Method for determining operating state of sensorless motor using signal injection

Abstract

A method of determining an instantaneous operating state of a sensorless controlled electric machine with signal injection comprises injecting an HF supplemental excitation into a drive voltage of the electric machine, thereby modulating a drive current (y) of the electric machine by a modulation signal (z), measuring the drive current (y) of the electric machine, and estimating a state variable (x) of the electric machine using the drive current (y), wherein the estimating step comprises generating a modulation basis (s) from the excitation, multiplying (P1) the drive current (y) by a demodulation basis (r) to obtain a first intermediate signal (ry), multiplying (P2) a transpose (sT) of the modulation basis (s) by the demodulation basis (r) to obtain a second intermediate signal (rsT), applying (F1) a set of finite-length filters to the first intermediate signal (ry), and applying (F2) a set of finite-length filters to the second intermediate signal (ry). And applying (F2) the same set of finite length filters and their moments to the second intermediate signal (rsT) to obtain a system of linear equations (L); the system of linear equations (L) is solved to obtain a modulated signal (z).

Description

Technical Field

[0001] This disclosure relates to sensorless control of a motor using signal injection. This disclosure also relates to a variable speed drive capable of performing said control. In a preferred application, the motor is a rotary AC motor, such as an AC electric motor. Background Technology

[0002] Methods for controlling electric motors (such as rotating AC motors or magnetic bearings) are well known in the art.

[0003] AC electric motors can be controlled, in particular, by a variable speed drive connected to the main unit. Classic voltage / frequency control methods are increasingly being replaced by sensorless control methods, which can control the speed and torque of the electric motor without the need for dedicated speed or position sensors.

[0004] In the context of this disclosure, "sensorless control" does not mean the complete absence of sensors, but rather the absence of some sensors, such as rotor speed or position sensors. "Sensorless control" typically relies on the measurement of the electric current (and potentially the electric voltage). In other words, "sensorless control" relies solely on sensors embedded in the transmission drive.

[0005] Sensorless control of electric motors, particularly electric motors, relies on extracting information from measured current values. One sensorless control technique, particularly suitable for controlling electric motors at low speeds, is based on signal injection and involves superimposing a supplementary high-frequency excitation onto the electric motor's drive voltage. The motor's current response to this supplementary excitation is then extracted from current measurements, and even at low or zero speeds, additional signal processing allows for the retrieval of the motor rotor's speed or angular position.

[0006] Document EP 3 709 500 A1 describes such a technique for sensorless electric motor control via signal injection. In this technique, a finite impulse response filter, made from a linear combination of moving averages, is used to extract the motor's current response to a supplementary excitation. This method relies on the assumption that the supplementary excitation is periodic.

[0007] In the method described in document EP 4 016 831 A1, the supplementary excitation is a high-frequency signal whose frequency varies with time. Preferably, the supplementary excitation is a square wave signal. In order to extract the current response of the motor to such a supplementary excitation with a varying frequency, EP 4 016 831 A1 relies on the calculation of the zero-mean primitive of the supplementary excitation.

[0008] Both EP 3 709 500 A1 and EP 4 016 831 A1 involve so-called "exogenous" signal injection. In exogenous signal injection, the supplementary excitation (high-frequency probe signal) is a well-controlled external signal that is specifically designed to probe electric motors.

[0009] In contrast, the paper "Sensorless rotor position estimation by PWM-induced signal injection" by D. Surroop, P. Combes, P. Martin, and P. Rouxon, The 46th Annual Conference of the IEEE Industrial Electronics Society (IECON 2020), Singapore, 2020, pp. 367-372, doi: 10.1109 / IECON43393.2020.9254909, focuses on so-called "intrinsic" signal injection. This type of signal injection occurs, for example, in applications where the drive voltage of an electric motor is generated by pulse width modulation. Due to the nature of pulse width modulation, current ripple is inherently present in the current response of the motor. This "natural" current ripple is used for sensorless control of electric motors. See their cited paper for more details. Figure 1 The PWM-induced current ripple is extracted from the motor's current response by multiplying it by a known signal and then using a low-pass filter. This process relies on the assumption that the complementary periodic high-frequency excitation of the PWM inducement has a slowly changing shape and suitable mathematical regularity.

[0010] The drawback of the aforementioned known techniques is that they can only be applied when the auxiliary excitation has suitable specific characteristics. These techniques fail when the auxiliary excitation has more general properties, such as when it is caused by pulse width modulation with varying periods, by direct torque control (DTC), or by space vector pulse width modulation, or when the auxiliary excitation has completely aperiodic exogenous properties.

[0011] The following prior art references are cited as general technical background:

[0012]

[0013]

[11] D. Surroop, P. Combes and P. Martin, "Towards an industriallyimplementable PWM-injection scheme," 2021 IEEE International ElectricMachines & Drives Conference (IEMDC), Hartford, CT, USA, 2021, pp. 1-6, doi:10.1109 / IEMDC47953.2021.9449593.

[0014]

[12] Dilshad Surroop, Pascal Combes, Philippe Martin, “Error analysis of a demodulation procedure for multicarrier signals with slowly-varying carriers”, 29th European Signal Processing Conference (EUSIPCO), Dublin,Ireland, 2021, pp. 1636-1640. Summary of the Invention

[0015] In view of the above, the purpose of this disclosure is to provide an improved method for determining the instantaneous operating state of a sensorless controlled motor by signal injection, which can be universally applied to a wide variety of endogenous or exogenous signal injection processes.

[0016] Another objective of this disclosure is to determine the operating status with the best possible accuracy.

[0017] According to this disclosure, these objectives are achieved by a method for determining the instantaneous operating state of a sensorless controlled motor using signal injection, the method comprising the following steps:

[0018] a. Inject high-frequency supplementary excitation into the drive voltage of the controlled motor, thereby modulating the drive current taken up by the controlled motor through the modulation signal;

[0019] b. Measure the instantaneous intensity of the drive current occupied by the controlled motor; and

[0020] c. Use the measured drive current intensity to estimate the instantaneous values ​​of the motor's state variables.

[0021] Step c includes the following sub-steps:

[0022] i. Generate a modulation basis that is mathematically related to the injected supplementary excitation.

[0023] ii. Multiply the measured drive current intensity by the demodulation basis to obtain a first intermediate signal, the demodulation basis being related to the generated modulation basis;

[0024] iii. Multiply the transpose of the generated modulation basis by the demodulation basis to obtain the second intermediate signal;

[0025] iv. Apply a set of m finite-length filters to the obtained first intermediate signal, where m is a positive integer greater than or equal to 2, and apply the same set of m finite-length filters and their first to (m-1) moments to the obtained second intermediate signal to obtain a system of linear equations;

[0026] v. Solve the resulting system of linear equations to obtain at least a modulation signal of the measured drive current intensity; and

[0027] vi. Estimate the instantaneous value of the state variable based on the obtained modulation signal.

[0028] In fact, by relying not only on the finite-length filter but also on the moment of the finite-length filter in the estimation of the motor's state variables, the method of this disclosure allows for sensorless control of the motor using signal injection with different high-frequency supplementary excitations.

[0029] The following features may be implemented, individually or in combination, in the disclosed methods:

[0030] - The demodulation basis is equal to the modulation basis or equal to the windowed version of the modulation basis;

[0031] - The ratio of the length of one finite-length filter to the length of another finite-length filter is less than about 0.8 or greater than about 1.2;

[0032] - The m finite-length filters are sequentially delayed versions of the same finite-length filter;

[0033] - The same finite-length filter is a window function, such as a B-spline function, Hann function, Welch function, or Hamming function;

[0034] - Sub-step v not only generates the modulated signal, but also its first to (m-1)th time derivatives;

[0035] - The motor is a rotating AC motor, such as an AC electric motor;

[0036] - The motor is an AC electric motor, and the state variable is the angular position of the motor's rotor;

[0037] - The motor is a magnetic bearing;

[0038] - The state variable is the gap between the magnetic bearing and the rotating shaft supported by the magnetic bearing.

[0039] This disclosure also relates to a variable speed drive for controlling an AC electric motor, wherein the variable speed drive is configured to perform the methods defined above.

[0040] This disclosure also relates to computer software that includes instructions for implementing the methods described above when the software is executed by a processor.

[0041] This disclosure also relates to a computer-readable non-transitory recording medium on which computer software is stored. Attached Figure Description

[0042] The above and other features, details and advantages of this disclosure are explained in the following detailed description and illustrated in the accompanying drawings, in which:

[0043] Figure 1 This is a schematic diagram showing a variable speed drive according to the present disclosure and a three-phase AC electric motor connected thereto.

[0044] Figure 2 This is a flowchart illustrating how the state variable x of the motor is estimated based on the current measurement y and the modulation basis s in the method of this disclosure.

[0045] Figure 3 yes Figure 2 A variation of the flowchart shows that the modulation basis can come from a signal generator.

[0046] Figure 4 This is a schematic diagram illustrating how the methods of this disclosure can be applied to sensorless control of magnetic bearings using signal injection. Detailed Implementation

[0047] Figure 1 The present disclosure illustrates a method of sensorless control using a three-phase AC electric motor with signal injection as an example. Therefore, in this example, the motor is a rotating AC motor, i.e., an AC electric motor, and the state variable to be estimated is the angular position of the motor's rotor.

[0048] Figure 1A variable speed drive (VSD) 1 is shown, which is connected to a power supply 3 on the input side 2 and to a three-phase AC electric motor M on the output side 4. VSD 1 includes a processor 5 and a memory 7.

[0049] The electric motor M includes the stator S M and rotor R M Rotor R M The angular position x indicates the operating state of the electric motor M. The three phases of the electric motor M are represented by the letters a, b, and c.

[0050] The operation of the electric motor M, particularly its speed or torque, is controlled by VSD 1 according to a given control law. To this end, VSD 1 converts the three-phase power supply voltage Us provided by power supply 3 into a three-phase drive voltage Ud = (Uda, Udb, Udc) to drive the electric motor M. VSD 1 performs sensorless control of the electric motor M. This means that VSD 1 only monitors the three-phase drive current y = (ya, yb, yc) occupied by the electric motor M and adjusts the drive voltage Ud accordingly to conform to the given control law. Sensorless control involves injecting a high-frequency supplementary excitation e into the drive voltage Ud. HF .

[0051] As part of sensorless control, VSD 1 continuously determines the instantaneous operating state of the electric motor M. In a given example, this means that VSD 1 continuously determines the rotor R M The instantaneous value of the angular position x.

[0052] Determining the instantaneous operational state includes the following steps:

[0053] a. High-frequency supplementary excitation e HF Injected drive voltage Ud;

[0054] b. Measure the instantaneous intensity of the driving current y;

[0055] c. Use the measured drive current intensity to estimate the instantaneous value of the rotor's angular position x.

[0056] The effect of step a is the modulation of the drive current y. Therefore, the drive current y can be written as follows:

[0057] Equation 1: y(t, t / ε) := s T (t, t / ε)z(t),

[0058] Where s is the modulation basis, z is the modulating signal, t is time, and ε is a small parameter. HF And it can be calculated from it. The modulation basis s is the supplementary excitation e. HF The zero-mean primitive.

[0059] According to this disclosure, step c (i.e., estimating the angular position x using the drive current y) follows the method described by... Figure 2 The specific process shown is used to complete this.

[0060] from Figure 2 As can be seen, the specific process of this disclosure is divided into four consecutive steps, labeled Step 1, Step 2, Step 3, and Step 4. This process is actually an algorithm that takes three variables as input.

[0061] The first input variable is y(t, t / ε), which corresponds to the measured driving current intensity.

[0062] The second input variable is r(t, t / ε), which is the demodulation basis. This demodulation basis r is related to the modulation basis s. The demodulation basis r can simply be chosen to be equal to the modulation basis s. Alternatively, the demodulation basis r can also be a windowed version of the modulation basis s.

[0063] The third input variable is s T (t, t / ε), which is the transpose of the modulation basis s.

[0064] Step 1 is a multiplication step, which involves two multiplications. In one multiplication, denoted as P1, the current intensity y is multiplied by the demodulation basis r to obtain the first intermediate signal ry. In the other multiplication, denoted as P2, the transpose s of the modulation basis s... T Also multiply by the demodulation basis r to obtain the second intermediate signal rs T .

[0065] Step 2 is the filtering step, which filters the two previously obtained intermediate signals ry and rs. T As input, each intermediate signal is filtered individually.

[0066] like Figure 2 As shown in box F1, a set of m finite-length filters is applied to the first intermediate signal ry. In this context, m is a positive integer greater than or equal to 2.

[0067] like Figure 2 As shown in box F2, the same set of m finite-length filters and their first to (m-1)th moments are applied to the second intermediate signal rs. T .

[0068] The finite-length filter for each application is defined by a time function F(t), called its kernel, also known as the impulse response. To apply a finite-length filter to a signal g(t), the kernel F of the filter is convolved with the signal g(t), which is written as... .

[0069] The k-th moment (k is a positive integer) of a finite-length filter is another finite-length filter whose kernel F [k] Defined as

[0070] Equation 2 F [k] = t k F(t).

[0071] Preferably, in the group of m finite-length filters, the ratio of the length of one finite-length filter to the length of another finite-length filter is less than about 0.8 or greater than about 1.2.

[0072] m finite-length filters can be sequentially delayed versions of the same finite-length filter. In this case, the same finite-length filter can be a window function, such as a B-spline function, a Hann function, a Welch function, or a Hamming function.

[0073] The result of filtering is a system of linear equations; see [link / reference]. Figure 2 The box L in the middle.

[0074] Step 3 of the process includes solving the obtained system of linear equations to obtain at least the modulation signal z. For example... Figure 2 As shown, solving the linear equation system L can also generate the first to (m-1)th time derivatives of the modulated signal z. .

[0075] Step 4 of the process estimates the instantaneous value of the state variable x based on the obtained modulation signal z. A known algorithm exists to perform step 4, therefore further description of this step will be omitted.

[0076] Now go to Figure 3 The above process can be executed by a digital signal processor (DSP), a field-programmable gate array (FPGA), or an application-specific integrated circuit (ASIC). The DSP, FPGA, or ASIC can be... Figure 1 Part of VSD 1.

[0077] As from Figure 3 It is also evident that the demodulation basis r and the transpose s of the modulation basis s are... T This can be generated by a signal generator G, which receives a clock signal CK as input. The signal generator G can also generate supplementary excitation e. HF .

[0078] Turn now Figure 4 The method disclosed herein can also be applied to sensorless control of the magnetic bearing B using signal injection. In this example, the magnetic bearing B includes a support ring 9 and a set of circumferential electromagnetic coils 11 disposed on the support ring 9. The rotating shaft A is supported by the magnetic bearing B by suspension.

[0079] The controller 13 provides a drive voltage Ud to the electromagnetic coil 11, causing the rotating shaft A to remain centered on the magnetic bearing B. This is equivalent to maintaining a sufficient gap x between the rotating shaft A and the magnetic bearing B. The gap x is a state variable estimated using the method of this disclosure.

[0080] To optimize the sensorless control of magnetic bearing B, a high-frequency supplementary excitation e is injected into the drive voltage Ud. HF .

[0081] A current sensor (not shown) continuously measures the instantaneous intensity y of the drive current drawn by the electromagnetic coil 11. These measurements are fed into the gap estimator 15. The gap estimator 15 performs... Figure 2 The process involves four steps to estimate the instantaneous value of the gap x. This estimate is then output to controller 13. Based on this output, controller 13 adjusts the drive voltage Ud to maintain the required gap.

[0082] The following is an additional description of the procedures used in the methods of this disclosure:

[0083] Process Description

[0084] We propose a process for demodulating composite signals.

[0085]

[0086] in And s are of size The vector function, and It is a small parameter; s T It is the transpose of s. The components of s, known as the modulation basis, will be considered as a fast-oscillating carrier with a slowly changing shape, by Slowly varying component modulation.

[0087] The goal is to recover the y and s at each time t using only the knowledge of y and s on [0, t]. The accuracy is , where m is any positive integer; O denotes the "Big O" notation for analysis, i.e., for some K independent of t and s, if ,but .

[0088] The main novelty lies in the fact that carriers can be quite common, provided they are exciting enough in some sense. In particular, they do not need to be periodic in the second variable as in other methods, nor do they enjoy regularity.

[0089] An interesting feature of this process is that it not only covers the signal Moreover, it covers its derivative. Each has a precision .

[0090] When the composite signal y is of magnitude The process is equally effective even when disrupted by minor disturbances.

[0091] It is also easily applicable to composite signals. This refers to the case where the signal is a vector or matrix signal rather than a scalar signal.

[0092] The process includes the following three steps, detailed below.

[0093] 1) Multiplication steps:

[0094] 1a) Composite signal Multiplying by a vector function whose dimension n is the same as and related to the modulation basis s is called the demodulation basis. This produces an n × 1 vector signal.

[0095] 1b) will transpose multiplied by This generates an n × n matrix signal. .

[0096] 2) Filtering steps:

[0097] 2a) For vector signals Apply a previously obtained set of m sufficiently distinct finite-length filters and stack them into an mn × 1 vector signal.

[0098] 2b) Applied to matrix signals The same set of m filters and their first m-1 moments obtained previously are arranged into an mn × mn matrix signal.

[0099] 3) The mn × 1 vector signal and the mn × mn matrix signal obtained in the previous stage constitute the mn unknown at each time t. The linear mn equation system, until Error; if the modulation basis s is sufficiently excited, the system of equations can be solved, which provides the desired error. The precisions are respectively .

[0100] In the first step of this process, the simplest procedure is to select a demodulation base r equal to the modulation base s. However, different choices are possible, provided that r is sufficiently correlated with s: for example, when the composite signal y is corrupted by a large disturbance with a known temporal location (e.g., a commutation transient in a switching power electronics device), it is advantageous to select a windowed version of s for r in order to discard the corrupted data.

[0101] In the second step of this process, m sufficiently different finite-length filters must be selected. In this case, "sufficiently different" basically means that their length ratio is not too close to 1 (typically less than 0.8 or more than 1.2). On the other hand, to ensure the recovery... Precision, filter length must be Longer lengths, for example It will still work, but at the cost of lower recovery accuracy. Otherwise, any filter sufficient to suppress all frequencies except zero will do. The trade-off is to make the filter long enough for good frequency suppression, but not too long to avoid losing accuracy in recovery. Well-performing filter choices are as follows: The first filter, F1, is a typical window function used in signal processing (B-spline, Welch, Hann, Hamming, etc.), with a length of... ,in The second filter, F2, is delayed. (A portion) of the F1 version; the third filter F3 is delayed. (A portion) of the F2 version, and so on.

[0102] In some applications, such as signal injection, the vector signal to be recovered according to The power of "gradation" is as follows:

[0103]

[0104] in It is the size of The vector function. If we use the standard demodulation procedure, only In the middle mn0+(m-1)n1+…+2n m-2 +n m-1 and its derivative from The data was correctly restored; "correctly restored" means that there was an error during the restoration process. Or better yet. This is a waste of computational power because the process involves filtering in the second step. Scalar signal, and solve for its size in the third step. A linear group.

[0105] However, due to the hierarchical structure, the dimensionality can be reduced by a simple modification to the standard process: in fact, only mn0 + (m-1)n1 + ... + 2n is filtered in the second step. m-2 +n m-1 Appropriate selection of scalar signals produces signals with dimensions of mn0 + (m-1)n1 + ... + 2n. m-2 +n m-1The system produces a linear set of equations mn0 + (m-1)n1 + ... + 2n that can be correctly recovered by standard procedures. m-2 +n m-1 The quantity is large, but the amount of calculation is much smaller.

[0106] Adapting to discrete time cases

[0107] This process is easily applicable to discrete-time scenarios. If the signal is not continuous-time... and We only know their discrete-time versions. and T s If it is the sampling time, the process is as follows:

[0108] 1) Multiplication steps:

[0109] 1a) Discrete-time signals Multiplied by a discrete-time vector function of the same dimension n as the modulation basis s

[0110] 1b) will transpose multiplied by This generates an n×n matrix signal. .

[0111] 2) Filtering steps:

[0112] 2a) Apply the previously obtained set of m sufficiently different finite-length filters to the vector signal And stack them into an mn × 1 vector signal.

[0113] 2b) Take the matrix signal of the same set of m filters and their first m-1 moments obtained earlier. And arrange them into an mn × mn matrix signal.

[0114] 3) The mn × 1 vector signal and the mn × mn matrix signal obtained in the previous stage constitute mn unknowns at each time t. The system of mn linear equations in the equations, until... Error; if the modulation basis s is sufficiently excited, the system of equations can be solved, which provides respectively having The required precision of the discrete-time signal .

[0115] Note that finite-length discrete-time filters are often referred to as finite impulse response (FIR) filters. All comments made in the continuous-time case remain valid after obvious adaptations.

[0116] A key feature of this process is that it is, in a sense, unaffected by aliasing: even for discrete-time signals... and Significant spectral folding exists as long as the discrete-time carrier maintains sufficient excitation. Therefore, an anti-aliasing filter is not required before sampling the continuous-time signal. Furthermore, this allows for fairly coarse sampling, i.e., a sampling time T that is much shorter than the filter length used in the second step of the process. s It's not that small.

[0117] Potential uses of the program

[0118] In the context of signal injection, the composite signal y described above is encountered in the control of the motor:

[0119] 1) When an external periodic excitation is injected for sensorless control of an electric motor [2] (so-called "external signal injection"); in this case, the measured current exhibits some small, rapidly changing ripple, i.e., has the following form

[0120]

[0121] in It is periodic. More generally, if the shape of the excitation signal is essentially periodic, but also changes slowly, then the measured current has the following form.

[0122]

[0123] In the second variable, s1 is periodic.

[0124] 2) Similarly, when an external non-periodic excitation is injected for “sensorless” control of an electric motor

[10] ; in this case, the measured current also has the following form

[0125]

[0126] in The second variable is bounded, but not periodic. Note that while this expression is formally similar to the periodic case, the mathematical proof is far more complex.

[0127] 3) When using current ripple generated by constant period PWM (so-called "intrinsic signal injection") [3]; in this case, the measured current has the following form

[0128]

[0129] In the second variable It is periodic.

[0130] 4) Similarly, when utilizing current ripple generated by a non-constant period PWM; in this case, the measured current has the following form

[0131]

[0132] in The second variable is bounded, not periodic. Note that while this expression is formally similar to the periodic case, the mathematical proof is far more complex. More generally, any type of rapidly changing modulation of the input voltage, such as singular PWM, is... Modulation, DTC, etc., will result in this form of current.

[0133] Depending on the measurement quality, higher-order expansions can also be used [4]. For example, the second-order expansion of the measured current.

[0134] ,

[0135] in With Same attributes.

[0136] The above-mentioned signal injection techniques all rely on the composite signal y and the carrier wave. Knowledge estimation signal The possibility. In fact, due to The additional information provided allows the motor's state to be recovered using only current measurements. Due to this invention, Even their derivatives can be determined with the best possible accuracy.

[0137] The scope of this invention is not limited to the control of electric motors, but potentially covers many engineering applications, particularly in the field of electromechanical systems [7]; in fact, the invention can be considered a fundamental building block in signal processing. Therefore, it can be used in any application involving the extraction of information modulated by a periodic function. This includes, in particular:

[0138] • Other applications using signal injection [7]

[0139] • Extract harmonics at known frequencies (RMS value calculation, THDI calculation in sensors). Once these values ​​have been calculated, they can be used for monitoring (e.g., energy consumption) or assessing compliance with electromagnetic compatibility regulations.

[0140] This disclosure is not limited to the embodiments described herein, which are merely examples. This disclosure covers every alternative that will be conceived by those skilled in the art as covered by the appended claims.

Claims

1. A method for determining the instantaneous operating state of a motor (M) for sensorless control using signal injection, the method comprising the steps of: a. High-frequency supplementary excitation (e) HF The driving voltage (Ud) applied to the controlled motor (M) is injected, thereby modulating the driving current occupied by the controlled motor (M) through the modulation signal (z); b. Measure the instantaneous intensity (y) of the drive current drawn by the controlled motor (M); and c. Use the measured drive current intensity (y) to estimate the instantaneous value of the state variable (x) of the motor (M). Step c includes the following sub-steps: i. Generating mathematically complementary stimuli (e) HF The related modulation basis(s); ii. Multiply the measured drive current intensity (y) by the demodulation basis (r) (P1) to obtain a first intermediate signal (ry), the demodulation basis (r) being related to the generated modulation basis (s); iii. Transpose the generated modulation basis(s) T The signal is multiplied by the demodulated basis (r) (P2) to obtain the second intermediate signal (rs). T ); iv. Apply a set of m finite-length filters (F1) to the obtained first intermediate signal (ry), where m is a positive integer greater than or equal to 2, and apply the same set of m finite-length filters and their first to (m-1) moments (F2) to the obtained second intermediate signal (rs). T ), to obtain a system of linear equations (L); v. Solve the obtained system of linear equations (L) to obtain at least the modulation signal (z) of the measured drive current intensity (y); and vi. Estimate the instantaneous value of the state variable (x) based on the obtained modulation signal (z).

2. The method according to the preceding claim, wherein the demodulation basis (r) is equal to the modulation basis (s) or equal to a windowed version of the modulation basis (s).

3. The method according to any one of the preceding claims, wherein the ratio of the length of one finite-length filter to the length of the other finite-length filter is less than about 0.8 or greater than about 1.

2.

4. The method according to any one of the preceding claims, wherein the m finite-length filters are sequentially delayed versions of the same finite-length filters.

5. The method of claim 4, wherein the same finite-length filter is a window function, such as a B-spline function, a Hann function, a Welch function, or a Hamming function.

6. The method according to any one of the preceding claims, wherein sub-step v generates not only the modulation signal (z), but also its first to (m-1)th time derivatives.

7. The method according to any one of the preceding claims, wherein the motor is a rotary AC motor, such as an AC electric motor (M).

8. The method according to claim 7, wherein the motor is an AC electric motor (M), and the state variable (x) is the rotor (R) of the electric motor. M The angular position of ).

9. The method according to any one of claims 1 to 6, wherein the motor is a magnetic bearing (B).

10. The method according to claim 9, wherein the state variable (x) is the gap between the magnetic bearing (B) and the rotating shaft (A) supported by the magnetic bearing.

11. A variable speed drive (1) for controlling an AC electric motor (M), wherein the variable speed drive (1) is configured to perform the method according to any one of claims 1 to 8.

12. A computer software comprising instructions which, when executed by a processor (5), are used to implement the method according to any one of claims 1 to 10.

13. A computer-readable non-transitory recording medium (7) storing the computer software according to claim 12.

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