Offline flux-linkage and moment-of-inertia identification method for permanent magnet synchronous motor

Abstract

An offline flux-linkage and moment-of-inertia identification method for a permanent magnet synchronous motor, the method comprising: on the premise that a pole-pair number Pn, a stator resistance Rs, and a stator inductance Ls of a motor are known, tuning PI parameters of a current loop and a speed loop; in a dual closed-loop mode for current and speed, identifying the flux linkage of the motor by using a recursive least squares method with a forgetting factor; in a current closed-loop mode, injecting a low-frequency current signal having progressively increasing amplitude and frequency, and determining a current magnitude required to start the motor and rotate same to a preset rotation speed threshold; and using acceleration / deceleration methods to identify the moment of inertia of the motor, wherein the motor is rotated forward and backward and identification is performed multiple times, and a median value is obtained by ranking to improve identification accuracy. The flux-linkage and moment-of-inertia identification processes are simple, stable, and reliable, the accuracy of identification results is high, one-click parameter identification can be achieved, and the method has a wide range of applications and is applicable to permanent magnet synchronous motors with various parameters.

Description

An offline method for identifying flux linkage and moment of inertia of permanent magnet synchronous motors Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to an offline permanent magnet synchronous motor flux linkage and moment of inertia identification method. Background Art

[0002] As one of the supporting technologies for modern industrial automation and motion control, servo control systems, with their high-precision control performance, high dynamic performance, and wide range of applications, are widely used in industrial fields such as machine tools, textiles, robotics, and robotics, as well as in military fields such as aviation, aerospace, and marine. The accuracy of motor parameters is crucial for stable and efficient drive systems. Advanced control strategies such as predictive control, parameter self-tuning, and sensorless position control require prior knowledge of the motor's intrinsic parameters. Therefore, parameter identification of permanent magnet synchronous motors has been a research focus for scholars both domestically and internationally.

[0003] Magnetic flux and moment of inertia are the primary parameters influencing the speed loop controller. Magnetic flux is also often used in current loop decoupling compensation and back-EMF compensation, playing a crucial role in PMSM control systems. There are two primary methods for identifying magnetic flux and moment of inertia: offline and online. Online inertia identification offers high precision and speed, but it does not require the motor to be in a specific state to determine the required inertia value. When the motor system is in normal operation, an online identification algorithm can be used to accurately identify the value. Offline identification offers the advantages of simple structure, ease of implementation, and stability and reliability. It is the mainstream method in industrial applications where accuracy and dynamic performance are not critical. However, offline methods are not currently widely used.

[0004] Summary of the Invention

[0005] The purpose of the present invention is to provide an offline permanent magnet synchronous motor flux linkage and moment of inertia identification method to address the deficiencies of the prior art. n , stator resistance R s , stator inductance L s Under the premise of accurate identification, the least squares method with a forgetting factor is used to identify the flux linkage offline in the speed closed-loop mode. In the current closed-loop mode, the acceleration and deceleration method is used to identify the motor's moment of inertia offline. This invention accurately and reliably identifies the parameters of permanent magnet synchronous motors and has universal applicability.

[0006] The technical solution to achieve the purpose of the present invention is: an offline permanent magnet synchronous motor flux and moment of inertia identification method, the method comprising:

[0007] Step 1: In the speed closed-loop mode, the motor flux is identified offline using the recursive least squares method with forgetting factor.

[0008] Step 2: In the current closed-loop mode, use the acceleration and deceleration method to identify the motor's moment of inertia offline.

[0009] Furthermore, step 1 specifically includes the following steps:

[0010] Step 1-1, according to the quadrature-axis stator voltage equation of the motor:

[0011] When the motor speed and load remain unchanged, Also adopt i d = 0 current control strategy, ignore Item and i d Item, formula (1) can be arranged as follows: q =R s i q +ω e ψ f (2)

[0012] Among them, u q is the motor quadrature axis voltage, R s is the stator resistance, i q is the quadrature axis current, i d is the excitation current, L s is the stator inductance, ω e is the motor angular velocity, ψ f is the permanent magnet flux linkage;

[0013] Step 1-2, use the recursive least squares method with forgetting factor to identify the flux linkage, establish the least squares model of the permanent magnet synchronous motor, and determine the output u q 、i q 、R s , the parameter to be identified is ψ f , the observation matrix is ​​ω e , then the least squares equation is as follows:

[0014] Among them, ψ k is the permanent magnet flux at the current moment, ψ k-1 is the permanent magnet flux at the previous moment, is the gain at the current moment, u qk 、i qk They are the quadrature-axis voltage and quadrature-axis current of the motor at the current moment, R k The motor stator resistance at the current moment;

[0015] Steps 1-3: Adjust the normalized PI parameters of the current loop and speed loop, and identify the motor flux in the speed and current dual closed-loop mode.

[0016] Furthermore, the recursive least squares method in steps 1-2 specifically includes:

[0017] For an observable system, its n sets of input and output observation data are expressed as: {y(k),u(k),k=1,2,3…,n}; where y(k),u(k) are the kth set of input and output observation data respectively;

[0018] Assume that the input and output of the system are expressed as:

[0019] Among them, y(k) is the output matrix of the system corresponding to the kth group of input and output observation data, is the observable matrix corresponding to the k-th group of input and output observation data, θ(k) is the matrix of parameters to be identified corresponding to the k-th group of input and output observation data, and ε(k) is the random variable matrix with an average value of 0 corresponding to the k-th group of input and output observation data;

[0020] The objective function of the system J(θ) is constructed as:

[0021] Let its partial derivative be 0, then the recursive least squares method is expressed as:

[0022] Among them, P(k) and P(k-1) are the covariance matrices corresponding to the k-th and k-1-th groups of input and output observation data, respectively; K(k) is the gain matrix corresponding to the k-th group of input and output observation data; θ(k-1) is the matrix of the parameters to be identified corresponding to the k-1-th group of input and output observation data;

[0023] As long as we can get y(k) and You can start the recursive least squares method, and the identification result is θ(k);

[0024] Combining equations (2) and (4), the output matrix of the flux identification system y(k) = u qk -i qk R k 、Parameter to be identified θ(k)=ψ k , observation matrix Thus, the least squares recursive equation for flux linkage identification of formula (3) is obtained.

[0025] Furthermore, the recursive least squares method in step 1-2 introduces a forgetting factor, specifically including:

[0026] Introducing the forgetting factor λ, the covariance matrix and gain matrix of the least squares method in formula (6) are updated as follows:

[0027] Furthermore, the steps 1-3 of adjusting the normalized PI parameters of the current loop and the speed loop specifically include:

[0028] Establish the transfer function G of the PI controller pi (s) is:

[0029] The PI parameters of the current loop closed loop are set as follows:

[0030] The closed-loop PI parameters of the speed loop are tuned as follows:

[0031] Among them, K p is the proportionality coefficient, K i is the integration coefficient, K pCur , K iCur They are the proportional coefficient and integral coefficient of the current loop controller, K pVel , K iVel They are the proportional coefficient and integral coefficient of the speed loop controller, ω c is the current loop cutoff frequency, T s is the current loop control period, I N 、U N 、n N They are the motor rated current, rated voltage and rated speed.

[0032] Furthermore, step 2 specifically includes the following steps:

[0033] Step 2-1, given a sinusoidal quadrature-axis current i with increasing amplitude and frequency qref , determine the current required to start the motor and rotate to the set threshold;

[0034] Step 2-2, according to the mechanical motion equation of the motor:

[0035] Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient;

[0036] In T e and 1.5 times T e When the motor is constantly accelerating, convert equation (11) into:

[0037] Take ω2=ω4, ω1=ω3, then ω 12 Approximately equal to ω 34 According to formula (12), the moment of inertia can be calculated as follows:

[0038] Among them, t1 and t2 are the electromagnetic torque T e At the moment of acceleration to the mechanical angular velocity ω1, ω2, t3 and t4 are respectively the electromagnetic torque 1.5T e When the acceleration reaches the mechanical angular velocity ω3, ω4, ω 12 is the difference between the mechanical angular velocities ω1 and ω2, ω 34 is the difference between the mechanical angular velocities ω3 and ω4;

[0039] Step 2-3, according to the electromagnetic torque equation of the motor:

[0040] Adopt i d =0, the current control strategy is written as:

[0041] Among them, P n is the number of pole pairs of the motor;

[0042] Combining equations (13) and (15), the motor moment of inertia is calculated by equation (16):

[0043] Furthermore, the sinusoidal quadrature-axis current i qref The current required to set the threshold value I q The relationship is: i qref =I q sin(2πf0·n) n=1,2,3…

[0044] Where f0 is the initial frequency of the current.

[0045] Furthermore, in step 2-2, the e and 1.5 times T e The motor is made to rotate at a constant acceleration to identify the moment of inertia, specifically including:

[0046] 1) First acceleration stage: given i qref =I q , so that the motor is constantly accelerated to the set speed threshold, and the time t1 and t2 corresponding to the speed ω1 and ω2 are recorded;

[0047] 2) First deceleration stage: given i qref =0, making the motor decelerate to 0;

[0048] 3) Second acceleration stage: given i qref =1.5I q , so that the motor is constantly accelerated to the set speed threshold, and the time t3 and t4 corresponding to the speed of ω1 and ω2 are recorded;

[0049] 4) Second deceleration stage: given i qref =0, making the motor decelerate to 0;

[0050] 5) Complete the moment of inertia identification process once and calculate the moment of inertia identification result according to formula (16).

[0051] Furthermore, when identifying the moment of inertia, given i qref =I q After the motor rotates forward and the moment of inertia is identified, set i again. qref =-I q The motor is reversed to complete the moment of inertia identification. This is repeated multiple times to obtain multiple identification results. The final identification result is obtained by sorting and taking the median.

[0052] Compared with the prior art, the present invention has the following significant advantages:

[0053] (1) The present invention identifies magnetic flux in a dual closed-loop mode of current and speed. The PI parameters of the current loop and speed loop are self-tuned, resulting in a better closed-loop control effect. The current and speed can be controlled during the identification process, improving the safety and reliability of the identification process.

[0054] (2) The present invention adopts the recursive least square method with forgetting factor to identify the magnetic flux, which not only improves the accuracy of the identified magnetic flux, but also ensures the convergence time of the identification algorithm.

[0055] (3) When identifying the moment of inertia, the present invention uses a sinusoidal quadrature-axis current method with a given amplitude and increasing frequency to determine the current required to start the motor and rotate it to a set threshold. This method avoids the problem of poor identification accuracy caused by inaccurate speed and time acquisition during the acceleration process when using the acceleration and deceleration method to identify the moment of inertia, thereby improving the accuracy of the moment of inertia identification.

[0056] (4) The acceleration and deceleration identification of the moment of inertia adopted by the present invention identifies the forward acceleration and deceleration and the reverse acceleration and deceleration respectively, and repeats these two processes multiple times to obtain multiple groups of rotational inertia identification values; and then adopts the method of sorting and taking the median value to reduce the error caused by the asymmetry of the forward and reverse rotation of the motor and the error of speed and time acquisition, thereby greatly improving the accuracy of the rotational inertia identification.

[0057] (5) The present invention adopts a parameter standardization design for universal servo drives, which can identify the magnetic flux and moment of inertia of motors with different parameters. It has strong versatility and can realize a one-button parameter identification function.

[0058] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is an offline permanent magnet synchronous motor flux and moment of inertia identification control block diagram.

[0060] Figure 2 is a diagram of current and speed tracking during the flux identification process.

[0061] FIG3 is a control flow chart of the recursive least squares method with a forgetting factor.

[0062] FIG4 is a diagram of the flux identification process, wherein (a) and (b) in FIG4 are the current and speed tracking conditions of the flux identification process, respectively.

[0063] FIG5 is a flow chart of the moment of inertia identification control.

[0064] FIG6 is a diagram of current and speed tracking during the moment of inertia process, wherein (a) and (b) in FIG6 are the current and speed tracking conditions during the flux linkage identification process, respectively. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0066] It should be noted that if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or suggesting their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the fact that they can be implemented by ordinary technicians in this field. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0067] The present invention provides an offline permanent magnet synchronous motor flux linkage and moment of inertia identification method. The basic principle is as follows: when the number of pole pairs P of the motor is known, n , stator resistance R s , stator inductance L sBased on this premise, the PI parameters of the current and speed loops are tuned. In the current and speed dual closed-loop mode, the motor flux is identified using a recursive least squares method with a forgetting factor. In the current closed-loop mode, a low-frequency current signal with increasing amplitude and frequency is first injected to determine the current required to start the motor and rotate it to the set speed threshold. Acceleration and deceleration are then used to identify the motor's moment of inertia. The motor is rotated forward and reversed, and multiple identifications are performed. The median method is used to improve identification accuracy. Combining flux identification using the recursive least squares method with a forgetting factor and moment of inertia identification using the acceleration and deceleration method creates a complete offline permanent magnet synchronous motor flux and moment of inertia identification method.

[0068] In one embodiment, an offline permanent magnet synchronous motor flux linkage and moment of inertia identification method is provided, the control block diagram of which is shown in FIG1 . The method specifically includes the following steps:

[0069] (1) The flow chart of flux linkage identification control based on the recursive least squares method with forgetting factor is shown in Figure 2.

[0070] First, adjust the normalized PI parameters of the current loop and speed loop, and identify the motor flux in the speed and current dual closed-loop mode;

[0071] The transfer function of the PI controller is established as:

[0072] The per-unit PI parameters of the current loop closed loop can be adjusted as follows:

[0073] The closed-loop PI parameters of the speed loop can be adjusted as follows:

[0074] Among them, K p is the proportionality coefficient, K i is the integration coefficient, K pCur , K iCur They are the proportional coefficient and integral coefficient of the current loop controller, K pVel , K iVel They are the proportional coefficient and integral coefficient of the speed loop controller, ω c is the current loop cutoff frequency, T s is the current loop control period, I N 、U N 、n N They are the motor rated current, rated voltage and rated speed.

[0075] Figure 4 shows the speed and current tracking during the flux identification process. It can be seen that the adjusted PI parameters of the current loop and speed loop can achieve good steady-state tracking of current and speed, fully meeting the requirements of flux identification in closed-loop mode.

[0076] (2) According to the quadrature axis stator voltage equation of the motor:

[0077] When the motor speed and load remain unchanged, Also adopt i d = 0 current control strategy, ignore Item and i d Item, we can get: u q =R s i q +ω e ψ f (twenty one)

[0078] Among them, u q is the motor quadrature axis voltage, R s is the stator resistance, i q is the quadrature axis current, L s is the stator inductance, ω e is the electrical angular velocity, ψ f is the permanent magnet flux linkage;

[0079] (3) Establish a recursive least squares model of the permanent magnet synchronous motor, and its control flow chart is shown in Figure 3:

[0080] For an observable system, its n sets of input and output observation data can be expressed as: {y(k), u(k), k = 1, 2, 3…n}, where y(k) and u(k) are the kth set of input and output observation data respectively.

[0081] Assume that the input and output of the system can be expressed as:

[0082] Among them, y(k) is the output matrix of the system corresponding to the kth group of input and output observation data, is the observable matrix corresponding to the kth group of input and output observation data, θ(k) is the matrix of parameters to be identified corresponding to the kth group of input and output observation data, and ε(k) is the random variable matrix with an average value of 0 corresponding to the kth group of input and output observation data.

[0083] The objective function is constructed as:

[0084] Let its partial derivative be 0, then the recursive least squares method can be expressed as:

[0085] Among them, P(k) and P(k-1) are the covariance matrices corresponding to the k-th and k-1-th groups of input and output observation data, respectively; K(k) is the gain matrix corresponding to the k-th group of input and output observation data; θ(k-1) is the matrix of the parameters to be identified corresponding to the k-1-th group of input and output observation data;

[0086] As long as we can get y(k) and You can start recursive least squares, and the identification result is θ(k).

[0087] Combining equations (21) and (22), the output matrix of the flux identification system y(k) = u qk -i qk R k 、Parameter to be identified θ(k)=ψ k , observation matrix

[0088] (4) In order to speed up the convergence of calculation and reduce the amount of calculation, the recursive least squares method introduces a forgetting factor, which is generally set to 0.8 to 1. After the forgetting factor is introduced, the covariance matrix and gain matrix of the least squares method in formula (24) can be updated as follows:

[0089] By adding the forgetting factor, the controller "forgets" the data accumulated during each iteration, reducing the saturation of the covariance matrix and highlighting the role of new data. When the forgetting factor is small, the least squares method converges quickly but is susceptible to noise in steady-state conditions. Conversely, a larger forgetting factor slows the least squares algorithm's convergence but improves steady-state performance and reduces noise interference.

[0090] (5) Based on the recursive least squares method with forgetting factor, the permanent magnet synchronous motor flux identification is performed, and its recursive equation is as follows:

[0091] Among them, ψ k is the permanent magnet flux at the current moment, ψ k-1 is the permanent magnet flux at the previous moment, is the gain at the current moment, R k The motor stator resistance at the current moment;

[0092] (6) The flow chart of the moment of inertia identification control based on the acceleration and deceleration method is shown in Figure 5. First, a sinusoidal quadrature-axis current i with increasing amplitude and frequency is given. qref , determine the current I required to start the motor and rotate to the set threshold q The size of i qref =I q sin(2πf0·n) (n=1,2,3…) (27)

[0093] (7) According to the mechanical motion equation of the motor:

[0094] Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient;

[0095] In T e and 1.5 times T e When the motor is constantly accelerating, equation (28) can be converted into the following:

[0096] Take ω2=ω4, ω1=ω3, then ω 12 Can be approximately equal to ω 34 According to formula (29), the moment of inertia can be calculated as follows:

[0097] Among them, t1 and t2 are based on the electromagnetic torque T e The moment of acceleration to the mechanical angular velocity ω1, ω2, t3, t4 is the electromagnetic torque 1.5T e When the acceleration reaches the mechanical angular velocity ω3, ω4, ω 12 is the difference between the mechanical angular velocities ω1 and ω2, ω 34 is the difference between the mechanical angular velocities ω3 and ω4;

[0098] (8) According to the electromagnetic torque equation of the motor:

[0099] Due to the use of i d = 0, the current control strategy, equation (31) can be written as:

[0100] Combining equations (30) and (32), the motor moment of inertia can be calculated as follows:

[0101] (9) Using the acceleration and deceleration method, T e and 1.5 times T e The motor is made to rotate at a constant acceleration to identify the moment of inertia, specifically including:

[0102] a. First acceleration segment: given i qref =I q , so that the motor is constantly accelerated to the set speed threshold, and the time t1 and t2 corresponding to the speed ω1 and ω2 are recorded;

[0103] b. First deceleration stage: given i qref =0, making the motor decelerate to 0;

[0104] c. Second acceleration stage: given i qref =1.5I q , so that the motor is constantly accelerated to the set speed threshold, and the time t3 and t4 corresponding to the speed of ω1 and ω2 are recorded;

[0105] d. Second deceleration stage: given i qref =0, making the motor decelerate to 0;

[0106] After completing the moment of inertia identification process, the moment of inertia identification result is calculated according to formula (33).

[0107] (10) When identifying the moment of inertia, given i qref =I q After the motor rotates forward and the moment of inertia is identified, set i again. qref =-I q The motor is rotated in reverse to complete the moment of inertia identification. This process is repeated 10 times, resulting in 20 identification results. The method of sorting and taking the median value is used to improve the identification accuracy. Figure 6 shows the moment of inertia identification process.

[0108] In one embodiment, an offline permanent magnet synchronous motor flux linkage and moment of inertia identification system is provided, the system comprising:

[0109] The first module is used to implement offline identification of motor flux linkage using the recursive least squares method with forgetting factor in the speed closed-loop mode;

[0110] The second module is used to realize offline identification of motor moment of inertia by using acceleration and deceleration methods in current closed-loop mode.

[0111] The specific limitations of the offline permanent magnet synchronous motor flux and moment of inertia identification system can be found in the limitations of the offline permanent magnet synchronous motor flux and moment of inertia identification method described above and will not be further elaborated here. Each module in the aforementioned offline permanent magnet synchronous motor flux and moment of inertia identification system can be implemented in whole or in part through software, hardware, or a combination thereof. Each of these modules can be embedded in or independent of a processor in a computer device in hardware form, or stored in a computer device memory in software form, so that the processor can call and execute the corresponding operations of each of these modules.

[0112] The magnetic flux and moment of inertia identification process of the method of the present invention is simple, stable and reliable, the identification result is highly accurate, a one-button parameter identification function can be realized, and it has universality.

[0113] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only illustrative of the principles of the present invention. Without departing from the spirit and scope of the present invention, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. An offline permanent magnet synchronous motor flux linkage and moment of inertia identification method, characterized in that: The method comprises: when the number of pole pairs P of the motor is known n , stator resistance R s , stator inductance L s Under the premise of , the PI parameters of the current loop and speed loop are determined. In the current and speed dual closed-loop mode, the recursive least squares method with forgetting factor is used to identify the motor magnetic flux. In the current closed-loop mode, a low-frequency current signal with increasing amplitude and frequency is first injected to determine the current required to start the motor and rotate to the set speed threshold. Then, the acceleration and deceleration method is used to identify the motor's rotational inertia.

2. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 1, characterized in that: The method of identifying the motor flux linkage using the recursive least squares method with a forgetting factor specifically includes the following steps: Step 1-1, according to the quadrature-axis stator voltage equation of the motor: When the motor speed and load remain unchanged, Also adopt i d = 0 current control strategy, ignore Item and i d Term, formula (1) is sorted as follows: you q =R s I q +oh e ψ f (2) Among them, u q is the motor quadrature axis voltage, R s is the stator resistance, i q is the quadrature axis current, i d is the excitation current, L s is the stator inductance, ω e is the motor angular velocity, ψ f is the permanent magnet flux linkage; Step 1-2, use the recursive least squares method with forgetting factor to identify the flux linkage, establish the least squares model of the permanent magnet synchronous motor, and determine the output u q 、i q 、R s , the parameter to be identified is ψ f , the observation matrix is ω e , then the least squares equation is as follows: Among them, ψ k is the permanent magnet flux at the current moment, ψ k-1 is the permanent magnet flux at the previous moment, is the gain at the current moment, u qk 、i qk They are the quadrature-axis voltage and quadrature-axis current of the motor at the current moment, R k The motor stator resistance at the current moment; Steps 1-3: Adjust the normalized PI parameters of the current loop and speed loop, and identify the motor flux in the speed and current dual closed-loop mode.

3. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 2, characterized in that: The recursive least squares method described in steps 1-2 specifically includes: For an observable system, its n sets of input and output observation data are expressed as: {y(k),u(k),k=1,2,3…,n}; where y(k),u(k) are the kth set of input and output observation data respectively; Assume that the input and output of the system are expressed as: Among them, y(k) is the output matrix of the system corresponding to the kth group of input and output observation data, is the observable matrix corresponding to the k-th group of input and output observation data, θ(k) is the matrix of parameters to be identified corresponding to the k-th group of input and output observation data, and ε(k) is the random variable matrix with an average value of 0 corresponding to the k-th group of input and output observation data; The objective function of the system J(θ) is constructed as: Let its partial derivative be 0, then the recursive least squares method is expressed as: Among them, P(k) and P(k-1) are the covariance matrices corresponding to the kth and k-1th groups of input and output observation data, respectively; K(k) is the gain matrix corresponding to the kth group of input and output observation data; θ(k-1) is the matrix of the parameters to be identified corresponding to the k-1th group of input and output observation data. As long as we can get y(k) and You can start the recursive least squares method, and the identification result is θ(k); Combining equations (2) and (4), the output matrix of the flux identification system y(k) = u qk -i qk R k 、Parameter to be identified θ(k)=ψ k , observation matrix Thus, the least squares recursive equation for flux linkage identification of formula (3) is obtained.

4. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 3, characterized in that: The recursive least squares method in step 1-2 introduces the forgetting factor, which specifically includes: Introducing the forgetting factor λ, the covariance matrix and gain matrix of the least squares method in formula (6) are updated as follows:

5. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 4, characterized in that: Steps 1-3 are to adjust the normalized PI parameters of the current loop and speed loop, specifically including: Establish the transfer function G of the PI controller pi (s) is: The PI parameters of the current loop closed loop are set as follows: The closed-loop PI parameters of the speed loop are tuned as follows: Among them, K p is the proportionality coefficient, K i is the integration coefficient, K pCur , K iCur They are the proportional coefficient and integral coefficient of the current loop controller, K pVel , K iVel They are the proportional coefficient and integral coefficient of the speed loop controller, ω c is the current loop cutoff frequency, T s is the current loop control period, I N 、U N 、n N They are the motor rated current, rated voltage and rated speed.

6. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 5, characterized in that: The method of using acceleration and deceleration to identify the motor moment of inertia specifically includes the following steps: Step 2-1, given a sinusoidal quadrature-axis current i with increasing amplitude and frequency qref , determine the current required to start the motor and rotate to the set threshold; Step 2-2, according to the mechanical motion equation of the motor: Where J is the moment of inertia, ω m is the mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, B is the viscous friction coefficient; In T e and 1.5 times T e When the motor is constantly accelerating, convert equation (11) into: Take ω2=ω4, ω1=ω3, then ω 12 Approximately equal to ω 34 According to formula (12), the moment of inertia can be calculated as follows: Among them, t1 and t2 are the electromagnetic torque T e At the moment of acceleration to the mechanical angular velocity ω1 and ω2, t3 and t4 are respectively the electromagnetic torque 1.5T. e The moment when the acceleration reaches the mechanical angular velocity ω3, ω4; 12 is the difference between the mechanical angular velocities ω1 and ω2, ω 34 is the difference between the mechanical angular velocities ω3 and ω4; Step 2-3, according to the electromagnetic torque equation of the motor: Adopt i d =0, the current control strategy is written as: Among them, P n is the number of pole pairs of the motor; Combining equations (13) and (15), the motor moment of inertia is calculated by equation (16):

7. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 6, characterized in that: The sinusoidal quadrature-axis current i described in step 2-1 qref The current required to set the threshold value I q The relationship is: i qref =I q sin(2πf0·n) n=1,2,3… Where f0 is the initial frequency of the current.

8. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 7, characterized in that: Step 2-2 is described in T e and 1.5 times T e The motor is made to rotate at a constant acceleration to identify the moment of inertia, specifically including: 1) First acceleration stage: given i qref =I q , so that the motor is constantly accelerated to the set speed threshold, and the time t1 and t2 corresponding to the speed ω1 and ω2 are recorded; 2) First deceleration stage: given i qref =0, making the motor decelerate to 0; 3) Second acceleration stage: given i qref =1.5I q , so that the motor is constantly accelerated to the set speed threshold, and the time t3 and t4 corresponding to the speed of ω1 and ω2 are recorded; 4) Second deceleration stage: given i qref =0, making the motor decelerate to 0; 5) Complete the moment of inertia identification process once and calculate the moment of inertia identification result according to formula (16).

9. The offline permanent magnet synchronous motor flux linkage and moment of inertia identification method according to claim 8, characterized in that: When identifying the moment of inertia, given i qref =I q After the motor rotates forward and the moment of inertia is identified, set i again. qref =-I q The motor is reversed to complete the moment of inertia identification. This is repeated multiple times to obtain multiple identification results. The final identification result is obtained by sorting and taking the median.

10. An offline permanent magnet synchronous motor flux linkage and moment of inertia identification system based on the method according to any one of claims 1 to 9, characterized in that: The system comprises: The first module is used to implement offline identification of motor flux linkage using the recursive least squares method with forgetting factor in the speed closed-loop mode; The second module is used to realize offline identification of motor moment of inertia by using acceleration and deceleration methods in current closed-loop mode.

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