Synchronous identification method of motor speed and stator resistance based on adaptive observer

Abstract

The application relates to the technical field of motor driving control, in particular to a synchronous identification method for motor rotating speed and stator resistance based on an adaptive observer, which comprises the following steps: constructing an induction motor mathematical model containing stator resistance variation based on the state equation of the induction motor; establishing an extended high-gain observer including unknown parameter identification and system state estimation according to the induction motor mathematical model; transforming the dynamic weight matrix of the extended high-gain observer to obtain an adaptive gain dynamic equation group; and substituting the adaptive gain dynamic equation group into the extended high-gain observer to establish an adaptive high-gain observer for synchronous identification of the stator resistance and the rotating speed. The real-time estimation of the rotor flux, the rotating speed and the stator resistance of the induction motor at the low-speed section is realized, and the robustness of the control system is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of motor drive control, in particular to a synchronous identification method for motor speed and stator resistance based on an adaptive observer. BACKGROUND

[0002] As the core equipment in the industrial drive field, the induction motor has the characteristics of nonlinearity, strong coupling and multivariable, which leads to inherent defects such as dynamic response lag and parameter sensitivity of traditional speed regulation methods. The key to high-performance vector control lies in accurate acquisition of speed and flux linkage information. However, due to the low reliability and limited installation space of the speed sensor in the traditional scheme, the speed sensorless technology emerges as the times require, aiming to get rid of the dependence on the speed sensor, and to realize accurate estimation of the flux and speed by analyzing the relationship between various electrical quantities of the motor and using the easily measured voltage and current signals.

[0003] In the observer design based on the ideal model of the motor, it is usually assumed that the parameters used in the design strictly correspond to the parameters of the motor. However, under actual working conditions, the internal electromagnetic characteristics of the motor are affected by multiple dynamic disturbances, such as nonlinear drift of inductance caused by magnetic saturation, frequency variation characteristics of rotor impedance caused by skin effect, and continuous shift of resistance value caused by winding temperature rise. Such parameter perturbations cause essential deviations between the dynamic equation of the observer and the real motor. Among them, the change of stator resistance is the most concerned, which will drift due to factors such as temperature change, winding aging or manufacturing deviation. This parameter uncertainty may lead to a decrease in observer performance or even system instability. Especially at low speed, the back electromotive force decreases, resulting in a relatively increased proportion of stator resistance voltage drop in the terminal voltage, and the mismatch of stator resistance parameters will directly lead to the decoupling error of stator current, and then cause the system to lose control. SUMMARY

[0004] To solve the above problems, the present application provides a synchronous identification method for motor speed and stator resistance based on an adaptive observer, which introduces online identification of stator resistance to realize real-time tracking of stator resistance and motor speed in the low speed domain.

[0005] The first aspect of the present application provides a synchronous identification method for motor speed and stator resistance based on an adaptive observer, comprising:

[0006] Based on the state equation of the induction motor, a mathematical model of the induction motor containing the change of stator resistance is constructed;

[0007] According to the mathematical model of the induction motor, an extended high-gain observer including unknown parameter identification and system state estimation is established;

[0008] The dynamic weight matrix of the extended high-gain observer is transformed to obtain the adaptive gain dynamic equation set; the adaptive gain dynamic equation set is then substituted into the extended high-gain observer to establish an adaptive high-gain observer that synchronously identifies stator resistance and rotational speed.

[0009] The mathematical model of the induction motor is as follows:

[0010] ,

[0011] ,

[0012] ,

[0013] ,

[0014] ,

[0015] In the formula, x Represents the system state matrix. ; y represents the output variable matrix, C represents the output matrix. ; u Indicates control input, ; θ For unknown parameters, ; F(u, x, θ ) is the coefficient matrix; , ε ( u, x, θ These are nonlinear matrices; For rotational speed, This represents the number of pole pairs of the motor. J This is the total moment of inertia of the rotor and the load. This is the load torque; , These represent the stator currents respectively. Axial components; , These represent the rotor flux linkages. Axial components; , These represent the stator voltages respectively. Axial components; The leakage flux coefficient of the motor. ; The rotor electromagnetic time constant is ; R s Stator resistance; R r For rotor resistance; L s For the stator inductance of the motor; Lr is the rotor inductance; L m is the mutual inductance between stator and rotor.

[0016] The extended high gain observer is:

[0017] ,

[0018] ,

[0019] ,

[0020] wherein, represents the observer state, ; represents the unknown parameters of the observer, ; is the adjustable gain parameter; , and are the scaling matrices of state estimation and parameter estimation respectively; H represents the dynamic weight matrix; F ( u, x, θ ) is the coefficient matrix; , ε ( u, x, θ ) are the nonlinear matrices respectively; is the rotor speed; , represent the axis components of the stator current respectively; , represent the axis components of the rotor flux respectively; u represents the control input, ; , represent the axis components of the stator voltage respectively; R s is the stator resistance.

[0021] The specific operation of transforming the dynamic weight matrix of the extended high gain observer to obtain the adaptive gain dynamic equation set is:

[0022] The dynamic weight matrix H of the extended high gain observer is divided to obtain the decomposed symmetric positive definite matrix H 1 after division, and the Schur complement H 1 of the symmetric positive definite matrix W is obtained;

[0023] Based on the Schur complement, the dynamic weight matrixH transforming to obtain a transformed regression matrix;

[0024] obtaining an inverse matrix of the transformed dynamic weight matrix H obtaining a symmetric positive definite inverse matrix from the inverse matrix H 1 -1 corresponding inverse matrix Schur complement W -1 based on the inverse matrix Schur complement W -1 obtaining a gain matrix;

[0025] obtaining an adaptive gain dynamic equation group composed of the dynamic weight matrix, the regression matrix and the gain matrix according to a solving formula of the dynamic weight matrix.

[0026] The formula of the adaptive gain dynamic equation group is:

[0027] .

[0028] The expression of the adaptive high-gain observer is:

[0029] .

[0030] The synchronous identification method of the motor speed and the stator resistance further comprises judging the stability of the adaptive high-gain observer through a Lyapunov function after establishing the adaptive high-gain observer for synchronous identification of the stator resistance and the speed.

[0031] The second aspect provides a synchronous identification system of a motor speed and a stator resistance based on an adaptive observer, comprising:

[0032] An initial module is configured to construct an induction motor mathematical model containing stator resistance variation based on a state equation of the induction motor.

[0033] A processing module is configured to establish an extended high-gain observer including unknown parameter identification and system state estimation according to the induction motor mathematical model.

[0034] The processing module is further configured to transform a dynamic weight matrix of the extended high-gain observer to obtain an adaptive gain dynamic equation group, and to establish an adaptive high-gain observer for synchronous identification of the stator resistance and the speed by substituting the adaptive gain dynamic equation group into the extended high-gain observer.

[0035] The third aspect provides a synchronous identification device of a motor speed and a stator resistance based on an adaptive observer, comprising a processor and a memory, wherein the processor realizes the synchronous identification method of the motor speed and the stator resistance as described above when executing a computer program saved in the memory.

[0036] The fourth aspect provides a computer readable storage medium for storing a computer program, wherein the computer program is executed by a processor to implement the synchronous identification method of motor speed and stator resistance as described above.

[0037] Beneficial effects: The application is a synchronous identification method of motor speed and stator resistance based on an adaptive observer, which considers the actual situation of stator resistance variation, sets the stator resistance as an unknown parameter, and the established induction motor mathematical model is more in line with the actual operation state of the induction motor; by establishing an extended high-gain observer, the dynamics of the induction motor system state is extended to the dynamics of the unknown parameter to estimate the parameter, which can realize the synchronous identification of the system state and the time-varying characteristics of the unknown parameter, and the dynamic weight matrix is obtained by solving the ordinary differential equation, which is used to adjust the sensitivity of the extended high-gain observer in the error correction term, so that the observer can adapt to the dynamic change of the induction motor state system and the parameter uncertainty at the same time, and the adaptability and accuracy of the observer are improved; at the same time, the adaptive high-gain observer for synchronous identification of stator resistance and speed is established based on the extended high-gain observer, the state estimation convergence is judged by Lyapunov stability theory, and the real-time estimation of rotor flux, speed and stator resistance of the induction motor at the low speed stage is realized. BRIEF DESCRIPTION OF DRAWINGS

[0038] The schemes and advantages of the present application will become clear to those skilled in the art from the following detailed description of the preferred embodiments. The accompanying drawings are merely intended to illustrate the preferred embodiments and should not be considered as limiting the present application.

[0039] In the drawings:

[0040] Figure 1 Flow chart of the synchronous identification method of induction motor speed and stator resistance based on adaptive high-gain observer;

[0041] Figure 2 System block diagram of the synchronous identification method of induction motor speed and stator resistance. DETAILED DESCRIPTION

[0042] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings.

[0043] Referring to Figure 1 The embodiment provides a synchronous identification method of motor speed and stator resistance based on an adaptive observer, and specific steps of the method include:

[0044] S1, based on the state equation of the induction motor, constructing an induction motor mathematical model containing stator resistance variation;

[0045] Firstly, the induction motor is in α-βThe state equation in the coordinate system is:

[0046] ,

[0047] , , ,

[0048] , , ,

[0049] In the formula, is the rotating speed, is the pole pair number of the motor, J is the total moment of inertia of the rotor and the load, is the load torque; , respectively represent the axis components of the stator current; , respectively represent the axis components of the rotor flux linkage; , respectively represent the axis components of the stator voltage; is the leakage coefficient of the motor, ; is the rotor electromagnetic time constant, ; R s is the stator resistance; R r is the rotor resistance; L s is the stator inductance of the motor; L r is the rotor inductance; L m is the mutual inductance between the stator and the rotor.

[0050] Considering the change of the stator resistance, the stator resistance is set as an unknown parameter, and the mathematical model of the induction motor containing the change of the stator is established as:

[0051] ,

[0052] ,

[0053] ,

[0054] ,

[0055] ,

[0056] In the formula, xRepresents the system state matrix. ; y represents the output variable matrix, C represents the output matrix. ; u Indicates control input, ; θ For unknown parameters, ; F(u, x, θ ) is the coefficient matrix; , ε ( u, x, θ ) are nonlinear matrices.

[0057] S2. Based on the mathematical model of the induction motor, establish an extended high-gain observer that includes the identification of unknown parameters and the estimation of system state;

[0058] To ensure the validity of the observer's estimation of unknown parameters, assumptions must be declared to prepare for subsequent stability proofs of the observer.

[0059] First, to avoid divergence caused by unbounded functions and to ensure the rationality of system state, control input, and unknown parameters, we must assume the existence of compact sets. , , ( ) makes , , .

[0060] Secondly, the coefficient matrix in the mathematical model of the induction motor and nonlinear matrices , about x They are Lipschitz continuous, and their Lipschitz constants are respectively , and This ensures the differentiability of the state equations.

[0061] Finally, by ensuring that the solution of the nonlinear matrix ordinary differential equation remains positive definite in any time, the singularity of the observer gain is avoided; at the same time, by using the continuous excitation condition to ensure that the control input can provide sufficient information to estimate the state and parameters, the stability and convergence of the observer are ensured.

[0062] The extended high-gain observer, based on the high-gain observer, extends the dynamics of the induction motor system state to the dynamics of unknown parameters to estimate parameters, achieving synchronous identification of the time-varying characteristics of the system state and unknown parameters. It is suitable for MIMO nonlinear systems containing unknown parameters. Therefore, the extended high-gain observer is established, and its formula is:

[0063] ,

[0064] ,

[0065] ,

[0066] wherein, represents the observer state, ; represents the unknown parameters of the observer, ; is an adjustable gain parameter; , and are scaling matrices of state estimation and parameter estimation, respectively; H represents a dynamic weight matrix.

[0067] The dynamic weight matrix of the extended high-gain observer is obtained by solving an ordinary differential equation, which is used to adjust the sensitivity of the extended high-gain observer in the error correction term, so that the extended high-gain observer can adapt to the dynamic changes of the state system and parameter uncertainty of the induction motor at the same time.

[0068] The dynamic weight matrix H is:

[0069] .

[0070] S3, transform the dynamic weight matrix of the extended high-gain observer to obtain an adaptive gain dynamic equation group; substitute the adaptive gain dynamic equation group into the extended high-gain observer to establish an adaptive high-gain observer for synchronous identification of stator resistance and speed;

[0071] The dynamic weight matrix of the extended high-gain observer is transformed to obtain an adaptive gain dynamic equation group, and the specific operation is:

[0072] S3.1, divide the dynamic weight matrix of the extended high-gain observer to obtain a divided and decomposed symmetric positive definite matrix, and obtain the Schur complement of the symmetric positive definite matrix;

[0073] The dynamic weight matrix H is divided into:

[0074] .

[0075] In this embodiment, the dynamic weight matrix H is a symmetric positive definite matrix , so is divided into a symmetric positive definite matrix , is divided into a matrix , is divided into one symmetric positive definite matrix.

[0076] by giving in Schur complement exists, the H 1 in H Schur complement W is expressed as:

[0077] .

[0078] S3.2, transform the dynamic weight matrix based on the Schur complement, to obtain the transformed regression matrix;

[0079] According to the positive definite matrix and its Schur complement W , the dynamic weight matrix H is transformed by using the Schur complement, and the dynamic weight matrix H is transformed into:

[0080] ,

[0081] In the formula, I n and I m are unit matrices, n =4, m =2; is the regression matrix, .

[0082] S3.3, obtain the inverse matrix of the transformed dynamic weight matrix, obtain the inverse matrix Schur complement corresponding to the symmetric positive definite inverse matrix according to the inverse matrix, and obtain the gain matrix based on the inverse matrix Schur complement;

[0083] Since the dynamic weight matrix H is a symmetric positive definite matrix, the inverse matrix of the transformed dynamic weight matrix H is determined as:

[0084]

[0085] In the formula , P denotes the gain matrix.

[0086] S3.4, according to the solving formula of the dynamic weight matrix, obtain the adaptive gain dynamic equation composed of the dynamic weight matrix, the regression matrix and the gain matrix, and the equation group formula is:

[0087] .

[0088] Substitute the adaptive gain dynamic equation into the extended high-gain observer to obtain an adaptive high-gain observer;

[0089] Substituting the adaptive gain dynamic equation obtained in S3.4 into the correction term of the extended high-gain observer, we obtain the adaptive high-gain observer, whose expression is:

[0090] ,

[0091] According to the expression of the adaptive high-gain observer, the estimation of unknown parameters depends entirely on the terms containing the gain matrix P. When P=0, the unknown parameter estimation terms are 0. However, the pure state estimation correction (without the gain matrix P) and the parameter coupling terms (containing the gain matrix P) in the system state estimation are related. Even if P is 0, it can still be corrected by the pure state estimation.

[0092] To avoid the computational complexity caused by calculating the inverse matrix, we utilize... Substituting into the Lyapunov differential equation for indirect calculation, the following equation is the final derived adaptive high-gain observer:

[0093]

[0094] In the formula, the upper triangular matrix is: The nonlinear matrix is ​​represented as: , .

[0095] like Figure 2 The diagram shown is a system block diagram for synchronous identification of induction motor speed and stator resistance based on an adaptive high-gain observer. The control system of the induction motor adds simultaneous identification of speed and stator resistance on the basis of the adaptive high-gain observer, realizing real-time estimation of rotor flux, speed and stator resistance of the induction motor in the low-speed range, which effectively improves the robustness of the control system.

[0096] Furthermore, in constructing an adaptive high-gain observer that synchronously identifies stator resistance and rotational speed, the stability of the observer is determined using a Lyapunov function. The specific operation is as follows:

[0097] One of the necessary conditions for the convergence of system state and unknown parameter estimation is that the continuous excitation condition is satisfied, namely: , , ,right and ,satisfy:

[0098] ,

[0099] in, The minimum time required for continuous excitation; if this time is less, the system cannot converge. Minimum gain to ensure stability; is the lower bound of excitation strength constant; is the state transition matrix; is the parameter gain scaling matrix; is the excitation amplitude adjustment function, , the upper limit of integration prevents the system from being unstable due to excessive excitation signal amplitude. When the system is in the working condition of rotating magnetic field excitation and non-zero load torque, the continuous excitation condition of simultaneous estimation of speed and stator resistance parameters is met.

[0100] On the basis of the system having met the continuous excitation condition, the convergence of the system state and unknown parameter estimation error is proved. First, the state error equation is obtained by subtracting the induction motor model established by S1 and the adaptive high-gain observer constructed by S3:

[0101]

[0102] In the formula, the system state and unknown parameters are represented as , the estimated system state and unknown parameters are , and the system state and unknown parameter estimation error is . The nonlinear disturbance matrix is and , and the coefficient matrix is: .

[0103] In order to simplify the calculation, let , according to the characteristics of the scaling matrix , the matrix can be converted to high-gain form:

[0104]

[0105] Using the above formula, further calculation is carried out:

[0106] .

[0107] The given Lyapunov function is , and the first derivative is:

[0108] ,

[0109] Using the Lipschitz continuity condition, the nonlinear disturbance term is constrained as:

[0110]

[0111] where, The minimum eigenvalue of , substitute it into the above formula to get

[0112]

[0113] The first-order partial derivative of the final Lyapunov function can be expressed as:

[0114]

[0115] wherein, .

[0116] and denote the upper bounds of the system state and unknown parameters, According to the above analysis, it can be seen that when the sustained excitation condition is met and the observer gain is large enough, the system state and parameter estimation error converge exponentially to zero, which shows that the method can realize the simultaneous identification of the state, speed and stator resistance of the induction motor.

[0117] Then, the application further provides a motor speed and stator resistance synchronous identification system based on an adaptive observer, comprising:

[0118] An initial module is configured to construct an induction motor mathematical model containing stator resistance variation based on the state equation of the induction motor.

[0119] A processing module is configured to establish an extended high-gain observer including unknown parameter identification and system state estimation according to the induction motor mathematical model.

[0120] The processing module is further configured to transform the dynamic weight matrix of the extended high-gain observer to obtain an adaptive gain dynamic equation set; and substitute the adaptive gain dynamic equation set into the extended high-gain observer to establish an adaptive high-gain observer for synchronous identification of the stator resistance and the speed.

[0121] In addition, a motor speed and stator resistance synchronous identification device based on an adaptive observer is provided, comprising a processor and a memory, wherein the processor implements the motor speed and stator resistance synchronous identification method as described above when executing the computer program stored in the memory.

[0122] Finally, a computer readable storage medium for storing a computer program is provided, wherein the computer program is executed by the processor to implement the motor speed and stator resistance synchronous identification method as described above.

Claims

1. A method for synchronous identification of motor speed and stator resistance based on an adaptive observer, characterized in that, include: Based on the state equation of the induction motor, a mathematical model of the induction motor with stator resistance variation is constructed. Based on the mathematical model of the induction motor, an extended high-gain observer is established, which includes the identification of unknown parameters and the estimation of system state. The extended high-gain observer is as follows: ， ， ， In the formula, Indicates the observer state. ; This represents the unknown parameters of the observer. , where ∧ represents the observed value of the corresponding parameter; This is an adjustable gain parameter; , and These are the scaling matrices for state estimation and parameter estimation, respectively; H C represents the dynamic weight matrix; C represents the output matrix. ; F ( u, x,θ ) is the coefficient matrix; , ε ( u,x,θ ) are nonlinear matrices; Rotational speed; , These represent the stator currents respectively. Axial components; , These represent the rotor flux linkages. Axial components; u Indicates control input, ; , These represent the stator voltages respectively. Axial components; R s Stator resistance; Transform the dynamic weight matrix of the extended high-gain observer to obtain the adaptive gain dynamic equation set; substitute the adaptive gain dynamic equation set into the extended high-gain observer to establish an adaptive high-gain observer that synchronously identifies stator resistance and rotational speed. The specific operation of transforming the dynamic weight matrix of the extended high-gain observer to obtain the adaptive gain dynamic equation system is as follows: Dynamic weight matrix for extended high-gain observer H The partitioning process yields a symmetric positive definite matrix after the partitioning. H 1 And obtain the symmetric positive definite matrix. H 1 Shuer Supplement W ; Based on the Shure complement dynamic weight matrix H Perform the transformation to obtain the transformed regression matrix; Obtain the transformed dynamic weight matrix H The inverse matrix, and the symmetric positive definite inverse matrix obtained from the inverse matrix. H 1 -1 The corresponding inverse matrix Schul complement W -1 Based on the Schur complement of the inverse matrix W -1 Obtain the gain matrix; Based on the formula for solving the dynamic weight matrix, we obtain the adaptive gain dynamic equation system consisting of the dynamic weight matrix, the regression matrix, and the gain matrix.

2. The method for synchronously identifying motor speed and stator resistance according to claim 1, characterized in that, The mathematical model of the induction motor is as follows: ， ， ， ， ， ， ， ， ， ， In the formula, x Represents the system state matrix. ; y represents the output variable matrix, C represents the output matrix. ; u Indicates control input, ; θ For unknown parameters, ; F(u,x,θ ) is the coefficient matrix; , ε ( u,x,θ ) are nonlinear matrices; For rotational speed, This represents the number of pole pairs of the motor. J This is the total moment of inertia of the rotor and the load. This is the load torque; , These represent the stator currents respectively. Axial components; , These represent the rotor flux linkages. Axial components; , These represent the stator voltages respectively. Axial components; The leakage flux coefficient of the motor. ; The rotor electromagnetic time constant is ; R s Stator resistance; R r For rotor resistance; L s For the stator inductance of the motor; L r For rotor inductance; L m This refers to the mutual inductance between the stator and rotor.

3. The method for synchronously identifying motor speed and stator resistance according to claim 1, characterized in that, The formula for the adaptive gain dynamic equation set is: ， in, This is the regression matrix; , P This represents the gain matrix.

4. The method for synchronously identifying motor speed and stator resistance according to claim 3, characterized in that, The expression for the adaptive high-gain observer is: ， Where y represents the output variable matrix, .

5. The method for synchronously identifying motor speed and stator resistance according to claim 1, characterized in that, After establishing an adaptive high-gain observer that synchronously identifies stator resistance and rotational speed, the method also includes using Lyapunov functions to determine the stability of the adaptive high-gain observer.

6. A synchronization identification system for motor speed and stator resistance based on an adaptive observer, implemented using the synchronization identification method for motor speed and stator resistance based on an adaptive observer as described in claim 1, characterized in that, include: The initial module is used to construct a mathematical model of an induction motor with stator resistance variation based on the state equation of the induction motor. The processing module is used to establish an extended high-gain observer, including the identification of unknown parameters and the estimation of system state, based on the mathematical model of the induction motor. The processing module is also used to transform the dynamic weight matrix of the extended high-gain observer to obtain an adaptive gain dynamic equation set; and to substitute the adaptive gain dynamic equation set into the extended high-gain observer to establish an adaptive high-gain observer that synchronously identifies stator resistance and rotational speed.

7. A synchronization identification device for motor speed and stator resistance based on an adaptive observer, characterized in that, It includes a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the synchronous identification method for motor speed and stator resistance as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the synchronous identification method for motor speed and stator resistance as described in any one of claims 1-5.

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