A method and system for parameter identification and position correction of permanent magnet synchronous motor under position-free control

Abstract

The present invention provides a method and system for parameter identification and position correction under positionless control of a permanent magnet synchronous motor. The method comprises establishing a sinusoidal small-signal impedance model; designing a multi-parameter adaptive observer; finding a unique solution through continuous excitation conditions; designing an optimizer based on the gradient descent method; and using an extended electromotive force (EEMF) full-state observer to perform sensorless motor control using estimated parameters and position observation errors. The above steps are repeated continuously to achieve online parameter estimation and real-time correction of position errors. By introducing a robust adaptive observer and an inductance optimizer, the present invention achieves parameter identification and position correction for both surface-mount and internal permanent magnet synchronous motors under position sensorless control, overcoming the drawbacks of traditional methods and enabling parameter identification at high speeds. Furthermore, the method can observe and optimize inductance, further improving the accuracy of position observation results, thereby achieving precise control of the permanent magnet synchronous motor.

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] Currently, various industries are undergoing a transformation towards electrification and intelligentization. The electrification of household appliances, more electric aircraft, and electric vehicles is rapidly gaining popularity. As the key power source of electrified systems, motors naturally face more challenges and opportunities.

[0003] Compared to traditional industrial motors, motors for these applications must have a wider speed range and stronger overload capacity to meet the speed regulation and traction requirements of the powertrain. Furthermore, due to space constraints, they must possess higher power density and efficiency to reduce the volume of the cooling system. Among various motor types, permanent magnet synchronous motors (PMSMs) are the preferred choice for electric vehicle main drive motors due to their strong overload capacity and wide-range field weakening capability. Furthermore, electric drive control must not only achieve high-efficiency operation but also precise speed and torque control across 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 operating conditions to achieve precise and intelligent control of the system. However, existing methods and mathematical models have the following drawbacks:

[0005] 1. Both the traditional electric drive control system and the parameter identification system are based on the mathematical model of the linear permanent magnet synchronous motor, which is expressed as follows:

[0006]

[0007] where R s is the motor stator winding resistance, 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 frequency of the injected high-frequency signal cannot be increased infinitely. Therefore, this solution can only realize parameter identification at zero speed and low speed. When the motor runs at high speed, this assumption does not hold. In addition, due to the characteristics of the 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 large errors in the observation of inductance. Summary of the Invention

[0010] In response to the shortcomings of the existing technology, 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 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 of a permanent magnet synchronous motor under positionless control, comprising the following steps:

[0012] S1) A unified sinusoidal small signal impedance model of the 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 injection including the AC component; based on the sensorless control technology, the rotor position angle is outputted.

[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 the 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 position mis-observation error is calculated based on the observed position mis-observation error. Use the optimizer to iteratively calculate and adjust the d-axis and q-axis inductance estimates and Position observation error Converges to zero;

[0016] S5) By extending the electromotive force EEMF full state observer and using the estimated parameters and position observation error Sensorless control of the motor;

[0017] 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. The multi-parameter adaptive observer and gradient descent optimizer run in parallel with the model-based sensorless control. By real-time estimation of the resistance R s and q-axis inductance to ensure that the system achieves 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 rotation 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 represents the moment of inertia; ψ γδ is the permanent magnet 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] Where 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 ω 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] Where 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), formula (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 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 estimation error of the current on the γδ axes 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] Where, 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 velocity 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] Where, It represents the rate of change of the estimated value of the γ-axis current under high-frequency input; It represents the rate of change of the estimated value of the δ-axis current 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] As a preference, 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, When 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] Where, represents the derivative of V; 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; Indicates 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] Where, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for the resistor; represents the estimated value vector of the current on the γ and δ axes under high-frequency input; It represents the estimation error of the current on the γ and δ axes under high-frequency input; represents the estimated value of the electrical velocity 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; denote the estimated value and estimation error of the current on the γ axis, respectively; denote 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 eigenvalues ​​of Q are derived by the following formula, namely:

[0049]

[0050] Where 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 Indicates 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] Where, represents the estimated value of the electrical velocity 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] Where TA is a positive real number, indicating the length of the integration time interval; ζ is a positive real number, indicating the lower bound of the integration result; I represents the identity matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector is 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 preference, in 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] Where, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Indicates the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h 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] As an example, in step S4), for non-orthogonal isotropic synchronous motors SMs, due to the observation error at any given position There is 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 them are:

[0065]

[0066] Where, L δδ represents the self-inductance on the δ axis; L γγ Indicates 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] Where, 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; Represents the iterative position error of the kth step in the optimizer, and its initial value is α is a positive learning rate.

[0072] As a preference, in step S5), for an isotropic motor, since 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 parameters It can be directly used in the extended electromotive force (EEMF) full-state observer, feeding back only the estimated stator resistance. and each phase inductance To achieve accurate estimation of the motor state, thus 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 relationship is shown in Equation (22) as a convex function, so the general gradient descent optimizer shown in Equation (23) is used to determine the iterative position error of the kth step after a sufficient number of 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] Extended electromotive force full state observer is used to calculate the voltage according to the input signal 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 rotor position angle of the motor And the rotor position angle Perform differential operation to obtain the estimated value of the rotor angular velocity

[0076] Bandpass filter to extract the voltage u γδ and current I γδ 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 equations (3) and (6), the estimated values ​​of stator resistance, inductance and permanent magnet flux are obtained;

[0078] 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 Equation (14) through the multi-parameter adaptive observer. 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 the extended 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 for surface-mount and interior permanent magnet synchronous motors under position sensorless control, overcoming the drawbacks of traditional methods and enabling 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 embodiments of the present invention will be further described below with reference to 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 unified sinusoidal small signal impedance model of the synchronous motor in the non-orthogonal synchronous coordinate system γδ; calculate the estimated values ​​of the 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 including the DC component and the dynamic characteristics of the system after the injection of the small signal including the 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 represents the moment of inertia; ψγδ is the permanent magnet flux on the γ and δ axes;

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

[0092] This embodiment uses a second-order Butterworth bandpass filter, whose 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 attenuation of high-frequency signals is also greater. 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 injection signal frequency and noise frequency range, the center frequency is calculated as ω n The initial value of the voltage u is 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, namely:

[0096]

[0097] Where 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 ω 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] Where 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] Where, 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 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 estimation error of the current on the γδ axes 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] Where, 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 velocity 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] Where, It represents the rate of change of the estimated value of the γ-axis current under high-frequency input; It represents the rate of change of the estimated value of the δ-axis current 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 and estimate the current, stator resistance, and inductance through the feedback matrix, and design the 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] Where, 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 Indicates 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] Where, represents the derivative of V; 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; Indicates 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), we can obtain the multi-parameter adaptive observer shown in formula (15):

[0128]

[0129] Where, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for the resistor; represents the estimated value vector of the current on the γ and δ axes under high-frequency input; It represents the estimation error of the current on the γ and δ axes under high-frequency input; represents the estimated value of the electrical velocity 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; denote the estimated value and estimation error of the current on the γ axis, respectively; denote 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 eigenvalues ​​of Q are derived by the following formula, namely:

[0131]

[0132] Where 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 Indicates 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] Where, represents the estimated value of the electrical velocity 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; the details are as follows:

[0139] In this embodiment, 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:

[0140] for exist So that:

[0141]

[0142] Where TA is a positive real number, indicating the length of the integration time interval; ζ is a positive real number, indicating the lower bound of the integration result; I represents the identity matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector is 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, assuming that a pair of small current signals in Equation (19) are injected into the γγ-axis, and Equation (19) is substituted into Equation (18), 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] Where, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Indicates the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h 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 position mis-observation error is calculated based on the observed position mis-observation error. Use the optimizer to iteratively calculate 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 is L below δδ =L γγ =L d =L q =L s , the parameters estimated by the adaptation rule of Equation (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 them are:

[0151]

[0152] Where, L δδ represents the self-inductance on the δ axis; L γγ Indicates 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] Where, 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; Represents the iterative position error of the kth step in the optimizer, and its initial value is α is a positive learning rate.

[0158] S5) By extending the electromotive force EEMF full state observer and using the estimated parameters and position observation error The motor is controlled without sensors, based on the estimated current and parameters, as well as 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 parameters It can be directly used in the extended electromotive force (EEMF) full-state observer, feeding back only the estimated stator resistance. and each phase inductance To achieve accurate estimation of the motor state, thus 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 relationship is shown in Equation (22) as a convex function, so the general gradient descent optimizer shown in Equation (23) is used to determine the iterative position error of the kth step after a sufficient number of 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 error. 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 achieves 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] Extended electromotive force full state observer is used to calculate the voltage according to the input signal 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 rotor position angle of the motor And the rotor position angle Perform differential operation to obtain the estimated value of the rotor angular velocity

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

[0165] This embodiment uses a second-order Butterworth bandpass filter, whose 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 attenuation of high-frequency signals is also greater. 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 injection signal frequency and noise frequency range, the center frequency is calculated as ω n The initial value of the voltage u is 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] Where 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 ω 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 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 estimation error of the current on the γδ axes 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] 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] Where, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for the resistor; represents the estimated value vector of the current on the γ and δ axes under high-frequency input; It represents the estimation error of the current on the γ and δ axes under high-frequency input; represents the estimated value of the electrical velocity 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; denote the estimated value and estimation error of the current on the γ axis, respectively; denote 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 non-orthogonal anisotropic synchronous 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 Equation (14) through the multi-parameter adaptive observer. 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 the extended EMF full state observer.

[0175]

[0176] in:

[0177]

[0178] Where, 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; Represents the iterative position error of the kth step in the optimizer, and its initial value is α is a positive learning rate.

[0179] The above embodiments and descriptions are only for explaining 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, which shall fall within the scope of the 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 the synchronous motor in the non-orthogonal synchronous coordinate system γδ; and divide the sinusoidal small signal impedance model into a large signal model and a small signal model. Based on the sensorless control technology, the observed rotor position angle is output. 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 the 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, according to the observed position observation error Use the optimizer to iteratively calculate and adjust the d-axis and q-axis inductance estimates and Position observation error Converges to zero; S5) By extending the electromotive force EEMF full state observer and using the estimated parameters and position observation error Sensorless control of the motor; 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. The 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 represents the moment of inertia; ψ γδ is the permanent magnet 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) Where 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 ω 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: Where 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 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 estimation 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: Where, 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 velocity 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; Rewrite (7) into the parameter error vector form, that is: in, Where, It represents the rate of change of the estimated value of the γ-axis current under high-frequency input; It represents the rate of change of the estimated value of the δ-axis current 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.

4. The method for parameter identification and position correction of a permanent magnet synchronous motor under position-free control according to claim 3, 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: Where, represents the derivative of V; 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; Indicates 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), the multi-parameter adaptive observer shown in formula (15) is obtained: Where, represents the rate of change of the estimated value of the stator resistance; Γ R Positive gain element estimated for the resistor; represents the estimated value vector of the current on the γ and δ axes under high-frequency input; It represents the estimation error of the current on the γ and δ axes under high-frequency input; represents the estimated value of the electrical velocity 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; denote the estimated value and estimation error of the current on the γ axis, respectively; denote 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) is to find the only 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: Where TA is a positive real number, indicating the length of the integration time interval; ζ is a positive real number, indicating the lower bound of the integration result; I represents the identity matrix; Φ(τ) represents a Φ matrix that changes with time, as defined in formula (9); then the parameter estimation error vector is 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 ; Where, I γδh Represents the current on the γ and δ axes under high-frequency input; I mγ Indicates the current amplitude on the γ axis; I mδ represents the current amplitude on the δ axis; ω h 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 is 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 them are: Where, L δδ represents the self-inductance on the δ axis; L γγ Indicates 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: Where, 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 the self-inductance on the γ axis after the k-th iteration in the optimizer; Represents the iterative position error of the kth step 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, since 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 parameters 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 motor status 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 relationship is shown in Equation (22) as a convex function, so the general gradient descent optimizer shown in Equation (23) is used to determine the iterative position error of the kth step after a sufficient number of 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 according to any one of claims 1 to 9 to perform parameter identification and position correction, and the system includes: Extended electromotive force full state observer is used to calculate the voltage according to the input signal 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 rotor position angle of the motor And the rotor position angle Perform differential operation to obtain the estimated value of the rotor angular velocity Bandpass filter to extract the voltage u γδ and current I γδ 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 equations (3) and (6), the estimated values ​​of stator resistance, inductance and permanent magnet flux are obtained; 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 non-orthogonal anisotropic synchronous 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 Equation (14) through the multi-parameter adaptive observer. 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 the extended EMF full state observer.

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