Permanent magnet synchronous motor parameter identification method and system based on recursive least squares method

Abstract

The invention discloses a permanent magnet synchronous motor parameter identification method and system based on a recursive least squares method, belonging to the technical field of permanent magnet synchronous motor control. Firstly, the basic equation of the recursive least squares method is derived; secondly, an electrical dynamic model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system is established, and the resistance and inductance of the stator winding, and the permanent magnet flux are identified; then, a mechanical dynamic model of the permanent magnet synchronous motor is established, and the moment of inertia and the viscous friction coefficient, as well as the load torque disturbance are identified and estimated; the invention can accurately identify the parameters of the permanent magnet synchronous motor online, and only requires the initial value of the external load disturbance to achieve its estimation, and is suitable for the design of a high-performance servo control system for the permanent magnet synchronous motor.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control, and in particular relates to a permanent magnet synchronous motor parameter identification method and system based on a recursive least squares method. Background Art

[0002] In recent years, with the development of power electronics, automatic control and computer technologies, AC speed control systems have gradually replaced DC speed control systems in the field of high-performance speed regulation. Permanent magnet synchronous motors have a dominant position in AC speed regulation systems due to their high power density, large torque-to-inertia ratio and fast dynamic response speed. Online and accurate identification of permanent magnet synchronous motor parameters is the basis for achieving high-performance motor control and also provides a basis for system fault diagnosis. At the same time, the influence of load disturbances during motor operation and changes in motor parameters will cause controller parameters to mismatch, thereby affecting system performance. In order to enable the designed controller to have parameter self-tuning function, parameter online identification technology has become a research hotspot in the field of motor control. The design of permanent magnet synchronous motor parameter identification algorithm plays a vital role in improving the dynamic performance of the control system.

[0003] Parameter identification algorithms can be roughly divided into two categories, namely offline identification and online identification. Offline identification refers to a method in which the servo system runs for a period of time according to a predetermined instruction, and calculates based on relevant data such as torque and speed to obtain the estimated value of the system parameters. Offline identification can obtain a phased identification result at the end of a given instruction operation cycle. The obtained identification result has high accuracy, but its application occasions are relatively limited. As an online identification algorithm, the recursive least squares (RLS) method can obtain unbiased estimates of parameters in real time in a system containing white noise, and it is easy to implement. Therefore, it is necessary to design a permanent magnet synchronous motor parameter identification method and system based on the recursive least squares method. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a permanent magnet synchronous motor parameter identification method and system based on recursive least squares method, which can identify the electrical parameters and mechanical parameters of the permanent magnet synchronous motor and realize the estimation of external load disturbance.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A permanent magnet synchronous motor parameter identification system based on recursive least squares method, the system comprising an electrical angular velocity module, a low-pass filter, an electrical RLS module, an electromagnetic torque module, a unit delay module and a mechanical RLS module;

[0007] The electrical angular velocity module is used to obtain the electrical angular velocity ω e, and the electrical angular velocity ω e Send to low pass filter;

[0008] The low-pass filter filters the input signal to obtain a corresponding steady-state value, and sends the steady-state value to the electrical RLS module;

[0009] The electrical RLS module obtains the resistance and inductance of the stator winding and the estimated value of the permanent magnet flux linkage based on the electrical dynamic model of the permanent magnet synchronous motor. and

[0010] The electromagnetic torque module is used to obtain the electromagnetic torque T e , and the electromagnetic torque T e Send to the unit delay module;

[0011] The unit delay module delays the input signal by a discrete period, obtains the signal value at the previous moment, and sends the signal value to the mechanical RLS module;

[0012] The mechanical RLS module obtains the estimated values ​​of the moment of inertia, viscous friction coefficient and load torque disturbance based on the mechanical dynamic model of the permanent magnet synchronous motor. and

[0013] A method for identifying parameters of a permanent magnet synchronous motor based on a recursive least squares method, the method comprising the following steps:

[0014] Step 1: Establish the basic model of recursive least squares method;

[0015] Step 2: Establish an electrical dynamic model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system and identify the electrical parameters;

[0016] Step 3: Establish the mechanical dynamic model of the permanent magnet synchronous motor, and identify and estimate the mechanical parameters.

[0017] Furthermore, the basic model equation of the recursive least squares method in step 1 is:

[0018]

[0019] Furthermore, the identification of electrical parameters in step 2 is performed based on a steady-state system of electrical dynamic equations, and the identification of electrical parameters includes identifying the resistance and inductance of the stator winding and identifying the flux linkage of the permanent magnet.

[0020] Furthermore, the electrical dynamic model established in the two-phase synchronous rotating orthogonal coordinate system in the step 2 is based on the mathematical model of the surface mounted permanent magnet synchronous motor in the three-phase stationary ABC coordinate system. The voltage equation of the permanent magnet synchronous motor in the two synchronous rotating orthogonal dq coordinate systems is obtained by vector transformation, and the voltage equation and the magnetic flux equation of the surface mounted permanent magnet synchronous motor are combined to obtain the electrical dynamic equation:

[0021]

[0022] Among them, u d and u q are the voltages of the d-axis and q-axis stator windings, R s is the resistance of the stator winding, i d and i q are the currents of the d-axis and q-axis stator windings, L s is the inductance of the stator winding, d / dt is the differential operator, ω e is the electrical angular velocity, ψ f is the permanent magnet flux.

[0023] Furthermore, the mechanical dynamic equation of the permanent magnet synchronous motor in step 3 is:

[0024]

[0025] Where J is the moment of inertia, ω m is the mechanical angular velocity, K T =3p n ψ f / 2 is the electromagnetic torque coefficient, p n is the pole pair number, F is the viscous friction coefficient, T m is the load torque disturbance.

[0026] Furthermore, the identification and estimation of mechanical parameters in step three includes identification and estimation of the moment of inertia, viscous friction coefficient and load torque disturbance.

[0027] Beneficial effects of the present invention:

[0028] 1. Based on the electrical and mechanical dynamic models in the two-phase synchronous rotating orthogonal coordinate system, the permanent magnet synchronous motor parameters are identified and the external load disturbance is estimated.

[0029] 2. Make full use of the d-axis voltage equation information to give the identification algorithm richer excitations, thereby obtaining accurate parameter estimates.

[0030] 3. Derive the basic equations of the recursive least squares method and apply it to the system of permanent magnet synchronous motor parameter identification and load disturbance estimation.

[0031] 4. It can accurately identify the parameters of permanent magnet synchronous motors online, and only requires the initial value of the external load disturbance to estimate it, which is suitable for the design of high-performance servo control systems for permanent magnet synchronous motors. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0033] Figure 1 The system principle diagram of the permanent magnet synchronous motor parameter identification method based on the recursive least squares method of the present invention. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] A permanent magnet synchronous motor parameter identification system based on recursive least squares method, such as Figure 1 As shown, it includes an electrical angular velocity module, a low-pass filter (LPF), an electrical RLS module, an electromagnetic torque module, a unit delay module and a mechanical RLS module, wherein:

[0036] The electrical angular velocity module is based on the mechanical angular velocity ω m , multiply it by the pole logarithm p n Get the electrical angular velocity ω e , and send it to a low-pass filter (LPF);

[0037] The low-pass filter (LPF) filters the input signal to obtain the corresponding steady-state value and sends it to the electrical RLS module;

[0038] The electrical RLS module obtains the resistance and inductance of the stator winding and the estimated value of the permanent magnet flux linkage based on the electrical dynamic model of the permanent magnet synchronous motor. and

[0039] The electromagnetic torque module is based on the q-axis current i q , multiply it by the electromagnetic torque coefficient K T Get the electromagnetic torque T e , and send it to the unit delay module;

[0040] The unit delay module delays the input signal by a discrete period, obtains the signal value at the previous moment, and sends it to the mechanical RLS module;

[0041] The mechanical RLS module obtains the estimated values ​​of the moment of inertia and viscous friction coefficient as well as the load torque disturbance based on the mechanical dynamic model of the permanent magnet synchronous motor. and

[0042] A method for identifying parameters of a permanent magnet synchronous motor based on a recursive least squares method, the method being executed by the above system, and the identification method comprising the following steps:

[0043] Step 1: Establish the basic model of recursive least squares method. First, establish the basic model of least squares method as shown below:

[0044] ψ(k)Θ(k)=y(k) (1)

[0045] Among them, k represents the current moment, ψ is the input matrix, Θ is the model parameter to be estimated, and y is the system output column vector.

[0046] The essence of the recursive least squares method is to make the Euclidean norm ||ψ(k)Θ(k)-y(k)|| 2 Based on the concept of Moore-Penrose generalized inverse (pseudo-inverse) matrix, the solution of equation (1) is

[0047] Θ(k)=ψ Γ (k)y(k)=[ψ T (k)ψ(k)] -1 ψ T (k)y(k) (2)

[0048] The superscripts Γ, T, and -1 represent the pseudo-inverse, transpose, and inverse operations of the matrix, respectively.

[0049] According to the current moment Θ(k), and the next moment ψ(k+1) and y(k+1), we can optimize the next moment Θ(k+1), that is,

[0050]

[0051] Among them, k+1 represents the next moment.

[0052] Define the update matrix as shown below:

[0053] G(k)=ψ T (k)ψ(k) (4)

[0054] Where G(k) represents the update matrix.

[0055] Combining (2) and (4) we get

[0056] Θ(k)=G -1 (k)ψ T (k)y(k)=P(k)ψ T (k)y(k) (5)

[0057] Where, the covariance matrix P(k) = G -1 (k).

[0058] Combining (3) and (4) we get

[0059]

[0060] Combining (3), (5) and (6), we can get

[0061]

[0062] Where P(k+1)=G -1 (k+1), gain matrix K(k+1)=P(k+1)ψ T (k+1).

[0063] Since the matrix K(k+1) contains the inverse of the larger matrix G(k+1), this undoubtedly increases the complexity of the identification algorithm. To this end, the Sherman-Morrison-Woodbury formula is introduced, that is,

[0064] [A+UV] -1 =A -1 -A -1 U[I+VA -1 U] -1 VA -1 (8)Where I is the unit matrix.

[0065] Combining (6) and (8) we get

[0066]

[0067] Combining (8) and (9) we get

[0068]

[0069] Combining (9) and (10) we get

[0070]

[0071] According to the above derivation process, as well as (7), (10) and (11), for model (1), the basic equation of the recursive least squares method is

[0072]

[0073] According to (4), the initial value of the covariance matrix P(0) = G -1 (0) = [ψ T (0)ψ(0)] -1 , whose dimension is equal to the number of rows of Θ (i.e. the number of identification parameters), and according to (5), the initial value of the model parameter to be estimated Θ(0) = P(0)ψ T (0)y(0).

[0074] Step 2: Establish an electrical dynamic model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system and identify the electrical parameters.

[0075] First, a mathematical model is established on a two-phase synchronous rotating orthogonal dq coordinate system. The present invention is based on the mathematical model of a surface-mounted permanent magnet synchronous motor in a three-phase stationary ABC coordinate system. Through vector transformation, the voltage equation of the permanent magnet synchronous motor in two synchronous rotating orthogonal dq coordinate systems is obtained.

[0076]

[0077] Among them, u d and u q are the voltages of the d-axis and q-axis stator windings, R s is the resistance of the stator winding, i d and i q are the currents of the d-axis and q-axis stator windings, L s is the inductance of the stator winding, d / dt is the differential operator, ω e is the electrical angular velocity, ψ f is the permanent magnet flux.

[0078] For a surface mounted permanent magnet synchronous motor, the flux equation can be simplified to

[0079]

[0080] Among them, L s is the inductance of the stator winding, ψ f is the permanent magnet flux.

[0081] Combining the voltage equation (13) and the flux equation (14) of the surface-mounted permanent magnet synchronous motor, the electrical dynamic equation is:

[0082]

[0083] Then, the electrical parameter identification based on the recursive least squares method ignores the influence of the current change rate on the identification accuracy, that is, it is assumed that the electrical parameter identification based on the recursive least squares method is based on the steady-state system of (15).

[0084]

[0085] Electrical parameters Stator winding resistance R s and inductor L s After identification, the steady-state system (16) is written in the form of model (1), and we can get

[0086]

[0087] Similarly, in order to identify the electrical parameters of the stator winding inductance Ls and the permanent magnet flux ψf based on the recursive least squares method, the steady-state system (16) is written in the form of model (1), and we can get

[0088]

[0089] Step 3: Establish the mechanical dynamic model of the permanent magnet synchronous motor, and identify and estimate the mechanical parameters.

[0090] First, the mechanical dynamic equation of the surface-mounted permanent magnet synchronous motor is established. For the surface-mounted permanent magnet synchronous motor, the electromagnetic torque can be simplified as

[0091] T e =K T i q (19)

[0092] Among them, T e and K T =3p n ψ f / 2 are electromagnetic torque and electromagnetic torque coefficient respectively, p n is the pole pair number.

[0093] The motion equation of a permanent magnet synchronous motor is

[0094]

[0095] Where J is the moment of inertia, ω m is the mechanical angular velocity, F is the viscous friction coefficient, T m is the load torque disturbance. Combining the electromagnetic torque (19) and the motion equation (20), the mechanical dynamic equation can be obtained as follows:

[0096]

[0097] Then, based on the recursive least squares method, the mechanical parameters are identified and estimated, and the mechanical dynamic equation (21) is Laplace transformed to obtain the transfer function shown below:

[0098]

[0099] Among them, Gs (s) is the transfer function of the mechanical dynamic equation, s is the Laplace operator, W m (s), I q (s) and T m (s) are ω m ,i q and T m The Laplace transform of .

[0100] The transfer function of the zero order holder (ZOH) is

[0101]

[0102] Among them, G s (s) is the transfer function of the zero-order holder, exp(·) is the exponential function, T s For walking distance.

[0103] For the transfer function (22) with a zero-order holder, we can perform a Z-transform with respect to the unit pulse function and obtain

[0104]

[0105] Where Z[·] is the Z transform.

[0106] According to the displacement theorem of Z transform and the Z transform formula table, we can get

[0107]

[0108] Combining (22), (24) and (25), we can get

[0109]

[0110] Wherein, z is the Z-transform operator, and Z[1]=1.

[0111] From (26), we can get the discretization model of the mechanical dynamic equation (21) as follows:

[0112] ω m (k) = ω m (k-1)Θ1+K T i q (k-1)Θ2-Θ3 (27)

[0113] Among them, variable θ1 = exp(-T s F / J), Θ2=(1-Θ1) / F, Θ3=Θ2T m .

[0114] Writing system (27) in the form of model (1), we can obtain

[0115]

[0116] Among them, k-1 represents the previous moment.

[0117] From Θ1 to Θ3, the estimated values ​​of the moment of inertia, viscous friction coefficient, and load torque disturbance are

[0118]

[0119] in, represents the estimated value, and ln(·) is the logarithm operation with the constant e as the base.

[0120] In this implementation, in order to verify the effectiveness and advantages of the designed system, take T s =0.1ms (the inverter switching frequency is 10kHz), and the control strategy of equalizing the d-axis current to its given value is adopted, that is,

[0121] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A permanent magnet synchronous motor parameter identification system based on recursive least squares method, characterized in that: The system includes an electrical angular velocity module, a low-pass filter, an electrical RLS module, an electromagnetic torque module, a unit delay module and a mechanical RLS module; The electrical angular velocity module is used to obtain the electrical angular velocity ω e , and the electrical angular velocity ω e Send to low pass filter; The low-pass filter filters the input signal to obtain a corresponding steady-state value, and sends the steady-state value to the electrical RLS module; The electrical RLS module obtains the resistance and inductance of the stator winding and the estimated value of the permanent magnet flux linkage based on the electrical dynamic model of the permanent magnet synchronous motor. , and ; The electromagnetic torque module is used to obtain the electromagnetic torque T e , and the electromagnetic torque T e Send to the unit delay module; The unit delay module delays the input signal by a discrete period, obtains the signal value at the previous moment, and sends the signal value to the mechanical RLS module; The mechanical RLS module obtains the estimated values ​​of the moment of inertia, viscous friction coefficient and load torque disturbance based on the mechanical dynamic model of the permanent magnet synchronous motor , and ; The basic model equation of the recursive least squares method is: in, k Indicates the current moment, k + 1 means the next moment, K is the gain matrix, P is the covariance matrix, ψ is the input matrix, I is the identity matrix, Θ are the model parameters to be estimated, y is the system output column vector, T and -1 represent the matrix transposition and inversion operations respectively; The mechanical dynamic model equation of the permanent magnet synchronous motor is: in, J is the moment of inertia, ω m is the mechanical angular velocity, F is the viscous friction coefficient; K T = 3 p n ψ f / 2 is the electromagnetic torque coefficient, ψ f is the permanent magnet flux, p n is the pole pair number; T m is the load torque disturbance; i q is the current of the q-axis stator winding.

2. A method for identifying parameters of a permanent magnet synchronous motor based on a recursive least squares method, the method being executed by a permanent magnet synchronous motor parameter identification system based on a recursive least squares method as claimed in claim 1, characterized in that: The method comprises the following steps: Step 1: Establish the basic model of recursive least squares method; Step 2: Establish an electrical dynamic model of the permanent magnet synchronous motor in a two-phase synchronous rotating orthogonal coordinate system and identify the electrical parameters; Step 3: Establish the mechanical dynamic model of the permanent magnet synchronous motor, and identify and estimate the mechanical parameters.

3. A permanent magnet synchronous motor parameter identification method based on recursive least squares method according to claim 2, characterized in that: The identification of electrical parameters in the second step is performed based on a steady-state system of electrical dynamic equations. The identification of electrical parameters includes the identification of resistance and inductance of the stator winding and the identification of the flux linkage of the permanent magnet.

4. A method for identifying parameters of a permanent magnet synchronous motor based on recursive least squares method according to claim 2, characterized in that: The electrical dynamic model established in the two-phase synchronous rotating orthogonal coordinate system in the step 2 is based on the mathematical model of the surface mounted permanent magnet synchronous motor in the three-phase stationary ABC coordinate system. The voltage equation of the permanent magnet synchronous motor in the two synchronous rotating orthogonal dq coordinate systems is obtained by vector transformation, and the voltage equation and the magnetic flux equation of the surface mounted permanent magnet synchronous motor are combined to obtain the electrical dynamic equation: in, u d and u q are the voltages of the d-axis and q-axis stator windings, R s is the resistance of the stator winding, i d and i q are the currents of the d-axis and q-axis stator windings, respectively. L s is the inductance of the stator winding, d / d t is the differential operator, ω e is the electrical angular velocity, ψ f is the permanent magnet flux.

5. The method for identifying parameters of a permanent magnet synchronous motor based on recursive least squares method according to claim 2, characterized in that: The identification and estimation of mechanical parameters in step three include the identification and estimation of the moment of inertia, the viscous friction coefficient and the load torque disturbance.

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