Parameter identification and position correction method and system for permanent magnet synchronous motor under position-free control

Abstract

The invention provides a parameter identification and position correction method and system for a permanent magnet synchronous motor under position-free control. The parameter identification and position correction method comprises the following steps: establishing a sine small signal impedance model; designing a multi-parameter adaptive observer; finding a unique solution through a continuous excitation condition; designing an optimizer based on a gradient descent method; and performing sensorless control on the motor by using the estimated parameters and the position observation error through an extended electromotive force (EEMF) full-state observer, and continuously repeating the steps to realize online estimation of the parameters and real-time correction of the position error. According to the method, the robust adaptive observer and the inductance optimizer are introduced, so that parameter identification and position correction are carried out on the surface-mounted permanent magnet synchronous motor and the built-in permanent magnet synchronous motor without control of a position sensor, the defects of a traditional method are overcome, and parameter identification is carried out under the high-speed condition; inductance can be observed and optimized, the accuracy of a position observation result is further improved, and therefore accurate control over the permanent magnet synchronous motor is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor parameter identification, and in particular to a method and system for parameter identification and position correction of a permanent magnet synchronous motor under position-free control. Background Art

[0002] At present, various industries are undergoing the transformation of electrification and intelligence. Among them, the electrification of household appliances, more electric aircraft and electric vehicles is rapidly becoming popular. As the key power part of the electrification system, the motor naturally faces more challenges and opportunities.

[0003] Compared with traditional industrial motors, motors for this type of application must have a wider speed range and stronger overload capacity to meet the speed regulation and traction requirements of the power system, and due to space limitations, they must have higher power density and efficiency to reduce the volume share of the cooling system. Among the many types of motors, permanent magnet synchronous motors have become the first choice for electric vehicle main drive motors because of their strong overload capacity and wide range of weak magnetic field capabilities. In addition, the electric drive control must not only achieve high-efficiency operation, but also achieve precise speed and torque control over the entire operating speed range.

[0004] In order to meet the above application requirements, it is necessary to obtain accurate parameters of the motor under running state to achieve precise and intelligent control of the system. However, the existing methods and mathematical models have the following disadvantages:

[0005] 1. The traditional electric drive control system and parameter identification system are both based on the mathematical model of the linear permanent magnet synchronous motor, and its expression is shown in formula (1):

[0006]

[0007] Where R s is the stator winding resistance of the motor, Ψ f is the permanent magnet flux, L d and L q Respectively represent the dq axis inductance, ω e Indicates the operating frequency of the motor.

[0008] This simplified mathematical model can facilitate the design of the controller, but in fact, the motor is a highly coupled and strongly nonlinear system. When the motor runs at high current, the model cannot reflect the actual electromagnetic conditions inside the motor.

[0009] 2. The traditional parameter identification algorithm based on high frequency injection is not only based on the linear mathematical model of formula (1), but also based on the injection voltage signal frequency ω. h Much larger than the motor's fundamental frequency ω e Ignore ωe L d i d and ω e L q i q Due to the limitation of inverter switching frequency, the injected high-frequency signal frequency cannot be infinitely increased. Therefore, this scheme can only realize parameter identification under zero speed and low speed conditions. When the motor runs at high speed, this assumption does not hold. In addition, due to the characteristics of embedded permanent magnet synchronous motor, L d < <L q , so ignoring ω e L d i d and ω e L q i q This will also lead to larger errors in the observation of inductance. Summary of the invention

[0010] In view of the deficiencies in the prior art, the present invention provides a method and system for parameter identification and position correction under position-free control of a permanent magnet synchronous motor. The present invention can realize parameter identification under high-speed conditions and further improve the accuracy of the position observation results by observing the inductance, thereby realizing precise control of the permanent magnet synchronous motor.

[0011] The technical solution of the present invention is: a method for parameter identification and position correction under position-free control of a permanent magnet synchronous motor, comprising the following steps:

[0012] S1) A unified sinusoidal small signal impedance model of synchronous motor is established in the non-orthogonal synchronous coordinate system γδ; the sinusoidal small signal impedance model is divided into a large signal model and a small signal model; they are used to describe the dynamic characteristics of the system including the DC component and the dynamic characteristics of the system after the small signal is injected including the AC component; based on the sensorless control technology, the rotor position angle obtained by the observation is output

[0013] S2), design a multi-parameter adaptive observer, and estimate the current, stator resistance, and inductance through a feedback matrix, and design a feedback matrix to adjust the convergence speed of the current estimation;

[0014] S3) Track the current trajectory in the estimated current and find the unique solution through the continuous excitation condition For orthogonal motors, a small signal is injected only in the γ-axis to satisfy continuous excitation. For non-orthogonal motors, a small signal is injected simultaneously in the γ-axis and the δ-axis, and the phase difference ∈ cannot be 0 or π;

[0015] S4) For non-orthogonal synchronous motors, an optimizer based on the gradient descent method is designed, and the observed position mis-observation error Use the optimizer to iterate and adjust the d-axis and q-axis inductance estimates and Position observation error Converges to zero;

[0016] S5) By extending the EEMF full state observer, the estimated parameters and position observation error Sensorless control of motors;

[0017] S6) During the operation of the system, steps S2)-S5) are repeated continuously to achieve online estimation of parameters and real-time correction of position errors. The multi-parameter adaptive observer and gradient descent optimizer run in parallel with the model-based sensorless control. s and q-axis inductance to ensure that the system can achieve accurate position observation results within the rated speed and torque range.

[0018] Preferably, in step S1), in order to realize multi-parameter estimation under sensorless control, the state equation of the unified synchronous motor on the synchronous rotating γδ axis with position error misalignment is established:

[0019]

[0020] Where: u γδ Represents the voltage on the γ and δ axes; R s is the stator resistance; I γδ Indicates the current on the γ and δ axes; L γδ represents the mutual inductance on the γ and δ axes; Represents the current derivative on the γ and δ axes, that is, the rate of change of current; ω e is the electrical speed; J is the moment of inertia; ψ γδ is the permanent magnetic flux on the γ and δ axes;

[0021] The sinusoidal small signal impedance model is obtained from equation (2) by multiplying the specific injection frequency and the velocity change of the basic flux component, namely:

[0022]

[0023] In the formula, u γδh Represents the voltage on the γ and δ axes under high-frequency input; I γδh Represents the current on the γ and δ axes under high-frequency input; Indicates the rate of change of current on the γ and δ axes under high-frequency input; ω e0 is the electrical speed ω e The DC component of eh is the electrical velocity fluctuation at a specific injection frequency; I γδ0is the DC component of the current on the γ and δ axes.

[0024] Preferably, in step S1), in order to reduce the extended unknown state, equation (3) is expressed as the large signal model, that is:

[0025]

[0026] In the formula, u γδ0 Represents the DC component of the voltage on the γ and δ axes; I γδ0 Represents the DC component of the current on the γ and δ axes.

[0027] Preferably, in step S1), equation (3) is expressed as the small signal model, that is:

[0028]

[0029] middle, represents the estimated value of stator resistance; It represents the estimated value of the current on the γ and δ axes under high frequency input; represents the estimated value of mutual inductance on the γ-axis and the δ-axis; Indicates electrical speed ω e An estimate of the DC component of ; represents an estimate of the electrical speed fluctuation at a specific injection frequency; It represents the estimated error of the current on the γδ axis under high frequency input, which is expressed as the difference between the actual current and the estimated current; K1 and K2 are feedback matrices; sgn is the sign function.

[0030] Preferably, in step S1), by comparing the difference between formula (5) and formula (6), formula (7) is obtained, that is:

[0031]

[0032] In the formula, It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated error of the electrical speed fluctuation at a specific injection frequency; represents the estimated error of the stator resistance; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis; It represents the rate of change of the estimated current value on the γ and δ axes under high frequency input;

[0033] Rewrite (7) into the parameter error vector form, that is:

[0034]

[0035] in,

[0036]

[0037] In the formula, It represents the rate of change of the estimated value of the current on the γ axis under high frequency input; It represents the rate of change of the estimated value of the current on the delta axis under high frequency input; It represents the estimated value of the current on the γ axis under high frequency input; I γ0 Represents the DC component of the current on the γ axis; It represents the estimated value of the current on the delta axis under high frequency input; I δ0 Represents the DC component of the current on the δ axis; represents the estimated error of the stator resistance; represents the estimated error of the self-inductance on the γ axis; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the self-inductance on the δ-axis; T represents the transposition operation.

[0038] Preferably, in step S2), the Lyapunov candidate function is used to ensure that the estimated current signal Tracking actual current small signal I γδh And the estimated parameters converge to the actual value, the expression of the Lyapunov candidate function V is:

[0039]

[0040] Where V represents the Lyapunov candidate function, which is used to ensure the stability of the system; represents the estimated error of the current on the γδ axis under high frequency input; L γδ represents the mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the mutual inductance on the γ axis and the δ axis; Γ R is the positive gain element estimated by the resistor; Γ L is the symmetric positive definite gain matrix for inductance estimation; tr(·) is the trace of the square matrix, defined by the sum of its diagonal elements;

[0041] From formula (10), we can see that V is greater than 0 unless the current small signal estimation error is zero, that is, , V=0.

[0042] Preferably, in step S2), by assuming that the electrical parameters are constant in a short time, Get the derivative of the Lyapunov candidate function Right now:

[0043]

[0044] In the formula, represents the derivative of V; It represents the estimation error of the current on the γδ axis under high frequency input; It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; Represents the rate of change of the mutual inductance estimation value on the γ and δ axes; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis.

[0045] Preferably, in step S2), by selecting the parameter adaptation rule of formula (14) and removing the parameter error term in formula (13), a multi-parameter adaptive observer shown in formula (15) is obtained:

[0046]

[0047] In the formula, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for resistor; represents the estimated value vector of the current on the γ and δ axes under high frequency input; It represents the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated value of the electrical speed fluctuation at a specific injection frequency; I γδ0 Represents the DC component of the current on the γ and δ axes; represents the rate of change of the estimated value of the self-inductance on the γ axis; Γ L,11 , Γ L,22 , Γ L,12 denote the symmetric positive definite gain matrices associated with the self-inductance on the γ axis, the self-inductance on the δ axis, and the mutual inductance on the γ axis and the δ axis respectively; represent the estimated value and estimation error of the current on the γ axis respectively; They represent the estimated value and estimation error of the current on the δ axis respectively; represents the rate of change of the estimated value of the current on the γ axis; represents the rate of change of the estimated value of the current on the δ axis; represents the rate of change of the estimated value of the self-inductance on the δ-axis; Indicates the rate of change of the estimated value of the mutual inductance on the γ-axis and the δ-axis.

[0048] Preferably, in step S2), in order to ensure the stability of the estimation system, the feedback matrix K1 needs to ensure Q = K1 + JL γδ is positive definite, by choosing K1 as a diagonal matrix with the same scalar value, K1 = k1I; then the eigenvalue of Q is derived by the following formula, namely:

[0049]

[0050] In the formula, λ Qrepresents the eigenvalue of matrix Q; Q is composed of feedback matrix K1 and inductance matrix JL γδ The matrix composed of is defined as Q = K1 + JL γδ ; L γγ represents the self-inductance on the γ axis; L δδ represents the self-inductance on the δ axis; L γδ represents the mutual inductance on the γ axis and the δ axis; L q , L d are the q-axis and d-axis inductances, respectively; j represents the imaginary unit; I represents the unit matrix;

[0051] To ensure system stability in the presence of sampling noise, system delays, and other unmodeled dynamics, k1 is positive.

[0052] Preferably, in step S2), the feedback matrix K2 is selected as a diagonal matrix k2I with uniform scalar values; to ensure that the second line in equation (15) is negative, k2 is selected as:

[0053]

[0054] In the formula, represents the estimated value of the electrical speed fluctuation at a specific injection frequency; ω e0 is the electrical speed ω e The DC component of u γδ0 Represents the DC component of the voltage on the γ and δ axes; I γδ0 Represents the DC component of the current on the γ and δ axes;

[0055] According to equations (16) and (17), the derivative of the Lyapunov candidate function (10) is negative definite, which proves that the adaptive observer can track the actual current trajectory.

[0056] As a preferred step, step S3) is to find a unique solution A sufficient condition for is that the matrix Φ in equation (9) is continuously excited, which is based on the continuous excitation condition lemma of equation (18), namely:

[0057] for exist So that:

[0058]

[0059] In the formula, TA is a positive real number, which indicates the length of the time interval of the integration, ζ is a positive real number, which indicates the lower bound of the integration result; I represents the unit matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector Converge the exponential to 0 4×1 ;

[0060] Due to the d-axis inductance L d and q-axis inductance L q Equal, that is, L d =L q =L s ,For an isotropic synchronous motor SM, continuous excitation regulation can be satisfied simply by injecting a small signal in the γ-axis.

[0061] As a preferred step, step S3), for a non-orthogonal motor, assuming that a pair of small current signals in equation (19) are injected into the γδ-axis, and equation (19) is substituted into equation (18) to obtain that both the γ-axis and the δ-axis contain additional sinusoidal components, and the phase difference ∈ cannot be 0 or π, then the parameter estimation error vector The exponential converges to 0 4×1 ;

[0062]

[0063] In the formula, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Represents the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h It represents the angular frequency of the corresponding signal under the input; t is the time variable, which represents the time elapsed from a certain initial moment; ∈ is the phase difference relative to the first component.

[0064] Preferably, in step S4), for non-orthogonal isotropic synchronous motors SMs, due to the observation error at any given position There are L below δδ =L γγ =L d =L q =L s , the parameters estimated by the adaptation law of Eq. (14) are directly used in the model-based position observer. For non-orthogonal anisotropic synchronous motors, L γγ and L δδ The differences between are:

[0065]

[0066] Where, L δδ represents the self-inductance on the δ axis; L γγ represents the self-inductance on the γ axis; L q represents the q-axis inductance; L d represents the d-axis inductance; represents the position observation error;

[0067] From formula (22), we can see that due to the anisotropy of the rotor, Lγγ and L δδ The difference is a convex function, and the general gradient descent optimizer shown in Equation (23) is used to find the model-based position observation error caused by parameter mismatch Once the position observation error is found for anisotropic synchronous motors (SMs) Then the estimated d-axis and q-axis inductances converge to their actual values, and the position observation error will be 0, and the expression of the general gradient descent optimizer is:

[0068]

[0069] in:

[0070]

[0071] In the formula, represents the estimated value of the self-inductance on the δ-axis after the k-th iteration in the optimizer; represents the estimated value of self-inductance on the γ axis after the k-th iteration in the optimizer; It represents the iterative position error at step k in the optimizer, and its initial value is α is a positive learning rate.

[0072] Preferably, in step S5), for an isotropic motor, due to L γγ =L δδ =L d =L q =L s , L d and L q The value of does not change with the rotor position, and no position correction is required, so the estimated parameter It can be directly used in the extended electromotive force EEMF full state observer, only feeding back the estimated value of the stator resistance And each phase inductance Accurate estimation of the motor state is achieved, thereby achieving precise control of the motor. For anisotropic motors, due to L d ≠L q , the observed rotor position angle Not accurate, considering the self-inductance L on the δ axis δδ , self-inductance on the γ axis l γγ The existence relationship is a convex function as shown in formula (22). Therefore, the general gradient descent optimizer shown in formula (23) is used to determine the iterative position error of the kth step after performing enough iterations. At the same time, the estimated values ​​of d-axis inductance and q-axis inductance are It also converges to the actual value, that is, Feedback to the extended electromotive force EEMF full state observer, position observation error will be 0.

[0073] The present invention also provides a parameter identification and position correction system for a permanent magnet synchronous motor under position-free control, the system comprising:

[0074] The extended electromotive force full state observer is used to calculate the input signal voltage u αβ and current I αβ Calculate the estimated electromotive force e αβ ;

[0075] The inverse tangent module is used to calculate the electromotive force e αβ Calculate the motor's rotor position angle And the rotor position angle Perform differential operation to obtain the estimated value of the rotor's angular velocity

[0076] Bandpass filter to extract the voltage u γδ and current I γδ The high frequency voltage u γδh and high frequency current I γδh ;

[0077] Sinusoidal small signal impedance model module, used to extract the high-frequency voltage signal u according to the bandpass filter γδh and high frequency current signal I γδh , calculated by equation (3) and equation (6), the estimated values ​​of stator resistance, inductance and permanent magnet flux are obtained;

[0078] A multi-parameter adaptive observer is used to calculate the high-frequency voltage u γδh and I γδh , and the angular velocity of the rotor Combined with the sinusoidal small signal impedance model module, the estimated value is updated using formula (14), thereby realizing online estimation of motor parameters;

[0079] The gradient descent optimizer is used to further adjust the estimated values ​​of the motor parameters according to equations (23) and (24). The specific parameters directly adjusted are: and They represent the estimated values ​​of self-inductance on the δ-axis and γ-axis after the k-th iteration in the optimizer, and are substituted into and Directly estimate each parameter and finally output the estimated value of stator resistance Estimated value of permanent magnet flux linkage Estimated d-axis and q-axis inductance and rotor position angle To expand the EMF full state observer.

[0080] The beneficial effects of the present invention are:

[0081] 1. The present invention introduces a robust adaptive observer and an inductance optimizer to achieve parameter identification and position correction of surface-mount and built-in permanent magnet synchronous motors under position sensorless control, overcomes the drawbacks of traditional methods, and achieves parameter identification at high speeds;

[0082] 2. The present invention can also observe and optimize the inductance, further improving the accuracy of the position observation results, thereby achieving precise control of the permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a schematic diagram of the structural framework of the present invention. DETAILED DESCRIPTION

[0084] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0085] Example 1

[0086] like Figure 1 As shown, this embodiment provides a parameter identification and position correction method for a permanent magnet synchronous motor under position-free control, comprising the following steps:

[0087] S1) Establish a sinusoidal small signal impedance model of a unified synchronous motor in the non-orthogonal synchronous coordinate system γδ; calculate the estimated values ​​of stator resistance, inductance and permanent magnet flux through the sinusoidal small signal impedance model; and divide the sinusoidal small signal impedance model into a large signal model and a small signal model; respectively used to describe the dynamic characteristics of the system containing a DC component and the dynamic characteristics of the system after injecting a small signal containing an AC component; based on the sensorless control technology, output the observed rotor position angle The details are as follows:

[0088] In order to realize multi-parameter estimation under sensorless control, the state equation of the unified synchronous motor on the synchronous rotation γδ axis with position error misalignment is established:

[0089]

[0090] Where: u γδ Represents the voltage on the γ and δ axes; R s is the stator resistance; I γδ Indicates the current on the γ and δ axes; L γδ represents the mutual inductance on the γ and δ axes; Represents the current derivative on the γ and δ axes, that is, the rate of change of current; ω e is the electrical speed; J is the moment of inertia; ψγδ is the permanent magnetic flux on the γ and δ axes;

[0091] During operation, the voltage u γδ and current I γδ The high frequency voltage u γδh and high frequency current I γδh ;

[0092] This embodiment adopts a second-order Butterworth bandpass filter, and its transfer function is as follows:

[0093]

[0094] Where s is the Laplace transform operator, ω n is the natural frequency of the filter, which determines the bandwidth of the filter. The higher the natural frequency, the narrower the bandwidth, but the greater the attenuation of high-frequency signals. ζ is the damping ratio of the filter, which determines the attenuation speed of the filter. The higher the damping ratio, the faster the attenuation speed, but the wider the transition band. At this time, according to the estimated value of the rotor angular velocity Select the appropriate natural frequency ω of the filter n , generally based on the injected signal frequency and noise frequency range, the center frequency is calculated as ω n The initial value of the voltage u γδ and current I γδ Filter and subtract the voltage u from it γδ and current I γδ The low-frequency signal in the high-frequency voltage u is obtained γδh and high frequency current I γδh .

[0095] In this embodiment, the sinusoidal small signal impedance model is obtained from equation (2) by multiplying the specific injection frequency and the velocity change of the basic flux component, that is:

[0096]

[0097] In the formula, u γδh Represents the voltage on the γ and δ axes under high-frequency input; I γδh Represents the current on the γ and δ axes under high-frequency input; Indicates the rate of change of current on the γ and δ axes under high-frequency input; ω e0 is the electrical speed ω e The DC component of eh is the electrical velocity fluctuation at a specific injection frequency; I γδ0 is the DC component of the current on the γ and δ axes.

[0098] In order to reduce the extended unknown state, equation (3) is expressed as the large signal model, that is:

[0099]

[0100] In the formula, u γδ0 Represents the DC component of the voltage on the γ and δ axes; I γδ0 Represents the DC component of the current on the γ and δ axes.

[0101] Formula (3) is expressed as the small signal model, that is:

[0102]

[0103] In the formula, represents the estimated value of stator resistance; It represents the estimated value of the current on the γ and δ axes under high frequency input; represents the estimated value of mutual inductance on the γ-axis and the δ-axis; Indicates electrical speed ω e An estimate of the DC component of ; represents an estimate of the electrical speed fluctuation at a specific injection frequency; It represents the estimated error of the current on the γδ axis under high frequency input, which is expressed as the difference between the actual current and the estimated current; K1 and K2 are feedback matrices; sgn is the sign function.

[0104] By comparing the differences between formula (5) and formula (6), we get formula (7), namely:

[0105]

[0106] In the formula, It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated error of the electrical speed fluctuation at a specific injection frequency; represents the estimated error of the stator resistance; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis; It represents the rate of change of the estimated current value on the γ and δ axes under high frequency input;

[0107] Rewrite (7) into the parameter error vector form, that is:

[0108]

[0109] in,

[0110]

[0111] In the formula, It represents the rate of change of the estimated value of the current on the γ axis under high frequency input; It represents the rate of change of the estimated value of the current on the delta axis under high frequency input; It represents the estimated value of the current on the γ axis under high frequency input; I γ0 represents the DC component of the current on the γ axis; It represents the estimated value of the current on the delta axis under high frequency input; I δ0 Represents the DC component of the current on the δ axis; represents the estimated error of the stator resistance; represents the estimated error of the self-inductance on the γ axis; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the self-inductance on the δ-axis; T represents the transposition operation.

[0112] S2) Design a multi-parameter adaptive observer, estimate the current, stator resistance, and inductance through a feedback matrix, and design a feedback matrix to adjust the convergence speed of the current estimation; the details are as follows:

[0113] This embodiment uses the Lyapunov candidate function to ensure that the estimated current signal Tracking actual current small signal I γδh And the estimated parameters converge to the actual value, the expression of the Lyapunov candidate function V is:

[0114]

[0115] Where V represents the Lyapunov candidate function, which is used to ensure the stability of the system; represents the estimated error of the current on the γδ axis under high frequency input; L γδ represents the mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the mutual inductance on the γ axis and the δ axis; Γ R is the positive gain element estimated by the resistor; Γ L is the symmetric positive definite gain matrix for inductance estimation; tr(·) is the trace of the square matrix, defined by the sum of its diagonal elements;

[0116] in,

[0117]

[0118] For any nonzero vector x, x T Γ L x>0;

[0119] In the formula, Γ L,11 , Γ L,12 , Γ L,21 , Γ L,22denote the symmetric positive definite gain matrices related to the self-inductance on the γ axis, the self-inductance on the v axis, and the mutual inductance on the γ axis and the δ axis respectively; x denotes any non-zero vector, which is generally a current vector or magnetic flux, etc., considering the physical meaning;

[0120] From formula (10), we can see that V is greater than 0 unless the current small signal estimation error is zero, that is, When V=0, this is because L γδ is a positive definite matrix, as shown in formula (12):

[0121]

[0122] Where, L γδ[1,1] , L γδ[2,2] Respectively represent; L q , L d q-axis and d-axis inductance respectively; represents the position observation error;

[0123] L γγ represents the self-inductance on the γ axis; L δδ represents the self-inductance on the δ axis; L γδ Represents the mutual inductance on the γ-axis and the δ-axis.

[0124] By assuming that the electrical parameters are constant over short periods of time, Get the derivative of the Lyapunov candidate function Right now:

[0125]

[0126] In the formula, represents the derivative of V; It represents the estimated error of the current on the γδ axis under high frequency input; It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; Represents the rate of change of the mutual inductance estimation value on the γ and δ axes; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis.

[0127] By selecting the parameter adaptation rule of formula (14) and removing the parameter error term in formula (13), the multi-parameter adaptive observer shown in formula (15) is obtained:

[0128]

[0129] In the formula, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for resistor; represents the estimated value vector of the current on the γ and δ axes under high frequency input; It represents the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated value of the electrical speed fluctuation at a specific injection frequency; I γδ0 Represents the DC component of the current on the γ and δ axes; represents the rate of change of the estimated value of the self-inductance on the γ axis; Γ L,11 , Γ L,22 , Γ L,12 denote the symmetric positive definite gain matrices associated with the self-inductance on the γ axis, the self-inductance on the δ axis, and the mutual inductance on the γ axis and the δ axis respectively; represent the estimated value and estimation error of the current on the γ axis respectively; They represent the estimated value and estimation error of the current on the δ axis respectively; represents the rate of change of the estimated value of the current on the γ axis; represents the rate of change of the estimated value of the current on the δ axis; represents the rate of change of the estimated value of the self-inductance on the δ-axis; Indicates the rate of change of the estimated value of the mutual inductance on the γ-axis and the δ-axis.

[0130] In this embodiment, in order to ensure the stability of the estimation system, the feedback matrix K1 needs to ensure Q = K1 + JL γδ is positive definite, by choosing K1 as a diagonal matrix with the same scalar value, K1 = k1I; then the eigenvalue of Q is derived by the following formula, namely:

[0131]

[0132] In the formula, λ Q represents the eigenvalue of matrix Q; Q is composed of feedback matrix K1 and inductance matrix JL γδ The matrix composed of is defined as Q = K1 + JL γδ ; L γγ represents the self-inductance on the γ axis; L δδ represents the self-inductance on the δ axis; L γδ represents the mutual inductance on the γ axis and the δ axis; j represents the imaginary unit; I represents the unit matrix; L q , L d q-axis and d-axis inductance respectively;

[0133] To ensure system stability in the presence of sampling noise, system delays, and other unmodeled dynamics, k1 is positive.

[0134] In this embodiment, the feedback matrix K2 is selected as a diagonal matrix k2I with uniform scalar values; to ensure that the second line in equation (15) is negative, k2 is selected as:

[0135]

[0136] In the formula, represents the estimated value of the electrical speed fluctuation at a specific injection frequency; ω e0 is the electrical speed ω e The DC component of u γδ0 Represents the DC component of the voltage on the γ and δ axes; I γδ0 Represents the DC component of the current on the γ and δ axes;

[0137] According to equations (16) and (17), the derivative of the Lyapunov candidate function (10) is negative definite, which proves that the adaptive observer can track the actual current trajectory.

[0138] S3) Track the current trajectory in the estimated current and find the unique solution through the continuous excitation condition For orthogonal motors, a small signal is injected only in the γ-axis to satisfy continuous excitation. For non-orthogonal motors, a small signal is injected simultaneously in the γ-axis and the δ-axis, and the phase difference ∈ cannot be 0 or π; as follows:

[0139] In this embodiment, to find a unique solution A sufficient condition for is that the matrix Φ in equation (9) is continuously excited, which is based on the continuous excitation condition lemma of equation (18), namely:

[0140] for exist So that:

[0141]

[0142] In the formula, TA is a positive real number, which indicates the length of the time interval of the integration, ζ is a positive real number, which indicates the lower bound of the integration result; I represents the unit matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector Converge the exponential to 0 4×1 ;

[0143] Due to the d-axis inductance L d and q-axis inductance L q Equal, that is, L d =L q =L γ ,For an isotropic synchronous motor SM, continuous excitation regulation can be satisfied simply by injecting a small signal in the γ-axis.

[0144] For non-orthogonal motors, assume that a pair of small current signals in equation (19) are injected into the γγ-axis, and substitute equation (19) into equation (18) to obtain that both the γ-axis and the δ-axis contain additional sinusoidal components, and the phase difference ∈ cannot be 0 or π, then the parameter estimation error vector The exponential converges to 04×1 ;

[0145]

[0146] In the formula, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Represents the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h It represents the angular frequency of the corresponding signal under the input; t is the time variable, which represents the time elapsed from a certain initial moment; ∈ is the phase difference relative to the first component.

[0147] When is 0 or π, the third column of the matrix Φ in equation (9) becomes linearly correlated with the first and second columns, which impairs the system's ability to perform multi-parameter estimation.

[0148] S4) For non-orthogonal synchronous motors, an optimizer based on the gradient descent method is designed, and the observed position mis-observation error Use the optimizer to iterate and adjust the d-axis and q-axis inductance estimates and Position observation error Converges to zero; specifically as follows:

[0149] For non-orthogonal isotropic synchronous motors (SMs), due to the observation error at any given position There are L below δδ =L γγ =L d =L q =L s , the parameters estimated by the adaptation rule of formula (14) are directly used in the model-based position observer;

[0150] For non-orthotropic synchronous motors SMs, L γγ and L δδ The differences between are:

[0151]

[0152] Where, L δδ represents the self-inductance on the δ axis; L γγ represents the self-inductance on the γ axis; L q represents the q-axis inductance; L d represents the d-axis inductance; represents the position observation error;

[0153] From formula (22), we can see that due to the anisotropy of the rotor, L γγ and L δδThe difference is a convex function, and the general gradient descent optimizer shown in Equation (23) is used to find the model-based position observation error caused by parameter mismatch Once the position observation error is found for anisotropic synchronous motors (SMs) Then the estimated d-axis and q-axis inductances converge to their actual values, and the position observation error will be 0, and the expression of the general gradient descent optimizer is:

[0154]

[0155] in:

[0156]

[0157] In the formula, represents the estimated value of the self-inductance on the δ-axis after the k-th iteration in the optimizer; represents the estimated value of self-inductance on the γ axis after the k-th iteration in the optimizer; It represents the iterative position error at step k in the optimizer, and its initial value is α is a positive learning rate.

[0158] S5) By extending the EEMF full state observer, the estimated parameters and position observation error The motor is controlled sensorlessly based on the estimated current and parameters and the observed voltage information. For an isotropic motor, due to L γγ =L δδ =L d =L q =L s , L d and L q The value of does not change with the rotor position, and no position correction is required, so the estimated parameter It can be directly used in the extended electromotive force EEMF full state observer, only feeding back the estimated value of the stator resistance And each phase inductance Accurate estimation of the motor state is achieved, thereby achieving precise control of the motor. For anisotropic motors, due to L d ≠L q , the observed rotor position angle Not accurate, considering the self-inductance L on the δ axis δδ , self-inductance L on the γ axis γγ The existence relationship is a convex function as shown in formula (22). Therefore, the general gradient descent optimizer shown in formula (23) is used to determine the iterative position error of the kth step after performing enough iterations. At the same time, the estimated values ​​of d-axis inductance and q-axis inductance are It also converges to the actual value, that is, Feedback to the extended electromotive force EEMF full state observer, position observation error will be 0.

[0159] S6) During the operation of the system, steps S2)-S5) are continuously repeated to achieve online parameter estimation and real-time correction of position errors. The multi-parameter adaptive observer and gradient descent optimizer of this embodiment run in parallel with the model-based sensorless control. s and q-axis inductance to ensure that the system can achieve accurate position observation results within the rated speed and torque range.

[0160] Example 2

[0161] like Figure 1 As shown, this embodiment provides a parameter identification and position correction system for a permanent magnet synchronous motor under position-free control, the system comprising:

[0162] The extended electromotive force full state observer is used to calculate the input signal voltage u αβ and current I αβ Calculate the estimated electromotive force e αβ ;

[0163] The inverse tangent module is used to calculate the electromotive force e αβ Calculate the motor's rotor position angle And the rotor position angle Perform differential operation to obtain the estimated value of the rotor's angular velocity

[0164] Bandpass filter to extract the voltage u γδ and current I γδ The high frequency voltage u γδh and high frequency current I γδh ;

[0165] This embodiment adopts a second-order Butterworth bandpass filter, and its transfer function is as follows:

[0166]

[0167] Where s is the Laplace transform operator, ω n is the natural frequency of the filter, which determines the bandwidth of the filter. The higher the natural frequency, the narrower the bandwidth, but the greater the attenuation of high-frequency signals. ζ is the damping ratio of the filter, which determines the attenuation speed of the filter. The higher the damping ratio, the faster the attenuation speed, but the wider the transition band. At this time, according to the estimated value of the rotor angular velocity Select the appropriate natural frequency ω of the filter n, generally based on the injected signal frequency and noise frequency range, the center frequency is calculated as ω n The initial value of the voltage u γδ and current I γδ Filter and subtract the voltage u from it γδ and current I γδ The low-frequency signal in the high-frequency voltage u is obtained γδh and high frequency current I γδh .u γδh ,I γδh

[0168] Sinusoidal small signal impedance model module, used to extract the high-frequency voltage signal u according to the bandpass filter γδh and high frequency current signal I γδh , calculated by equations (3) and (6), the estimated values ​​of stator resistance, inductance and permanent magnet flux are obtained;

[0169]

[0170] In the formula, u γδh Represents the voltage on the γ and δ axes under high-frequency input; I γδh Represents the current on the γ and δ axes under high-frequency input; Indicates the rate of change of current on the γ and δ axes under high-frequency input; ω e0 is the electrical speed ω e The DC component of eh is the electrical velocity fluctuation at a specific injection frequency; I γδ0 is the DC component of the current on the γ and δ axes; represents the estimated value of stator resistance; It represents the estimated value of the current on the γ and δ axes under high frequency input; represents the estimated value of mutual inductance on the γ-axis and the δ-axis; Indicates electrical speed ω e An estimate of the DC component of ; represents an estimate of the electrical speed fluctuation at a specific injection frequency; It represents the estimated error of the current on the γδ axis under high frequency input, which is expressed as the difference between the actual current and the estimated current; K1 and K2 are feedback matrices; sgn is the sign function.

[0171] A multi-parameter adaptive observer is used to calculate the high-frequency voltage u γδh and I γδh , and the angular velocity of the rotor Combined with the sinusoidal small signal impedance model module, the estimated value is updated using formula (14), thereby realizing online estimation of motor parameters;

[0172]

[0173] In the formula, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for resistor; represents the estimated value vector of the current on the γ and δ axes under high frequency input; It represents the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated value of the electrical speed fluctuation at a specific injection frequency; I γδ0 Represents the DC component of the current on the γ and δ axes; represents the rate of change of the estimated value of the self-inductance on the γ axis; Γ L,11 , Γ L,22 , Γ L,12 denote the symmetric positive definite gain matrices associated with the self-inductance on the γ axis, the self-inductance on the δ axis, and the mutual inductance on the γ axis and the δ axis respectively; represent the estimated value and estimation error of the current on the γ axis respectively; They represent the estimated value and estimation error of the current on the δ axis respectively; represents the rate of change of the estimated value of the current on the γ axis; represents the rate of change of the estimated value of the current on the δ axis; represents the rate of change of the estimated value of the self-inductance on the δ-axis; Indicates the rate of change of the estimated value of the mutual inductance on the γ-axis and the δ-axis.

[0174] The gradient descent optimizer is used to further adjust the estimated values ​​of the parameters of the non-orthogonal anisotropic synchronous motor according to equations (23) and (24). The specific parameters directly adjusted are: and They represent the estimated values ​​of self-inductance on the δ-axis and γ-axis after the k-th iteration in the optimizer, and are substituted into and Directly estimate each parameter and finally output the estimated value of stator resistance Estimated value of permanent magnet flux linkage Estimated d-axis and q-axis inductance and rotor position angle To expand the EMF full state observer.

[0175]

[0176] in:

[0177]

[0178] In the formula, represents the estimated value of the self-inductance on the δ-axis after the k-th iteration in the optimizer; represents the estimated value of self-inductance on the γ axis after the k-th iteration in the optimizer; It represents the iterative position error at step k in the optimizer, and its initial value is α is a positive learning rate.

[0179] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control, characterized in that: The following steps are involved: S1) Establish a unified sinusoidal small signal impedance model of synchronous motor in non-orthogonal synchronous coordinate system γδ; divide the sinusoidal small signal impedance model into large signal model and small signal model, and output the observed rotor position angle based on sensorless control technology. S2), design a multi-parameter adaptive observer, and estimate the current, stator resistance, and inductance through a feedback matrix, and design a feedback matrix to adjust the convergence speed of the current estimation; S3) Track the current trajectory in the estimated current and find the unique solution through the continuous excitation condition For orthogonal motors, a small signal is injected only in the γ-axis to satisfy continuous excitation. For non-orthogonal motors, a small signal is injected simultaneously in the γ-axis and the δ-axis, and the phase difference ∈ cannot be 0 or π; S4) For non-orthogonal anisotropic synchronous motors, an optimizer based on the gradient descent method is designed. Use the optimizer to iterate and adjust the d-axis and q-axis inductance estimates and Position observation error Converges to zero; S5) By extending the EEMF full state observer, the estimated parameters and position observation error Sensorless control of motors; S6) During the operation of the system, steps S2)-S5) are continuously repeated to achieve online estimation of parameters and real-time correction of position errors.

2. A method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 1, characterized in that: In step S1), in order to realize multi-parameter estimation under sensorless control, the state equation of the unified synchronous motor on the synchronous rotation γδ axis with position error misalignment is established: Where u γδ Represents the voltage on the γ and δ axes; R s is the stator resistance; I γδ Indicates the current on the γ and δ axes; L γδ represents the mutual inductance on the γ and δ axes; Represents the current derivative on the γ and δ axes, that is, the rate of change of current; ω e is the electrical speed; J is the moment of inertia; ψ γδ is the permanent magnetic flux on the γ and δ axes; The sinusoidal small signal impedance model is obtained from equation (2) by multiplying the specific injection frequency and the velocity change of the basic flux component, namely: u γδh =R s I γδh +L γδ and γδh +ω e0 JL γδ I γδh +ω eh (L γδ I γδ0 +ψ γδ ) (3) In the formula, u γδh Represents the voltage on the γ and δ axes under high-frequency input; I γδh Represents the current on the γ and δ axes under high-frequency input; Indicates the rate of change of current on the γ and δ axes under high-frequency input; ω e0 is the electrical speed ω e The DC component of eh is the electrical velocity fluctuation at a specific injection frequency; I γδ0 is the DC component of the current on the γ and δ axes.

3. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 2, characterized in that: In step S1), in order to reduce the extended unknown state, equation (3) is expressed as the large signal model, that is: In the formula, u γδ0 Represents the DC component of the voltage on the γ and δ axes; I γδ0 Represents the DC component of the current on the γ and δ axes; Formula (3) is expressed as the small signal model, that is: middle, represents the estimated value of stator resistance; It represents the estimated value of the current on the γ and δ axes under high frequency input; represents the estimated value of mutual inductance on the γ-axis and the δ-axis; Indicates electrical speed ω e An estimate of the DC component of ; represents an estimate of the electrical velocity fluctuation at a specific injection frequency; represents the estimated error of the current on the γδ axis under high frequency input, which is expressed as the difference between the actual current and the estimated current; K1 and K2 are feedback matrices; sgn is the sign function; By comparing the differences between formula (5) and formula (6), we get formula (7), namely: In the formula, It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated error of the electrical speed fluctuation at a specific injection frequency; represents the estimated error of the stator resistance; represents the estimated error of mutual inductance on the γ-axis and the δ-axis; It represents the rate of change of the estimated current value on the γ and δ axes under high frequency input; Rewrite (7) into the parameter error vector form, that is: in, In the formula, It represents the rate of change of the estimated value of the current on the γ axis under high frequency input; It represents the rate of change of the estimated value of the current on the delta axis under high frequency input; It represents the estimated value of the current on the γ axis under high frequency input; I γ0 Represents the DC component of the current on the γ axis; It represents the estimated value of the current on the delta axis under high frequency input; I δ0 Represents the DC component of the current on the δ axis; represents the estimated error of the stator resistance; represents the estimated error of the self-inductance on the γ axis; represents the estimated error of mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the self-inductance on the δ-axis; T represents the transposition operation.

4. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 3 is characterized in that: In step S2), the estimated current signal is ensured by using the Lyapunov candidate function Tracking actual current small signal I γδh And the estimated parameters converge to the actual value, the expression of the Lyapunov candidate function V is: Where V represents the Lyapunov candidate function, which is used to ensure the stability of the system; represents the estimated error of the current on the γδ axis under high frequency input; L γδ represents the mutual inductance on the γ-axis and the δ-axis; represents the estimated error of the mutual inductance on the γ axis and the δ axis; Γ R is the positive gain element estimated by the resistor; Γ L is the symmetric positive definite gain matrix for inductance estimation; tr(·) is the trace of the square matrix, defined by the sum of its diagonal elements; From formula (10), we can see that V is greater than 0 unless the current small signal estimation error is zero, that is, When V=0; By assuming that the electrical parameters are constant over short periods of time, Get the derivative of the Lyapunov candidate function Right now: In the formula, represents the derivative of V; It represents the estimated error of the current on the γδ axis under high frequency input; It represents the rate of change of the estimated error of the current on the γ and δ axes under high frequency input; Represents the rate of change of the mutual inductance estimation value on the γ and δ axes; represents the estimated error of the mutual inductance on the γ-axis and the δ-axis.

5. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 4, characterized in that: In step S2), by selecting the parameter adaptation rule of formula (14) and removing the parameter error term in formula (13), a multi-parameter adaptive observer shown in formula (15) is obtained: In the formula, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for resistor; Represents the estimated value vector of the current on the γ and δ axes under high frequency input; It represents the estimated error of the current on the γ and δ axes under high frequency input; represents the estimated value of the electrical speed fluctuation at a specific injection frequency; I γδ0 Represents the DC component of the current on the γ and δ axes; represents the rate of change of the estimated value of the self-inductance on the γ axis; Γ L,11 , Γ L,22 , Γ L,12 denote the symmetric positive definite gain matrices associated with the self-inductance on the γ axis, the self-inductance on the δ axis, and the mutual inductance on the γ axis and the δ axis respectively; represent the estimated value and estimation error of the current on the γ axis respectively; They represent the estimated value and estimation error of the current on the δ axis respectively; represents the rate of change of the estimated value of the current on the γ axis; represents the rate of change of the estimated value of the current on the δ axis; represents the rate of change of the estimated value of the self-inductance on the δ-axis; Indicates the rate of change of the estimated value of the mutual inductance on the γ-axis and the δ-axis.

6. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 5, characterized in that: Step S3), to find the unique solution A sufficient condition for is that the matrix Φ in equation (9) is continuously excited, which is based on the continuous excitation condition lemma of equation (18), namely: for exist So that: In the formula, TA is a positive real number, which indicates the length of the time interval of the integration, ζ is a positive real number, which indicates the lower bound of the integration result; I represents the unit matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector Converge the exponential to 0 4×1 ; Due to the d-axis inductance L d and q-axis inductance L q Equal, that is, L d =L q =L s ,For an isotropic synchronous motor SM, continuous excitation regulation can be satisfied simply by injecting a small signal in the γ-axis.

7. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 6, characterized in that: Step S3), for non-orthogonal motors, assume that a pair of small current signals in equation (19) are injected into the γδ-axis, and substitute equation (19) into equation (18) to obtain that both the γ-axis and the δ-axis contain additional sinusoidal components, and the phase difference ∈ cannot be 0 or π, then the parameter estimation error vector The exponential converges to 0 4×1 ; In the formula, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Represents the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h It represents the angular frequency of the corresponding signal under the input; t is the time variable, which represents the time elapsed from a certain initial moment; ∈ is the phase difference relative to the first component.

8. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 7, characterized in that: In step S4), for non-orthogonal isotropic synchronous motors SMs, due to the observation error at any given position There are L below δδ =L γγ =L d =L q =L s , the parameters estimated by the adaptation rule of Eq. (14) are directly used in the model-based position observer. For non-orthogonal anisotropic synchronous motors SMs, L γγ and L δδ The differences between are: Where, L δδ represents the self-inductance on the δ axis; L γγ represents the self-inductance on the γ axis; L q represents the q-axis inductance; L d represents the d-axis inductance; represents the position observation error; From formula (22), we can see that due to the anisotropy of the rotor, L γγ and L δδ The difference is a convex function, and the general gradient descent optimizer shown in Equation (23) is used to find the model-based position observation error caused by parameter mismatch Once the position observation error is found for anisotropic synchronous motors SMs Then the estimated d-axis and q-axis inductances converge to their actual values, and the position observation error will be 0, and the expression of the general gradient descent optimizer is: in: In the formula, represents the estimated value of the self-inductance on the δ-axis after the k-th iteration in the optimizer; represents the estimated value of self-inductance on the γ axis after the k-th iteration in the optimizer; It represents the iterative position error at step k in the optimizer, and its initial value is α is a positive learning rate.

9. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 8, characterized in that: In step S5), for an isotropic motor, due to L γγ =L δδ =L d =L q =L s , L d and L q The value of does not change with the rotor position, and no position correction is required, so the estimated parameter Directly used in the extended electromotive force EEMF full state observer, only feeding back the stator resistance estimate And each phase inductance Achieve accurate estimation of the motor state and precise control of the motor; For anisotropic motors, due to L d ≠L q , the observed rotor position angle Not accurate, considering the self-inductance L on the δ axis δδ , self-inductance L on the γ axis γγ The existence relationship is a convex function as shown in formula (22), so the general gradient descent optimizer shown in formula (23) is used to determine the iterative position error of the kth step after performing enough iterations. At the same time, the estimated values ​​of d-axis inductance and q-axis inductance are Converges to the actual value, that is Feedback to the extended electromotive force EEMF full state observer, position observation error will be 0.

10. A parameter identification and position correction system for a permanent magnet synchronous motor under position-free control, characterized in that: The system uses the method described in any one of claims 1 to 9 to perform parameter identification and position correction, and the system includes: The extended electromotive force full state observer is used to calculate the input signal voltage u αβ and current I αβ Calculate the estimated electromotive force e αβ ; The inverse tangent module is used to calculate the electromotive force e αβ Calculate the motor's rotor position angle And the rotor position angle Perform differential operation to obtain the estimated value of the rotor's angular velocity Bandpass filter to extract the voltage u γδ and current I γδ The high frequency voltage u γδh and high frequency current I γδh ; Sinusoidal small signal impedance model module, used to extract the high-frequency voltage signal u according to the bandpass filter γδh and high frequency current signal I γδh , calculated by equation (3) and equation (6), the estimated values ​​of stator resistance, inductance and permanent magnet flux are obtained; A multi-parameter adaptive observer is used to calculate the high-frequency voltage u γδh and I γδh , and the angular velocity of the rotor Combined with the sinusoidal small signal impedance model module, the estimated value is updated using formula (14), thereby realizing online estimation of motor parameters; The gradient descent optimizer is used to further adjust the estimated values ​​of the parameters of the non-orthogonal anisotropic synchronous motor according to equations (23) and (24). The specific parameters directly adjusted are: and They represent the estimated values ​​of self-inductance on the δ-axis and γ-axis after the k-th iteration in the optimizer, and are substituted into and Directly estimate each parameter and finally output the estimated value of stator resistance Estimated value of permanent magnet flux linkage Estimated d-axis and q-axis inductance and rotor position angle To expand the EMF full state observer.

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