Improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification

Abstract

The invention relates to an improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification, and belongs to the field of permanent magnet synchronous motor control. The method comprises the following steps: building a reference model and an adjustable model of an improved position observer according to a state equation of a motor by taking built-in permanent magnet synchronization as a control object; defining an error vector, constructing a nonlinear time-varying error feedback system, and deriving a parameter adaptive law, a forward channel gain matrix and a feedback gain matrix according to the Popov hyperstability theorem; identifying parameters influencing the parameter sensitivity of the observer are analyzed, and then a reference model and an adjustable model of the parameter identifier are constructed according to a state equation of the built-in permanent magnet synchronous motor; and deriving a parameter adaptive law according to the Popov hyperstability theorem, and updating the identified parameters to the observer adjustable model, thereby realizing estimation of the rotor position of the permanent magnet synchronous motor. According to the invention, sensorless control of the built-in permanent magnet synchronous motor can be realized, and the control precision is improved.

Description

Technical Field

[0001] The invention belongs to the field of permanent magnet synchronous motor control and relates to an improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) is widely used in industrial applications such as servo systems, automotive industry, wind power generation, etc. due to its high power density, high starting torque, good dynamic performance, and low maintenance requirements. To achieve closed-loop control of permanent magnet synchronous motors, it is necessary to obtain the rotor position information of the motor, including motor speed and rotor angle. However, the use of mechanical sensors will increase the cost of the system, make installation and wiring difficult, and reduce the reliability of the system. Therefore, it is necessary to select a suitable sensorless control strategy to improve the reliability of the system. For example, sliding mode observer, extended Kalman filter, adaptive full-order observer, model reference adaptive system (MRAS), etc.

[0003] Although the existing MRAS position sensorless PMSM control method has achieved certain results, the identification accuracy of the model reference adaptive observer depends on the accuracy of the adjustable model, which requires various parameters of the motor. However, there are many factors that limit the accuracy of the nominal parameters of the permanent magnet synchronous motor when it leaves the factory. Due to manufacturing tolerances, the parameters of the motor will have errors compared to the values ​​on the nameplate. In addition, the parameters will be affected by load changes, electromagnetic interference, and environmental factors, resulting in nonlinear changes. Therefore, the uncertainty caused by the motor parameters greatly reduces the control accuracy of the MRAS observer. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide an improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification, which uses a parameter identification system to update the motor parameters, reduce the estimation error of the observer caused by parameter changes, improve the dynamic performance of the parameter change system, and improve the control accuracy.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] An improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification includes the following steps:

[0007] S1. Taking the built-in permanent magnet synchronous machine as the control object, the reference model and adjustable model of the improved position observer are constructed according to the state equation of the motor;

[0008] S2. Define the error vector, construct a nonlinear time-varying error feedback system, and derive the parameter adaptation law, forward channel gain matrix and feedback gain matrix according to Popov's superstability theorem;

[0009] S3, analyzing the identification parameters that affect the designed observer parameter sensitivity, and then constructing a reference model and an adjustable model of the parameter identifier according to the state equation of the built-in permanent magnet synchronous motor;

[0010] S4. According to Popov's superstability theorem, the parameter adaptation law is derived, and the identified parameters are updated to the observer adjustable model, thereby realizing the estimation of the rotor position of the permanent magnet synchronous motor.

[0011] Furthermore, in step S1, the construction of the reference model and the adjustable model of the improved position observer includes: taking the current equation of the interior permanent magnet synchronous motor in the synchronous rotating coordinate system as the reference model:

[0012]

[0013] In the formula, i d 、i q Respectively represent the d-axis and q-axis currents; u d 、u q Respectively represent the d-axis and q-axis voltages; L d , L q Respectively represent the d-axis and q-axis inductances; R represents the stator resistance; ψ f represents the magnetic flux of the rotor permanent magnet; ω e represents the electrical angular velocity; t represents the differential variable;

[0014] Rewrite the above formula into matrix form:

[0015]

[0016] Replace the current and electrical angular velocity values ​​in the matrix form with the corresponding estimated values, and then add the proportional error feedback term and the integral error feedback correction term to obtain an adjustable model based on the current equation:

[0017]

[0018] In the formula, Represent the estimated values ​​of d-axis and q-axis currents, respectively. represents the estimated value of electrical angular velocity, represents the reconstruction matrix, K represents the coefficient matrix of the proportional error feedback term, and F represents the coefficient matrix of the integral error feedback correction term.

[0019] Further, step S2 includes defining a current error vector Considering that the integral term in the adjustable model will take effect when the model parameters are mismatched, in order to simplify the calculation, when deriving the adaptive law, the coefficient matrix F of the integral error feedback correction term is set to 0, and the adjustable model is subtracted from the reference model to construct a nonlinear time-varying error feedback system:

[0020]

[0021] In the formula, represents the current error vector, I represents the unit matrix, W t represents the nonlinear feedback matrix, C represents the forward channel gain matrix, and v represents the output of the nonlinear time-varying error feedback system.

[0022] After the nonlinear time-varying error feedback system is constructed, the parameter adaptation law is derived according to Popov's superstability theorem while ensuring the stability of the system. Among them, in order to ensure the stability of the system, two conditions of Popov's superstability theorem must be met. The first condition is that the forward path transfer function matrix of the nonlinear time-varying error feedback system must be strictly positive and real, and the forward channel gain matrix C is derived as:

[0023]

[0024] The coefficient matrix K of the proportional error feedback term is derived as:

[0025]

[0026] Where k is the feedback gain coefficient.

[0027] The second condition is that the nonlinear feedback path satisfies the Popov integral inequality. When the Popov integral inequality is satisfied, the parameter adaptation law ω is derived. e for:

[0028]

[0029] In the formula, K i Indicates the integral coefficient, K p Represents the scale of the parameter adaptation law.

[0030] Furthermore, in step S3, the identification parameters affecting the observer parameter sensitivity include the q-axis inductance L q and permanent magnet flux ψ f , then the reference model and adjustable model for constructing the parameter identifier include:

[0031] Taking the motor current state equation as the reference model, it is expressed as:

[0032]

[0033] In the formula, i d 、i q Respectively represent the d-axis and q-axis currents, u d 、u q Respectively represent the d-axis and q-axis voltages, ω e represents the electrical angular velocity, R represents the stator resistance, L d represents the d-axis inductance;

[0034] Then the adjustable model of the parameter identifier is expressed as:

[0035]

[0036] In the formula, represents the estimated value of q-axis inductance, Represents the estimated value of the permanent magnet flux.

[0037] Further, in step S4, after the reference model and the adjustable model of the parameter identifier are constructed, the parameter adaptation law is derived according to Popov's superstability theorem; first, the state equation of the linear steady-state forward path is obtained by subtracting the adjustable model from the reference model of the parameter identifier:

[0038]

[0039] Where W l represents the nonlinear feedback channel matrix, C l represents the forward channel gain matrix, represents the estimated value of current;

[0040] According to the first condition of Popov's superstability theorem, that is, the system forward path transfer function matrix must be strictly positive and real, the forward channel gain matrix C is obtained l for:

[0041]

[0042] According to the second condition of Popov's superstability theorem, that is, the nonlinear feedback path of the system satisfies the Popov integral inequality, the parameter adaptive law is derived. The parameter adaptive law is taken as the proportional integral mode and substituted into the Popov integral inequality. The inverse solution obtains the parameter adaptive law as follows:

[0043]

[0044] In the formula, K i Indicates the integral coefficient, K p represents the ratio of the parameter adaptation law,

[0045] The identified parameters are updated to the observer adjustable model to achieve the estimation of the rotor position of the permanent magnet synchronous motor.

[0046] The beneficial effects of the present invention are as follows: the present invention proposes an improved model reference adaptive observer, designs a new MRAS adjustable model, adds the proportional and integral terms of the observed current error as feedback correction, and uses the Popov superstability theorem to perform stability analysis and derivation, wherein the integral term can play a role when the adjustable model does not match the actual parameters of the PMSM, so as to reduce the observer estimation error and weaken the system jitter. At the same time, the present invention designs a parameter identifier based on MRAS for the analyzed parameters with greater sensitivity, updates the identified parameters to the adjustable model, improves the dynamic performance of the parameter change system, and improves the control accuracy. The present invention can identify the q-axis inductance and permanent magnet flux of the motor under the influence of load changes, electromagnetic interference, and environmental factors, and update them to the adjustable model of the observer, thereby realizing sensorless control of the built-in permanent magnet synchronous motor and improving the control accuracy.

[0047] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0049] Figure 1 This is the structural block diagram of the improved model reference adaptive sensorless control system with parameter identification;

[0050] Figure 2 The block diagram of the position estimator based on improved model reference adaptation;

[0051] Figure 3 This is the structural block diagram of the parameter identifier based on model reference adaptation. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] See also Figure 1 to Figure 3 , is an improved model reference adaptive PMSM observer design method with parameter identification proposed by the present invention, the method is specifically as follows:

[0054] 1. The current equation of the built-in permanent magnet synchronous motor in the synchronous rotating coordinate system is selected as the reference model, which is expressed as:

[0055]

[0056] Among them, i d 、i q are d-axis and q-axis currents respectively; u d 、u q are d-axis and q-axis voltages respectively; L d , L q are the d-axis and q-axis inductances respectively; R is the stator resistance; ψ f is the magnetic flux of the rotor permanent magnet; ω e is the electrical angular velocity; t represents the differential variable. Formula (1) is written in matrix form as follows:

[0057]

[0058] in:

[0059] The current and electrical angular velocity in equation (2) are expressed as estimated values, and the proportional error feedback term and the integral error feedback correction term are added to obtain the adjustable model based on the current equation:

[0060]

[0061] in: represents the estimated value of current, represents the estimated value of electrical angular velocity, Contains the value to be estimated , K is the coefficient matrix of the proportional error feedback term, and F is the coefficient matrix of the integral error feedback correction term.

[0062] 2. Define the current error vector Considering that the integral term in the adjustable model will take effect when the model parameters are mismatched, in order to simplify the calculation, when deriving the adaptive law, let F = 0, subtract equation (3) from equation (2), and obtain the state equation of the nonlinear time-varying error feedback system:

[0063]

[0064] Where: W t is the nonlinear feedback matrix, I is the identity matrix, C is the forward channel gain matrix.

[0065] In order to ensure the stability of the system, two conditions of Popov's superstability theorem must be met. The first condition is that the forward path transfer function matrix of the system represented by equation (4) must be strictly positive and real. The matrices C and K can be derived as follows:

[0066]

[0067] Where k is the feedback gain coefficient. To satisfy the requirement that the sequential principal minors of the linear forward path transfer function matrix Q are all greater than zero, the value range of k is: k>0. At this time, the matrix Q is:

[0068]

[0069] The second condition to ensure the stability of the system is that the nonlinear feedback path of the system satisfies Popov's integral inequality, which is used to derive the speed adaptation law. In the form of proportional integral, the speed adaptive law is derived as shown in formula (8), which satisfies the Popov integral inequality and the system remains stable:

[0070]

[0071] The block diagram of the position estimator based on improved model reference adaptation is as follows Figure 2 After analysis, the main parameters affecting the identification accuracy of the improved model reference adaptive observer are the q-axis inductance L q and permanent magnet flux ψ f , now design L q and ψ f The online identification method is as follows:

[0072] 3. Select the motor current state equation, that is, equation (2) as the reference model, and design the adjustable model of the parameter identifier as follows:

[0073]

[0074] in:

[0075] 4. According to Popov's superstability theorem, the parameter adaptation law is derived. Specifically, the state equation of the linear steady-state forward path is obtained by subtracting equation (10) from equation (2):

[0076]

[0077] Where: W l is the nonlinear feedback channel matrix, C l is the forward channel gain matrix.

[0078] In order to ensure that the forward path transfer function is strictly positive and real, the first condition of Popov's superstability theorem is satisfied, that is, the system forward path transfer function matrix must be strictly positive and real, thus the matrix C can be obtained l for:

[0079]

[0080] The second condition to ensure the stability of the system is that the nonlinear feedback path of the system satisfies the Popov integral inequality, which is used to derive the parameter adaptive law. The parameter adaptive law is taken as the proportional integral mode and is brought into the Popov integral inequality. The parameter adaptive law is inversely solved as follows:

[0081]

[0082] Among them, K i Indicates the integral coefficient, K p represents the ratio of the parameter adaptation law,

[0083] The block diagram of the parameter identifier based on model reference adaptation is as follows: Figure 3 As shown, the identified motor parameters are finally updated to the observer adjustable model to achieve high-precision rotor position estimation of the permanent magnet synchronous motor in a complex environment, thereby improving the control accuracy.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. An improved model reference adaptive permanent magnet synchronous motor observer design method based on parameter identification, characterized in that: The method includes: Taking the built-in permanent magnet synchronous motor as the control object, the reference model and adjustable model of the improved position observer are constructed according to the state equation of the motor. Define the error vector, construct a nonlinear time-varying error feedback system, and derive the parameter adaptation law, forward channel gain matrix and feedback gain matrix according to Popov's superstability theorem; The identification parameters that affect the parameter sensitivity of the designed observer are analyzed, and then the reference model and adjustable model of the parameter identifier are constructed according to the state equation of the interior permanent magnet synchronous motor. According to Popov's superstability theorem, the parameter adaptation law is derived, and the identified parameters are updated to the observer adjustable model, thereby realizing the estimation of the permanent magnet synchronous motor rotor position.

2. The method according to claim 1, characterized in that: The construction of the reference model and adjustable model of the improved position observer includes: taking the current equation of the interior permanent magnet synchronous motor in the synchronous rotating coordinate system as the reference model: In the formula, i d 、i q Respectively represent the d-axis and q-axis currents; u d 、u q Respectively represent the d-axis and q-axis voltages; L d , L q Respectively represent the d-axis and q-axis inductances; R represents the stator resistance; ψ f represents the magnetic flux of the rotor permanent magnet; ω e represents the electrical angular velocity; t represents the differential variable; Rewrite the above formula into matrix form: Replace the current and electrical angular velocity values ​​in the matrix form with the corresponding estimated values, and then add the proportional error feedback term and the integral error feedback correction term to obtain an adjustable model based on the current equation: In the formula, Respectively represent the estimated values ​​of d-axis and q-axis currents, represents the estimated value of electrical angular velocity, represents the reconstruction matrix, K represents the coefficient matrix of the proportional error feedback term, and F represents the coefficient matrix of the integral error feedback correction term.

3. The method according to claim 2, characterized in that The coefficient matrix F of the integral error feedback correction term is set to 0, and the adjustable model is subtracted from the reference model to construct the nonlinear time-varying error feedback system: In the formula, represents the current error vector, I represents the unit matrix, W t represents the nonlinear feedback matrix, C represents the forward channel gain matrix, and v represents the output of the nonlinear time-varying error feedback system.

4. The method according to claim 3, characterized in that After the nonlinear time-varying error feedback system is constructed, the parameter adaptation law is derived according to Popov's superstability theorem while ensuring the stability of the system. Among them, in order to ensure the stability of the system, two conditions of Popov's superstability theorem must be met. The first condition is that the forward path transfer function matrix of the nonlinear time-varying error feedback system must be strictly positive and real, and the forward channel gain matrix C is derived as: The coefficient matrix K of the proportional error feedback term is derived as: Where k represents the feedback gain coefficient; The second condition is that the nonlinear feedback path satisfies the Popov integral inequality. When the Popov integral inequality is satisfied, the parameter adaptation law is derived: for: In the formula, K i Indicates the integral coefficient, K p Represents the scale of the parameter adaptation law.

5. The method according to claim 1, characterized in that The identification parameters that affect the observer parameter sensitivity include the q-axis inductance L q and permanent magnet flux ψ f , then the reference model and adjustable model for constructing the parameter identifier include: Taking the motor current state equation as the reference model, it is expressed as: In the formula, i d 、i q Respectively represent the d-axis and q-axis currents, u d 、u q Respectively represent the d-axis and q-axis voltages, ω e represents the electrical angular velocity, R represents the stator resistance, L d represents the d-axis inductance, R represents the stator resistance; Then the adjustable model of the parameter identifier is expressed as: In the formula, denote the estimated values ​​of d-axis and q-axis currents, respectively, represents the estimated value of q-axis inductance, Represents the estimated value of the permanent magnet flux.

6. The method according to claim 5, characterized in that After the reference model and the adjustable model of the parameter identifier are constructed, the parameter adaptation law is derived according to Popov's superstability theorem; first, the state equation of the linear steady-state forward path is obtained by subtracting the adjustable model from the reference model of the parameter identifier: Where W l represents the nonlinear feedback channel matrix, C l represents the forward channel gain matrix, represents the estimated value of current; According to the first condition of Popov's superstability theorem, that is, the system forward path transfer function matrix must be strictly positive and real, the forward channel gain matrix C is obtained l for: According to the second condition of Popov's superstability theorem, that is, the nonlinear feedback path of the system satisfies the Popov integral inequality, the parameter adaptive law is derived. The parameter adaptive law is taken as the proportional integral mode and substituted into the Popov integral inequality. The inverse solution obtains the parameter adaptive law as follows: In the formula, K i Indicates the integral coefficient, K p represents the ratio of the parameter adaptation law, The identified parameters are updated to the observer adjustable model to achieve the estimation of the rotor position of the permanent magnet synchronous motor.

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