Observer design method for self-learning identification of induction motor parameters

Abstract

The application provides an observer design method for self-learning identification of induction motor parameters. Through design and simplification of the observer, all parameters of the induction motor can be quickly and accurately identified under the test conditions of induction motor static test or shaft rotation and the like in cooperation with the induction motor.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and more specifically, to an observer design method for self-learning and identifying parameters of an induction motor. Background Technology

[0002] High-performance operation of motor drives requires complex control algorithms and corresponding motor parameter information. However, existing technologies lack sufficient skills and tools to obtain the precise motor parameters required for high-performance motor control. Motor parameters include rotor resistance, stator resistance, rotor inductance, stator inductance, magnetizing inductance, and moment of inertia. These parameters are used to implement the motor's vector control algorithm. Therefore, motor drives must know the motor parameters from the outset. This is especially true for commercial motor drives, which cannot adapt to different types of motors and cannot accurately obtain motor parameter information in a short time. Traditional motor parameter identification methods involve a series of extensive motor tests under specified power supply and environmental conditions. When the motor cannot be isolated from the load or testing equipment is unavailable, the available hardware included in standard motor drives must be used to fully define the motor parameters, and self-learning must be used to automatically determine the motor parameters. However, self-learning requires special testing conditions such as a freely rotating rotor or a stationary motor. Existing technologies, such as sensorless control based on high-frequency signal injection, sensorless control based on observers, and control methods based on improving energy efficiency, such as maximum torque-to-current ratio (MTPA) control, have the following problems:

[0003] • It is not possible to fully identify all the parameters of the induction motor;

[0004] The long testing time makes it difficult for the entire parameter identification process to converge.

[0005] • Rotation testing requires the induction motor to be running; parameters of the induction motor cannot be obtained when the induction motor is stationary. Summary of the Invention

[0006] The problem solved by this invention is how to quickly and accurately identify all the identification parameters of an induction motor without the need for rotation testing.

[0007] To address the above problems, this invention provides an observer design method for self-learning identification of induction motor parameters, comprising:

[0008] Step 1: Construct the mathematical model of the induction motor:

[0009]

[0010] In the formula, i=(i a i b ) T For stator current, ia i represents the stator current component along the a-axis. b Represents the stator current component along the b-axis, ψ=(ψ a ,ψ b ) T Let ψ be the flux linkage vector. a ψ represents the flux linkage component of the flux linkage vector along the a-axis. b Let u represent the flux linkage vector along the b-axis, where u = (u a ,u b ) T Let u be the stator voltage vector. a u represents the stator voltage component along the a-axis. b This represents the stator voltage component along the b-axis, ω is the angular velocity, R1 is the stator resistance, and b, d, and γ0 are unknown characteristic parameters, where b = dα. γ0=αL m β+α, σ, α, and β are constants, defined by the motor parameters as follows:

[0011]

[0012] In the formula, R2 is the rotor inductance, L1 is the stator inductance, L2 is the rotor inductance, and L... m It is a magnetized inductor;

[0013] Step 2: Set the estimated values ​​of the sub-current and flux linkage vector pairs as follows: The error between the estimated values ​​of stator current and flux linkage vector and the actual identified parameters is calculated based on the mathematical model of the induction motor:

[0014]

[0015]

[0016]

[0017] In the formula, Indicates the error in stator current. This represents the error in the flux linkage vector. These represent the current component error of the stator current along the a-axis and the current component error along the b-axis, respectively. Let represent the flux linkage component error along the a-axis and the flux linkage component error along the b-axis, respectively. This represents the estimated value of b. This represents the estimated value of d. This represents the estimated value of γ0;

[0018] Step 3: Ensure the stator current error satisfies The error estimate of the flux linkage vector satisfies The errors of the unknown characteristic parameters b, d, γ0 satisfy... The mathematical model of the observer, derived from the mathematical model of the induction motor, is as follows:

[0019]

[0020] In the formula, k f >0 and k i >0 and all are adjustable coefficients; This is an estimate of the flux linkage vector error. It also serves as an auxiliary variable vector;

[0021] Step 4: Use Lyapunov functions Prove the global exponential stability of the observer's parameter identification and estimates, where Γ=diag[k f1 ,k f1 [γ1,γ2,γ3,γ4,γ4]>0,k f1 γ1, γ2, γ3, and γ4 are all adjustable coefficients;

[0022] Step 5: Solve for the identification parameters of the induction motor based on the mathematical model of the observer;

[0023] Step 6: Simplify the observer. The mathematical model of the simplified observer is as follows:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Step 7: Use Lyapunov functions to prove the local stability of the induction motor identification parameters and estimates of the simplified observer;

[0030] Step 8: Solve for the identification parameters of the induction motor based on the simplified mathematical model of the observer.

[0031] The beneficial effects of this invention are: by designing a simplified observer to work with the induction motor, all parameters of the induction motor can be quickly and accurately identified under test conditions such as static testing or shaft rotation testing. At the same time, the simplified observer can be integrated into the industrial drive or frequency converter as a separate functional module, making it easy to use.

[0032] Preferably, step 4 specifically includes:

[0033] Step 401: Based on the mathematical model of the induction motor and the mathematical model of the observer, the dynamic error of the estimated values ​​of the stator current and flux linkage vector is:

[0034]

[0035]

[0036] In the formula:

[0037]

[0038]

[0039]

[0040]

[0041] W(t) is the regression matrix; D = diag[b -1 ,b -1 ,1,1,1,d -1 ,d -1 ]>0, D∈| 7×7 ;

[0042] Step 402: Construct the Lyapunov function In the formula, Γ=diag[k f1 ,k f1 ,γ1,γ2,γ3,γ4,γ4]>0, Γ∈| 7×7 k f1 =(R1+k f ), P = diag[1,1], P = I∈| 2×2 ;

[0043] Step 403: Differentiate the Lyapunov function using the dynamic error formula for the estimated values ​​of stator current and flux linkage vector obtained in Step 401:

[0044]

[0045] Therefore, the formula for parameter identification and estimation of induction motors is obtained as follows:

[0046] Step 404: Based on the derivative formula in step 403 and the formula for parameter identification and estimation of the induction motor, the condition for satisfying the stability of the Lyapunov function is obtained as follows: Furthermore, when the condition for the stability of the Lyapunov function is satisfied, and It is bounded. For bounded u, i, ψ, and ω, the estimated value is... and Regression function W(t) and It is also bounded; therefore, for step 403... and in step 401 It is globally exponentially stable.

[0047] Preferably, step 5 specifically includes:

[0048] Using the formula for parameter identification and estimation of the induction motor obtained in step 403, the formula for solving the parameter identification and dynamic error estimation of the auxiliary variables of the induction motor is as follows:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] The dynamic equation for the auxiliary variable is:

[0055]

[0056] Preferably, step 7 specifically includes:

[0057] Step 701: Based on the simplified mathematical model of the observer, the dynamic error formulas for the flux linkage vector, stator current, and unknown parameters are obtained as follows:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] in:

[0065]

[0066] Г=diag[k1,k1,γ1,γ2,γ3]>0

[0067] P = diag[1,1],

[0068]

[0069]

[0070] Step 702, Ignored Items The stability of the dynamic error formulas for flux linkage vector, stator current, and unknown parameters is studied. Specifically, based on the dynamic error formulas for flux linkage vector, stator current, and unknown parameters in step 701, the quadratic equation of the Lyapunov function is used. The derivation shows that V is negative, then...

[0071] Step 703: Repeat steps 402 to 404 to obtain the equilibrium point. hour, It is globally exponentially stable.

[0072] Preferably, step 8 specifically includes: based on the estimated value Given R1 and parameters L = L1 = L2, solve for L using the following formula. m ,

[0073] Attached Figure Description

[0074] Figure 1 This refers to the motor parameter identification system in a specific embodiment;

[0075] Figure 2 This is a flowchart of parameter identification using the observer in step 3;

[0076] Figure 3 This is a flowchart of parameter identification using the simplified observer from step 6;

[0077] Figure 4 According to Figure 1 The test bench that was set up;

[0078] Figure 5 According to Figure 4 The test bench identified the parameter results of three motor samples;

[0079] Figure 6 A comparison chart of simulation data and experimental results for identifying a 2.2KW induction motor;

[0080] Figure 7 This is a comparison chart of the experimental results of a 2.2KW induction motor with and without rotation testing. Detailed Implementation

[0081] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0082] An observer design method for self-learning identification of induction motor parameters includes:

[0083] Step 1: Construct a mathematical model of the induction motor, specifically including:

[0084] Step 101: Define a linear magnetic system and construct a mathematical model of the induction motor under a stationary reference:

[0085]

[0086]

[0087]

[0088] In the formula, i=(i a i b ) T For stator current, i a i represents the stator current component along the a-axis. b Represents the stator current component along the b-axis, ψ=(ψ a ,ψ b ) T Let ψ be the flux linkage vector. a ψ represents the flux linkage component of the flux linkage vector along the a-axis. b Let u represent the flux linkage vector along the b-axis, where u = (u a ,u b ) T Let u be the stator voltage vector. a u represents the stator voltage component along the a-axis. b This represents the stator voltage component along the b-axis, where ω is the angular velocity, R1 is the stator resistance, and σ, α, and β are constants defined by the motor parameters:

[0089]

[0090] In the formula, R2 is the rotor inductance, L1 is the stator inductance, L2 is the rotor inductance, and L... m It is a magnetized inductor;

[0091] Step 102: Set the values ​​of the sub-inductance and rotor inductance to be equal, i.e., L1 = L2, and when u a =const and u b When = 0,

[0092] Step 103: Since angular velocity ω and angular acceleration are bounded functions, and the applied voltage u... a ,u b and its total derivative du a / dt and du b / dt is also bounded; therefore, the constants σ, α, β that need to be determined include R1, R2, L1, L2, and L m For ease of identification, let the unknown feature parameter b = dα. γ0=αL m Based on the mathematical model of the induction motor under a stationary reference, the mathematical model of the induction motor is obtained as follows: β+α

[0093]

[0094]

[0095] Step 2: Set the estimated values ​​of the sub-current and flux linkage vector pairs as follows: The error between the estimated values ​​of stator current and flux linkage vector and the actual identified parameters is calculated based on the mathematical model of the induction motor:

[0096]

[0097]

[0098]

[0099] In the formula, Indicates the error in stator current. This represents the error in the flux linkage vector. These represent the current component error of the stator current along the a-axis and the current component error along the b-axis, respectively. Let represent the flux linkage component error along the a-axis and the flux linkage component error along the b-axis, respectively. This represents the estimated value of b. This represents the estimated value of d. This represents the estimated value of γ0;

[0100] Step 3: Ensure the stator current error satisfies The error estimate of the flux linkage vector satisfies The errors of the unknown characteristic parameters b, d, γ0 satisfy... The mathematical model of the observer, derived from the mathematical model of the induction motor, is as follows:

[0101]

[0102]

[0103] In the formula, kf >0 and k i >0 and all are adjustable coefficients; This is an estimate of the flux linkage vector error. It also serves as an auxiliary variable vector;

[0104] Step 4: Use Lyapunov functions Prove the global exponential stability of the observer's parameter identification and estimates, where Γ=diag[k f1 ,k f1 [γ1,γ2,γ3,γ4,γ4]>0,k f1 γ1, γ2, γ3, and γ4 are all adjustable coefficients; specifically including:

[0105] Step 401: Based on the mathematical model of the induction motor and the mathematical model of the observer, the dynamic error of the estimated values ​​of the stator current and flux linkage vector is:

[0106]

[0107]

[0108] In the formula:

[0109]

[0110]

[0111]

[0112]

[0113] W(t) is the regression matrix; D = diag[b -1 ,b -1 ,1,1,1,d -1 ,d -1 ]>0, D∈| 7×7 ;

[0114] Step 402: Construct the Lyapunov function In the formula, Γ=diag[k f1 ,k f1 ,γ1,γ2,γ3,γ4,γ4]>0, Γ∈| 7×7 k f1 =(R1+k f ), P = diag[1,1], P = I∈| 2×2 ;

[0115] Step 403: Differentiate the Lyapunov function using the dynamic error formula for the estimated values ​​of stator current and flux linkage vector obtained in Step 401:

[0116]

[0117] Therefore, the formula for parameter identification and estimation of induction motors is obtained as follows:

[0118] Step 404: Based on the derivative formula in step 403 and the formula for parameter identification and estimation of the induction motor, the condition for satisfying the stability of the Lyapunov function is obtained as follows: Furthermore, when the condition for the stability of the Lyapunov function is satisfied, and It is bounded. For bounded u, i, ψ, and ω, the estimated value is... and Regression function W(t) and It is also bounded; therefore, for step 403... and in step 401 It is globally exponentially stable;

[0119] After proving the global exponential stability of the observer's parameter identification and estimates, the observer is integrated into an existing motor parameter identification system, such as... Figure 1 As shown, it mainly includes a controllable voltage source, a transformer, an encoder, and an induction motor. The specific operation procedure is as follows: Figure 2 As shown, the controllable voltage input initial voltage u a and u b After Clarke transformation, the output is a three-phase DC voltage. and Then the PWM controller outputs the duty cycle t. u t v t u Then, it is converted by a transformer into a three-phase AC voltage u for use as input to the induction motor. u u v u w The encoder reads the angular velocity ω of the induction motor and inputs it to the observer, while simultaneously solving for the current i input to the observer. u and i v Current i u and i v After inverse Clarke transformation to i a and i b The input is then the observer, which is combined with u a u b Unknown parameter estimates Auxiliary variable vector and stator current error value The estimated value of the flux linkage vector is obtained by solving the problem. and stator current estimate Then, with the flux linkage vector estimate... and stator current estimate and u a u b Stator current error value Proceed to step 5;

[0120] Step 5: Solve for the identification parameters of the induction motor based on the mathematical model of the observer; specifically including:

[0121] Using the formula for parameter identification and estimation of the induction motor obtained in step 403, the formula for solving the parameter identification and dynamic error estimation of the auxiliary variables of the induction motor is as follows:

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] The dynamic equation for the auxiliary variable is:

[0128]

[0129] After combining the mathematical model of the observer, a result equation for parameter identification and adaptive estimation is obtained. The result equation is very long and complex. In order to reduce the complexity of the result, improve the convergence speed and simplify the coefficient adjustment, the observer is simplified and proceeds to step 6.

[0130] Step 6: Simplify the observer. The mathematical model of the simplified observer is as follows:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] In the formula, γ1, γ2, and γ3 are constants;

[0137] Step 7: Use Lyapunov functions to prove the local stability of the simplified observer's induction motor identification parameters and estimates; specifically including:

[0138] Step 701: Based on the simplified mathematical model of the observer, the dynamic error formulas for the flux linkage vector, stator current, and unknown parameters are obtained as follows:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] in:

[0146]

[0147] Г=diag[k1,k1,γ1,γ2,γ3]>0

[0148] P = diag[1,1],

[0149]

[0150]

[0151] Step 702, Ignored Items The stability of the dynamic error formulas for flux linkage vector, stator current, and unknown parameters is studied. Specifically, based on the dynamic error formulas for flux linkage vector, stator current, and unknown parameters in step 701, the quadratic equation of the Lyapunov function is used. The derivation shows that V is negative, then...

[0152] Step 703: Repeat steps 402 to 404 to obtain the equilibrium point. hour, It is globally exponentially stable;

[0153] The specific operating procedures are as follows: Figure 3 As shown, the controllable voltage input initial voltage u a and u b After Clarke transformation, the output is a three-phase DC voltage. and Then the PWM controller outputs the duty cycle t. u t v t u Then, it is converted by a transformer into a three-phase AC voltage u for use as input to the induction motor. u u v u w The encoder reads the angular velocity ω of the induction motor and inputs it into the simplified observer, while simultaneously solving for the current i input to the observer. u and i v Current i u and i v After inverse Clarke transformation to i a and i b The simplified observer is then input, and the simplified observer is combined with u a u b Unknown parameter estimates Auxiliary variable vector and stator current error value The estimated value of the flux linkage vector is obtained by solving the problem. and stator current estimate Then, with the flux linkage vector estimate... and stator current estimate and u a u b Stator current error value Proceed to step 8; The Clarke variation, anti-Clarke variation, PWM controller output duty cycle, and transformer conversion technology mentioned above are all existing technologies and will not be elaborated on here.

[0154] Step 8: Solve for the identification parameters of the induction motor based on the simplified mathematical model of the observer, specifically including: based on the estimated values... Given R1 and parameters L = L1 = L2, solve for L using the following formula. m ,

[0155]

[0156] Experiments have shown that:

[0157] like Figure 4 As shown, Figure 1 The devices were connected in sequence, and using a simplified observer, three motor samples were successfully identified, with parameters as follows: Figure 5 As shown; and as Figure 6 As shown, parameter identification is performed on a 2.2KW induction motor using... Figure 2The simulated data obtained by the observer for parameter identification shows high consistency with the actual experimental results, and the entire identification process converges quickly without affecting the actual parameters due to test conditions; furthermore, the method employs... Figure 2 The parameter identification process shown was used to test a 2.2kW induction motor with and without rotation, and the results are as follows. Figure 7 As shown, the parameter identification results with and without rotation tests exhibit high consistency. Furthermore, it is demonstrated that the observer designed in this invention helps to avoid the saturation region by correcting the excitation signal in the identification of the flux linkage vector of the induction motor.

[0158] While the disclosure is as stated above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this disclosure, and all such changes and modifications will fall within the protection scope of this invention.

Claims

1. A method for designing an observer for self-learning identification of induction motor parameters, characterized in that, include: Step 1: Construct the mathematical model of the induction motor: In the formula, i=(i a i b ) T For stator current, i a i represents the stator current component along the a-axis. b Represents the stator current component along the b-axis, ψ=(ψ a ,ψ b ) T Let ψ be the flux linkage vector. a ψ represents the flux linkage component of the flux linkage vector along the a-axis. b Represents the flux linkage vector along the b-axis, u = (u a ,u b ) T Let u be the stator voltage vector. a u represents the stator voltage component along the a-axis. b This represents the stator voltage component along the b-axis, ω is the angular velocity, R1 is the stator resistance, and b, d, and γ0 are unknown characteristic parameters, where b = dα. γ0=αL m β+α, σ, α, and β are constants, defined by the motor parameters as follows: In the formula, R2 is the rotor inductance, L1 is the stator inductance, L2 is the rotor inductance, and L... m It is a magnetized inductor; Step 2: Set the estimated values ​​of the sub-current and flux linkage vector pairs as follows: The error between the estimated values ​​of stator current and flux linkage vector and the actual identified parameters is calculated based on the mathematical model of the induction motor: In the formula, Indicates the error in stator current. This represents the error in the flux linkage vector. These represent the current component error of the stator current along the a-axis and the current component error along the b-axis, respectively. Let represent the flux linkage component error along the a-axis and the flux linkage component error along the b-axis, respectively. This represents the estimated value of b. This represents the estimated value of d. This represents the estimated value of γ0; Step 3: Ensure the stator current error satisfies The error estimate of the flux linkage vector satisfies The errors of the unknown characteristic parameters b, d, γ0 satisfy... The mathematical model of the observer, derived from the mathematical model of the induction motor, is as follows: In the formula, k f >0 and k i >0 and all are adjustable coefficients; This is an estimate of the flux linkage vector error. It is also used as an auxiliary variable vector; Step 4: Use Lyapunov functions Prove the global exponential stability of the observer's parameter identification and estimates, where Γ=diag[k f1 ,k f1 [γ1,γ2,γ3,γ4,γ4]>0,k f1 γ1, γ2, γ3, and γ4 are all adjustable coefficients; Step 5: Solve for the identification parameters of the induction motor based on the mathematical model of the observer; Step 6: Simplify the observer. The mathematical model of the simplified observer is as follows: Step 7: Use Lyapunov functions to prove the local stability of the induction motor identification parameters and estimates of the simplified observer; Step 8: Solve for the identification parameters of the induction motor based on the simplified mathematical model of the observer.

2. The observer design method for self-learning identification of induction motor parameters according to claim 1, characterized in that, Step 4 specifically includes: Step 401: Based on the mathematical model of the induction motor and the mathematical model of the observer, the dynamic error of the estimated values ​​of the stator current and flux linkage vector is: In the formula: W(t) is the regression matrix; D = diag[b -1 ,b -1 ,1,1,1,d -1 ,d -1 ]>0, D∈| 7×7 ; Step 402: Construct the Lyapunov function In the formula, Γ=diag[k f1 ,k f1 ,γ1,γ2,γ3,γ4,γ4]>0, Γ∈| 7×7 k f1 =(R1+k f ), P = diag[1,1], P = I∈| 2×2 ; Step 403: Differentiate the Lyapunov function using the dynamic error formula for the estimated values ​​of stator current and flux linkage vector obtained in Step 401: Therefore, the formula for parameter identification and estimation of induction motors is obtained as follows: Step 404: Based on the derivative formula in step 403 and the formula for parameter identification and estimation of the induction motor, the condition for satisfying the stability of the Lyapunov function is obtained as follows: Furthermore, when the condition for the stability of the Lyapunov function is satisfied, and It is bounded. For bounded u, i, ψ, and ω, the estimated value is... and Regression function W(t) and It is also bounded; therefore, for step 403... and in step 401 It is globally exponentially stable.

3. The observer design method for self-learning identification of induction motor parameters according to claim 2, characterized in that, Step 5 specifically includes: based on the formula for parameter identification and estimation of the induction motor obtained in step 403, the formula for solving the dynamic error estimation value of the parameter identification and auxiliary variables of the induction motor is as follows: The dynamic equation for the auxiliary variable is:

4. The observer design method for self-learning identification of induction motor parameters according to claim 3, characterized in that, Step 7 specifically includes: Step 701: Based on the simplified mathematical model of the observer, the dynamic error formulas for the flux linkage vector, stator current, and unknown parameters are obtained as follows: in: Г=diag[k1,k1,γ1,γ2,γ3]>0 Step 702, Ignored Items The stability of the dynamic error formulas for flux linkage vector, stator current, and unknown parameters is studied. Specifically, based on the dynamic error formulas for flux linkage vector, stator current, and unknown parameters in step 701, the quadratic equation of the Lyapunov function is used. The derivation shows that V is negative, then... Step 703: Repeat steps 402 to 404 to obtain the equilibrium point. hour, It is globally exponentially stable.

5. The observer design method for self-learning identification of induction motor parameters according to claim 4, characterized in that, Step 8 specifically includes: based on the estimated value Given R1 and parameters L = L1 = L2, solve for L using the following formula. m ,

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