Sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine with reduced parameter sensitivity

Abstract

The invention relates to a method for the sensorless determination of the angular frequency (ω e ) and / or position (φ e ) of a permanent magnet rotor of a brushless electric machine (1), in particular a linear or rotary machine, wherein the electric machine (1) is provided with a d-voltage (u d) and a q-voltage (u q ), wherein on the basis of an, in particular mathematical, motor model (9), a d-voltage deviation (Δu d ) and a q-voltage deviation (Auq) is determined, wherein, in a tracking controller (6), the angular frequency (ω e ) and / or position (φ e ) of the permanent magnet rotor is determined on the basis of the d-voltage deviation (Δu d ) and the q-voltage deviation (Δu q ), wherein the tracking controller (6) has a first element (6.1) to which the d-voltage deviation (Δu d ) is supplied in order to obtain an intermediate value, and a second element (6.2) to which a combination, in particular a difference, of the q-voltage deviation (Δu q ) and the intermediate value is supplied, in order to obtain the angular frequency (ω e ), wherein the first element (6.1) of the tracking controller (6) has an I-component.

Description

[0001] Sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine with reduced parameter sensitivity

[0002] The invention relates to a method for sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine according to the preamble of claim 1. Furthermore, the invention relates to a drive system with a device for sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine according to the preamble of claim 5.

[0003] Brushless electric machines with a permanent magnet rotor are also known as permanent magnet electric machines and are increasingly used in the automotive industry, particularly in the form of permanent magnet synchronous motors. Controlling such electric machines requires knowledge of the permanent magnet rotor's position. Conventionally, this position is determined using a position sensor, but this involves additional costs and installation space. Therefore, there is a need for sensorless alternatives for controlling these machines.

[0004] An exemplary method for the sensorless determination of the position and angular frequency of a permanent magnet rotor is known from EP 2019482 A1. The method is used within the framework of field-oriented control (vector control) and enables the determination of the rotor's angular frequency based on multiphase current measurements at the machine. A mathematical machine model is used for estimating the angular frequency and position.

[0005] Figure 1 shows a block diagram of a drive system implementing the method disclosed in EP 2019482 A1. A d-voltage u is applied to the electric machine 1. d and a q-voltage u q provided in the rotor-related dq coordinate system. A d-stress deviation Au is determined using a motor model 9. d and a q-voltage deviation Au q determined. Both signals Au d , Au q are fed to a tracking controller 6. This controls the signals Au.d , Au q to zero, so that the position p e The constant velocity of the permanent magnet runner is correctly estimated. The tracking controller 6 consists of three elements connected in series. The first element 6.1 is a proportional amplifier with the transfer function G(s) = k. p trained, whereby k pThe amplification factor is denoted. The second term 6.2 and the third term 6.3 are each implemented as integrators. A significant disadvantage of the known drive system is its sensitivity to changes in the parameters of motor model 9, such as the ohmic resistance, inductances, and flux of the permanent magnets. The actual motor parameters can deviate considerably from the values ​​used in the model. Reasons for this can include, for example, parameter variations in mass production, temperature changes, or the aging of the permanent magnets under the influence of heat, vibrations, or external magnetic fields. These discrepancies between the actual parameters and those used in the motor model can lead to errors in the rotor angle estimation.An incorrect angle, passed to the field-oriented control system, causes unnecessary reactive components in the current and thus increased ohmic losses in the motor windings. In some cases, an incorrect angle can lead to instability or even a crash of the control system.

[0006] Against this background, the task arises to improve the stability of the control system and to avoid reactive components in the power supply.

[0007] The problem is solved by a method for sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine, in particular a linear or rotary machine, wherein a d-voltage and a q-voltage are provided to the electric machine, wherein a d-voltage deviation and a q-voltage deviation are determined on the basis of a motor model, in particular a mathematical one, wherein the angular frequency and / or position of the permanent magnet rotor is determined in a tracking controller on the basis of the d-voltage deviation and the q-voltage deviation, wherein the tracking controller has a first element to which the d-voltage deviation is supplied in order to obtain an intermediate value, and a second element to which a combination, in particular a difference, of the q-voltage deviation and the intermediate value is supplied in order to obtain the angular frequency, wherein the first element of the tracking controller has an integral term.

[0008] It was found that, in contrast to the prior art, the angle estimation of the tracking controller is insensitive to parameter deviations of the flux chaining in the steady-state or steady-state condition of the tracking controller.

[0009]

[0010] the permanent magnets and the longitudinal inductance L d is also the sensitivity to changes in ohmic resistance and transverse inductance L. qis significantly reduced. Consequently, the risk of errors in rotor angle estimation and the danger of instabilities can be reduced. Reactive components in the current can be avoided, thereby reducing ohmic losses in the motor windings. This advantageous behavior of the tracking controller is achieved by the fact that the first stage of the tracking controller has an integral component, i.e., an integrating component. The transfer functions of the tracking controller for disturbance components of the d-voltage and the q-voltage can be influenced by this integral component in such a way that the influence of the respective disturbance components on the estimated position p is minimized. e in the steady or steady state of the tracking controller, it is either greatly reduced or even becomes zero.

[0011] According to an advantageous embodiment of the invention, the first element is a proportional (P) element. A proportional (P) element is understood to be an element with a proportional component (P) and an integrating component (I). In contrast to an element with an I but without a P, such an embodiment provides a controller whose step response includes an initial step, such that the effect of the I component occurs earlier by a reset time of the I component.

[0012] According to an advantageous embodiment of the invention, the first element implements a transfer function G(s) with

[0013] r _ 1 + T N S ) k i,

[0014] G(s) — - - - — — F k p ,

[0015] T N SS

[0016] k

[0017] where k p an amplification factor, T Na reset time and k t = ^-an integral gain.

[0018] According to an advantageous embodiment of the invention, the tracking controller includes a third element to which the angular frequency is applied in order to maintain the position. The third element can have an integral component, and in particular can be configured as an integral component.

[0019] A further object of the invention is a drive system with a device for sensorless determination of the angular frequency and / or position of a permanent magnet rotor of a brushless electric machine, in particular a linear or rotary machine, which is configured to provide the electric machine with a d-voltage and a q-voltage, and to determine a d-voltage deviation and a q-voltage deviation on the basis of a motor model, in particular a mathematical one, wherein the device comprises a tracking controller by which the angular frequency and / or position of the permanent magnet rotor can be determined on the basis of the d-voltage deviation and the q-voltage deviation, wherein the tracking controller has a first element to which the d-voltage deviation can be supplied in order to obtain an intermediate value, and a second element to which a combination, in particular a difference, of the q-voltage deviation and the intermediate value can be supplied.to obtain the angular frequency, where the first element of the tracking controller has an integral component.

[0020] The same technical advantages and effects can be achieved with the drive system as have been discussed in connection with the method according to the invention.

[0021] According to an advantageous embodiment of the invention, the first element is a pl element. A pl element is understood to be an element with a proportional component (P component) and an integrating component (I component).

[0022] According to an advantageous embodiment of the invention, the first element implements a transfer function G(s) with

[0023] r _ 1 + T N S ) k i,

[0024] G(s) — - - - — — F k p ,

[0025] T N SS

[0026] k

[0027] where k pan amplification factor, T N a reset time and k t = ^-an integral gain.

[0028] According to an advantageous embodiment of the invention, the tracking controller includes a third element to which the angular frequency can be supplied in order to maintain the position. The third element preferably has an integral component; it is particularly preferred that the third element is designed as an integral component.

[0029] Further details and advantages of the invention will be explained below with reference to the exemplary embodiment shown in the drawings. This shows:

[0030] Fig. 1 shows a block diagram of a drive system according to the prior art;

[0031] Fig. 2 Equivalent circuit diagrams of the tracking controller; and

[0032] Fig. 3 shows exemplary time courses of the angular error A. <p und der Winkelgeschwindigkeit ü) ewhen using an embodiment of the method according to the invention.

[0033] Figure 1 shows a drive system that can be used, for example, in the automotive industry. The drive system comprises an electric machine 1 with a stator and a permanent magnet rotor, such as a brushless synchronous machine. A control device implementing field-oriented control (vector control) is provided to regulate the position and angular frequency of the rotor of the electric machine 1.

[0034] The control device comprises two controllers 111, 112, via which a d-voltage u d and a q-voltage u q These stresses are provided in the rotor-related dq coordinate system. d and u qare fed to a transformation unit 7, in which a transformation from the rotor-related dq coordinate system to the stator-related a-β coordinate system is performed. The stator-related voltages u obtained at the output of transformation unit 7 a and u ß are fed to a unit 8, which controls a converter 2 by means of pulse width modulation (PWM). This converter 2 provides several, here two, phase currents for the winding of the stator of the electric machine 1.

[0035] Two phase currents i ± The phase currents i2 of the stator are measured via current sensors 41, 42 and fed to further transformation units 3, 4, which transform the phase currents into the rotor-related dq coordinate system. The actual currents i are obtained in this process. d and i q These actual flows i d , i q are supplied to controllers 111 and 112 as actual values.

[0036] Further input signals of the controllers 111, 112 are the setpoint values, i. dso u, i qS oii-

[0037] For sensorless determination of the angular frequency G) e and location p e The permanent magnet rotor of the drive system, according to the state of the art, relies on a mathematical motor model 9. The actual currents i are assigned to the mathematical motor model 9. d and i q as well as the control variables d-voltage u d and q-voltage u q supplied. Furthermore, the angular frequency G determined within the framework of the procedure is e traced back to motor model 9. The mathematical motor model 9 determines a d-voltage deviation Au. d and a q-voltage deviation Au q , which are output to a tracking controller 6. The tracking controller 6 determines an angular frequency G) e and derives from this the position p eof the permanent magnet rotor. The tracking controller 6 regulates the d-voltage deviation Au. d and the q-voltage deviation Au q to zero.

[0038] The tracking controller 6 consists of three elements 6.1, 6.2, 6.3 connected in series. The first element 6.1 is, according to the prior art according to EP 2019482 A1, a proportional amplifier with a gain factor k. p formed. Thus, the first term 6.1 implements the transfer function G(s) = k according to the state of the art. p The second element 6.2 of the tracking controller 6 is implemented as an integrating element with the transfer function — - —, where is a time constant and 'Pp^p of the

[0039]

[0040] Calculated value of the flow chain (ideally)

[0041]

[0042] = ^PMO

[0043] According to the publication by V. Barnberg and F.-R. Götz, "Improved voltage model for sensorless control of drives with permanent magnet synchronous motors," SPS / IPC / DRIVES 2008, Trade Fair & Congress - November 25-27, 2008, Nuremberg - the conference proceedings apply in case of minor deviations. <p = <p - <p e between the estimated p e and the actual p rotor angle:

[0044] Au d = sin A <p «

[0045] A

[0046]

[0047] lZ q = Tp M ( <1> COs A <p — 60g) « — 'Pp M Aü),

[0048] where Aw = (ü - o) e the deviation between the estimated angular velocity o e and the true angular velocity w. The illustration in Fig. 2a shows an equivalent circuit diagram of the tracking controller 6 known from the prior art, taking into account these simplifications for Au. d and Au q .

[0049] If the parameters in the model deviate from their actual values, the signals contain Au d , Au q Each interference component is 8 d and 8 q According to the aforementioned publication, these can be obtained under stationary conditions (or...

[0050]

[0051]

[0052] = 0 ) can be represented as follows: <5 d Art de + Lq() e iq e ,

[0053] 8q 8riq e + AL d ü) e J de ATp^tOg.

[0054] where Ar, AL d , AL q , A'PpM = ^PMO ~ ^PM are the deviations of the corresponding parameters from their calculated values. The disturbance components 8 d and 8 q act as disturbances for the tracking controller 6, as shown in Fig. 2a. The equivalent circuit diagram in Fig. 2a can be further reduced under the assumption w = const, as shown in Fig. 2b, where

[0055] , _ VPM _ VPM

[0056] K\IJ — - — -.

[0057]

[0058] w % M o VPM + ATP M

[0059] Ideally, k = 1.

[0060] To reduce parameter sensitivity and thus improve the stability of the control and avoid reactive components in the current, according to an embodiment of the present invention, the first element 6.1 is provided as a Pl element with the reset time T. N The transfer function G(s) of the first term 6.1 is as follows:

[0061] r _ M 1 + k i,,

[0062] G(s) — - - - — — F k p ,

[0063]

[0064] T N SS

[0065] k

[0066] where k p an amplification factor, T N a reset time and k t= ^-an integral gain.

[0067] To reduce the influence of the disturbance variable 8 d , 8 q based on the estimated results and <p e , a) e To assess this, the following transfer functions can be derived:

[0068] n = ^e(s) = 1 _ k p s(l + T w s) _

[0069] “ d{S) 8 d (s) W PM T N s 2 (k^s + l) + k p öj(l + T N s)'

[0070] to e (s) _ 1 _ T N S 2 _

[0071] 3 q (s) W PM T N s 2 (,k w T (O s + 1) + k p o)(l + T N S) '

[0072] < Pe(s) _ 1 _ M 1 + T N S~) _

[0073] (3)

[0074] 5 d (s) + 1) + k p a)(l + T w s) '

[0075] < Pe(s) _ 1 _ T N S _

[0076]

[0077] 3 q (s) W PM T N s 2 (,k w T (O s + 1) + kpO)(l + T N s)'

[0078] Since the transfer functions (1), (2) have zeros at s = 0, the speed estimation in steady state is insensitive to parameter changes. This behavior is also observed in the prior art. However, it is noteworthy that, in contrast to the prior art described in the aforementioned publication, the transfer function G w (s) according to equation (4) also has a zero at s = 0. This means that the angle estimation is insensitive to parameter deviations of

[0079]

[0080] and L d is, which is in the disturbance variable 8 qto enter. Therefore, this is an insensitivity in the steady or steady state. The factor k w , which the transfer functions (1)-(4) contain, is indeed of ^ PM dependent, but it obviously has no effect on the steady state or only influences the dynamic behavior of the tracking controller. The transfer function G^ d (s) has no zero at s=0 and therefore the sensitivity of parameter deviations remains via the disturbance variable 8 d These are, according to (3), the ohmic resistance r and the transverse inductance L. q The corresponding steady-state angular errors are obtained by applying the above definition of the disturbance component 8 d Substituting into equation (3)(3) at s = 0. Taking into account that in the steady state a> e = applies, results

[0081] Arp = A(p r + A(p Lq ,

[0082] where

[0083] A &ri de

[0084] Vr ~

[0085] AL„j„g

[0086] A< Pz,q = —

[0087]

[0088] the angular errors due to the inaccuracies of the resistance Ar and the transverse inductance AL q are. It can be seen that in the basic speed range without field weakening with i de = 0 the angular deviation Acp r = 0. In the field weakness range, the motor speed is comparatively high, therefore the denominator is

[0089]

[0090] , which represents the induced voltage, usually much larger than the ohmic losses in the counter, and the error Acp r is negligibly small. In other words, the method according to the invention either has no sensitivity to changes in resistance at all, or this sensitivity is very low.

[0091] Fig. 3 shows a comparison of the rotational speed curves a> e and the angular error Acp in the sensorless control according to Fig. 1 without integral component (i.e. k) L = 0) and with an integral term (Zcj = 20) in the first term 6.1 of the tracking controller 6. The curves were recorded on a motor from a pump drive, a typical automotive application. The proportional gain was the same value k in both cases. p = 1.5. The calculated value of the river linkage was intentionally reduced by 31% compared to the "real" value. o = 0.69^^. Therefore, with a first term 6.1 without an I-component, an angular error of approximately 11° (electrical) resulted.

[0092] As soon as the I-component was switched on in the first element 6.1 (i.e. kt = 20), the error Acp was reduced to zero.

Claims

Patent claims 1. Method for sensorless determination of the angular frequency (o> e ) and / or location ( <p e ) of a permanent magnet rotor of a brushless electric machine (1), in particular a linear or rotary machine, wherein the electric machine (1) is supplied with a d-voltage (u d ) and a q-voltage (u q ) is provided, wherein a d- voltage deviation (Au) is determined using a motor model, in particular a mathematical one (9). d ) and a q-voltage deviation (Au q ) is determined, wherein the angular frequency (<» is determined in a tracking controller (6) e ) and / or location ( <p e ) of the permanent magnet rotor based on the d-voltage deviation (Au d ) and the q-voltage deviation (Au q ) is determined, wherein the tracking controller (6) has a first element (6.1) to which the d-voltage deviation (Au) d) is supplied to obtain an intermediate value, and has a second term (6.2) to which a link, in particular a difference, is derived from the q-voltage deviation (Au q ) and the intermediate value is supplied to determine the angular frequency (<» e ) to obtain, characterized by the fact that the first element (6.1) of the tracking controller (6) has an I-component.

2. Method according to claim 1, characterized in that the first member (6.1) is a Pl member.

3. Method according to claim 2, characterized in that the first member (6.1) implements a transfer function G(s) with k where k p an amplification factor, T N a reset time and k t = a Integral amplification is.

4. Method according to one of the preceding claims, characterized in that the tracking controller (6) has a third element (6.3) to which the angular frequency (ü) e ) is supplied to improve the situation ( <p e ) to obtain.

5. Drive system with a device for sensorless determination of the angular frequency (o> e ) and / or location ( <p e ) of a permanent magnet rotor of a brushless electric machine (1), in particular a linear or rotary machine, which is configured to supply the electric machine (1) with a d-voltage (u d ) and a q-voltage (u q ) to provide, using a motor model, in particular a mathematical one (9), a d-voltage deviation (Au d ) and a q-voltage deviation (Au q ) to determine, wherein the device includes a tracking controller (6) by which the angular frequency (o> e ) and / or location ( <p e) of the permanent magnet rotor based on the d-voltage deviation (Au d ) and the q-voltage deviation (Au q ) can be determined, wherein the tracking controller (6) has a first element (6.1) to which the d-voltage deviation (Au) d ) can be supplied to obtain an intermediate value, and has a second term (6.2) to which a link, in particular a difference, is derived from the q-voltage deviation (Au q ) and the intermediate value can be supplied to determine the angular frequency (o> e ) to obtain, characterized by the fact that the first element (6.1) of the tracking controller (6) has an I-component.

6. Drive system according to claim 5, wherein the first member (6.1) is a Pl member.

7. Drive system according to claim 6 characterized in that the first member (6.1) implements a transfer function G(s) with k where k p an amplification factor, TN a reset time and k t = a Integral amplification is.

8. Drive system according to one of claims 5 to 7, characterized in that the tracking controller (6) has a third element (6.3) to which the angular frequency (o> e ) can be supplied to determine the location ( <p e ) to obtain.

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