METHOD FOR DETERMINING THE RPM AND / OR ENGINE PARAMETERS
Patent Information
- Application Number
- DE502023001872
- Authority / Receiving Office
- DE · DE
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-05-17
- Publication Date
- 2025-10-16
- Estimated Expiration
- 2043-05-17
AI Technical Summary
Existing methods for determining the speed and motor parameters of frequency converter-fed three-phase drives are unreliable at low speeds and require additional test signals, leading to noise pollution and increased motor losses, and they lack a consistent solution across all speed ranges.
A method that converts space vector components into a nonlinear system with complex-valued input and output variables, using a nonlinear regression analysis to determine motor parameters and rotor position without test signals, allowing reliable determination across the entire speed range.
Enables accurate and efficient determination of motor parameters and rotor position without additional test signals, suitable for highly dynamic control of three-phase motors.
Description
[0001] The invention relates to a method for determining the speed and / or motor parameters of a three-phase drive operated with a frequency converter.
[0002] For highly dynamic control of electrical drives, frequency converter-fed three-phase drives are used in many areas of industrial drive technology. The basic principle of these drives is that torque-generating and flux-generating variables can be controlled separately. To achieve this, precise information about the rotor position or speed and / or motor parameters is essential. Field-oriented control is the most well-known method, and this information is essential. Examples of drive types include synchronous, synchronous-reluctance, and asynchronous motors.
[0003] According to EP 3 723 273 B1, a method for determining the rotor position of a three-phase drive operated with a frequency converter is known from the prior art, comprising the following steps: a) Providing motor currents in stator coordinates (i α , i β ) as the first input variable of a first computing unit (11), b) Determining motor setpoint voltages in stator coordinates from a current intermediate circuit voltage of the frequency converter and PWM signals (S 1 - S 6 ) and providing the motor setpoint voltages in stator coordinates as the second input variable of the first computing unit (11) and c) Calculating the rotor position (φ) in stator coordinates, wherein starting from the general voltage equation u _ s s = R s ⋅ i _ s s + L s ⋅ d i _ s s dt + ω ⋅ ψ _ s s the rotating field machine in space vector representation a division into the two voltage space vector components u α s = R s ⋅ i α s + L 0 ⋅ di α i dt + L 1 ⋅ di α s dt ⋅ cos 2 φ + di β s dt ⋅ sin 2 φ + L dq ⋅ di β s dt ⋅ cos 2 φ − di φ s dt ⋅ sin 2 φ − ω ⋅ ψ β s − ω ⋅ L dq ⋅ i α s ⋅ cos 2 φ + i β s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i β s ⋅ cos 2 φ − i α s ⋅ sin 2 φ + ω ⋅ L 0 ⋅ i β s u β s = R s ⋅ i β s + L 0 ⋅ di β i dt − L 1 ⋅ di β s dt ⋅ cos 2 φ + di α s dt ⋅ sin 2 φ + L dq ⋅ di α s dt ⋅ cos 2 φ − di β s dt ⋅ sin 2 φ − ω ⋅ ψ α s − ω ⋅ L dq ⋅ i β s ⋅ cos 2 φ + i α s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i α s ⋅ cos 2 φ − i β s ⋅ sin 2 φ + ω ⋅ L 0 ⋅ i α s is carried out, the voltage setpoint space vector ( u α s , u β s ) and the current actual value space vectors (i α , i β ) are converted into a linear system with complex-valued input and output variables and, using the input variables of the first computer unit (11), the rotor position (φ) is determined as the output variable of this system by means of a linear regression analysis.
[0004] Another way to obtain information about the rotor position is to equip the machine with a position sensor. However, this measure increases the cost of the machine. It also increases the probability of failure, as the sensor signal can be corrupted due to interference, for example. In the worst case, the sensor signal can be completely unusable, for example, due to a cable break.
[0005] For this reason, so-called "sensorless" methods are often used. These methods use the motor as a sensor to determine the rotor position from the available electrical signals. Sensorless methods, which are based solely on a fundamental shaft model of the machine, fail at zero speed. At low speeds, they are also inaccurate and can lead to drive instability. For this reason, there are numerous alternative methods that exploit the anisotropy of the motor to determine the rotor position of the motor up to and including zero speed.
[0006] The causes of anisotropy can be explained primarily by two physical effects. First, an asymmetrical rotor structure causes the permeability of the iron material to vary spatially. This leads to the motor's stator inductance being dependent on the rotor position. Second, anisotropy can arise from the motor's magnetization state. This manifestation is then caused by the saturation of the iron material and also leads to a rotor-position-dependent stator inductance.
[0007] Taking anisotropic properties into account, methods for determining engine parameters are also known from the state of the art. These can be divided into different categories.
[0008] For example, methods are known in which a high-frequency test signal is impressed into the motor. This test signal can be implemented as an alternating or rotating space vector. Motor parameters can be extracted by demodulating the high-frequency signal. One such method is disclosed, for example, in DE 10 2017 221 610 A1. DE 10 2017 221 610 A1 relates to a method for field-oriented operation of a converter-fed, permanent-magnet synchronous machine, wherein an estimated rotor position angle and an estimated rotor angular frequency are continuously corrected using a test signal superimposed on a target current space vector.
[0009] The methods in this category have the disadvantage that the test signal is usually continuously impressed, which can lead to considerable noise pollution and increases the losses of the motor.
[0010] Methods are also known that operate without requiring a specific excitation pattern. For example, the motor excitation provided by an existing current and speed control can be used directly. Therefore, under certain conditions, adaptation of motor parameters is possible even without additional test signals. One such method is disclosed, for example, in DE 10 2011 112 647 A1.
[0011] Another distinguishing feature of the methods for determining motor parameters is the type of motor current measurement. In many applications, only the average current over one switching period is required. However, since averaging is complex and expensive, current sampling synchronous with pulse width modulation is usually used. Assuming that the current changes linearly within a switching period, the fundamental oscillation of the motor current can be recorded. A maximum of two measurements per switching period are possible.
[0012] However, it is advantageous to obtain more information about the electrical state within a switching period. For this purpose, a current oversampling method can be used, as described, for example, in EP 3 054 583 A1. Current sampling at up to 20 MHz is known from industrial practice.
[0013] A final distinguishing feature between the various methods for determining speed and / or motor parameters is the reference system in which the calculation is performed. Here, the calculation can be performed in field coordinates (for example, according to EP 3 054 583 A1) or, alternatively, in stator coordinates (for example, according to WO 2017 / 045810 A1).
[0014] The methods listed above for determining speed and / or motor parameters all have in common that they use the so-called space vector representation as the basis for their description. This form of representation allows the consideration of a three-phase system within a more easily handled two-phase system. The space vector representation is obtained by applying the so-called Clarke transformation.
[0015] A disadvantage of these known methods is that they require a separation into the two space vector components to enable calculations. However, a consistently closed-form solution, i.e., determining the speed and / or engine parameters across all speed ranges, is not possible with the space vector representation.
[0016] In summary, various methods are known for determining speed and / or motor parameters. These methods have in common that they only provide reliable values for a specific speed range. For example, the so-called EMF method is typically used, particularly in a comparatively high speed range. However, this method fails in the lower speed range close to zero because the input parameters required to carry out the method are missing due to the lack of rotor speed. This can be compensated for in a cumbersome manner by using test signals or by determining the speed and / or motor parameters based on known operating points and / or motor characteristics.
[0017] It is therefore the TaskThe invention aims to provide a method for determining the speed and / or motor parameters of a rotating field machine operated with a frequency converter, which provides reliable results over the entire speed range.
[0018] To Solution To achieve this object, the invention proposes a method for determining the speed and / or motor parameters of a three-phase drive operated with a frequency converter, which is characterized by the features of claim 1. Features of advantageous embodiments of the invention are specified in the further claims.
[0019] Engine parameters in the sense of the invention, ie engine parameters that can be determined by means of a method according to the invention are in particular the secant inductances L d and L q , whereby the size of these inductances depends on the fundamental current, the transverse inductance L dq , whereby this so-called coupling inductance arises due to cross saturation of the magnetic axes, the tangent inductances L dd and L qq , which result from partial derivatives of the magnetic flux equations, the rotor flux, which arises from the magnets of the permanent magnet synchronous machine and the motor resistance
[0020] The method implementation according to the invention provides, among other things, for the space vector components to be converted into a nonlinear system with complex-valued input and output variables. The method implementation according to the invention thus takes advantage of the fact that the conversion into a nonlinear system with complex-valued input and output variables results in an equation that can be solved as such, without neglecting individual equation terms. The advantageous result is that output variables can be determined for all equation terms based on the previously provided input variables.
[0021] This avoids neglecting individual equation terms in order to generate a solvable equation before determining the desired output variables. Instead, the idea is to generate an equation that is solvable with respect to all terms, so that rejection or neglect only occurs with respect to results obtained as a result of a calculation. This creates a closed system that enables reliable determination of the speed and / or engine parameters across the entire speed range.
[0022] The result of the procedure is that neither test signals nor any operating points or motor properties are required to determine the speed and / or motor parameters. Simply specifying current and voltage values is sufficient.
[0023] The starting point for the procedure is the general voltage equation of a three-phase drive in space vector representation, which is as follows. u _ s s = R s ⋅ i _ s s + L s ⋅ d i _ s s dt + ω ⋅ ψ _ s s
[0024] Taking anisotropy into account, this results in u _ s s = R s ⋅ i _ s s + L αα L αβ L βα L ββ ⋅ d i _ s s dt + 0 − 1 1 0 ⋅ ω ⋅ ψ _ s s − L αα L αβ L βα L ββ ⋅ 0 − 1 1 0 ⋅ ω ⋅ d i _ s s dt with L αα = L dd ⋅ cos 2 φ + L qq ⋅ sin 2 φ − 2 ⋅ L dq ⋅ sin φ ⋅ cos φ L ββ = L dd ⋅ sin 2 φ + L qq ⋅ cos 2 φ + 2 ⋅ L dq ⋅ sin φ ⋅ cos φ L αβ = L dd − L qq ⋅ sin φ ⋅ cos φ + L dq ⋅ cos 2 φ − sin 2 φ = L βα
[0025] For the two space vector components this results in u α s = R s ⋅ i α s + L αα ⋅ di α s dt + L αβ ⋅ di β s dt − ω ⋅ ψ β s − L αβ ⋅ ω ⋅ i α s + L αα ⋅ ω ⋅ i β s u β s = R s ⋅ i β s + L ββ ⋅ di β s dt + L βα ⋅ di α s dt + ω ⋅ ψ α s + L βα ⋅ ω ⋅ i β s − L ββ ⋅ ω ⋅ i α s where L αα = L 0 + L 1 ⋅ cos 2 φ − L dq ⋅ sin 2 φ L ββ = L 0 − L 1 ⋅ cos 2 φ + L dq ⋅ sin 2 φ L αβ = L 1 ⋅ sin 2 φ + L dq ⋅ cos 2 φ = L βα with L 0 = L dd + L qq 2 and L 1 = L dd − L qq 2 so that it results u α s = R s ⋅ i α s + L 0 ⋅ di α s dt + L 1 ⋅ di α s dt ⋅ cos 2 φ + di β s dt ⋅ sin 2 φ + L dq ⋅ di β s dt ⋅ cos 2 φ − di α s dt ⋅ sin 2 φ − ω ⋅ ψ β s − ω ⋅ L dq ⋅ i α s ⋅ cos 2 φ + i β s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i β s ⋅ cos 2 φ − i α s ⋅ sin 2 φ + ω ⋅ L 0 ⋅ i β s u β s = R s ⋅ i β s + L 0 ⋅ di β s dt − L 1 ⋅ di β s dt ⋅ cos 2 φ − di α s dt ⋅ sin 2 φ + L dq ⋅ di α s dt ⋅ cos 2 φ + di β s dt ⋅ sin 2 φ + ω ⋅ ψ α s + ω ⋅ L dq ⋅ i β s ⋅ cos 2 φ − i α s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i α s ⋅ cos 2 φ + i β s ⋅ sin 2 φ − ω ⋅ L 0 ⋅ i α s
[0026] The space vector components determined in this way, ie the voltage setpoint space vectors ( u α s , u β s ) and the current actual value space vectors (i α , i β ) are now converted into a non-linear system with complex-valued input and output variables, in contrast to the EP 3 723 273 B1 mentioned at the beginning. u _ αβ = L d ⋅ 1 2 di α dt + j di β dt + 1 2 di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + L q ⋅ 1 2 di α dt + j di β dt − 1 2 di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + L dq ⋅ j di α dt − j di β dt − ω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + ∂ L d ∂ i d ⋅ i d ⋅ 1 2 di α dt + j di β dt − jω i α + ji β + di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + ∂ L q ∂ i q ⋅ i q ⋅ 1 2 di α dt + j di β dt − jω i α + ji β − di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + ψ p ⋅ jω ⋅ e jωt ⋅ e jφ 0 + R ⋅ i α + ji β
[0027] This provides the advantage of a system with coefficients described by complex numbers, which enables a closed-form solution using, for example, a nonlinear regression analysis. Motor parameters, the speed, and also the position can be determined using a suitable method. The position is implicitly contained in the complex-valued exponential function. Speed and motor parameters are multiplicatively linked to each other and to the exponential function of the position dependence. Therefore, it is a nonlinear system.
[0028] The input variables for the method are motor setpoint voltages transformed into the stator-fixed coordinate system and motor currents also transformed into the stator-fixed coordinate system. The motor setpoint voltages are determined based on the DC link voltage currently applied to the frequency converter and the PWM signals. The motor currents are preferably available as oversampled signals. Depending on the hardware used, sampling rates of up to 1 MHz can be provided. In general, oversampling occurs when the current is sampled more than twice per switching period. At a switching frequency of 8 kHz, this corresponds to 125 measured values per switching period. The measured data is processed without delay, so that the rotor position determined from the calculations can be used for highly dynamic control of the three-phase motor. For this purpose, it is preferable to outsource the calculations to an FPGA.
[0029] The following categorization can be given for the inventive method. Any test signals: Oversampling current measurement with double the switching frequency up to 100 MHz, preferably 32 kHz to 20 MHz, even more preferably 200 kHz to 4 MHz, most preferably 1 MHz, for example. Other sampling rates are also possible. All that is required is that the motor is excited via the PWM signals, and that this excitation is recorded by the current measurement. Determination of the speed and motor parameters in stator coordinates.
[0030] As a result of the method's transformation of the space vector components into a nonlinear system with complex-valued input and output variables, terms are obtained that are multiplicatively related to the speed. Thus, the system is nonlinear with respect to the speed and the motor parameters to be determined. u ^ _ αβ = L d L q L dq L dd L qq Ψ p R T ⋅ f d i _ αβ dt d i _ αβ * dt i _ α , β * ω φ f d i _ αβ dt d i _ αβ * dt i _ α , β * ω φ f d i _ αβ * dt i _ α , β * ω φ f d i _ αβ dt d i _ αβ * dt i _ αβ i _ α , β * ω φ f d i _ αβ dt d i _ αβ * dt i _ αβ i _ α , β * ω φ f ω φ f i _ αβ = W T ⋅ X
[0031] The above equation shows the structure of the proposed complex-valued engine model. The goal is to create a model that has a relationship f between the real- and complex-valued inputs and the complex-valued estimated output. The superscript asterisk indicates a complex conjugation.
[0032] Saturation effects of the motor are taken into account by differential self-inductances (L dd , L qq ) and transverse inductances (L dq ). According to the invention, a suitable recursive method for parameter and state estimation of systems is used as a starting point to determine motor parameters, speed, and position.
[0033] According to a further feature of the invention, the least-mean-squares method, based on a stochastic gradient method, is used as a nonlinear regression analysis search algorithm. It simplifies the so-called steepest-descent algorithm by replacing the expectations of the correlation and cross-correlation matrix with instantaneous estimates. This approximation leads to the following general equations. The three calculations required for one iteration step can be referred to as "filtering," "error estimation," and "parameter vector adaptation." y n = w T n ⋅ x n e _ n = d n − y n w n + 1 = w n + 2 μ ⋅ e _ n ⋅ x n
[0034] The algorithm is intended for use with real-valued parameters and signals. Therefore, the algorithm must be modified to make it applicable to the proposed complex-valued motor model. Additionally, the algorithm must be adapted due to the nonlinear nature of the motor equation. This is achieved by adding partial derivatives of the complex-valued output voltage. u ^ _ αβ n = W ^ T n ⋅ X n e _ n = u _ αβ n − u ^ _ αβ n W n + 1 φ n + 1 ω n + 1 = W n φ n ω n + 2 ⋅ μ ⋅ e _ n ⋅ X * n d u _ ^ αβ * d φ ^ d u _ ^ αβ * d ω ^
[0035] A particular advantage of the least-mean-squares method compared to other regression algorithms is the low computational effort required for the individual iteration steps.
[0036] According to a further feature of the invention, an "extended Kalman filter" algorithm can be used for the calculation instead of the "least mean squares" method. However, the computational effort is higher, making real-time calculation more difficult to implement and requiring appropriate hardware, making the application comparatively expensive.
[0037] For the reasons already explained, the regression analysis provided according to the invention as a suitable recursive method is preferably based on a nonlinear, complex-valued least-mean-square algorithm, which enables the determination of position, speed, and electrical motor parameters in real time. According to the invention, the speed is not determined by differentiating the rotor position. Rather, the rotor position and speed are adapted independently of each other, so that the relationship between rotor position and speed is only indirectly determined.
[0038] According to a further feature of the invention, real-time Max Torque Per Ampere (MTPA) control can also be implemented based on a real-time calculation of the motor parameters. This is enabled by a gradient-based search algorithm.
[0039] Real-time MTPA control is designed to minimize the apparent motor current for a given torque setpoint. The starting point for the derivation is the following equation. M ^ = f I d I q L d L q Ψ p z p
[0040] This equation establishes a relationship f between signals and parameters required for calculating the motor torque and the motor torque. The derivatives of this equation with respect to the actual current components in the field-synchronous reference frame are calculated as follows. ∂ M ^ d ∂ I d = f I d I q L d L q L dq L dd z p ∂ M ^ q ∂ I q = f I d I q L d L q L dq L qq Ψ p z p
[0041] These two equations above must be rearranged to minimize the apparent current ∂ M ^ d ∂ I = ∂ M ^ d ∂ I d ⋅ ∂ I d ∂ I = ∂ M ^ d ∂ I d ⋅ I d 2 + I q 2 I d ∂ M ^ q ∂ I = ∂ M ^ q ∂ I q ⋅ ∂ I q ∂ I = ∂ M ^ q ∂ I q ⋅ I d 2 + I q 2 I q
[0042] The quotient of these two equations is ∂ M ^ d ∂ I ∂ M ^ q ∂ I = ∂ M ^ d ∂ I d ⋅ I q ∂ M ^ q ∂ I q ⋅ I d
[0043] Values greater than one indicate that increasing the reactive current I d would decrease the apparent current for a given motor torque. Values less than one would increase the apparent current. This information can therefore be used for an adaptation algorithm.
[0044] Further features and advantages are evident from the following description based on the only Figure 1 , which shows a current control in a purely schematic representation.
[0045] Figure 1 shows a schematic circuit diagram of a sensorless, field-oriented current control system. The superimposed speed control loop and any position control loop are not shown here for clarity.
[0046] The actual current values required for field-oriented control are measured at the power level using current sensors 6 on a rotating field machine 7. These currents are converted at the signal level using a third coordinate converter 10, so that actual current value space vectors are available in the stator coordinate system. A coordinate rotator connected downstream of the third coordinate converter 10 serves as a second vector rotator 13 in the field-oriented coordinate system. The resulting actual current value space vectors in field coordinates are fed into an adder 1 with the current setpoint space vectors provided by a higher-level speed controller. The actual current value space vector is first inverted for this purpose. The resulting difference between the current setpoint space vector and the actual current value space vector is fed to a control device 2.At the output of this control device 2, a voltage setpoint space vector is available in field coordinates, which is rotated into the stator coordinate system using the first vector rotator 3. A pulse width modulator 4 then calculates the control signals for the power semiconductors in actuator 5 from this voltage setpoint space vector.
[0047] The six control signals provided by the pulse width modulator 4 are transformed into a three-phase voltage system using the first coordinate converter 8 and taking into account the current intermediate circuit voltage of the frequency converter. This first coordinate converter 8 is followed by a second coordinate converter 9, which converts the transformation of this three-phase voltage system into the space vector representation in stator coordinates.
[0048] In a first computing unit 11, the voltage setpoint space vectors from the second coordinate converter 9 and the current actual value space vectors from the third coordinate converter 10 are then converted into a linear system with complex-valued input and output variables.
[0049] In a second computing unit 12, the speed and motor parameters such as the secant inductances L d and L q , the shunt inductance L dq , the tangent inductances L dd and L qq , the rotor flux, and / or the motor resistance are then determined using a nonlinear regression analysis. The rotor position is also determined. This is required for field-oriented control to perform the vector rotation from field coordinates to stator coordinates in the first vector rotator 3. This rotor position is also required to perform the vector rotation from stator coordinates to field coordinates in the second vector rotator 13. Reference symbol
[0050] 1Adder 2Control device 3First vector rotator 4Pulse width modulator 5Actuator 6Current sensor 7Rotating field machine 8First coordinate converter 9Second coordinate converter 10Third coordinate converter 11First arithmetic unit 12Second arithmetic unit 13Second vector rotator
Claims
1. Method for determining the rotational speed and / or motor parameters of a three-phase drive operated with a frequency converter, comprising the following steps: a) providing motor currents in stator coordinates (iα, iβ) as a first input variable of a first arithmetic unit (11), wherein the provision of the motor currents takes place by means of an oversampling current measurement, b) determining set value voltages of the motor in stator coordinates from a current intermediate circuit voltage of the frequency converter and PWM signals (S1 - S6) as well as providing the set value voltages of the motor in stator coordinates as a second input variable of the first arithmetic unit (11), c) calculating the rotational speed and / or motor parameters in stator coordinates, wherein - starting from the general voltage equation u _ s s = R s ⋅ i _ s s + L s ⋅ d i _ s s dt + ω ⋅ ψ _ s s of the induction machine in space vector representation, a division into the voltage space vector components u α s = R s ⋅ i α s + L 0 ⋅ dij α s dt + L 1 . di α s dt ⋅ cos 2 φ + di β s dt ⋅ sin 2 φ + L dq ⋅ di β s dt ⋅ cos 2 φ − di α s dt ⋅ sin 2 φ − ω ⋅ ψ β s − ω ⋅ L dq ⋅ i α s ⋅ cos 2 φ + i β s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i β s ⋅ cos 2 φ − i α s ⋅ sin 2 φ + ω ⋅ L 0 ⋅ i β s u β s = R s ⋅ i β s + L 0 ⋅ di β s dt − L 1 . di β s dt ⋅ cos 2 φ − di α s dt ⋅ sin 2 φ + L dq ⋅ di α s dt ⋅ cos 2 φ + di β s dt ⋅ sin 2 φ + ω ⋅ ψ α s + ω ⋅ L dq ⋅ i β s ⋅ cos 2 φ − i α s ⋅ sin 2 φ + ω ⋅ L 1 ⋅ i α s ⋅ cos 2 φ + i β s ⋅ sin 2 φ − ω ⋅ L 0 ⋅ i α s is carried out and - using the input variable of the first arithmetic unit (11), the rotational speed and / or motor parameter(s) as output variable(s) of this system is(are) determined by means of a suitable recursive process, the method being characterized in that - the voltage setpoint space vectors ( u α s , u β s ) and the current actual value space vectors (iα, iβ) are transferred into a non-linear system with complex-valued input and output variables u _ αβ = L d ⋅ 1 2 di α dt + j di β dt + 1 2 di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + L q ⋅ 1 2 di α dt + j di β dt − 1 2 di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + L dq ⋅ j di a dt − j di β dt − ω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + ∂ L d ∂ i d ⋅ i d ⋅ 1 2 di α dt + j di β dt − jω i α + ji β + di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + ∂ L q ∂ i q ⋅ i q ⋅ 1 2 di α dt + j di β dt − jω i α + ji β − di α dt − j di β dt + jω i α − ji β ⋅ e j 2 ωt ⋅ e j 2 φ 0 + Ψ P ⋅ jω ⋅ e jωt ⋅ e jφ 0 + R ⋅ i α + ji β 2. Method according to claim 1, characterized in that the rotational speed and / or motor parameters is (are) determined by means of a non-linear regression analysis.
3. Method according to claim 2, characterized in that the rotational speed and / or motor parameters is (are) determined by means of a non-linear least mean squares method.
4. Method according to claim 2, characterized in that an extended Kalman filter algorithm is used for the determination of the rotational speed and / or motor parameters.
5. Method according to any of the preceding claims, characterized in that a real-time maximum torque per ampere control (MTPA) is performed.
6. Method according to any of the preceding claims, characterized in that a rotational speed is determined undifferentiated.
7. Method according to claim 6, characterized in that a rotational speed and a rotor position are adapted independently of each other.