Method for identifying parameters of permanent magnet synchronous motor

Abstract

The invention discloses a method for identifying parameters of a permanent magnet synchronous motor, in particular the inductance and resistance of a stator winding and the magnetic flux generated by a rotor magnet, and the method can be used for compensating for the nonlinearity and driving delay of an inverter supplying power to the motor. The method comprises: identifying a steady state of the electric machine (102) and extracting an operating condition of the steady state (104); and, at least when the stator winding resistance and the magnetic flux generated by the rotor magnet are identified, using data of two operating conditions in different steady states, and selecting said operating conditions to minimize the estimation error of the parameter to be identified.

Description

Technical Field

[0001] This invention relates to motors and their control systems, and more specifically, to a method for identifying parameters of a permanent magnet synchronous motor (hereinafter also abbreviated as PMSM, derived from its English name "Permanent Magnet Synchronous Motor"), particularly a method for identifying parameters of an isotropic motor with surface-mount magnets.

[0002] Preferably, but not exclusively, the present invention is applied to identifying parameters of a motor used in a capping device for applying a cap or closure to a container such as a bottle. Background Technology

[0003] At several stages of a motor's lifespan, such as design verification, control system commissioning, operating condition monitoring, and fault diagnosis, it is essential to understand the parameters of a permanent magnet synchronous motor, such as stator winding inductance and resistance, and the magnetic flux generated by the rotor magnets. Given that these parameters can change significantly during the operation of the equipment in which the motor operates, monitoring these changes over time provides invaluable insights for preventative and predictive maintenance, as well as for fault prevention.

[0004] Existing literature reveals various methods for estimating PMSM parameters, which can be broadly categorized into two types: offline methods and online methods.

[0005] The offline method is based on post-hoc processing of data obtained through various motor tests, which typically require the motor to be removed from its host equipment.

[0006] In contrast, the online approach is based on an algorithm executed in real time by the control unit of the electric drive in the device where the motor is located, and utilizes measurement data that is typically available in such drives (phase current, rotor position and speed, and reference values ​​of the supply voltage fed to the inverter), which is collected and processed during normal operation of the motor without removing the motor from its device.

[0007] While offline methods offer high accuracy, their drawbacks include the need for experienced personnel to remove the motor from its host equipment and the use of specialized laboratory instruments. This makes offline methods particularly costly in industrial production environments where multiple motors operate in parallel on different devices. Furthermore, the method requires continuous shutdown of the motor under test for disassembly and reinstallation, which is detrimental to the production efficiency of factories using these motors.

[0008] While existing online methods avoid the aforementioned problems, they themselves have two prominent issues.

[0009] The first problem is that they are difficult to implement from scratch on commercial drives that are not specifically designed for this purpose. In fact, the software of commercial drive control units is often not modifiable to implement customized recognition algorithms. Furthermore, the computational load required for online recognition algorithms may be too large for the control unit.

[0010] The second problem is that the estimation accuracy of online methods is affected by the rank deficiency problem of the identified system and insufficient measurement of the actual voltage applied to the motor.

[0011] Rank deficiency arises because the number of parameters to be identified exceeds the number of motor equations available in each sampling step for the measured quantities (current, position, speed, and voltage), leading to ambiguity in parameter identification. Two different methods have been proposed to address this problem.

[0012] The first approach is based on reducing the parameters to be identified, which is achieved by associating a portion of these parameters with nameplate values ​​or values ​​obtained from other estimations and measurements. However, this first approach is less accurate because it does not account for how these parameters change with variations in motor operating conditions (current, speed, and temperature).

[0013] The second method, which is also the method adopted in this invention, is based on increasing the available equations. For this purpose, it is suggested to use additional data obtained by perturbing the motor's operating point through the injection of current, voltage, or position signals. Such an example is disclosed in CN111030534A. Aside from the fact that signal injection is not always feasible in commercial drive systems, a key problem with this solution is its invasiveness. In fact, signal injection reduces the energy efficiency and control accuracy of the motor driver.

[0014] To address the lack of measurement of the actual voltage applied to the motor, online parameter identification algorithms typically use a reference supply voltage sent to the inverter by the control unit as an estimate of this missing measurement. However, due to inverter nonlinearity and drive delay, a deviation exists between the actual voltage and the reference voltage, potentially introducing non-negligible estimation errors. Theoretically, existing research has shown that inverter nonlinearity can be compensated for by introducing other parameters to be identified into the motor model equations. As the ratio of the motor's electric speed to the inverter's pulse width modulation frequency increases, the deviation caused by drive delay also increases. This problem is generally overlooked in existing literature on online identification methods, but it can lead to significant estimation errors in low-to-medium speed to high-speed applications.

[0015] CN113141140A discloses an online identification method for PMSM parameters of surface-mount magnets, which considers the problems of rank deficiency and drive delay. It addresses the rank deficiency problem by using data obtained under single motor operating conditions. However, this solution is inherently inaccurate because it does not include compensation for inverter nonlinearity. Furthermore, using data obtained under single motor operating conditions cannot minimize the estimation error.

[0016] CN108183648A discloses an online method for identifying PMSM parameters, which can compensate for inverter nonlinearity and drive delay. This method identifies parameters by performing experimental DC tests on the motor and employs a specially designed electric drive control scheme to compensate for inverter nonlinearity. Therefore, this method is invasive and becomes complex and costly due to the need to design new drive control schemes, which often require adjustments based on specific circumstances.

[0017] The paper "PMSM Parameter Identification Considering VSI Nonlinearity and Coupled Adaptive Linear Element Neural Networks (CoupledAdalineNNs)" by BRESCIAELIA et al. (3rd International Conference on Power Electronics and Computer Applications (ICPECA) 2023, IEEE, January 29, 2023, pp. 259-265, XP034319234) discloses a method for identifying parameters of permanent magnet synchronous motors. Other related methods are disclosed in BRESCIAELIAET et al.’s “Automatic Parameter Identification of SPMSM Bistable Systems Using Cloud Computing Resources” (International Conference on Electrical, Computer and Energy Technologies (ICECET) 2021, IEEE, December 9, 2021, pp. 1-6, XP034082182) and LIFUMIN et al.’s “Optimal FOPID Error Voltage Control Dead Zone Compensation for PMSM Servo Systems Based on FOPI Current Control” (International Conference on Fractional Differentials and Their Applications (ICFDA) 2023, IEEE, March 14, 2023, pp. 1-6, XP034362840). Summary of the Invention

[0018] The purpose of this invention is to provide a method for identifying parameters of permanent magnet synchronous motors that solves problems such as rank deficiency, inverter nonlinearity, and drive delay in the prior art.

[0019] To achieve the above objectives, the method employed in this invention includes: identifying the steady state of the motor and extracting the operating conditions of the steady state, namely current, speed, and temperature; wherein, in order to identify at least the stator winding resistance and the magnetic flux generated by the rotor magnet, data from two operating conditions under different steady states are used, and these operating conditions are selected to minimize the estimation error of the parameters to be identified.

[0020] Preferably, the R-statistic algorithm is used for steady-state identification, and the extraction of the operating conditions includes dividing the data of each steady state into a data subset related to a time interval, wherein the motor temperature keeps the parameters related to the motor temperature basically constant within the time interval; for each operating condition, the data of each data subset is used for parameter identification.

[0021] Advantageously, the inverter nonlinear compensation includes identifying a voltage representing this nonlinear effect, hereinafter referred to as the distortion voltage, which is achieved by minimizing the difference between the voltage actually applied to the motor and the reference voltage in all samples of each operating condition under each steady state.

[0022] According to a preferred embodiment of the present invention, minimizing the estimation error of the stator winding resistance and the magnetic flux generated by the rotor magnet includes minimizing the error comprising a first error component and a second error component, wherein the first error component is caused by the difference in resistance and magnetic flux values ​​under two operating conditions; and the second error component is caused by the reference voltage being affected by the drive delay compensation error due to inverter nonlinearity.

[0023] Advantageously, in this case, the first error component is determined by a rough estimate of the stator winding resistance and the magnetic flux generated by the rotor magnets, obtained by using preset values ​​of motor temperature and rotor speed coefficients.

[0024] According to another embodiment of the invention, minimizing the estimation error of the stator winding resistance and the magnetic flux generated by the rotor magnets includes applying a constraint that makes the major portion of the estimation error lower than the expected portion of the corresponding motor parameters, and that the values ​​of the parameters used to evaluate the linear independence of the equations describing the mathematical model of the motor under two selected operating conditions are not close to values ​​indicating a lack of independence in the equations.

[0025] Another object of the present invention is to provide a sealing device actuated by a permanent magnet synchronous motor and controlled by a control system, wherein the control system includes at least one processing unit programmed to perform the method described in the present invention.

[0026] Another object of the present invention is to provide a computer program product that is loaded into the memory of at least one processing unit, particularly belonging to the memory of a processing unit of a control system for a device for sealing containers such as bottles, actuated by a permanent magnet synchronous motor, the program product including software code portions for implementing the above-described method when the program product is executed on at least one processing unit. Attached Figure Description

[0027] These and other features and advantages of the invention will become apparent from the following description of preferred embodiments given by way of non-limiting example, in conjunction with the accompanying drawings, which illustrate an overall flowchart of the method of the invention. Detailed Implementation

[0028] The following describes a parameter identification method using an isotropic PMSM with surface-mounted magnets. This method is based on a static mathematical model of the motor, particularly for the d and q systems. This model only requires measurement data obtained under steady-state operating conditions, i.e., when the motor's absorbed current and speed remain constant over time.

[0029] As described above, the first step 101 of the method of the present invention includes collecting data from the control unit of the electric drive of the motor. As described above, this data is typically available in the PMSM control unit, namely, phase current, rotor angular position and speed, motor temperature, and reference values ​​of the supply voltage provided to the inverter.

[0030] The collected data is used in subsequent step 102 to identify the steady state of the motor. To distinguish between data obtained in steady state and data obtained in transient state, an algorithm called the R-statistic is applied to two different measured variables of the motor, namely the q-axis current and the rotor's mechanical speed ω. r For each sample k, the algorithm independently evaluates whether the two variables are in transient or steady state by using the previous sample kN, where N is chosen by the user. This is used to identify only the mechanical rotational speed ω. r The steady-state R-statistic formula is shown below:

[0031] Where ωr,n represents the measured rotational speed, with a small amount of noise added to improve detection performance. This algorithm is actually designed to analyze variables affected by noise. If If the motor speed is considered to be in a steady state at step k, then Rcrt is an index close to 1 (typically 1.2-1.4), which can be arbitrarily selected by the user through trial and error.

[0032] To facilitate understanding of the subsequent steps of the method, the equations of the discrete-time model of the motor in the d and q coordinate systems are given below: u*d(k)=-Lqω(k)iq(k)-Dd(k)Vdead(1a) u*q(k)=Riq(k)+ψmω(k)-Dq(k)Vdead(1b) Where: k represents the kth sample; u*d and u*q are the reference voltages of the d-axis and q-axis, respectively; iq is the current of the q-axis; ω is the electric speed of the rotor (mechanical speed multiplied by the number of pole pairs); Lq, R, and ψm are the stator inductance, stator resistance, and rotor concatenated magnetic flux of the q-axis, respectively; Vdead, also known as the distortion voltage, is an unknown voltage that takes into account the nonlinearity introduced by the inverter; and the coefficients Dd and Dq are obtained from the literature by studying pulse width modulation inverters, and are functions of phase current and rotor position, and therefore can be calculated from existing measurements.

[0033] According to the present invention, it is also necessary to identify the voltage Vdead in order to compensate for nonlinear phenomena.

[0034] It is important to note that the equation does not include the d-axis current id, because in isotropic motors, this current is typically kept to zero through appropriate control measures: in fact, as those skilled in the art know, in these motors, the current id does not generate torque and therefore does not do any useful work, but only increases power losses, thus reducing motor efficiency. Additionally, there is only one inductive component because in isotropic motors, under magnetic unsaturation conditions, the inductances Ld and Lq of both axes are the same.

[0035] After identifying the steady state, the drive delay is compensated in step 103, that is, the control unit compensates for the delay at time k. The inverter control voltage calculated by Ts is actually at time (k+1.5). The voltage is applied to the motor only after Ts, where Ts is the sampling time of the control unit. This delay is caused by two different reasons. The first reason is related to the digital implementation of the control algorithm, because the voltage calculated at a certain sampling moment is first stored in memory and then sent to the inverter at subsequent sampling moments; therefore, this reason is a pure delay equal to Ts. The second reason is that the inverter needs an average of 0.5 seconds after receiving the voltage in step k+1. The voltage is applied to the motor only after Ts. Due to this drive delay, relating the voltage detected in step k to other variables measured in the same step k in the motor's mathematical model is inaccurate because, as mentioned above, the voltage in step k needs to be 1.5... The voltage is applied after Ts, therefore it is not actually equal to 1.5. The voltage applied after Ts. In fact, the voltage in step k is calculated based on the rotor's electrical position θ(k) at step k; however, when at 1.5... When these voltages are applied after Ts, the rotor will rotate approximately by an angle, which is: Δθ = 1.5.Ts.ω(k) = 1.5(θ(k)) θ(k 1)), Where ω(k) is the electric rotational speed measured in step k. Since θ(k) and θ(k-1) are both known quantities, the rotational angle Δθ is also known.

[0036] Then, compensation for the drive delay includes using the actual applied voltage. d, q is used to replace the reference voltages u*d and u*q, and the actual applied voltage is... d, q is derived from the projection of the reference voltage onto an orthogonal coordinate system by a precise rotation of Δθ. The actual applied voltage... d, The evaluation of q can be calculated using the following rotation matrix:

[0037] in, Both dq and u*dq are column vectors, with the first element being the d-axis voltage and the other element being the q-axis voltage.

[0038] In the subsequent step 104, the motor's operating conditions, namely speed, current, and temperature, are extracted from the steady state. It is important to note that different operating conditions can have the same speed and current values ​​(i.e., they can belong to the same steady state), but will have a certain temperature difference Δθ. However, the operating conditions actually used to identify stator resistance and magnet flux must belong to different steady states for the following reasons. By using two steady states, two sets of equations (1a) and (1b) can be established, resulting in four equations with four unknowns, and the rank deficiency problem can be solved without the aid of signal injection.

[0039] To extract operating conditions, thermal transients must be considered. In fact, the R-statistic algorithm can easily detect only rapid transients, such as electrical or mechanical transients, and, in fact, the current and speed acting on the motor to eliminate measurements obtained during these transients. However, motors are also affected by thermal transients, and their duration is much longer than that of electrical and mechanical transients. Therefore, at each steady state of the motor detected by the algorithm, temperature changes will have a significant impact on the two parameters to be identified (resistance and flux). This means that if the temperature changes, these two parameters will also change in the same steady state. Therefore, it is appropriate to divide the data for each steady state into subsets associated with more or less uniform temperature ranges, within which the two parameters can be considered constant. Then, from these subsets, distinct operating conditions uniquely identified by temperature, current, and speed are obtained. This data on operating conditions will be used to identify the parameters in subsequent steps.

[0040] Given that each steady-state data point needs to be divided into multiple subsets, in order to perform these subsequent steps, it is necessary to calculate the average value of each variable in each subset. , q, , , where θ is the motor temperature.

[0041] Once the operating conditions are extracted, the stator inductance can be immediately identified based on formula (1a) for each operating condition (step 105), where Vdead is not considered. When id=0, Vdead is a periodic function with a mean of zero within the period. Therefore, Lqj=- / j q(3) Where j represents the running condition.

[0042] At this point, Vdead can be identified, and therefore the inverter's nonlinearity can be compensated by solving a minimization problem expressed by the following relation for each operating condition (step 106):

[0043] Where i, h, and j represent the i-th steady state, the h-th subset, and the j-th operating condition, respectively; ksi,h and kei,h represent the first and last samples of the h-th subset under the i-th steady state, respectively. Clearly, combining formula (1a), formula (4) applies the least squares method to the actually applied voltage. The difference between d and the reference voltage u*d. It should be noted that the effectiveness of this method depends on the availability of samples within the DdVdead period. Since the sampling time Ts is fixed, DdVdead decreases as the motor speed increases.

[0044] In the subsequent step 107, R and ψm are identified. As mentioned above, this requires data from two operating conditions, thus yielding two equations (1b). The system of equations consisting of these two equations can be represented in matrix form:

[0045] In this context, the symbols “^” and “-” above the variables represent the estimated value of the variable and the average value obtained after dividing each steady-state data into subsets, respectively; α and β represent the two operating conditions used, which are selected according to the criteria shown below. To solve this system of equations, the two equations must be linearly independent, which means that the determinant of the current and speed matrices in the second end of equation system (5) is not 0, i.e., the following conditions must be met: r = iqαωβ / iqβωα ≠ 1. (6) Obviously, satisfying condition (6) means that the selected operating conditions all belong to different steady states.

[0046] Under the condition that the above conditions are met, substituting equation (6) into equation (1b) corresponding to the two operating conditions, we can obtain R and ψm (or, more specifically, their estimated values) according to the following formula. and m):

[0047] Using the above formula will introduce estimation errors because parameter values ​​typically vary with operating conditions. Therefore, each operating condition may correspond to different resistance and magnetic flux values. Thus, when it is necessary to identify parameters under a specific operating condition α (primary condition), a second operating condition β (auxiliary condition) should be selected to minimize estimation errors as much as possible.

[0048] To account for the dependence of parameters on operating conditions and the errors present in the drive delay and nonlinear characteristics of the compensation inverter, a term εu representing the voltage error can be introduced into Equation (1b) for each operating condition. q Thus we get: q+ q dead=R q+ψm +εuq(8) For simplicity, the operating conditions are omitted in the above formula, and only one equation is written.

[0049] For the resistor, combining equation (8), the error term is decomposed into two components εR and εRM caused by the difference in resistance value under the two operating conditions and the compensation error of the q-axis voltage, respectively. Equation (7a) can be rewritten as: =Rα+εRα+εRM(9a) =Rβ+εRβ+εRM(9b), Right now, The value of is determined by the actual value of R under two operating conditions and by two error terms. These two error terms are given by the following formula:

[0050] Similarly, rewritable magnetic flux The formula for calculating m is determined by the actual value of ψm under two operating conditions, as well as by two error terms caused by the difference in the flux of the turn chain under the two operating conditions and the q-axis voltage compensation error.

[0051] From equation (10) and As can be seen from a similar formula for m, the estimation error depends on the rotational speed ω and the current iq. As mentioned earlier, the purpose of selecting two operating conditions is to minimize the estimation error as much as possible, more specifically, to minimize the major components of the error. Referring to the estimation of R under operating condition α, the major components of this error can be expressed as: Rtot= R+ RM(11) as well as

[0052] in, R and RM is the value of the aforementioned error components, which can be approximated using R and ψm. i, mi(i=α,β) is obtained. These approximate estimates are obtained using only temperature and rotational speed data and are calculated according to the following formula:

[0053] in, 0 and 0 represents the approximate estimated values ​​of R and ψm when the rotational speed is 0 and the temperature is 20℃, respectively; α0 is the temperature coefficient of copper resistivity; 0 represents the assumed second-order frequency coefficient; PM0 is the assumed temperature coefficient of the permanent magnet. uq、 0 and PM0 uses a preventative value to ensure Rtot> R+ RM.

[0054] To obtain 0. The selection of operating conditions α and β must satisfy the following formula:

[0055] Simultaneously, the following constraints must be met:

[0056] Where, flim and rlim are positive adjustment parameters. The derivation of equation (14) is based on: 0 is the estimated value of the resistance in operating condition α. α is obtained by correction. Therefore, it is easy to find the condition α in such a way that the value is... and Since α is close to each other, the temperature and speed in equation (13) are close to 20℃ and 0, respectively. Temperature correction is easier to achieve because α0 is independent of the motor used; however, frequency correction is different because... 0 depends on the motor. To avoid introducing an additional preventative factor into equation (14), it is only necessary to make α is close to 0 (the first constraint condition of equation (14)). Furthermore, the error must be minimized. R and RM should be minimized as much as possible. Since the estimated values ​​of the parameters are unknown, the first of the two errors cannot be explicitly minimized, but it can be reduced by choosing two operating conditions that make the value of |1-r| in the first of Equation (12) larger (the second constraint in Equation (14)). Conversely, by... RM is considered as the objective function to be minimized. Once the operating conditions α and β are selected according to equation (14), the calculation can be performed according to equation (7a). α. Finally, temperature and frequency corrections were performed to obtain... 0:

[0057] Using a similar approach, to obtain The selection of operating conditions α and β must satisfy the following formula:

[0058] Simultaneously, the following constraints must be met:

[0059] Where Θlim is the adjustment parameter; Noc is the total number of operating conditions. Once the operating conditions α and β are selected according to equation (16), they can be calculated according to equation (7b). mβ was finally obtained through temperature and frequency correction. 0:

[0060] The main part of the estimation error of the rotor's coil flux under operating condition β can be calculated using a method described by the stator resistance.

[0061] Once an approximate estimate is obtained, the principal component of the error can be calculated and explicitly minimized. For the resistor R, given a principal operating condition α that needs to be determined, auxiliary conditions β are chosen such that... Rαtot is minimized, that is:

[0062] Simultaneously, the following constraints must be satisfied: r < εr1 or r > εr2, and... Rjtot <xR α. Wherein: εr1 and εr2 are constants that are arbitrarily chosen according to specific circumstances, with the first constant being less than 1 and the second constant being greater than 1. This avoids choosing r too close to 1, thereby effectively ensuring that the equations describing the model under the two operating conditions have linear independence. xR is also an arbitrarily chosen parameter based on specific circumstances, with its value ranging from 0 to 1. This parameter requires that the main part of the error be smaller than a specific part of the approximate estimate of Rα.

[0063] Similarly, the above constraints can only be satisfied when the operating conditions come from different steady states.

[0064] If such auxiliary operating conditions do not exist, i.e., the main part of the error... Rtot is less than For a specific part of α, the estimation results under the main operating conditions can be discarded.

[0065] Once the auxiliary condition β is found, it can be actually identified using formula (7a).

[0066] A similar method can be used to identify the magnetic flux ψm.

[0067] This invention effectively overcomes the shortcomings of existing technologies. In fact, it provides a completely non-invasive method that requires neither experimental testing nor the design of new drive control schemes, but is based solely on the analysis of data generated by a standard drive during normal motor operation. Furthermore, by using data from two operating conditions, it is possible to identify parameter values ​​that effectively ensure the minimization of estimation errors.

[0068] Furthermore, as clearly seen from the foregoing description, this invention does not use nameplate values ​​for parameters. Firstly, this ensures a wider applicability of the method. In fact, in industrial plants involving motors of different specifications and from different manufacturers, obtaining datasheets for all motor models is not easy. This also makes the method more robust. In reality, nameplate values ​​are measured early in the motor's lifespan under specific environmental and operating conditions, which often differ from the actual operating conditions of the motor. Moreover, as the components of the PMSM wear out, its parameters also change over time.

[0069] Obviously, the above description is given only as a non-limiting example, and various changes and modifications can be made to the present invention without departing from the scope of protection of the present invention as defined by the appended claims.

Claims

1. A method for identifying parameters of a permanent magnet synchronous motor, particularly the stator winding inductance and resistance, and the magnetic flux generated by the rotor magnets, the method being used to compensate for nonlinearity and drive delay of an inverter supplying power to the motor, characterized in that: Identify the steady state of the motor (102) and extract the operating conditions of the steady state (104), namely, current, speed and temperature; and identify the parameters using data from two operating conditions under different steady states, and select the operating conditions to minimize the estimation error of the parameters to be identified.

2. The method according to claim 1, characterized in that: Steady-state identification is performed using the R-statistic algorithm (102); and, extracting the operating conditions (104) includes dividing the data of each steady state into a data subset related to a time interval, in which the temperature of the motor keeps the parameters related to the temperature of the motor basically constant; for each operating condition, the data of each of the data subsets is used to identify the parameters.

3. The method according to claim 2, characterized in that: Compensation for the nonlinearity of the inverter (106) includes identifying the voltage representing the effect of the nonlinearity, which is achieved by minimizing the difference between the voltage actually applied to the motor and the reference voltage in all samples of each operating condition under each steady state.

4. The method according to claim 1, characterized in that: Minimizing the estimation error of stator winding resistance and rotor magnet generated magnetic flux includes minimizing the error comprising a first error component and a second error component; wherein the first error component is caused by the difference in resistance and magnetic flux values ​​under two operating conditions, and the second error component is caused by the reference voltage being affected by drive delay compensation error due to inverter nonlinearity.

5. The method according to claim 4, characterized in that: The first error component is determined by a rough estimate of the stator winding resistance obtained using preset values ​​of motor temperature and rotor speed coefficient, and the magnetic flux generated by the rotor magnet.

6. The method according to any one of the preceding claims, characterized in that: Minimizing the estimation error of stator winding resistance and magnetic flux generated by rotor magnets includes employing the following constraints: the major portion of the estimation error is lower than the expected portion of the corresponding motor parameters; and, under the selected two operating conditions, the parameter values ​​of the two equations used to evaluate the linear independence of the mathematical model describing the motor and related to the current and speed under the two operating conditions are not close to a single value representing a lack of independence of the equations.

7. The method according to any one of the preceding claims, characterized in that: Parameters used to identify the permanent magnet synchronous motor used in a device for sealing containers.

8. A capping device driven by a permanent magnet synchronous motor and controlled by a control system, characterized in that: The control system includes at least one processing unit, which is programmed to perform the method described in any of the preceding claims.

9. A computer program product loaded into the memory of a processing unit, particularly belonging to a control system of a device for sealing containers such as bottles, driven by a permanent magnet synchronous motor, characterized in that: The product includes a software code portion that, when executed on the processing unit, enables the implementation of the method as claimed in any one of claims 1 to 7.

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