Fractional order modeling and identification method for motor drive system and application thereof

Abstract

The application belongs to the technical field of motor modeling, and discloses a fractional order modeling and identification method of a motor driving system and application thereof, which comprises the following steps: (1) a fractional order transfer function model of an electromagnetic link of a PMSM servo system is established; meanwhile, a nonlinear sigmoid function model of an inverter is established, and unknown parameters of the sigmoid function model are confirmed; the nonlinear of the inverter is preliminarily compensated based on the sigmoid function model, so that a new sigmoid function model is obtained, and parameters in the new sigmoid function model are confirmed; (2) a linear region of d-q axis voltage and current is obtained based on the obtained sigmoid function model, current sampling of the d-q axis is carried out in the obtained linear region, and unknown parameters in the fractional order transfer function model are calculated based on the obtained sampling data. The application simultaneously considers the dead zone nonlinearity of the inverter and the system delay existing in the digital system, and the accuracy is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of motor modeling, and more specifically, relates to a fractional-order modeling and identification method for motor drive systems and its application. Background Technology

[0002] Servo drives and permanent magnet synchronous motors (PMSMs) are widely used in many industrial fields, such as CNC machine tools, electric vehicles, and robots. The parameters of the PMSM are crucial for the tuning of controller parameters and are also essential for observer design, such as extended state observers (ESOs) based on model information. Furthermore, model predictive current control (MPCC) is a high-performance control strategy for PMSM drives, which is highly dependent on the PMSM parameters.

[0003] To obtain the parameters of PMSMs, some researchers have conducted very meaningful studies. However, most of these studies focus on PMSM models and their parameter identification methods, and are not detailed enough regarding the electromagnetic model of the PMSM servo system. Further research is needed to determine the true electromagnetic model of the PMSM servo system.

[0004] In traditional control strategies, PMSM models are integer-order. However, due to the fractional-order nature of the actual external characteristics of inductors, integer-order PMSM models are inaccurate. Servo drives typically use high-frequency PWM modulation, thus defining them as typical time-varying nonlinear systems. Representing nonlinear characteristics with integer-order transfer functions is challenging. At low switching frequencies, the inductor series resistance is frequency-independent, as are resistive losses, but due to the skin effect, the effective series resistance (ESR) of the inductor increases with the switching frequency. Using fractional-order operators, researchers have already accurately modeled the skin effect in inductors. Although fractional-order modeling of permanent magnet synchronous motor speed servo systems has been proposed in Chinese patents CN111786601A and CN110889240B, these patents do not consider digital delay and inverter nonlinearity.

[0005] Traditionally, stationary frequency response (SSFR) testing is performed to obtain accurate parameters of the PMSM (Polarization and Switching Mode). SSFR testing requires auxiliary instruments to acquire the PMSM model, but servo-driven model identification is more versatile. Due to the nonlinear characteristics of the inverter, servo drives introduce output voltage errors, which are detrimental to parameter identification. Therefore, inverter error voltage compensation for servo system electromagnetic parameter identification requires further research. Furthermore, digital delay significantly affects inductor parameter identification. Based on the above discussion, fractional-order modeling of the servo system electromagnetic components, considering inverter nonlinearity and digital delay, needs further development. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a fractional-order modeling and identification method for motor drive systems and its application. This method analyzes and eliminates the influence of the dead-zone nonlinearity of the inverter in the servo drive on parameter identification, and considers the system delay present in the digital system, thereby establishing a more accurate fractional-order model of the electromagnetic components of the servo system and obtaining more precise electromagnetic component model parameters.

[0007] To achieve the above objectives, according to one aspect of the present invention, a fractional-order modeling and identification method for a motor drive system is provided, the method comprising the following steps:

[0008] (1) Establish a fractional-order transfer function model for the electromagnetic components of the PMSM servo system. The mathematical expression of the fractional-order transfer function model is as follows:

[0009]

[0010] In the formula, Kv is the conversion factor from the per-unit voltage value to the actual output voltage; τ is the digital system delay; R s The resistor is denoted by λ, which includes the resistance of the permanent magnet synchronous motor, the inverter, and the circuitry; L is the inductance of the permanent magnet synchronous motor; s is the Laplace operator; λ is the fractional order; a0 = L; b0 = R s .

[0011] Simultaneously, a nonlinear sigmoid function model of the inverter is established, and the expression of the sigmoid function model is:

[0012]

[0013] In the formula, K is a parameter related to the voltage error constant, A is a parameter related to the inverter characteristics, and i xs Let x = a, b, c represent any one of the motor phase currents;

[0014] Based on d-axis reference voltage and the current i along the d-axis d The curve, and the d-axis reference voltage calculated using the particle swarm optimization algorithm. The parameters in the relationship between the phase current and the phase current are obtained, thus revealing the unknown parameters in the expression of the sigmoid function model.

[0015] Based on the confirmed parameters, the inverter nonlinearity is initially compensated using the sigmoid function model, thereby obtaining the d-axis reference voltage U. d1 and reference current i d1 The relationship curve, based on the d-axis reference voltage U d1 and reference current i d1The relationship curve and the sigmoid function model are used to calibrate the sigmoid function model to obtain a new sigmoid function model.

[0016] The voltage error compensation point is obtained based on the new sigmoid function model, and then the parameters in the new sigmoid function model are confirmed by the particle swarm algorithm.

[0017] (2) Based on the obtained sigmoid function model, obtain the linear region of dq axis voltage and current, sample the current of dq axis in the obtained linear region, and calculate the unknown parameters in the fractional transfer function model based on the sampled data.

[0018] Furthermore, by sequentially performing the inverse Laplace transform and approximation on the fractional transfer function model, we obtain:

[0019] y(t)=U T NED -1 ψ M (t)

[0020] In the formula, U is the input matrix, and D = (a0 + b0F) λ ), N = KvF λ E is the delay matrix, which is a function of the time constant τ, and F λ Let be the block impulse operation matrix, a function of fractional order λ, where ψ is the integral over the interval [0,T). M (t) is:

[0021]

[0022] Where t is a time variable and j is an integer,

[0023]

[0024] In the formula, M represents E and F. λ Dimensions.

[0025] Furthermore, the d-axis reference voltage The relationship between the phase current and the phase current is:

[0026]

[0027] In the formula, D represents the voltage drift of the voltage sampling measurement, and R A The resistor is the resistance of the electromagnetic link.

[0028] Furthermore, based on the obtained D(i) xs ) Calculate the error voltage D(i) caused by inverter nonlinearity. as ),D(i bs ),D(i csThe error voltage D(i) as ),D(i bs ),D(i cs The error voltage D(i) is transformed into a synchronously rotating coordinate system through Clark and Park transformations. ds ), D(i qs ), and the obtained error voltage D(i) ds ), D(i qs The error voltage is initially compensated by applying the compensation to the dq coordinate system.

[0029] Furthermore, based on the preliminary compensation, the d-axis reference voltage U is obtained. d1 and reference current i d1 The relationship curve is denoted as C. A For the d-axis, under zero initial conditions, performing an inverse Laplace transform on the current-to-voltage transfer function yields U. dideal =i ramp ·(L+S A ·t) / K v t is the time starting from 0; by D(i xs C A and U dideal The sigmoid function model is calibrated to obtain a new sigmoid function model.

[0030] Furthermore, the expression for the new sigmoid function model is:

[0031]

[0032] Furthermore, based on the expression of the new sigmoid function model, a series of more accurate voltage error compensation points are obtained, and then K can be obtained based on the PSO algorithm. ace and A ace .

[0033] Further, in step (2), a pseudo-random sequence is superimposed on the DC component, and the resulting composite signal is denoted as PRBSPDC; the pseudo-random sequence is denoted as PRBS; the value of the PRBSPDC signal is defined as us. prbspdc The value of the PRBS signal is defined as us. prbs Excitation signal u des Represented as:

[0034] u des =us prbspdc -us dc =us prbs

[0035] Excitation signal u des Current response i under actiondprbs Represented as:

[0036] i dprbs =i dprbspdc -i ddc

[0037] According to u des and i dprbs , let U=i dprbs y(t)=u des The particle swarm optimization algorithm is used to obtain the unknown parameters in the fractional transfer function model.

[0038] Furthermore, the unknown parameters in the fractional transfer function model include a0, b0, τ, and λ.

[0039] This invention provides an application of the transfer function model constructed using the fractional-order modeling and identification method for motor drive systems described above in the design of a current controller.

[0040] In summary, compared with the prior art, the fractional-order modeling and identification method for motor drive systems and its application provided by this invention have the following advantages:

[0041] 1. Taking advantage of the advantages of fractional-order modeling, a fractional-order model of the electromagnetic link of permanent magnet synchronous motor with delay element is proposed. The proposed model can not only describe the fractional-order behavior of inductor devices, but also reduce the impact of system delay on the inductance, resistance and fractional-order identification accuracy of inductor devices.

[0042] 2. Taking into account the nonlinear characteristics of the inverter, the actual relationship between the inverter phase error voltage and phase current is re-determined using the compensation-sampling-error voltage calibration method. Based on the actual relationship between the inverter phase error voltage and phase current, the sigmoid function is used to describe the nonlinear characteristics of the inverter.

[0043] 3. Based on the sigmoid function, and by compensating for the nonlinear characteristics of the inverter, the impact on the accuracy of electromagnetic model parameter identification of the permanent magnet synchronous motor servo system is suppressed. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the PMSM current control platform according to an embodiment of the present invention;

[0045] Figure 2 This is a schematic diagram of inverter nonlinearity identification and compensation according to an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the fractional-order electromagnetic model identification scheme according to an embodiment of the present invention;

[0047] Figure 4 This is a diagram illustrating the inverter model identification and inverter nonlinear compensation effect according to an embodiment of the present invention.

[0048] Figure 5 This is a flowchart of the PSO algorithm according to an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram of the excitation voltage and response current according to an embodiment of the present invention;

[0050] Figure 7 This is a block diagram of the current closed-loop control according to an embodiment of the present invention;

[0051] Figure 8 (a) and (b) in the figure are experimental results of the fractional-order model current closed loop in the embodiment of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0053] Please see Figure 1 and Figure 3 This invention provides a fractional-order modeling and identification method for motor drive systems, the method mainly including the following steps:

[0054] Step 1: Establish the fractional-order transfer function model of the electromagnetic components of the PMSM servo system. The mathematical expression of the fractional-order transfer function model is as follows:

[0055]

[0056] In the formula, Kv is the conversion factor from the per-unit voltage value to the actual output voltage; τ is the digital system delay; R s The resistor is represented by the resistance of the permanent magnet synchronous motor, the inverter, and the circuitry; L is the inductance of the permanent magnet synchronous motor; s is the Laplace operator; a0 = L; b0 = R s ;

[0057] Simultaneously, a nonlinear sigmoid function model of the inverter is established, and the expression of the sigmoid function model is:

[0058]

[0059] In the formula, K is a parameter related to the voltage error constant, A is a parameter related to the inverter characteristics, and i xsLet x = a, b, c represent any one of the motor phase currents;

[0060] Based on d-axis reference voltage and the current i along the d-axis d The curve, and the d-axis reference voltage calculated using the particle swarm optimization algorithm. The parameters in the relationship between the phase current and the phase current are obtained, thus revealing the unknown parameters in the expression of the sigmoid function model.

[0061] Based on the confirmed parameters, the inverter nonlinearity is initially compensated using the sigmoid function model, thereby obtaining the d-axis reference voltage U. d1 and reference current i d1 The relationship curve, based on the d-axis reference voltage U d1 and reference current i d1 The relationship curve and the sigmoid function model are used to calibrate the sigmoid function model to obtain a new sigmoid function model.

[0062] The voltage error compensation point is obtained based on the new sigmoid function model, and then the parameters in the new sigmoid function model are confirmed by the particle swarm algorithm.

[0063] In this embodiment, considering the skin effect of the inductor and the fact that its external characteristics are fractional, a fractional-order transfer function model of the electromagnetic components of the PMSM servo system is constructed. The mathematical expression of the fractional-order transfer function model is as follows:

[0064]

[0065] In the formula, Kv is the conversion factor from the per-unit voltage (pu) to the actual output voltage. In this example, Kv = 181.6. τ is the digital system delay. In this embodiment, τ is 1.0 to 1.5 times T. PWM T PWM The carrier period is 10kHz in this embodiment, R. s The resistance is defined as the resistance of the permanent magnet synchronous motor, the inverter, and the circuitry; L is the inductance of the permanent magnet synchronous motor; s is the Laplace operator; a0 = L; b0 = R. s .

[0066] The fractional operator is approximated using a block impulse function. An inverse Laplace transform of the fractional transfer function model yields:

[0067]

[0068] Approximating the above equation using a block impulse function, we obtain:

[0069] y(t)=UT NED -1 ψ M (t)

[0070] In the formula, U is the input matrix, and D = (a0 + b0F) λ ), N = KvF λ E is the delay matrix, which is a function of the time constant τ, and F λ Let be the block impulse operation matrix, a function of fractional order λ, where ψ is the integral over the interval [0,T). M (t) is defined as:

[0071]

[0072] Where t is a time variable and j is an integer,

[0073]

[0074] M represents E and F. λ The dimensions. In this embodiment, the carrier period is 10kHz, the current sampling frequency is 20kHz, M=4000, and T=0.2s.

[0075] In another implementation, a nonlinear sigmoid function model of the inverter is established. This sigmoid function model can represent the phase voltage error caused by the inverter's nonlinearity error, and its corresponding mathematical expression is:

[0076]

[0077] In the formula, K is a parameter related to the voltage error constant, A is a parameter related to the inverter characteristics, and i xs Let x = a, b, c represent any one of the motor phase currents a, b, c.

[0078] For a permanent magnet synchronous motor servo system, when the d-axis coincides with the a-axis, its d-axis reference voltage V d * s The relationship between phase current and phase current can be expressed as:

[0079]

[0080] In the formula, D represents the voltage drift of the voltage sampling measurement, and R A The resistor is the resistance of the electromagnetic link.

[0081] In a synchronous rotating coordinate system, a positive voltage of 0.1 pu is first applied to the d-axis, while the q-axis voltage is kept at 0 p.u. and the electrical angle is 0°. The permanent magnet synchronous motor rotor will rotate to a position with an electrical angle of 0° under the influence of electromagnetic force. After several cycles of oscillation, it will stop rotating, at which point the a-axis coincides with the d-axis. Then, a voltage starting from 0 and varying according to an arithmetic sequence with a tolerance of 0.0025 pu is applied to the d-axis, while maintaining the q-axis voltage at 0 p.u. and the electrical angle at 0°. Throughout this process, it is essential to ensure that the d-axis voltage allows the d-axis current to reach a steady state; at this point, the d-axis current i... d The current is the same as that of phase a. Finally, the d-axis current is acquired, and then... and the current i along the d-axis d The curve can be drawn. (Reference) Figure 4 , and i d The relationship curve is denoted as C. O C O The slope of the linear region is S A Record S A .

[0082] Based on the obtained and the current i along the d-axis d The relationship curve can be obtained using the particle swarm optimization (PSO) algorithm. The parameters in the expression, and D(i) xs The parameters in () can also be obtained. PSO algorithm execution reference Figure 5 ,for Given four parameters K, A, R, and D, and a particle swarm of 200 particles, where the i-th particle is represented as a 4-dimensional vector, X... i =(x i1 ,x i2 ,x i3 ,x i4 The velocity of the i-th particle is also a 4-dimensional vector, denoted as V, where (K, A, R, D) = (K, A, R, D). i =(v i1 ,v i2 ,v i3 ,v i4 The best position found so far by the i-th particle is called the individual extreme value, denoted as Pbest = (p i1 ,p i2 ,p i3 ,p i4 The optimal position found so far by the entire particle swarm is the global extremum, denoted as gbest = (g1, g2, g3, g4), and its evolutionary process is as follows:

[0083]

[0084] Where c1 and c2 are learning factors, r1 and r2 are random functions, ω is the inertia weight, and v ij It's the particle velocity. X i The feasible region is divided into several sub-regions. It is assumed that there is no more than one local optimum in each sub-region. An initial parameter vector X is selected from each sub-region (located at the midpoint of the sub-region). i .

[0085] The fitness function is the root mean square (RMS) error, which is defined as:

[0086]

[0087] Among them, H e (k) is the experimental measurement result, H d (k) is the model value, and n is the data length.

[0088] Inverter nonlinearity preliminary compensation:

[0089] refer to Figure 2 According to the obtained D(i) xs The error voltage D(i) caused by inverter nonlinearity can be calculated. as ),D(i bs ),D(i cs The error voltage D(i) as ),D(i bs ),D(i cs Through Clark and Park transformations, the error voltage D(i) in a synchronously rotating coordinate system can be transformed. ds ),D(i qs This error voltage is then compensated to the dq coordinate system to achieve preliminary error voltage compensation. The effect of the preliminary compensation is shown in the reference diagram. Figure 4 The curve CA in the figure.

[0090] Further compensation for inverter nonlinearity:

[0091] Based on the initial compensation, the PMSM electrical angle is equal to 0, the q-axis voltage is 0, and a voltage signal U is applied to the d-axis. d The motor rotor will rotate to a position with an electrical angle of 0 under the action of electromagnetic force, oscillate several times, and then stop. Then, take R... s ≈S A L represents the motor nameplate parameters. A current-controlled PID controller is designed, ensuring the PID controller's cutoff frequency is as high as possible. The d-axis reference current is a ramp current with a slope of i. ramp =1, the q-axis reference current is 0, and the motor rotor is kept at a position with an electrical angle of 0. Then, the d-axis reference voltage U can be obtained. d1 and reference current id1 The relationship. (Reference) Figure 4 U d1 and i d1 The relationship curve is denoted as C. A .

[0092] For the d-axis, under zero initial conditions, performing an inverse Laplace transform on the current-to-voltage transfer function yields the d-axis reference voltage U. dideal and the current i along the d-axis ramp The relationship between ·t, where t is the time starting from 0.

[0093] U dideal =i ramp ·(L+S A ·t) / K v

[0094] refer to Figure 4 The dotted line represents U. dideal The relationship between the current and the d-axis current. It can be seen that there is a gap between the initial compensation result and the ideal curve, and this gap needs further compensation.

[0095] By D(i) xs C A and U dideal A more accurate expression for the inverter's three-phase error voltage can be obtained:

[0096]

[0097] Based on this formula, a series of more accurate voltage error compensation points are obtained, and then K can be obtained based on the PSO algorithm. ace and A ace .

[0098] refer to Figure 2 Based on this new model, and using the phase current as input, the three-phase voltage errors (a, b, and c) caused by inverter nonlinearity can be obtained. These three-phase voltage errors are then transformed using Clark and Park methods to obtain D(i...). ds ) and D(i qs Then, this voltage is added to the dq-axis voltage and input to the motor. Following the method for tracking the d-axis ramp current mentioned above, the compensated d-axis voltage and current relationship can also be obtained. (Refer to...) Figure 4 The dotted lines represent the effect of further compensation.

[0099] Step 2: Based on the obtained sigmoid function model, obtain the linear region of dq axis voltage and current. In the obtained linear region, sample the current of dq axis and calculate the unknown parameters in the fractional transfer function model based on the sampled data.

[0100] refer to Figure 3 The inverter nonlinearity is compensated, and based on the compensation results, the linear regions of the dq-axis voltage and current can be obtained. The current linear region is referenced. Figure 4 In this region, the inverter's nonlinear characteristics will not affect parameter identification. Therefore, the following steps will involve applying an excitation voltage to the dq axis and then sampling the dq axis current during the linear interval.

[0101] In one implementation, firstly, voltage excitation and current sampling are performed on the d-axis:

[0102] The first step is to have a constant amplitude (d-axis voltage u). dref =0.1pu, q-axis voltage u qref =0p.u.) and direction (θ) e A current vector at θ = 0° is introduced into the stator coil. After a small oscillation, the rotor will eventually stop and remain at θ. e The position equal to zero. This step aligns the d-axis and a-axis.

[0103] The second step, to overcome the nonlinear region caused by current noise, is to superimpose a pseudo-random sequence (PRBS) onto the DC component. The resulting composite signal is denoted as PRBSPDC. PRBSPDC is then introduced into the d-axis stator voltage u. dref q-axis voltage u qref and electrical angle θ e Keep it at zero. Then, the signal of id can be sampled and labeled as i. dprbspdc The voltage component has an amplitude of 0.030 pu, and the voltage sequence has an amplitude of 0.008 pu.

[0104] Step 3, DC component u sdc The voltage u introduced into the d-axis stator dref In the middle, and the q-axis voltage u qref and electrical angle θ e Keep it at zero, then you can set i. d The signal is sampled and labeled as i. ddc .

[0105] The sampling method for q-axis data is the same as that for d-axis data:

[0106] The first step, before the sampling process, is to have a constant amplitude (q-axis voltage u). qref =0.1pu, d-axis voltage u dref =0p.u. and direction (θ) e A current vector of θ (-90°) is introduced into the stator coil. After a small oscillation, the rotor will eventually stop and remain at θ. eThe position is equal to -90 degrees. This step aligns the q-axis and a-axis.

[0107] In the second step, PRBSPDC is introduced into the q-axis stator voltage u. qref d-axis voltage u dref Keep it at zero, electrical angle θ e Keep it at -90 degrees; then you can do i q The signal is sampled and labeled as i. qprbspdc .

[0108] Step 3, DC component us dc The q-axis stator voltage u is introduced qref d-axis voltage u dref Keep it at zero, electrical angle θ e Keep it at -90 degrees; then you can do i q The signal is sampled and labeled as i. qdc .

[0109] The value of the PRBSPDC signal is defined as us. prbspdc The value of the PRBS signal is defined as us. prbs .

[0110] For the d-axis, the excitation signal u des Represented as:

[0111] u des =us prbspdc -us dc =us prbs

[0112] Excitation signal u des Current response i under action dprbs Represented as:

[0113] i dprbs =i dprbspdc -i ddc

[0114] For the q-axis, the excitation signal u des Represented as:

[0115] u qes =us prbspdc -us dc =us prbs

[0116] Excitation signal u des Current response i under action qprbs Represented as:

[0117] i qprbs =i dprbspdc -i ddc

[0118] To eliminate the back electromotive force generated by the rotation of the PMSM after power-on and to avoid the influence of the nonlinear region, when i ddc or i qdc When entering DC steady state, us prbs Superimposed on us dc Above. It is worth noting that once the PMSM axis is pulled to the set electrical angle by electromagnetic force, the PMSM will enter a stationary state. The experiment should be conducted with the PMSM stationary. This embodiment only specifically describes the sampling of the excitation voltage and response current of the d-axis. The excitation voltage and response current of the d-axis are referenced. Figure 6 .

[0119] According to u des and i dprbs , let U=i dprbs y(t)=u des Based on the PSO above, the unknown parameters (a0, b0, τ, λ) in the fractional transfer function model are obtained, thus obtaining the parameters of the d-axis. Similarly, the parameters of the q-axis can also be obtained.

[0120] refer to Figure 7 Different electromagnetic link models were used for testing, and the experimental results are referenced. Figure 8 In the figure, IOPTDMD represents a first-order integer-order model with delay, FOPTDMD represents the model proposed in this patent, and IOMD and FPMD represent the first-order integer-order model and fractional-order model, respectively. Figure 8 The results show that the electromagnetic model is more consistent with the physical system.

[0121] The present invention also provides an application of the transfer function model constructed using the fractional-order modeling and identification method of motor drive system described above in the design of current controllers, such as the design of current PID controllers.

[0122] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fractional-order modeling and identification method for a motor drive system, characterized in that, The method includes the following steps: (1) Establish a fractional-order transfer function model for the electromagnetic components of the PMSM servo system. The mathematical expression of the fractional-order transfer function model is as follows: In the formula, It is the conversion factor from the per-unit voltage value to the actual output voltage; It is the delay of the digital system; is the resistance, which includes the resistance of the permanent magnet synchronous motor, inverter, and circuit; L is the inductance of the permanent magnet synchronous motor; s is the Laplace operator; It is a fractional order; ; ; Simultaneously, a nonlinear sigmoid function model of the inverter is established, and the expression of the sigmoid function model is: In the formula, A is a parameter related to the voltage error constant, and A is a parameter related to the inverter characteristics. Let x = a, b, c represent any one of the motor phase currents, where a, b, c represent any one of the motor phases a, b, c. Based on d-axis reference voltage and d-axis current The curve, and the d-axis reference voltage calculated using the particle swarm optimization algorithm. The parameters in the relationship between the phase current and the phase current are obtained, thus revealing the unknown parameters in the expression of the sigmoid function model. Based on the confirmed parameters, the inverter nonlinearity is initially compensated using the sigmoid function model, thereby obtaining the d-axis reference voltage. and reference current The relationship curve, based on the d-axis reference voltage. and reference current The relationship curve and the sigmoid function model are used to calibrate the sigmoid function model to obtain a new sigmoid function model. The voltage error compensation point is obtained based on the new sigmoid function model, and then the parameters in the new sigmoid function model are confirmed by the particle swarm algorithm. (2) Based on the obtained sigmoid function model, obtain the linear region of dq axis voltage and current, sample the current of dq axis in the obtained linear region, and calculate the unknown parameters in the fractional transfer function model based on the sampled data; In step (2), a pseudo-random sequence is superimposed on the DC component, and the resulting composite signal is labeled PRBSPDC; the pseudo-random sequence is denoted as PRBS; the value of the PRBSPDC signal is defined as us. prbspdc The value of the PRBS signal is defined as us. prbs Excitation signal u des Represented as: Excitation signal u des Current response i under action dprbs Represented as: According to u des and i dprbs ,make , The particle swarm optimization algorithm is used to obtain the unknown parameters in the fractional transfer function model.

2. The fractional-order modeling and identification method for motor drive systems as described in claim 1, characterized in that: By sequentially performing the inverse Laplace transform and approximation on the fractional transfer function model, we obtain: In the formula, For the input matrix, , E is the delay matrix, which is the time constant. The function, The block impulse operation matrix is ​​of fractional order. The function, in the integration interval , for: Where t is a time variable and j is an integer, In the formula, M represents E and Dimensions.

3. The fractional-order modeling and identification method for motor drive systems as described in claim 2, characterized in that: d-axis reference voltage The relationship between the phase current and the phase current is: In the formula, This indicates the voltage drift in the voltage sampling measurement. The resistor is the resistance of the electromagnetic link.

4. The fractional-order modeling and identification method for motor drive systems as described in claim 2, characterized in that: Based on the obtained Calculate the error voltage caused by inverter nonlinearity. , , The error voltage , , The error voltage is transformed into a synchronous rotating coordinate system using Clark and Park transformations. , and the obtained error voltage , The initial compensation of the error voltage is achieved by compensating to the dq coordinate system.

5. The fractional-order modeling and identification method for motor drive systems as described in claim 4, characterized in that: Based on the initial compensation, the d-axis reference voltage is obtained. and reference current The relationship curve is denoted as ; For the d-axis, under zero initial conditions, performing an inverse Laplace transform on the current-to-voltage transfer function yields... , The time starts from 0; by , and The sigmoid function model is calibrated to obtain a new sigmoid function model.

6. The fractional-order modeling and identification method for motor drive systems as described in claim 5, characterized in that: The expression for the new sigmoid function model is: 。 7. The fractional-order modeling and identification method for motor drive systems as described in claim 6, characterized in that: Based on the expression of the new sigmoid function model, a series of more accurate voltage error compensation points are obtained, and then the PSO algorithm can be used to obtain... and .

8. The fractional-order modeling and identification method for motor drive systems as described in any one of claims 1-7, characterized in that: The unknown parameters in the fractional transfer function model include , , , .

9. An application of a transfer function model constructed using the fractional-order modeling and identification method for motor drive systems as described in any one of claims 1-8 in the design of a current controller.

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