阅读说明：本技术 永磁同步电机离散域电流环强鲁棒性二自由度控制方法 (Two-degree-of-freedom control method for discrete domain current loop high robustness of permanent magnet synchronous motor ) 是由 杨淑英 王奇帅 马铭遥 谢震 张兴 于 2020-07-02 设计创作，主要内容包括：本发明涉及永磁同步电机控制领域,具体涉及一种永磁同步电机离散域电流环强鲁棒性二自由度控制方法。该方法通过永磁同步电机在旋转dq坐标系下的离散域数学模型的系数矩阵F和输入矩阵G,设计电流控制器,并考虑了补偿数字控制一拍延迟造成的角度滞后问题。本发明使得永磁同步电机电流环跟随快速性的设计不受抗扰性能的约束,额外参数自由度的引入能够实现抗扰性能的主动配置,较好地克服了永磁同步电机电流跟踪快速性和抗扰性之间的矛盾,同时在不改变系统跟随快速性的情况下,极大地提升了系统的参数鲁棒性,进而提升了永磁同步电机电流控制系统的运行品质。(The invention relates to the field of permanent magnet synchronous motor control, in particular to a two-degree-of-freedom control method for discrete domain current loop robustness of a permanent magnet synchronous motor. According to the method, a current controller is designed through a coefficient matrix F and an input matrix G of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and the problem of angle lag caused by compensating digital control one-beat delay is considered. The invention ensures that the design of the following rapidity of the current loop of the permanent magnet synchronous motor is not restricted by the interference resistance, the active configuration of the interference resistance can be realized by introducing the additional parameter freedom degree, the contradiction between the current tracking rapidity and the interference resistance of the permanent magnet synchronous motor is better overcome, and meanwhile, the parameter robustness of the system is greatly improved under the condition of not changing the following rapidity of the system, thereby improving the operation quality of the current control system of the permanent magnet synchronous motor.)

1. A two-degree-of-freedom control method for discrete domain current loop robustness of a permanent magnet synchronous motor is characterized by comprising the following steps of:

step 1, collecting rotor electrical angular velocity omega of permanent magnet synchronous motor_eAnd rotor electrical angle theta_eAnd collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_cAnd obtaining a stator current dq component i of the permanent magnet synchronous motor under a rotating dq coordinate system through coordinate transformation_d,i_q；

Step 2, recording i_d,refFor d-axis given current, i_q,refA given current for the q-axis,

wherein the content of the first and second substances,

representing the integral action, z^-1Indicating a delay of one beat;

K_pis a matrix of scale coefficients, K_p＝G^-1(β₁β₂-β₁-β₂+1)；

K_iIs a matrix of integral coefficients, K_i＝G^-1(I-α₁F)(β₁β₂-β₁-β₂+1)；

M is a current feedback coefficient matrix, and M is G^-1((1-α₁)F²+(β₁+β₂-1)(α₁-1)F)；

A is a current controller delay output feedback coefficient matrix, and A is G^-1((1-α₁)F-(β₁+β₂-1)I)G；

In the scale factor matrix K_pIntegral coefficient matrix K_iA current feedback coefficient matrix M and a current controller delay output feedback coefficient matrix A,

i is an identity matrix and is a matrix of the identity,

β₁β for the desired follow and disturbance rejection closed loop pole one of the control system₂α following and disturbance rejection closed loop pole two desired for control system₁Adjustable coefficient of three poles of the anti-interference closed loop desired for the control system, β₁，β₂，α₁The value of (A) satisfies the restriction that 0 is not less than β₁＜1，0≤β₂＜1，0≤α₁＜1；

F is a coefficient matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as a coefficient matrix F;

g is an input matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as an input matrix G;

step 3, solving the expression of the current controller in the step 2 to obtain the d-axis output voltage of the current controllerAnd q-axis output voltage of current controller

wherein, T_sIs a sampling period;

step 4, the α axis output voltage u obtained in the step 3 is processed_α,refAnd β Axis output Voltage u_β,refAnd the input SVPWM module carries out space vector pulse width modulation and outputs PWM waves to the inverter module.

2. The two-degree-of-freedom control method for discrete domain current loop robustness of the permanent magnet synchronous motor according to claim 1, wherein the stator current dq component i of the permanent magnet synchronous motor in the step 1 is in a rotating dq coordinate system_d,i_qThe acquisition mode is as follows:

step 1.1, collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_c；

Step 1.2, the phase A of the permanent magnet synchronous motor stator acquired in the step 1.1Current i_aStator B phase current i_bStator C phase current i_cConverting the three-phase static coordinate system into a two-phase static coordinate system to obtain a stator current αβ component i of the permanent magnet synchronous motor under the two-phase static αβ coordinate system_α,i_β：

Step 1.3, the stator current αβ component i of the permanent magnet synchronous motor obtained in the step 1.2 in a two-phase static αβ coordinate system_α,i_βConverting the two-phase static coordinate system into a rotating coordinate system to obtain a stator current dq component i of the permanent magnet synchronous motor in the rotating dq coordinate system_d,i_q：

3. The two-degree-of-freedom control method for discrete domain current loop robustness of the permanent magnet synchronous motor according to claim 1, wherein the coefficient matrix F and the input matrix G in the step 2 are calculated as follows:

(1) the coefficient matrix F is expressed as follows:

wherein L is_dIs a stator straight axis inductor, L_qIs stator quadrature axis inductance, phi₁₁Is a variable 1, phi in the coefficient matrix F₁₂Is a variable 2, phi in the coefficient matrix F₂₁As a variable 3, phi in the coefficient matrix F₂₁＝-Φ₁₂，Φ₂₂Is variable 4 in the coefficient matrix F;

in the above-mentioned 3 formulae,for exponential function operation, sinh (), cosh () for hyperbolic function operation, R_sIs a stator resistor;

(2) the expression of the input matrix G is as follows:

wherein, γ₁₁For variables 1, gamma in the input matrix G₁₂For variables 2, gamma in the input matrix G₂₁For variables 3, gamma in the input matrix G₂₂For the variable 4 in the input matrix G, the expressions are respectively as follows:

Technical Field

The invention relates to the field of permanent magnet synchronous motor control, in particular to a two-degree-of-freedom control method for discrete domain current loop robustness of a permanent magnet synchronous motor.

Background

The permanent magnet synchronous motor is widely applied to high-performance driving occasions such as new energy automobiles, industrial servo systems and the like due to the characteristics of high efficiency, high power density, specific power, high starting torque and the like. For many years, a Proportional Integral (PI) controller based on a rotor magnetic field directional synchronous rotation coordinate system is an industrial standard for current control of an alternating current motor due to the advantages of wide speed regulation range, zero steady-state error and the like. However, the current controller in common use at present has the following problems when facing the high speed low carrier ratio operation state: 1) cross coupling disturbance terms introduced by rotation coordinate transformation between the d-axis subsystem and the q-axis subsystem are increased along with the increase of the operation rotating speed and even become main determining factors of current components of the d-axis subsystem and the q-axis subsystem, and great disturbance is brought to the control performance of the d-axis subsystem and the q-axis subsystem; 2) the carrier ratio corresponding to high-speed operation is lower due to the limitation of allowable switching frequency and heat dissipation conditions of a power device, so that discretization errors are prominent, the influence of sampling and control delay is aggravated, and even system instability is caused in severe cases.

Based on a motor discrete domain mathematical model, a controller is directly designed in a discrete domain, and the method becomes an effective way for improving the low-carrier-ratio operation performance of a motor control system. In recent years, with the increase of the demand for high-speed operation of a permanent magnet synchronous motor, a discrete domain control system design is emphasized.

Reference 1: an article of "Discrete-time current regulator design for ac modular drivers," (h.kim, m.w.degner, j.m.gurrero, f.briz, and r.d.lorenz, ieee transactions on industrial Applications, vol.46, No.4, pp.1425-1435, July 2010.) ("alternating current motor driven Discrete domain current regulator design" (h.kim, m.w.degner, j.m.gurrero, f.briz, and r.d.lorenz, institute of electrical and electronics engineers industrial Applications, volume 2010, volume 46, No.4, page 1435)). The article provides a discretization mathematical model of a surface-mounted permanent magnet synchronous motor current loop, and a current controller is directly designed in a discrete domain according to a zero-pole cancellation principle based on the model. The method better improves the following performance of the surface-mounted permanent magnet synchronous motor during high-speed low-carrier ratio operation, but cannot give consideration to the anti-interference performance of the system, so that the following performance is not high in practical application. In addition, the design scheme is not suitable for the design of the built-in permanent magnet synchronous motor current controller.

Reference 2: "A syndrome reference frame PI current controller with slave response" (Claudio A. Busada, Sebastian Gomez)and JorgeA. Solsona, IEEE Transactions on Power Electronics, vol.35, No.3, pp.3097-3105, March 2020.) ("a synchronous reference frame PI Current controller with minimum beat response" (Claudio A. Busada, Sebastian Gomez)

and Jorge a. solsona, proceedings of the institute of electrical and electronics engineers, 2020, volume 35, page 3 3097-3105)). The article is based on a discretization mathematical model of a current loop of a surface-mounted permanent magnet synchronous motor, a two-degree-of-freedom current controller is designed in a discretization domain, the method solves the problem that the system following performance of the surface-mounted permanent magnet synchronous motor is reduced under the condition of low carrier ratio, the minimum beat response of the current loop can be realized, the anti-interference performance of the system is improved, and the control freedom degree of the system is increased. But is difficult to be directly applicable to the interior permanent magnet synchronous motor.

Reference 3: an article of "Current Control for Synchronous Motor Drives" (M.Hinkkanen, H.Asad Ali Awan, Z.Qu, T.Tuovinen and F.Briz, IEEE Transactions on Industrial Applications, vol.52, No.2, pp.1530-1541, March-April 2016.) ("Current Control of Synchronous Motor drive System: direct discrete Domain Pole configuration Design" (M.Hinkkanen, H.Asad Ali Awan, Z.Qu, T.Tuovinen and F.Briz, institute of Electrical and electronics Engineers Industrial Applications, pp.2, 1541, No. 52, No.2, p.1530 1541). The article provides a discretization mathematical model of a current loop of a built-in permanent magnet synchronous motor, a current controller with an improved structure is designed in a discrete domain based on the model, the method solves the problem that the follow-up performance of the built-in permanent magnet synchronous motor is reduced under the condition of a low carrier ratio, the minimum beat response of the current loop can be realized theoretically, but the actual follow-up response speed is limited by the anti-interference performance and the parameter robustness, so that the actual operation effect is poor, and in case of non-punctual parameters, the dynamic response process of the system can generate larger overshoot.

In summary, the prior art has the following problems:

1. the built-in permanent magnet synchronous motor has uneven air gaps, so that the alternating-axis inductance and the direct-axis inductance are not equal, a permanent magnet motor voltage model cannot be simplified into a single-input single-output model by using a complex vector technology, the existing discrete domain design scheme is mostly based on a single-input single-output control object described by a complex vector, and the current controller discrete domain design scheme is not suitable for the built-in permanent magnet synchronous motor;

2. the design for the discrete domain current controller of the interior permanent magnet synchronous motor reported in reference 3 has the problems that the following performance and the anti-interference performance of a current loop cannot be considered simultaneously, and in actual use, parameter deviation seriously affects the dynamic response process of a system, a large overshoot is generated, overcurrent protection of the actual system can be caused, and the robustness of system parameters is insufficient.

Disclosure of Invention

The invention aims to solve the technical problem of how to realize the two-degree-of-freedom design of the current loop following property and the interference resistance of the built-in permanent magnet synchronous motor with strong parameter robustness under the condition of high speed and low carrier ratio, and greatly improve the dynamic response process of a control system when the motor parameters are not accurate under the condition of not changing the current following response, so that the overshoot of the control system is extremely small.

The invention aims to realize the purpose, and provides a two-degree-of-freedom control method for the discrete domain current loop strength and robustness of a permanent magnet synchronous motor, which comprises the following steps:

step 1, collecting rotor electrical angular velocity omega of permanent magnet synchronous motor_eAnd rotor electrical angle theta_eAnd collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_cAnd then the rotation of the permanent magnet synchronous motor is obtained through coordinate transformationStator current dq component i in dq coordinate system_d,i_q；

Step 2, recording i_d,refFor d-axis given current, i_q,refA given current for the q-axis,Outputs voltage for d axis of the current controller,

Designing a current controller in a z domain for a q-axis output voltage of the current controller by a complex variable z in the discrete domain, wherein the expression of the current controller is as follows:

wherein the content of the first and second substances,

representing the integral action, z^-1Indicating a delay of one beat;

K_pis a matrix of scale coefficients, K_p＝G^-1(β₁β₂-β₁-β₂+1)；

K_iIs a matrix of integral coefficients, K_i＝G^-1(I-α₁F)(β₁β₂-β₁-β₂+1)；

M is a current feedback coefficient matrix, and M is G^-1((1-α₁)F²+(β₁+β₂-1)(α₁-1)F)；

A is a current controller delay output feedback coefficient matrix, and A is G^-1((1-α₁)F-(β₁+β₂-1)I)G；

In the scale factor matrix K_pIntegral coefficient matrix K_iA current feedback coefficient matrix M and a current controller delay output feedback coefficient matrix A,

i is an identity matrix and is a matrix of the identity,

β₁β for the desired follow and disturbance rejection closed loop pole one of the control system₂α following and disturbance rejection closed loop pole two desired for control system₁Adjustable coefficient of three poles of the anti-interference closed loop desired for the control system, β₁，β₂，α₁The value of (A) satisfies the restriction that 0 is not less than β₁＜1，0≤β₂＜1，0≤α₁＜1；

F is a coefficient matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as a coefficient matrix F;

g is an input matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as an input matrix G;

step 3, solving the expression of the current controller in the step 2 to obtain the d-axis output voltage of the current controllerAnd q-axis output voltage of current controllerObtaining α axis output voltage u under a static αβ coordinate system through coordinate transformation and compensation of angle lag caused by one-beat delay of digital control_α,refAnd β Axis output Voltage u_β,refThe expression is as follows:

wherein, T_sIs a sampling period;

step 4, the α axis output voltage u obtained in the step 3 is processed_α，,refAnd β Axis output Voltage u_β，,refAnd the input SVPWM module carries out space vector pulse width modulation and outputs PWM waves to the inverter module.

Preferably, the stator current dq component i of the permanent magnet synchronous motor in the step 1 under a rotating dq coordinate system_d,i_qThe acquisition mode is as follows:

step 1.1, collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_c；

Step 1.2, the phase current i of the permanent magnet synchronous motor stator A acquired in the step 1.1 is compared_aStator B phase current i_bStator C phase current i_cConverting the three-phase static coordinate system into a two-phase static coordinate system to obtain a stator current αβ component i of the permanent magnet synchronous motor under the two-phase static αβ coordinate system_α,i_β：

Step 1.3, the stator current αβ component i of the permanent magnet synchronous motor obtained in the step 1.2 in a two-phase static αβ coordinate system_α,i_βConverting the two-phase static coordinate system into a rotating coordinate system to obtain a stator current dq component i of the permanent magnet synchronous motor in the rotating dq coordinate system_d,i_q：

Preferably, the coefficient matrix F and the input matrix G in step 2 are calculated as follows:

(1) the coefficient matrix F is expressed as follows:

wherein L is_dIs a stator straight axis inductor, L_qIs stator quadrature axis inductance, phi₁₁Is a variable 1, phi in the coefficient matrix F₁₂Is a variable 2, phi in the coefficient matrix F₂₁As a variable 3, phi in the coefficient matrix F₂₁＝-Φ₁₂，Φ₂₂Is variable 4 in the coefficient matrix F;

in the above-mentioned 3 formulae,

for exponential function operation, sinh (), cosh () for hyperbolic function operation, R_sIs a stator resistor;

(2) the expression of the input matrix G is as follows:

wherein, γ₁₁For variables 1, gamma in the input matrix G₁₂For variables 2, gamma in the input matrix G₂₁For variables 3, gamma in the input matrix G₂₂For the variable 4 in the input matrix G, the expressions are respectively as follows:

compared with the prior art, the invention has the beneficial effects that:

1. compared with the traditional surface-mounted permanent magnet synchronous motor discrete domain current controller, the invention utilizes a mathematical model based on the discrete domain of the built-in permanent magnet synchronous motor to carry out design, and the design result is suitable for the surface-mounted permanent magnet synchronous motor and the built-in permanent magnet synchronous motor;

2. compared with the discrete domain current controller of the built-in permanent magnet synchronous motor in reference 3, the current controller designed by the invention has extra parameter freedom, so that the design following rapidity is not restricted by the anti-interference performance, and the active configuration of the anti-interference performance can be realized by introducing the extra parameter freedom;

3. compared with the discrete domain current controller of the built-in permanent magnet synchronous motor in reference 3, the current controller designed by the invention can keep a very small overshoot in a dynamic response process of a control system when the motor parameter is deviated through reasonable configuration of an additional parameter degree of freedom on the premise of not changing the rapidity of the control system, and the control system has very strong parameter robustness.

Drawings

Fig. 1 is a control block diagram of a current loop control system of a permanent magnet synchronous motor according to the present invention.

Fig. 2 is a block diagram of a current controller of a permanent magnet synchronous motor according to the present invention.

Fig. 3 is an equivalent structure block diagram of a current loop control system of a permanent magnet synchronous motor in a rotating dq coordinate system.

Fig. 4 is a current response simulation diagram of the complex vector design current loop of the technical scheme described in reference 3 when the motor operates at a rated frequency and the motor inductance parameter is accurate, and the bandwidth of the complex vector design current loop is 50 Hz.

FIG. 5 is a current response simulation diagram of the technical scheme of the invention shown in FIG. 1 (expected following and anti-interference closed loop pole one β of the control system under the condition that the motor runs at a rated frequency and the motor inductance parameter is accurate₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0.8546, corresponding to a current loop bandwidth of 50 Hz).

FIG. 6 is a current response simulation diagram 2 (control system period) of the technical scheme of the invention under the condition that the motor runs at a rated frequency and the motor inductance parameter is accurateHopeful following and anti-interference closed loop pole one β₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0.5 corresponding to a current loop bandwidth of 50 Hz).

FIG. 7 is a current response simulation diagram of the technical solution of the present invention shown in FIG. 3 (select the first pole β of the desired follow and anti-interference closed loop of the control system under the condition that the motor operates at the rated frequency and the motor inductance parameter is accurate₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0, corresponding to a current loop bandwidth of 50 Hz).

FIG. 8 shows the stator quadrature axis inductance L when the motor is operated at a rated frequency_qIn the case of deviation, the internal model design in the technical solution described in reference 3 is configured as a current response simulation diagram when the current loop bandwidth is 100 Hz.

FIG. 9 shows the stator quadrature axis inductance L when the motor is operated at the rated frequency_qIn the case of deviation, the complex vector design in the technical solution described in reference 3 is configured as a current response simulation diagram when the current loop bandwidth is 100 Hz.

FIG. 10 shows the stator quadrature axis inductance L when the motor is operated at a rated frequency_qUnder the condition of deviation, the technical scheme of the invention is configured into a current response simulation graph when the current loop bandwidth is 100Hz (the expected following and anti-interference closed loop pole I of the control system is β)₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.7304, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁＝0.95)。

Detailed Description

The two-degree-of-freedom control method for the discrete domain current loop robustness of the permanent magnet synchronous motor is described in detail below with reference to the accompanying drawings and embodiments.

Fig. 1 is a control block diagram of a current loop control system of a permanent magnet synchronous motor according to the present invention, fig. 2 is a structural block diagram of a current controller of a permanent magnet synchronous motor according to the present invention, and fig. 3 is an equivalent structural block diagram of a current loop control system of a permanent magnet synchronous motor according to the present invention in a rotating dq coordinate system. As can be seen from fig. 1, 2 and 3, the present invention comprises the following steps:

step 1, collecting rotor electrical angular velocity omega of permanent magnet synchronous motor_eAnd rotor electrical angle theta_eAnd collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_cAnd obtaining a stator current dq component i of the permanent magnet synchronous motor under a rotating dq coordinate system through coordinate transformation_d,i_q。

Step 1.1, collecting stator A phase current i of the permanent magnet synchronous motor_aStator B phase current i_bStator C phase current i_c；

Step 1.2, the phase current i of the permanent magnet synchronous motor stator A acquired in the step 1.1 is compared_aStator B phase current i_bStator C phase current i_cConverting the three-phase static coordinate system into a two-phase static coordinate system to obtain a stator current αβ component i of the permanent magnet synchronous motor under the two-phase static αβ coordinate system_α,i_β：

Step 1.3, the stator current αβ component i of the permanent magnet synchronous motor obtained in the step 1.2 in a two-phase static αβ coordinate system_α,i_βConverting the two-phase static coordinate system into a rotating coordinate system to obtain a stator current dq component i of the permanent magnet synchronous motor in the rotating dq coordinate system_d,i_q：

Step 2, recording i_d,refFor d-axis given current, i_q,refA given current for the q-axis,Outputs voltage for d axis of the current controller,Designing a current controller in a z domain for a q-axis output voltage of the current controller by a complex variable z in the discrete domain, wherein the expression of the current controller is as follows:

wherein the content of the first and second substances,

representing the integral action, z^-1Indicating a delay of one beat;

K_pis a matrix of scale coefficients, K_p＝G^-1(β₁β₂-β₁-β₂+1)；

K_iIs a matrix of integral coefficients, K_i＝G^-1(I-α₁F)(β₁β₂-β₁-β₂+1)；

M is a current feedback coefficient matrix, and M is G^-1((1-α₁)F²+(β₁+β₂-1)(α₁-1)F)；

A is a current controller delay output feedback coefficient matrix, and A is G^-1((1-α₁)F-(β₁+β₂-1)I)G；

In the scale factor matrix K_pIntegral coefficient matrix K_iA current feedback coefficient matrix M and a current controller delay output feedback coefficient matrix A,

i is an identity matrix and is a matrix of the identity,

β₁β for the desired follow and disturbance rejection closed loop pole one of the control system₂α following and disturbance rejection closed loop pole two desired for control system₁Adjustable coefficient of three poles of the anti-interference closed loop desired for the control system, β₁，β₂，α₁The value of (A) satisfies the restriction that 0 is not less than β₁＜1，0≤β₂＜1，0≤α₁＜1；

F is a coefficient matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as a coefficient matrix F;

g is an input matrix of a discrete domain mathematical model of the permanent magnet synchronous motor under a rotating dq coordinate system, and is recorded as an input matrix G;

step 3, solving the expression of the current controller in the step 2 to obtain the d-axis output voltage of the current controller

And q-axis output voltage of current controller

Obtaining α axis output voltage u under a static αβ coordinate system through coordinate transformation and compensation of angle lag caused by one-beat delay of digital control_α,refAnd β Axis output Voltage u_β,refThe expression is as follows:

wherein, T_sIs the sampling period.

Step 4, the α axis output voltage u obtained in the step 3 is processed_α，,refAnd β Axis output Voltage u_β，,refAnd the input SVPWM module carries out space vector pulse width modulation and outputs PWM waves to the inverter module.

In the above step, the coefficient matrix F and the input matrix G in step 2 are calculated as follows:

(1) the coefficient matrix F is expressed as follows:

wherein L is_dIs a stator straight axis inductor, L_qIs stator quadrature axis inductance, phi₁₁Is a variable 1, phi in the coefficient matrix F₁₂Is a variable 2, phi in the coefficient matrix F₂₁As a variable 3, phi in the coefficient matrix F₂₁＝-Φ₁₂，Φ₂₂Is variable 4 in the coefficient matrix F.

In the above-mentioned 3 formulae,

for exponential function operation, sinh (), cosh () for hyperbolic function operation, R_sIs the stator resistance.

(2) The expression of the input matrix G is as follows:

wherein, γ₁₁For variables 1, gamma in the input matrix G₁₂For variables 2, gamma in the input matrix G₂₁For variables 3, gamma in the input matrix G₂₂For the variable 4 in the input matrix G, the expressions are respectively as follows:

in order to verify the effectiveness of the invention, the invention is subjected to simulation verification. Control system simulation parameters: rated power p of motor_n10kW, rated voltage U_N220V, stator resistance R_s0.428 Ω stator direct axis inductance L_d4.5mH, stator quadrature axis inductance L_q8.5mH, 5 pole pair number P, rated frequency f_e200Hz, switching frequency f_s2000Hz, sample period T_s＝0.5ms。

Fig. 4 is a simulation diagram of the motor running at a rated frequency, and in reference 3, in the case that the control system parameters are accurate, a complex vector design is selected, and the bandwidth of the control system is set to be 50 Hz. The control system firstly applies step setting and stabilizes, and then outputs voltage on the q axis

Step disturbance of 10V is applied, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

FIG. 5 is a current response simulation diagram of the technical scheme of the invention shown in FIG. 1 (expected following and anti-interference closed loop pole one β of the control system under the condition that the motor runs at a rated frequency and the motor inductance parameter is accurate₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0.8546, corresponding to a current loop bandwidth of 50 Hz). The control system firstly applies step setting and stabilizes, and then outputs voltage on the q axisStep disturbance of 10V is applied, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

FIG. 6 shows the motor operating at the rated frequencyUnder the condition that the motor inductance parameter is accurate, the current response simulation of the technical scheme of the invention is shown in figure 2 (the expected following and anti-interference closed loop pole I of the control system is β)₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0.5 corresponding to a current loop bandwidth of 50 Hz). The control system firstly applies step setting and stabilizes, and then outputs voltage on the q axisStep disturbance of 10V is applied, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

FIG. 7 is a current response simulation diagram of the technical solution of the present invention shown in FIG. 3 (select the first pole β of the desired follow and anti-interference closed loop of the control system under the condition that the motor operates at the rated frequency and the motor inductance parameter is accurate₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.8546, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0, corresponding to a current loop bandwidth of 50 Hz). The control system firstly applies step setting and stabilizes, and then outputs voltage on the q axisStep disturbance of 10V is applied, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

Comparing fig. 4, fig. 5, fig. 6, and fig. 7, it can be seen that the complex vector design in the technical solution described in reference 3 under the condition of accurate parameters and the technical solution of the present invention have the same control system bandwidth, but the complex vector design in the technical solution described in reference 3 has oscillation in the feedback current under the condition of sudden step disturbance,a certain time is needed for gradual stabilization, and the technical scheme of the invention can flexibly design the adjustable coefficient α of the three poles of the anti-interference closed loop expected by the control system₁The value of the variable coefficient α of the third pole of the anti-interference closed loop expected by the control system under the condition of not changing the following performance of the control system is proved by the technical scheme of the invention₁The flexible design of the control system improves the anti-interference performance of the control system.

FIG. 8 shows the stator quadrature axis inductance L when the motor is operated at a rated frequency_qIn the case of deviation, the internal model design in the technical solution described in reference 3 is configured as a current response simulation diagram when the current loop bandwidth is 100 Hz. The control system applies a step setting, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

FIG. 9 shows the stator quadrature axis inductance L when the motor is operated at the rated frequency_qIn the case of deviation, the complex vector design in the technical solution described in reference 3 is configured as a current response simulation diagram when the current loop bandwidth is 100 Hz. The control system applies a step setting, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current component i in_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

FIG. 10 shows the stator quadrature axis inductance L when the motor is operated at a rated frequency_qUnder the condition of deviation, the technical scheme of the invention is configured into a current response simulation graph when the current loop bandwidth is 100Hz (the expected following and anti-interference closed loop pole I of the control system is β)₁0, the desired following and disturbance rejection closed loop pole two β of the control system₂0.7304, the desired anti-interference closed loop pole three of the control system is adjusted by a factor α₁0.95 corresponding to a current loop bandwidth of 100 Hz). The control system applies a step setting, and the solid line waveform is a stator current dq component i_d,i_qQ-axis current ofQuantity i_qThe dotted line waveform is the stator current dq component i_d,i_qD-axis current component i in_dThe waveform of (2).

Comparing fig. 8, fig. 9, and fig. 10, it can be seen that in the case of the same current loop bandwidth, the feedback current dynamic process in the internal model design in the technical solution described in reference 3 has a large overshoot when the parameters are not aligned, while the complex vector design in the technical solution described in reference 3 reduces the overshoot of the control system but reduces the overshoot to a lower extent than the internal model design, and the technical solution of the present invention can utilize the adjustable coefficient α of the third pole of the anti-interference closed loop expected by the control system₁The flexible design of the control system obviously improves the dynamic response process of the control system when the parameters deviate, so that the overshoot of the control system is extremely small, and the technical scheme of the invention can expect the adjustable coefficient α of the third pole of the anti-interference closed loop through the control system under the condition of not changing the following rapidity of the control system₁The flexible design of the control system obviously improves the dynamic response process when the parameters of the control system deviate, so that the control system has extremely strong parameter robustness.