Method for determining a rotor position of a three-phase machine without using a rotary encoder and device for controlling a three-phase motor without using a rotary encoder

Abstract

In a method for determining the rotor position of a three-phase machine without using a rotary encoder, and to a device for controlling a three-phase motor without using a rotary encoder, the three-phase machine is fed by a converter that can be operated by pulse-width modulation, and the converter has model variables for the rotor angle and the current indicator of the three-phase machine, and the converter has device(s) by using which, in control operation, at least two values are measured which represent a measure of the local inductances of the machine which represent a measure of the local inductances of the machine, the error of the model rotor angle is determined in that, depending on the model rotor angle and the model current indicator, at least two weighting factors are determined, and in that a weighted sum is formed from the at least two measured values and the at least two weighting factors, and in that a further offset value is substracted from the sum, which is likewise determined on the basis of the model rotor angle and the model current indicator.

Claims

1. A device adapted for rotary encoderless determination of a rotor position of a three-phase motor, comprising: a converter, adapted to feed the three-phase motor, operable with pulse width modulation, and including model variables for a rotor angle and a current indicator of the three-phase motor, the converter including a device adapted to measure, in closed-loop controlled operation, at least two values that represent a measure of local inductances of the three-phase motor, the converter adapted to determine an error of the model rotor angle by determining at least two weighting factors as a function of the model rotor angle and the model current indicator, to form a weighted sum from the at least two measured values and the at least two weighting factors, and to subtract, from the sum, another offset value that is determined as a function of the model rotor angle and the model current indicator.

2. The device according to claim 1, wherein the three-phase motor is arranged as a rotary encoderless three-phase motor.

3. The device according to claim 1, wherein the converter is arranged as a pulse-controlled inverter.

4. The device according to claim 1, wherein the converter is adapted to use local admittances as a measure of the local inductances.

5. The device according to claim 1, wherein the function is determined offline.

6. The device according to claim 1, wherein the function is set one time preceding a positional determination.

7. The device according to claim 1, wherein the function is determined prior to the closed-loop controlled operation.

8. The device according to claim 7, wherein the weighting factors and the offset value are assigned by the function to the values of the two model variables online.

9. The device according to claim 7, wherein the weighting factors and the offset value are assigned by the function to the values of the two model variables during position determination.

10. The device according to claim 1, wherein the function is based on local inductances determined as a function of values of a rotor position and a current indicator.

11. The device according to claim 10, wherein the current indicator represents a trajectory.

12. The device according to claim 1, wherein the weighting factors and the offset value are assigned to the model variables as a function of a differential of the local inductances that is specific to rotor position.

13. The device according to claim 1, wherein the weighting factors and the offset value are assigned to the model variables as a function of a differential of local admittances that is specific to rotor position.

14. A system, comprising: a three-phase motor; and a device adapted for rotary encoderless determination of a rotor position of the three-phase motor, including a converter, adapted to feed the three-phase motor, operable with pulse width modulation, and including model variables for a rotor angle and a current indicator of the three-phase motor, the converter including a device adapted to measure, in closed-loop controlled operation, at least two values that represent a measure of local inductances of the three-phase motor, the converter adapted to determine an error of the model rotor angle by determining at least two weighting factors as a function of the model rotor angle and the model current indicator, to form a weighted sum from the at least two measured values and the at least two weighting factors, and to subtract, from the sum, another offset value that is determined as a function of the model rotor angle and the model current indicator.

15. The system according to claim 14, wherein the three-phase motor is arranged as a rotary encoderless three-phase motor.

16. The system according to claim 14, wherein the converter is arranged as a pulse-controlled inverter.

17. The system according to claim 14, wherein the converter is adapted to use local admittances as a measure of the local inductances.

18. The system according to claim 14, wherein the function is determined offline.

19. The system according to claim 14, wherein the function is set one time preceding a positional determination.

20. The system according to claim 14, wherein the function is determined prior to the closed-loop controlled operation.

21. The system according to claim 20, wherein the weighting factors and the offset value are assigned by the function to the values of the two model variables online.

22. The system according to claim 20, wherein the weighting factors and the offset value are assigned by the function to the values of the two model variables during position determination.

Description

BRIEF DECRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates the correlation in terms of signal engineering between the model variables known to the converter, the actual rotor position unknown to the converter, and the measurable admittance parameters derived as a function of these variables.

(2) FIG. 2 is a signal flow diagram of an exemplary embodiment of the method.

DETAILED DESCRIPTION

(3) The differential inductance matrix describes the relationship between current variations and the corresponding injection voltage u.sub.c. This matrix is symmetrical and, therefore, includes three independent parameters.

(4) $\begin{array}{cc}{u}_c=\left(\begin{array}{cc}{L}_a& L_{\mathrm{ab}}\\ L_{\mathrm{ab}}& L_b\end{array}\right).Math.\frac{d}{\mathrm{dt}}{i}_c& \left(1\right)\end{array}$

(5) Conversely, the current rise in response to an applied injection voltage u.sub.c is determined by the inverse matrix.

(6) $\begin{array}{cc}\frac{d}{\mathrm{dt}}{i}_c={\left(\begin{array}{cc}{L}_a& L_{\mathrm{ab}}\\ L_{\mathrm{ab}}& L_b\end{array}\right)}^{-1}.Math.u_c& \left(2\right)\end{array}$

(7) Inverse Y of inductance matrix L is often referred to as the admittance matrix here as well in the following. This is likewise symmetrical and determined by the three parameters Y.sub.a, Y.sub.b, and Y.sub.ab.

(8) $\begin{array}{cc}Y=L^{-1}={\left(\begin{array}{cc}{L}_a& L_{\mathrm{ab}}\\ L_{\mathrm{ab}}& L_b\end{array}\right)}^{-1}=\left(\begin{array}{cc}{Y}_a& Y_{\mathrm{ab}}\\ Y_{\mathrm{ab}}& Y_b\end{array}\right)& \left(3\right)\end{array}$

(9) Thus, the relationship between the applied injection voltage u, and the corresponding current rise is expressed as follows:

(10) $\begin{array}{cc}\frac{d}{\mathrm{dt}}{i}_c=\left(\begin{array}{cc}{Y}_a& Y_{\mathrm{ab}}\\ Y_{\mathrm{ab}}& Y_b\end{array}\right).Math.u_c=Y.Math.u_c& \left(4\right)\end{array}$

(11) Using the substitutions (5a)-(5c), the admittance matrix may be reduced as illustrated in (6).

(12) $\begin{array}{cc}{Y}_{.Math.}=\frac{Y_a+Y_b}{2}& \left(5a\right)\\ Y_{\Delta a}=\frac{Y_a-Y_b}{2}& \left(5b\right)\\ Y_{\Delta b}=Y_{\mathrm{ab}}& \left(5c\right)\\ Y=\left(\begin{array}{cc}{Y}_a& Y_{\mathrm{ab}}\\ Y_{\mathrm{ab}}& Y_b\end{array}\right)=Y_{.Math.}.Math.\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)+Y_{\Delta a}.Math.\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)+Y_{\Delta b}.Math.\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)& \left(6\right)\end{array}$

(13) In this reduction, Y.sub.Σ represents the isotropic component of the admittance matrix. On the other hand, the anisotropic component is a variable having magnitude and direction that is represented in (6) by Cartesian components Y.sub.Δa, and y.sub.Δb thereof.

(14) The exemplary embodiment may apply to a permanently excited synchronous machine. For such a machine, the local inductance matrix, respectively the local admittance matrix may be determined in the reduction thereof in accordance with (6) with the aid of a square injection, for example. In German Patent Document No. 10 2015 217 986, isotropic component Y.sub.Σ may be ascertained from the first component of equation (31) as follows:

(15) $\begin{array}{cc}{Y}_{.Math.}=\frac{{\Delta i}_{.Math.x}}{u_c.Math.\Delta t}=\frac{1}{4.Math.u_c.Math.\Delta t}.Math.\left({\Delta i}_{u\mathrm{\alpha 0}}+{\Delta i}_{u\mathrm{\beta 1}}-{\Delta i}_{u\mathrm{\alpha 2}}-{\Delta i}_{u\mathrm{\beta 3}}\right)& \left(7\right)\end{array}$

(16) This may be simplified to (8), whereby isotropic component Y.sub.Σ may be determined directly from the measured current rises.

(17) $\begin{array}{cc}{Y}_{.Math.}=\frac{1}{4.Math.u_c.Math.\Delta t}.Math.\left({\Delta i}_{\mathrm{\alpha 0}}+{\Delta i}_{\mathrm{\beta 1}}-{\Delta i}_{\mathrm{\alpha 2}}-{\Delta i}_{\mathrm{\beta 3}}\right)& \left(8\right)\end{array}$

(18) Apart from measurement errors, second component Δi.sub.Σy of equation (31) in the German Patent Document No.10 2015 217 986 is zero.

(19) The anisotropic components Y.sub.Δa, and K.sub.Δb are derived from the components of indicator equation (43) in German Patent Document No. 10 2015 217 986 as follows:

(20) $\begin{array}{cc}{Y}_{\Delta a}=\frac{1}{4.Math.u_c.Math.\Delta t}.Math.\left({\Delta i}_{\mathrm{\alpha 0}}-{\Delta i}_{\mathrm{\beta 1}}-{\Delta i}_{\mathrm{\alpha 2}}+{\Delta i}_{\mathrm{\beta 3}}\right)& \left(9\right)\\ Y_{\Delta b}=\frac{1}{4.Math.u_c.Math.\Delta t}.Math.\left({\Delta i}_{\mathrm{\alpha 0}}+{\Delta i}_{\mathrm{\beta 1}}-{\Delta i}_{\mathrm{\alpha 2}}-{\Delta i}_{\mathrm{\beta 3}}\right)& \left(10\right)\end{array}$

(21) Admittance components Y.sub.Σ, Y.sub.Δa and Y.sub.Δb may also be determined using other characteristics of the injection voltage, such as of a rotating injection, for example, as described, for example, in the publication A Comparative Analysis of Pulsating vs. Rotating Indicator Carrier Signal Injection-Based Sensorless Control, Applied Power Electronics Conference and Exposition, Austin, Feb. 24-28, 2008, pp. 879-885 by D. Raca et. al.

(22) The method according to an example embodiment of the present invention for rotor position identification is based on determining the three parameters of the admittance matrix. The implementation of the method is not bound to the selected form, respectively reduction in (6). Rather, any other form of representation of the information contained in the admittance matrix may be used as the basis for this.

(23) In particular, to implement the method, it is possible to acquire any three linear combinations from admittance components Y.sub.a, Y.sub.b, and Y.sub.ab, respectively Y.sub.Σ, Y.sub.Δa and Y.sub.Δb to the extent that they are mutually linearly independent.

(24) A component hereof is appropriately utilizing the realization that the three parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb of the local admittance matrix depend not only on rotor position θ.sub.r but, as a function of the operating points, also on components i.sub.d and i.sub.q of the instantaneous fundamental current indicator, thus they are influenced by the magnitude and direction thereof.
Y.sub.Σ=Y.sub.Σ(θ.sub.r,i.sub.d,i.sub.q)   (11)
Y.sub.Δn=hd Δa(θ.sub.r,i.sub.d,i.sub.q)   (12)
Y.sub.Δb=.sub.Δb(θ.sub.r,i.sub.d,i.sub.q)   (13)
θ.sub.r representing the electric angle of the rotor position and i.sub.d respectively i.sub.q the components of the fundamental current indicator.

(25) The following considerations are limited to the base speed range. Here, the machine is typically operated using a torque-generating current on the q-axis, i.e., i.sub.d=0 or along an MTPA (maximum torque per ampere) trajectory, which indicates a fixed association of the d-current as a function of the q-current. This is described by D. Schröder, for example, in Elektrische Antriebe—Regelung von Antriebssysteme [Electrical Drives—Closed-Loop Control of Drive Systems] 3rd edition, Berlin, Springer 2009. Thus the machine is operated in accordance with (14) or (15).
i.sub.d=0   (14)
respectively
i.sub.d=i.sub.d,MTPA(i.sub.q)   (15)

(26) In selecting the operating points, the converter is hereby limited to two remaining degrees of freedom, namely to electric rotor angle θ.sub.r and q-current i.sub.q, while associated d-current i.sub.d results from the q-current from a fixed association in accordance with (14) or (15), for example. For operating points in accordance with this selection, the dependency of admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb is also reduced to just two independent variables θ.sub.r and i.sub.q:
Y.sub.Σ=Y.sub.Σ(θ.sub.r, i.sub.d(i.sub.q),i.sub.q)=Y.sub.Σ(θ.sub.r,i.sub.q)   (16)
Y.sub.Δa=Y.sub.Δa(θ.sub.r,i.sub.d(i.sub.q),i.sub.q)=Y.sub.Δa(θ.sub.r,i.sub.q)   (17)
Y.sub.Δb=Y.sub.Δb(θ.sub.r,i.sub.d(i.sub.q),i.sub.q)=Y.sub.Δb(θ.sub.r,i.sub.q)   (18)

(27) In the case of rotary encoderless operation of the motor on a converter, deviations also inevitably arise between actual electric rotor angle θ.sub.r and corresponding model rotor angle θ.sub.r,mod in the converter. However, even when these ideally turn out to be very small, unstable operation may result in conventional rotary encoderless methods, as described by W. Hammel et. al. in Operating Point Dependent Anisotropies and Assessment for Position-Sensorless Control, European Conference on Power Electronics and Applications, Karlsruhe, Sep. 5-9, 2016.

(28) To orient the fundamental current indicator to be applied, the converter will only be able to revert to model rotor angle θ.sub.r,mod. If this does not conform to actual electric rotor angle θ.sub.r, the result is that the actual d- and q-current components no longer conform with the corresponding model variables. The d- and q-current components i.sub.d and i.sub.q actually flowing in the motor are dependent at this stage on the model variables in converter i.sub.d,mod and i.sub.q,mod as well as on the error of rotor angle model {tilde over (θ)}.sub.r, as follows:
i.sub.d=i.sub.d,mod.Math.cos({tilde over (θ)}.sub.r)−i.sub.q,mod.Math.sin({tilde over (θ)}.sub.r)   (19)
i.sub.q=i.sub.q,mod.Math.cos({tilde over (θ)}.sub.r)+i.sub.d,mod.Math.sin({tilde over (θ)}.sub.r)   (20)
{tilde over (θ)}.sub.r=θ.sub.r,mod−θ.sub.r   (21)

(29) If there is an error of model rotor angle {tilde over (θ)}.sub.r, the assignment according to (14), respectively (15) between the actual q- and d-current components does not take place, rather model d-current i.sub.d,mod is generated as a function of the model q-current i.sub.q,mod:
i.sub.d,mod=0   (22)
respectively
i.sub.d,mod=i.sub.d,MTPA(i.sub.q,mod)   (23)

(30) Since, in accordance with (11)-(13), the admittance parameters are dependent on actual d- and q-currents i.sub.d and i.sub.q, in comparison to (16)-(18), they will have an additional dependency on the error of model rotor angle {tilde over (θ)}.sub.r respectively on model rotor angle θ.sub.r,mod:
Y.sub.Σ=Y.sub.Σ(θ.sub.r,i.sub.q,mod,{tilde over (θ)}.sub.r)   (24)
Y.sub.Δa=Y.sub.Δa(θ.sub.r,i.sub.q,mod,{tilde over (θ)}.sub.r)   (25)
Y.sub.Δb=Y.sub.Δb(θ.sub.r,i.sub.q,mod,{tilde over (θ)}.sub.r)   (26)
respectively
Y.sub.Σ=Y.sub.Σ(θ.sub.r,i.sub.q,mod,θ.sub.r,mod)   (27)
Y.sub.Δa=Y.sub.Δa(θ.sub.r,i.sub.q,mod,θ.sub.r,mod)   (28)
Y.sub.Δb=Y.sub.Δb(θ.sub.r,i.sub.q,mod,θ.sub.r,mod)   (29)

(31) Thus, measurable admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb are dependent on the two model variables i.sub.q,mod and θ.sub.r,mod known in the converter as well as on a further variable, namely actual rotor angle θ.sub.r unknown in the converter.

(32) FIG. 1 shows the internal interaction of the relevant equations, which collectively lead to dependencies (27)-(29). The numbers of the equations, which represent the respective relationships, are indicated in parentheses here.

(33) Model d-current i.sub.d,mod is generated from model q-current i.sub.q,mod in accordance with selected MTPA characteristic 103 as expressed by equations (22) respectively (23). Actual motor current components i.sub.d and i.sub.q are derived from model current components i.sub.d,mod and i.sub.q,mod by the transformation of model rotor coordinates into actual rotor coordinates 102 in accordance with equations (19) and (20) using phase angle error {tilde over (θ)}.sub.r. In accordance with (21), the error of model rotor angle {tilde over (θ)}.sub.r is the difference between model rotor angle θ.sub.r,mod and actual rotor angle θ.sub.r. Finally, within the three-phase machine, measurable admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb are generated as a function of actual current components i.sub.d and i.sub.q as well as of actual rotor position θ.sub.r in accordance with equations (11)-(13).

(34) Overall, this results in a mapping 100 of the model variable of q-current i.sub.q,mod and of model rotor angle θ.sub.r,mod as well as of actual rotor angle θ.sub.r onto measurable admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb in accordance with equations (27)-(29).

(35) What is decisive is the realization that an error of the model rotor angle does, in fact, influence the admittance parameters, but they may nevertheless be measured, unaltered, using an injection process.

(36) Based on this realization, it is fundamentally possible to use the measured admittance parameters to identify the rotor position. This would be very simple to realize if one of the relationships (27)-(29) could be uniquely solved for rotor angle θ.sub.r in a reversible process. Generally, however, this is not the case for any of the three variables.

(37) In any case, however, it is necessary to know the dependencies of the admittance parameters on the operating point in accordance with (11)-(13). These may be ascertained, for example, by a preceding offline measurement, it being possible for measurement devices to also be used to determine the rotor position. However, there is no need for this to be determined over the entire d-q current plane to realize the method hereof. If the machine is operated on a current trajectory in accordance with (22), respectively (23), and it is also assumed that the phase angle errors occurring during operation remain small, it suffices to determine the admittance parameters on the current trajectory and in the vicinity thereof.

(38) In accordance with example embodiments of the present invention, the stability problem described by W. Hammel et al. in Operating Point Dependent Anisotropies and Assessment for Position-Sensorless Control, European Conference on Power Electronics and Applications, Karlsruhe, Sep. 5-9, 2016 is overcome by a converter internal error signal δ.sub.F initially being generated from variables θ.sub.r,mod and i.sub.q,mod , and which are available to the converter, as well as from measured admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb, whereby this error signal itself again depends only on model q-current i.sub.q,mod and model rotor angle θ.sub.r,mod as well as on unknown rotor angle θ.sub.r:
δ.sub.F=δ.sub.F(θ.sub.r,i.sub.q,mod,θ.sub.r,mod)   (30)

(39) In accordance with example embodiments of the present invention, this signal is generated to represent a measure of the deviation of model rotor angle θ.sub.r,mod from actual rotor angle θ.sub.r, and this signal is fed to a controller which adjusts model angle θ.sub.r,mod to the actual rotor angle. This may be accomplished by a simple PLL control loop, for example. Alternatively, error signal δ.sub.F may be used as a correction intervention in a fundamental wave model, which may thereby also be used in the low speed range and at standstill.

(40) In accordance with example embodiments of the present invention, error signal δ.sub.F is generated in accordance with FIG. 2 by a composite signal F which is a weighted sum of the three measured admittance parameters:
F=G.sub.Σ.Math.Y.sub.Σ+G.sub.Δa.Math.Y.sub.Δa+G.sub.Δb.Math.Y.sub.Δb   (31)

(41) A quantity F.sub.0 is subtracted from this composite signal F, resulting in error signal δ.sub.r:
δ.sub.F=F−F.sub.0   (32)

(42) Weights G.sub.Σ, G.sub.Δa and G.sub.Δb as well as quantity F.sub.0 are typically not constants, but rather operating point-dependent values. Significant thereby is that there is no need to use actual operating point θ.sub.r, i.sub.d and i.sub.q to determine these quantities. Rather, the use of the possibly faulty model operating point θ.sub.r,mod and i.sub.q,mod leads nevertheless in the result to a stable operation and, in fact, even in the case of a non-vanishing phase angle error.

(43) Thus, variables G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 are general functions of the model variables:
G.sub.Σ=G.sub.Σ(i.sub.q,mod,θ.sub.r,mod)   (33)
G.sub.Δa=G.sub.Δa(i.sub.q,mod,θ.sub.r,mod)   (34)
G.sub.Δb=G.sub.Δb(i.sub.q,mod,θ.sub.r,mod)   (35)
F.sub.0=F.sub.0(i.sub.q,mod,θ.sub.r,mod)   (36)

(44) As a function of the form of these functions G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0, a tabular or functional mapping or a combination of both is practical for the storing or calculation thereof in the converter. The following assumes a tabularly stored dependency of values G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 on the model operating point.

(45) Thus it follows for error signal δ.sub.F, which is dependent on model variables i.sub.q,mod and θ.sub.r,mod as well as on actual rotor angle θ.sub.r, that:
δ.sub.F=δ.sub.F(θ.sub.r,i.sub.q,mod,θ.sub.r,mod)   (37)

(46) It is possible to form functions G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 , and, in fact, solely in dependence upon the model variables such that error signal δ.sub.F acquires the following properties

(47) $\begin{array}{cc}\frac{\partial }{\partial {\theta }_r}{\delta }_F\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_{r,\mathrm{mod}}={\theta }_r}=1& \left(38\right)\\ \frac{\partial }{\partial {\theta }_{r,\mathrm{mod}}}{\delta }_F\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_{r,\mathrm{mod}}={\theta }_r}=-1& \left(39\right)\\ {\delta }_F\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_{r,\mathrm{mod}}={\theta }_r}=0& \left(40\right)\end{array}$
and this permits a stable operation because of the properties mentioned.

(48) Thus, in accordance with equation (38), the required property indicates how error signal δ.sub.F is to respond to a change in actual rotor angle θ.sub.r, namely with a slope 1 in response to a change in actual rotor angle θ.sub.r, proceeding from corrected operating point θ.sub.r,mod=θ.sub.r in the case of set model angle θ.sub.r,mod.

(49) Additionally, the required property in accordance with equation (39) indicates how error signal δ.sub.F is to respond to a change in model angle θ.sub.r,mod, proceeding from adjusted operating point θ.sub.r,mod=θ.sub.r in the case of set actual rotor angle θ.sub.r namely with a slope −1 in response to a change in model angle θ.sub.r,mod.

(50) Consequently, in the vicinity of corrected operating point θ.sub.r,mod=θ.sub.r, error signal δ.sub.F is proportional to phase angle error {tilde over (θ)}.sub.r=θ.sub.r,mod−θ.sub.r and is thus suited for adjusting the model angle to the actual motor angle with the aid of a closed-loop control circuit.

(51) Moreover, from required properties (38) and (39) of error signal δ.sub.F, it follows that the value of error signal δ.sub.F is constant, for example, as selected in (40), constantly zero for all corrected operating points θ.sub.q,mod=θ.sub.r independently of rotor position θ.sub.r and model q-current i.sub.q.

(52) In another step, G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 are formulated at this stage as a function of model variables i.sub.q,mod and θ.sub.r,mod provide error signal δ.sub.F in accordance with (31) and (32) with the required properties according to (38)-(40).

(53) This is accomplished by executing G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 as follows:

(54) 0$\begin{array}{cc}{G}_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{D_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}{D_{.Math.}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta a}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta b}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}& \left(41\right)\\ G_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{D_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}{D_{.Math.}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta a}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta b}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}& \left(42\right)\\ G_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{D_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}{D_{.Math.}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta a}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta b}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}& \left(43\right)\\ F_0\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{\begin{array}{c}{D}_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right).Math.Y_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+\\ D_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right).Math.Y_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+\\ D_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right).Math.Y_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)\end{array}}{D_{.Math.}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta a}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)+D_{\Delta b}^2\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)}& \left(44\right)\end{array}$

(55) D.sub.Σ, D.sub.Δa and D.sub.Δb thereby represent the differentials of local admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb in accordance with rotor position θ.sub.r. If the dependencies of local admittance parameters according to (27)-(29) are determined in the above described manner, then differentials D.sub.Σ, D.sub.Δa and D.sub.Δb thereof in accordance with rotor position θ.sub.r may also be indicated for the corrected operating point:

(56) $\begin{array}{cc}{D}_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{\partial }{\partial {\theta }_r}{Y}_{.Math.}\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_r={\theta }_{r,\mathrm{mod}}}& \left(45\right)\\ D_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{\partial }{\partial {\theta }_r}{Y}_{\Delta \alpha }\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_r={\theta }_{r,\mathrm{mod}}}& \left(46\right)\\ D_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)=\frac{\partial }{\partial {\theta }_r}{Y}_{\Delta b}\left({\theta }_r,i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right){|}_{{\theta }_r={\theta }_{r,\mathrm{mod}}}& \left(47\right)\end{array}$

(57) If the alternative representation according to (24)-(26) is used for the description of the admittance parameters, thus as a function of actual rotor angle θ.sub.r, of model q-current i.sub.q,mod and of error angle {tilde over (θ)}.sub.r, the relevant differentials present themselves as follows:

(58) $\begin{array}{cc}{D}_{.Math.}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)={\left[\frac{\partial }{\partial {\theta }_r}{Y}_{.Math.}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)-\frac{\partial }{\partial {\tilde{\theta }}_r}{Y}_{.Math.}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)\right]}_{{\theta }_r={\theta }_{r,\mathrm{mod}},{\tilde{\theta }}_r=0}& \left(48\right)\\ D_{\Delta a}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)={\left[\frac{\partial }{\partial {\theta }_r}{Y}_{\Delta a}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)-\frac{\partial }{\partial {\tilde{\theta }}_r}{Y}_{\Delta a}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)\right]}_{{\theta }_r={\theta }_{r,\mathrm{mod}},{\tilde{\theta }}_r=0}& \left(49\right)\\ D_{\Delta b}\left(i_{q,\mathrm{mod}},{\theta }_{r,\mathrm{mod}}\right)={\left[\frac{\partial }{\partial {\theta }_r}{Y}_{\Delta b}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)-\frac{\partial }{\partial {\tilde{\theta }}_r}{Y}_{\Delta b}\left({\theta }_r,i_{q,\mathrm{mod}},{\tilde{\theta }}_r\right)\right]}_{{\theta }_r={\theta }_{r,\mathrm{mod}},{\tilde{\theta }}_r=0}& \left(50\right)\end{array}$

(59) The setting of values G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 selected in accordance with (41)-(44) in conjunction with (45)-(47) or with (48)-(50) not only fulfills conditions (38)-(40) for the error signal, but also yields the best possible signal-to-noise ratio for error signal δ.sub.F, assuming that the measured values of the admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb generate noise in an uncorrelated and normally distributed manner and with the same standard deviation.

(60) Example embodiments of the present invention also include settings that deviate herefrom. Thus, for example, there may be a deviation from the above setting in the following variants: 1. A setting of G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 that is not optimal for the signal-to-noise ratio, so that properties (38)-(40) are nevertheless fulfilled for error signal δ.sub.F. 2. A setting, so that error signal δ.sub.F becomes noise-optimal for different noise characteristics of the measured admittance parameters. The measured admittance parameters may, for example, generate noise with different standard deviations, or the individual admittance parameters generate noise not in an uncorrelated, but in a mutually correlated manner, or the admittance parameters generate noise in accordance with a distribution that differs from the normal distribution. Under these conditions as well, the dependency of values G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 on the model variables for which error signal δ.sub.F has an optimal signal-to-noise ratio, is set in each case. 3. A setting so that the derivatives in (38)-(39) are not constantly +/−1, but deviate therefrom or even vary as a function of the operating point. In this case, an operating point-dependent control loop gain and thus an operating point-dependent transiet response results for the control loop which adjusts the modeled rotor position. 4. A setting in accordance with which an individual weight, for example, G.sub.Σ is selected to be lower in terms of absolute value or even down to zero. This would be beneficial, for example, if the associated admittance parameter has significant manufacturing tolerances, and different specimen from an ensemble of same motors are to be operated using one single set of parameters. The individual specimen of the ensemble thereby differ with respect to the respective admittance parameter on the basis of manufacturing tolerances. 5. A setting of values G.sub.Σ, G.sub.Δa, G.sub.Δb and F.sub.0 as a function of three model variables instead of the two model variables described here, for example, as a function of the model rotor angle and both model current components. This would be advantageous if the machine were to be operated not only along a fixed current trajectory, but in a larger range of the d-q current plane or in the entire d-q current plane, as is used, for example, in the field weakening range.

(61) In summary, the following steps are to be implemented to execute the method. The following steps are first performed in a preceding offline process: 1. Determination of the operation point dependency of local admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb along the set current trajectory and in the vicinity thereof. This may be done offline for a single specimen of a motor type on a test stand having a rotor position measuring device. 2. Determining the differentials of admittance parameters measured offline in accordance with the rotor position. 3. Setting of the table contents for weighting factors G.sub.Σ, G.sub.Δa and G.sub.Δb as well as of term F.sub.0 for all operating points.

(62) The subsequent rotary encoderless determination of the rotor position includes the following steps in online operation, as shown in FIG. 2: 1. Measuring local admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb using a suitable high frequency injection voltage. 2. Determining the current values for weighting factors G.sub.Σ, G.sub.Δa and G.sub.Δb by accessing the previously set tables as a function of instantaneous model variables i.sub.q,mod and θ.sub.r,mod. 3. Generating a weighted sum of the measured admittance parameters using the current weighting factors. 4. Determining the current value for term F.sub.0 to be subtracted as a function of the instantaneous model variables. 5. Generating error signal δ.sub.F by subtracting term F.sub.0 from the weighted sum. 6. Feeding error signal δ.sub.F to a control circuit or a fundamental wave machine model. 7. Adjusting model rotor angle θ.sub.r,mod by controlling error signal δ.sub.F toward zero. 8. Cyclically repeating online steps 1-7.

(63) For the described exemplary embodiment, FIG. 2 depicts the signal flow diagram for controlling a rotary encoderless three-phase machine 111 using the method hereof. Three-phase machine 111 is fed by power output stage 109 of an inverter. The currents flowing to the three-phase machine are measured by a two-phase or three-phase current acquisition 110.

(64) Corresponding setpoint d-current i.sub.d,soll is determined as a function of setpoint q-current i.sub.q,soll, which is dependent on the desired torque, in accordance with (14) or (15), via MTPA characteristic curve 103, and the setpoint current indicator derived therefrom is fed in model rotor coordinates i.sub.soll.sup.r to setpoint-actual comparison 104. The actual current indicator in model rotor coordinates i.sub.mod.sup.r is formed by inverse transformation 107 from the actual current indicator in stator coordinates i.sup.s using model rotor angle θ.sub.r,mod.

(65) Current controller 105 generates the fundamental wave voltage in model rotor coordinates u.sub.f.sup.r and thus adjusts actual current indicator i.sub.mod.sup.r to setpoint current indicator i.sub.soll.sup.r. Transformation device 106 transforms the fundamental wave voltage from model rotor coordinates into stator coordinates, for which purpose, model rotor angle θ.sub.r,mod is used, in turn.

(66) Injection voltage u.sub.c.sup.s is additively superimposed in stator coordinates u.sub.f.sup.s on fundamental voltage indicator by summation 108, whereby the entire motor voltage is generated in stator coordinates u.sub.m.sup.s which is [(sic.) are] amplified by power output stage 109 and fed to machine 111. The injection voltage may also be alternatively added already before transformation 106 into model rotor coordinates.

(67) The currents flowing in the machine are measured by current acquisition 110. Determined herefrom in separation unit 112 are both the fundamental wave current in stator coordinates i.sup.s as well as, from the high-frequency current components, admittance parameters Y.sub.Σ, Y.sub.Δa and Y.sub.Δb.

(68) Weights G.sub.Σ, G.sub.Δa and G.sub.Δb used for generating weighted sum F are formed via tables, respectively functional mappings 113-115 as a function of model rotor position θ.sub.r,mod and of model q-current i.sub.q,mod.

(69) Weights G.sub.Σ, G.sub.Δa and G.sub.Δb used for generating weighted sum F are formed via tables, respectively functional mappings 113-115 as a function of model rotor position θ.sub.r,mod and of model q-current i.sub.q,mod.

(70) Finally, offset F.sub.0, which is likewise formed as a function of model rotor position θ.sub.r,mod and of model q-current i.sub.q,mod in the table, respectively functional mapping 116 is subtracted from generated weighted sum F. Error signal δ.sub.F is ultimately hereby formed and is fed in the present exemplary embodiment to a PLL controller 119. This is usually composed of the series connection of a PI element 117 and of an I-element 118. The PLL controller adjusts model rotor angle θ.sub.r,mod formed at the output thereof to actual rotor angle θ.sub.r so that, in the corrected state, it ultimately agrees with the actual rotor angle, and error signal δ.sub.F then becomes zero. Additionally available at the output of PI element 117 is a model value of electric angular velocity ω.sub.mod which may be used, for example, as the actual value for a superimposed speed control loop.

LIST OF REFERENCE NUMERALS

(71) 100 generation of the admittance parameters as a function of the model variables and the actual rotor position

(72) 101 generation of the admittance parameters as a function of the actual motor sizes

(73) 102 transformation of model rotor coordinates into actual rotor coordinates

(74) 103 MTPA characteristic (maximum torque per ampere)

(75) 104 setpoint-actual comparison of the current control circuit

(76) 105 current controller

(77) 106 transformation of model rotor coordinates into stator coordinates

(78) 107 inverse transformation of stator coordinates into model rotor coordinates

(79) 108 additive application of the injection voltage

(80) 109 power output stage

(81) 110 current measurement

(82) 111 three-phase machine

(83) 112 means for determining the admittance parameters and the fundamental wave current

(84) 113 producing the weight factor for the isotropic admittance component

(85) 114 producing the weight factor for the anisotropic a-admittance component

(86) 115 producing the weight factor for the anisotropic b-admittance component

(87) 116 producing the offset to be subtracted

(88) 117 PI controller of the PLL controller for forming the model speed

(89) 118 I-controller of the PLL controller for forming the model rotor angle

(90) 119 PLL controller (phase-locked loop)

LIST OF SYMBOLS

(91) D.sub.Δa differential of the anisotropic admittance a-component in accordance with the rotor position

(92) D.sub.Δb differential of anisotropic admittance b-component in accordance with the rotor position

(93) D.sub.Σ differential of the isotropic admittance component in accordance with the rotor position

(94) F weighted sum of the measured admittance components

(95) F.sub.0 offset to be subtracted

(96) G.sub.Δa weighting factor for the a-component of the anisotropic admittance component

(97) G.sub.Δb weighting factor for the b-component of the anisotropic admittance component

(98) G.sub.Σ weighting factor for the isotropic admittance component

(99) i.sub.c carrier current indicator

(100) i.sub.d, i.sub.q actual fundamental wave current components in rotor coordinates

(101) i.sub.d,mod, i.sub.q,mod actual fundamental wave current components in model rotor coordinates

(102) i.sub.mod.sup.r actual fundamental wave current indicator in model rotor coordinates

(103) i.sup.s actual fundamental wave current indicator in stator coordinates

(104) i.sub.d,soll,i.sub.q,soll setpoint current components of the fundamental wave current

(105) i.sub.soll.sup.r setpoint current indicator of the fundamental wave current in model rotor coordinates

(106) Δi.sub.αn, Δi.sub.βn components of the current rises in stator coordinates

(107) Δi.sub.uαn, Δi.sub.uβn components of current rises in voltage coordinates

(108) Δ.sub.Σx,y current rises due to the isotropic admittance component

(109) L inductance matrix in stator coordinates

(110) L.sub.a a-component of the inductance matrix in stator coordinates

(111) L.sub.b b-component of the inductance matrix in stator coordinates

(112) L.sub.ab coupling inductance in stator coordinates

(113) Δt time interval

(114) u.sub.c amplitude of the injection voltage

(115) u.sub.c injection voltage indicator

(116) u.sub.c.sup.s injection voltage indicator in stator coordinates

(117) u.sub.f.sup.r fundamental wave current indicator in model rotor coordinates

(118) u.sub.f.sup.s, fundamental wave current indicator in stator coordinates

(119) u.sub.m.sup.s, machine voltage in stator coordinates

(120) Y admittance matrix in stator coordinates

(121) Y.sub.a a-component of the admittance matrix in stator coordinates

(122) Y.sub.b b-component of the admittance matrix in stator coordinates

(123) Y.sub.ab coupling admittance in stator coordinates

(124) Y.sub.Δa a-component of the anisotropic admittance component in stator coordinates

(125) Y.sub.Δb b-component of the anisotropic admittance component in stator coordinates

(126) Y.sub.Σ isotropic admittance component

(127) δ.sub.F error signal

(128) θ.sub.r rotor position

(129) θ.sub.r,mod model rotor position

(130) {tilde over (θ)}.sub.r error of the model rotor position