Permanent magnet synchronous motor multi-parameter online identification method based on double sampling principle

Abstract

The application discloses a permanent magnet synchronous motor multi-parameter online identification method based on a double sampling principle and belongs to the technical field of parameter identification. First, twice current sampling is carried out in a single SVPWM control period of the permanent magnet synchronous motor to obtain two groups of discrete current data. Second, a motor mathematical model is constructed according to the two groups of current data and corresponding voltage signals to form a full rank equation set. Finally, recursive least square method is adopted to perform parameter iterative calculation on the mathematical model to identify the stator resistance, stator inductance and rotor flux linkage parameters of the permanent magnet synchronous motor in real time. The application realizes the expansion of the permanent magnet synchronous motor model equation without additional injection signals, realizes the online simultaneous identification of the motor multi-parameters including the motor stator resistance, stator inductance and permanent magnet flux linkage, and is helpful to the design and implementation of the permanent magnet motor control strategy.

Description

Technical Field

[0001] This invention relates to the field of parameter identification technology, specifically to a method for online identification of multiple parameters of a permanent magnet synchronous motor based on the dual sampling principle. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial drives, electric vehicles, aerospace, and other fields due to their high efficiency, high power density, and excellent dynamic performance. However, accurate identification of motor parameters is a core prerequisite for achieving high-performance control. The stator resistance, stator inductance, and permanent magnet flux linkage of the motor directly affect the stability and efficiency of algorithms such as field-oriented control and model predictive control. Therefore, real-time online parameter identification methods have become a key technology for improving the robustness and adaptability of control systems.

[0003] Currently, high-precision control of permanent magnet synchronous motors relies on the real-time and accurate identification of parameters such as resistance, inductance, and flux linkage. However, during actual motor operation, these parameters can deviate due to factors such as temperature changes, magnetic saturation effects, and current fluctuations. If the control algorithm relies on fixed parameters, it will lead to increased torque ripple, reduced efficiency, and even system instability. Existing online identification methods have significant limitations. For example: 1. Traditional step-by-step identification methods require rotating fixed parameters, leading to error accumulation. 2. While active harmonic injection methods can simultaneously identify multiple parameters, they introduce additional torque ripple and electromagnetic interference, making them difficult to implement, especially at high speeds. 3. Passive methods based on current harmonics, while avoiding signal injection, rely on approximately discrete models and require sampling within the effective vector range where interference is severe, resulting in inaccurate parameter estimation. These shortcomings restrict the dynamic performance and stability of the control system. Therefore, a multi-parameter online identification technology for motors is urgently needed to solve these technical problems. Summary of the Invention

[0004] The purpose of this invention is to provide an online multi-parameter identification method for permanent magnet synchronous motors based on the dual sampling principle, so as to solve the problems mentioned in the background art.

[0005] To address the aforementioned technical problems, this invention provides a method for online multi-parameter identification of permanent magnet synchronous motors based on the dual-sampling principle, comprising:

[0006] The S100 permanent magnet synchronous motor performs two current samplings within a single SVPWM control cycle to obtain two sets of discrete current data.

[0007] Based on the interruption mechanism and the principle of double sampling and single update, the permanent magnet motor model is extended to address the problem of missing rank in the motor model, and a full-rank model is established for parameter identification to achieve simultaneous identification of multiple parameters.

[0008] A permanent magnet synchronous motor is a type of motor that uses the interaction between the static magnetic field generated by a permanent magnet and the torque generated by an electric current to achieve energy conversion. It mainly consists of a rotor, a stator, windings, and magnets. The rotor is composed of permanent magnets and a shaft, while the stator is composed of a series of windings.

[0009] Its working principle is based on the law of electromagnetic induction and the Lorentz force law. When the power is turned on, the magnetic field generated by the current flowing through the stator winding interacts with the magnetic field of the permanent magnet, generating torque according to the Lorentz force law, which makes the rotor start to move.

[0010] It has advantages such as high efficiency, high power density, high torque accuracy, fast response and low maintenance cost, and is widely used in industrial, transportation and home appliance fields.

[0011] The permanent magnet synchronous motor has a surface-mount structure. The two current sampling times are located at the beginning and midpoint of the space vector pulse width modulation (SVPWM) cycle, respectively. Within one SVPWM cycle, a single update means that the SVPWM duty cycle is updated only once using the current signal sampling data at the zero point.

[0012] The dual sampling principle refers to the dual-resistance sampling principle in the phase current detection of permanent magnet synchronous motors. The dual-resistance sampling phase current method involves connecting a sampling resistor in series with any two lower bridge arms of the full-bridge inverter circuit, acquiring voltage signals from both ends of the sampling resistors, passing them through the operational amplifier and AD device at the back end, and then calculating the magnitude of the phase current.

[0013] Typically, sampling is performed during the action of vector V000, when the three-phase upper bridge arms are cut off and the phase current freewheels through diodes. By sampling the freewheeling current, the true phase current can be obtained. Alternatively, sampling can be performed during the first half of the V000 action time in the PWM. After sampling two phase currents, the third phase current is obtained according to the formula Ia+Ib+Ic=0, thus reconstructing the three-phase current. However, dual-resistor sampling has an unobservable region, so the duty cycle of the maximum voltage phase is usually constrained to around 95% to ensure sufficient space for current sampling.

[0014] This approach employs a dual-sampling, single-update strategy, which differs from the traditional single-sampling, single-update SVPWM strategy. In the traditional strategy, sampling is performed only once at the zero point of the triangular carrier wave to obtain u. d u q And update the duty cycle. The dual-sampling strategy proposed in this invention performs sampling operations at the beginning and midpoint of the PWM cycle, respectively. Through these two samplings, two sets of current i can be obtained respectively. d i q information.

[0015] By using a dual sampling method, the sampling of motor current harmonics is avoided, and the motor resistance, inductance, and flux linkage parameters can be identified simultaneously without actively injecting harmonics, instead of identifying the motor resistance, inductance, and flux linkage parameters in turn.

[0016] S200. Based on the two sets of current data and the corresponding voltage signals, construct a mathematical model of the motor and form a full-rank equation system.

[0017] The specific implementation steps include:

[0018] S201. Based on the mathematical model of the motor and the sampled current and voltage signals at the start time, the first set of equations is generated.

[0019] In practical applications, the control of permanent magnet synchronous motors is usually implemented by digital circuits such as digital signal processors (DSPs) or microcontrollers (MCUs). Digital systems can only process discrete digital signals. Describing the permanent magnet synchronous motor model in the discrete time domain allows for easy interface with digital control systems, facilitating the solution and simulation of the motor's operating state through numerical calculation methods.

[0020] The mathematical model of the motor is chosen to be a discrete-time model, and the discrete-time mathematical model of the permanent magnet synchronous motor in the two-phase rotating dq coordinate system is derived as follows:

[0021] ;

[0022] ;

[0023] In the formula: i d i q These are the stator currents of the permanent magnet synchronous motor in a two-phase rotating coordinate system, u d u q These are the stator voltages of the permanent magnet synchronous motor in the dq coordinate system, e d e q These represent the back EMF of the motor under dq conditions, and R. s L is the stator resistance of the motor. s T is the stator inductance of the motor. s To control the period, ω e Let ω be the rotational electric angular velocity of the permanent magnet synchronous motor, and k be a certain moment in the discrete time domain.

[0024] This invention utilizes an accurate discrete model, thus avoiding the impact of modeling errors on the accuracy of parameter identification.

[0025] The first set of equations uses the sampled current signal i at the initial time. d i q and the corresponding voltage u d u q This forms the two traditional motor model equations:

[0026] ;

[0027] In the formula, , , . This refers to the rotor flux linkage of the motor.

[0028] S202. After rotating the voltage signal at the midpoint by half a control cycle, the second set of equations is generated by combining it with the sampled current.

[0029] The second set of equations uses the sampled current signal i at the midpoint. d i q At the same time, the voltage u d u q The values ​​calculated after half a control cycle are combined with these to form a new equation:

[0030] ;

[0031] The rotation of the voltage signal is achieved through coordinate transformation.

[0032] By constructing a second system of equations, the original two equations are expanded to four, thus extending the rank. This enables multi-parameter identification, thereby improving the capability and accuracy of parameter identification and optimizing the overall operational performance and control effect.

[0033] S203. Combine the first and second sets of equations to form a full-rank set of equations.

[0034] This invention achieves the extension of the permanent magnet synchronous motor model equations without the need for additional signal injection, and enables online simultaneous identification of multiple motor parameters, including stator resistance, stator inductance, and permanent magnet flux linkage, which helps in the design and implementation of permanent magnet motor control strategies.

[0035] S300 uses the recursive least squares method to perform parameter iteration calculations on the mathematical model, and identifies the stator resistance, stator inductance and rotor flux linkage parameters of the permanent magnet synchronous motor in real time.

[0036] In the operation and control of permanent magnet synchronous motors, parameter identification refers to the process of determining various electrical and mechanical parameters of the motor. Common parameters that need to be identified include stator resistance, dq inductance, rotor flux linkage, moment of inertia, coefficient of friction, and load torque.

[0037] Accurate parameter identification is crucial for optimizing the performance of motor control systems. It can make control strategies such as vector control and direct torque control of motors more precise, thereby improving motor operating efficiency, dynamic response, and stability.

[0038] Recursive least squares methods include:

[0039] ;

[0040] In the formula, θ(k) is the matrix to be identified, y(k) is the output matrix, φ(k) is the input matrix, K(k) is the gain matrix, and P(k) is the covariance matrix.

[0041] The iterative process includes:

[0042] S301. Initialize the covariance matrix P(k) and the parameter matrix to be identified θ(k). Set the covariance to be a sufficiently large positive real number and the parameter matrix to be identified to be a sufficiently small positive real number.

[0043] S302. Define the input matrix: ;

[0044] Parameter matrix to be identified: ;

[0045] Output matrix: .

[0046] S303. Substitute the input matrix, the parameter matrix to be identified, and the output matrix into the recursive least squares recursive equation to perform recursive operations.

[0047] By iteratively applying the recursive least squares method, the coefficients a, b, and c in the parameter matrix to be identified are obtained, and then substituted into the formula to calculate the parameter values ​​to be identified for the surface-mounted permanent magnet synchronous motor.

[0048] ;

[0049] In the formula, R s and L s These are the stator resistance and stator inductance parameters of the motor to be identified. This enables simultaneous identification of multiple parameters in a surface-mounted permanent magnet synchronous motor.

[0050] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0051] Harmonic-free multi-parameter synchronous identification: By employing a dual-sampling strategy to acquire two sets of discrete current data within a single SVPWM cycle, and combining this with a voltage signal to extend the mathematical model to full rank, simultaneous online identification of stator resistance, inductance, and flux linkage is achieved. This method eliminates the need for traditional active harmonic injection, avoiding additional torque ripple and electromagnetic interference, and is particularly suitable for high-speed scenarios.

[0052] Avoiding step-by-step defects without error accumulation: Traditional step-by-step identification methods require rotating fixed parameters, which leads to error propagation. However, this scheme constructs a complete full-rank equation system and integrates two sets of current and voltage signals to directly complete the synchronous solution of multiple parameters within a single cycle, thus eliminating the problem of accumulated errors in step-by-step iteration.

[0053] Precise discrete model enhances anti-interference capability: The discrete time domain precise modeling of a two-phase rotating coordinate system is adopted, combined with full-cycle voltage rotation compensation, to avoid parameter inaccuracies caused by the reliance on approximate models or sampling in the interference area in traditional methods, thus significantly improving dynamic robustness and identification accuracy.

[0054] Real-time identification efficiency and applicability optimization: Online iterative calculation using the recursive least squares method supports rapid updates of dynamic parameters. The dual-sampling single-update strategy takes into account constraints in the non-observation region, requiring only duty cycle constraints to ensure sampling reliability. It does not rely on complex harmonic decoupling or additional hardware compensation, simplifying the control architecture and improving engineering applicability. Attached Figure Description

[0055] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0056] Figure 1 This is a flowchart illustrating the online multi-parameter identification method for permanent magnet synchronous motors based on the dual-sampling principle of this invention.

[0057] Figure 2 This is a flowchart of the multi-parameter identification process for motors based on the dual sampling principle of this invention.

[0058] Figure 3 This is a schematic diagram of the multi-parameter sampling principle based on the dual sampling principle of the present invention.

[0059] Figure 4 This is a flowchart of the recursive least squares method of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Example 1: Please refer to Figure 1-2 This embodiment provides a method for online identification of multiple parameters of a permanent magnet synchronous motor based on the dual sampling principle, including:

[0062] The S100 permanent magnet synchronous motor performs two current samplings within a single SVPWM control cycle to obtain two sets of discrete current data.

[0063] Based on the interruption mechanism and the principle of double sampling and single update, the permanent magnet motor model is extended to address the problem of missing rank in the motor model, and a full-rank model is established for parameter identification to achieve simultaneous identification of multiple parameters.

[0064] A permanent magnet synchronous motor is a type of motor that uses the interaction between the static magnetic field generated by a permanent magnet and the torque generated by an electric current to achieve energy conversion. It mainly consists of a rotor, a stator, windings, and magnets. The rotor is composed of permanent magnets and a shaft, while the stator is composed of a series of windings.

[0065] Its working principle is based on the law of electromagnetic induction and the Lorentz force law. When the power is turned on, the magnetic field generated by the current flowing through the stator winding interacts with the magnetic field of the permanent magnet, generating torque according to the Lorentz force law, which makes the rotor start to move.

[0066] It has advantages such as high efficiency, high power density, high torque accuracy, fast response and low maintenance cost, and is widely used in industrial, transportation and home appliance fields.

[0067] The permanent magnet synchronous motor has a surface-mount structure. The two current sampling times are located at the beginning and midpoint of the space vector pulse width modulation (SVPWM) cycle, respectively. Within one SVPWM cycle, a single update means that the SVPWM duty cycle is updated only once using the current signal sampling data at the zero point.

[0068] The dual sampling principle refers to the dual-resistance sampling principle in the phase current detection of permanent magnet synchronous motors. The dual-resistance sampling phase current method involves connecting a sampling resistor in series with any two lower bridge arms of the full-bridge inverter circuit, acquiring voltage signals from both ends of the sampling resistors, passing them through the operational amplifier and AD device at the back end, and then calculating the magnitude of the phase current.

[0069] Typically, sampling is performed during the action of vector V000, when the three-phase upper bridge arms are cut off and the phase current freewheels through diodes. By sampling the freewheeling current, the true phase current can be obtained. Alternatively, sampling can be performed during the first half of the V000 action time in the PWM. After sampling two phase currents, the third phase current is obtained according to the formula Ia+Ib+Ic=0, thus reconstructing the three-phase current. However, dual-resistor sampling has an unobservable region, so the duty cycle of the maximum voltage phase is usually constrained to around 95% to ensure sufficient space for current sampling.

[0070] This approach employs a dual-sampling, single-update strategy, which differs from the traditional single-sampling, single-update SVPWM strategy. In the traditional strategy, sampling is performed only once at the zero point of the triangular carrier wave to obtain u. d u qAnd update the duty cycle. See also Figure 3 The dual-sampling strategy proposed in this invention performs sampling operations at the beginning and midpoint of the PWM cycle, respectively. Through these two samplings, two sets of current i can be obtained. d i q information.

[0071] By using a dual sampling method, the sampling of motor current harmonics is avoided, and the motor resistance, inductance, and flux linkage parameters can be identified simultaneously without actively injecting harmonics, instead of identifying the motor resistance, inductance, and flux linkage parameters in turn.

[0072] S200. Based on the two sets of current data and the corresponding voltage signals, construct a mathematical model of the motor and form a full-rank equation system.

[0073] The specific implementation steps include:

[0074] S201. Based on the mathematical model of the motor and the sampled current and voltage signals at the start time, the first set of equations is generated.

[0075] In practical applications, the control of permanent magnet synchronous motors is usually implemented by digital circuits such as digital signal processors (DSPs) or microcontrollers (MCUs). Digital systems can only process discrete digital signals. Describing the permanent magnet synchronous motor model in the discrete time domain allows for easy interface with digital control systems, facilitating the solution and simulation of the motor's operating state through numerical calculation methods.

[0076] The mathematical model of the motor is chosen to be a discrete-time model, and the discrete-time mathematical model of the permanent magnet synchronous motor in the two-phase rotating dq coordinate system is derived as follows:

[0077] ;

[0078] ;

[0079] In the formula: i d i q These are the stator currents of the permanent magnet synchronous motor in a two-phase rotating coordinate system, u d u q These are the stator voltages of the permanent magnet synchronous motor in the dq coordinate system, e d e q These represent the back EMF of the motor under dq conditions, and R. s L is the stator resistance of the motor. s T is the stator inductance of the motor. s To control the period, ω e Let ω be the rotational electric angular velocity of the permanent magnet synchronous motor, and k be a certain moment in the discrete time domain.

[0080] This invention utilizes an accurate discrete model, thus avoiding the impact of modeling errors on the accuracy of parameter identification.

[0081] The first set of equations uses the sampled current signal i at the initial time. d i q and the corresponding voltage u d u q This forms the two traditional motor model equations:

[0082] ;

[0083] In the formula, , , . This refers to the rotor flux linkage of the motor.

[0084] S202. After rotating the voltage signal at the midpoint by half a control cycle, the second set of equations is generated by combining it with the sampled current.

[0085] The second set of equations uses the sampled current signal i at the midpoint. d i q At the same time, the voltage u d u q The values ​​calculated after half a control cycle are combined with these to form a new equation:

[0086] ;

[0087] The rotation of the voltage signal is achieved through coordinate transformation.

[0088] By constructing a second system of equations, the original two equations are expanded to four, thus extending the rank. This enables multi-parameter identification, thereby improving the capability and accuracy of parameter identification and optimizing the overall operational performance and control effect.

[0089] S203. Combine the first and second sets of equations to form a full-rank set of equations.

[0090] This invention achieves the extension of the permanent magnet synchronous motor model equations without the need for additional signal injection, and enables online simultaneous identification of multiple motor parameters, including stator resistance, stator inductance, and permanent magnet flux linkage, which helps in the design and implementation of permanent magnet motor control strategies.

[0091] S300, please refer to Figure 4 The recursive least squares method is used to perform iterative calculation of parameters on the mathematical model, and the stator resistance, stator inductance and rotor flux linkage parameters of the permanent magnet synchronous motor are identified in real time.

[0092] In the operation and control of permanent magnet synchronous motors, parameter identification refers to the process of determining various electrical and mechanical parameters of the motor. Common parameters that need to be identified include stator resistance, dq inductance, rotor flux linkage, moment of inertia, coefficient of friction, and load torque.

[0093] Accurate parameter identification is crucial for optimizing the performance of motor control systems. It can make control strategies such as vector control and direct torque control of motors more precise, thereby improving motor operating efficiency, dynamic response, and stability.

[0094] Recursive least squares methods include:

[0095] ;

[0096] In the formula, θ(k) is the matrix to be identified, y(k) is the output matrix, φ(k) is the input matrix, K(k) is the gain matrix, and P(k) is the covariance matrix.

[0097] The iterative process includes:

[0098] S301. Initialize the covariance matrix P(k) and the parameter matrix to be identified θ(k). Set the covariance to be a sufficiently large positive real number and the parameter matrix to be identified to be a sufficiently small positive real number.

[0099] S302. Define the input matrix: ;

[0100] Parameter matrix to be identified: ;

[0101] Output matrix: .

[0102] S303. Substitute the input matrix, the parameter matrix to be identified, and the output matrix into the recursive least squares recursive equation to perform recursive operations.

[0103] By iteratively applying the recursive least squares method, the coefficients a, b, and c in the parameter matrix to be identified are obtained, and then substituted into the formula to calculate the parameter values ​​to be identified for the surface-mounted permanent magnet synchronous motor.

[0104] ;

[0105] In the formula, R s and L s These are the stator resistance and stator inductance parameters of the motor to be identified. This enables simultaneous identification of multiple parameters in a surface-mounted permanent magnet synchronous motor.

[0106] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0107] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for online identification of multiple parameters of a permanent magnet synchronous motor based on the dual sampling principle, characterized in that: The method includes: S100 permanent magnet synchronous motor performs two current samplings within a single SVPWM control cycle to obtain two sets of discrete current data; The permanent magnet synchronous motor is a surface-mount structure; the two current samplings are located at the beginning and midpoint of the space vector pulse width modulation (SVPWM) cycle, respectively, and the duty cycle signal is updated only at the zero point. S200. Construct a mathematical model of the motor based on the two sets of current data and the corresponding voltage signals, forming a full-rank system of equations; the specific implementation steps include: S201. Based on the mathematical model of the motor and the sampled current and voltage signals at the start time, generate the first set of equations; The mathematical model of the motor is a discrete-time model. The permanent magnet synchronous motor model is described in the discrete-time domain. The operating state of the motor is solved and simulated through numerical calculation methods, and the discrete-time mathematical model of the permanent magnet synchronous motor in the two-phase rotating dq coordinate system is derived: ； ； In the formula: i d i q These are the stator currents of the permanent magnet synchronous motor in a two-phase rotating coordinate system, u d u q These are the stator voltages of the permanent magnet synchronous motor in the dq coordinate system, e d e q These represent the back EMF of the motor under dq conditions, and R. s L is the stator resistance of the motor. s T is the stator inductance of the motor. s To control the period, ω e Let ω be the rotational electric angular velocity of the permanent magnet synchronous motor, and k be a certain moment in the discrete time domain. The first set of equations uses the sampled current signal i at the initial time. d i q and the corresponding voltage u d u q This forms the two traditional motor model equations: ； In the formula, , , ; For the rotor flux linkage of the motor; S202. After rotating the voltage signal at the midpoint by half a control cycle, the second set of equations is generated by combining it with the sampled current. The second set of equations uses the sampled current signal i at the midpoint. d i q At the same time, the voltage u d u q The values ​​calculated after half a control cycle are combined with these to form a new equation: ； The rotation of the voltage signal is achieved through coordinate transformation; S203. Combine the first and second sets of equations to form a full-rank set of equations; S300 uses the recursive least squares method to perform parameter iteration calculations on the mathematical model, and identifies the stator resistance, stator inductance and rotor flux linkage parameters of the permanent magnet synchronous motor in real time.

2. The online multi-parameter identification method for permanent magnet synchronous motors based on the dual-sampling principle according to claim 1, characterized in that: In S300, the recursive least squares method includes: ； In the formula, θ(k) is the matrix to be identified, y(k) is the output matrix, φ(k) is the input matrix, K(k) is the gain matrix, and P(k) is the covariance matrix.

3. The online multi-parameter identification method for permanent magnet synchronous motors based on the dual-sampling principle according to claim 2, characterized in that: The iterative process includes: S301. Initialize the covariance matrix P(k) and the identified parameter matrix θ(k), and set the covariance and the identified parameter matrix to positive real numbers; S302. Define the input matrix: ; Parameter matrix to be identified: ; Output matrix: ; S303. Substitute the input matrix, the parameter matrix to be identified, and the output matrix into the recursive least squares recursive equation to perform recursive operations.

4. The online multi-parameter identification method for permanent magnet synchronous motors based on the dual-sampling principle according to claim 3, characterized in that: By iteratively applying the recursive least squares method, the coefficients a, b, and c in the parameter matrix to be identified are obtained, and then substituted into the formula to calculate the parameter values ​​to be identified for the surface-mounted permanent magnet synchronous motor. ； In the formula, R s and L s These are the stator resistance and stator inductance parameters of the motor to be identified.

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