

[0047] Considering that the quadratic term is much smaller compared to the linear term, I will can be rewritten in the following form: E θ 1 ≈ i q 2 e θ E θ 2 ≈ − i q 2 e θ

[0048] It is clear that the electromagnetic torque and the current iq have similar behaviors. In the case where the torque is positive, the current iq will be positive, otherwise the current iq will be negative. E θ 1 ≈ λ e θ = i qm − i dm + i d ∗ 2 si i q ≥ 0 E θ 2 ≈ − λ e θ = i dm − i qm + i d ∗ 2 si i q < 0

[0049] With λ = i q 2 ,

[0050] We therefore note that the intermediate variables for estimating the position E i i are no longer dependent on anything other than the position estimation error e i and current iq .

[0051] So the sign of the intermediate variables I will depends only on the signs of e i and of iq.

[0052] For the sign to depend only on e i, we define the first intermediate variable E i 1 for the values ​​of iq positive and the second intermediate variable E i 2 for the values ​​of iq negative. Therefore, the signs of the intermediate variables E i 1 and E i 2 depend only on the position estimation error e i ( i - θ̂ ). sign E θ 1 = sign e θ = sign i qm − i dm + i d ∗ 2 si i q ≥ 0 sign E θ 2 = sign e θ = sign i dm − i qm + i d ∗ 2 si i q < 0

[0053] We can see that the position estimation error (15) is obtained independently of the machine parameters without injection of high-frequency signals or the use of filtering.

[0054] However, the error in estimating the position e i is not available for measurement, which makes its implementation not possible. On the other hand, the variables E i 1 and E i2 introduced in equation (8) are available through current measurements. The position estimation error e i used in the observer is thus replaced by E θ 1 λ For iq ≥ 0 and by E θ 2 λ For iq < 0 for the observer implementation, and a current sign detector is used to switch between these two variables ( E i 1 and E i 2).

[0055] To avoid the use of the mechanical model (and therefore the mechanical parameters of the machine), we propose to use the virtual model (15)-(16)-(17) for the estimation of the position, speed and acceleration of the machine: θ ˙ = ω ω ˙ = α α ˙ = 0

[0056] The observer proposed in this embodiment according to equations ((18)-(19)-(20)) is of the sliding mode type.

[0057] It allows to estimate the position and speed of the permanent magnet synchronous machine.

[0058] To reduce estimation deviations in transient phases, the observer used also estimates the acceleration of the machine, but this is not essential for implementing the invention.

[0059] This observer takes as inputs: the intermediate variables I will For i=1,2 (obtained by the measurements of the currents given by equation (8)) denominated by λ.

[0060] This observer is tuned by adaptive gain, so that only one parameter is used for its tuning. θ ^ ˙ = ω ^ + K 1 E θ i λ 2 3 sign E θ i λ ω ^ ˙ = α ^ + K 2 E θ i λ 1 3 sign E θ i λ α ^ ˙ = K 3 sign E θ i λ

[0061] With K 1 = 3L, K 2 = 2L 2< , K 2 = 2 3 2 L 3 And E θ i = E θ 1 si i q ≥ 0 E θ 2 si i q < 0 .

[0062] Where L is a positive constant.

[0063] The 3 observer gains are thus adjusted using the L parameter.

[0064] Experimental measurements demonstrate the performance of the present invention.

[0065] There figure 2 shows the load speed and torque profiles used to validate this invention. The profiles chosen allow the invention to be validated over different speed ranges with different torque values ​​(positive and negative).

[0066] There figure 3 shows the dynamics of the parameters proposed to validate the inventions. We introduced variations for the resistance, inductances and inertia of the machine to prove that the estimation of position and speed is independent of the electrical and mechanical parameters of the machine.

[0067] There figure 4 shows the estimated speeds measured (upper part) and the estimation error (lower part).

[0068] Finally, the figure 5shows the estimated positions measured (upper part) and the position estimation error (lower part).

[0069] It is noted from this experiment that the proposed technique makes it possible to give a relatively precise estimate of the position and speed of the permanent magnet synchronous machine.

[0070] Furthermore, this estimate is not affected by variations in the electrical and mechanical parameters of the machine.

[0071] The technique also enables robust and accurate estimation at very low speeds, which overcomes observability issues related to the machine model.

[0072] In order to compare the performance of the proposed method with that using high-frequency signal injection, another test is carried out under the same conditions. We note, with reference to the figure 6, that the injection-based method generates a position estimation deviation due to filtering. In addition, the estimation is particularly noisy, which is due to the injection of high-frequency signals.

Claims

1. Method (1) for estimating the position and the speed of the rotor of a permanent-magnet rotor synchronous electric machine, comprising: - a step (10) of measuring the three-phase currents (ia, ib, ic) of said electric machine; - a step (11) of transforming said measured three-phase currents into a two-phase rotating reference frame, comprising a direct component and a quadrature component; - a step (13) of defining two intermediate variables of the error in estimating the position of the rotor depending on the values of the current which is transformed into said two-phase reference frame; characterized in that the method comprises: - a step (14) of defining an observer to determine said position and speed of the rotor depending on the two intermediate variables of the estimation error and the value of the transformed currents, and the sign of the quadrature component of the two-phase current.

2. Method (1) according to Claim 1, characterized in that said transformation step implements a Park transformation.

3. Method (1) according to Claim 1 or 2, characterized in that said observer is a sliding-mode observer.

4. Method (1) according to Claim 3, characterized in that said observer furthermore makes it possible to estimate the acceleration of the electric machine.

5. Method (1) according to Claim 3 or 4, characterized in that the observer calculates the position and the speed of the rotor depending on the first or second intermediate variable, selected depending on the sign of the quadrature component of the two-phase current.

6. Device for estimating the position and the speed of the rotor of a permanent-magnet rotor synchronous electric machine, comprising: - means for measuring the three-phase currents (ia, ib, ic) of said electric machine; - means for transforming said measured three-phase currents into a two-phase rotating reference frame, comprising a direct component and a quadrature component; - means for defining two intermediate variables of the error in estimating the position of the rotor depending on the values of the current which is transformed into said two-phase reference frame; characterized in that the device comprises: - means for defining an observer to determine said position and speed of the rotor depending on the two intermediate variables of the estimation error and the value of the transformed currents, and the sign of the quadrature component of the two-phase current.

7. Electrical assembly comprising a permanent-magnet rotor synchronous electric machine and an estimation device according to Claim 6.

8. Motor vehicle comprising an electrical assembly according to Claim 7.