阅读说明：本技术 一种低载波比下新型的pmsm精确离散自抗扰控制方法 (Novel PMSM (permanent magnet synchronous motor) accurate discrete active-disturbance-rejection control method under low carrier ratio ) 是由 尹忠刚 黄文博 张彦平 原东昇 于 2020-12-24 设计创作，主要内容包括：本发明公开了一种低载波比下新型的PMSM精确离散自抗扰控制方法,具体包括如下步骤：步骤1,建立复矢量永磁同步电机模型,精确离散化后得到电流和电压之间的准确数学关系；步骤2,根据精确的离散域复矢量PMSM模型设计出具有扰动补偿的离散线性自抗扰控制器,并且对该自抗扰控制器进行数字延迟补偿；步骤3,依据极点配置设计保证全速范围内稳定运行的离散域扩展状态观测器反馈增益矩阵。本发明解决了目前高速低载波比下传统自抗扰控制存在控制精度低甚至失控的问题。(The invention discloses a novel PMSM (permanent magnet synchronous motor) accurate discrete active disturbance rejection control method under a low carrier ratio, which specifically comprises the following steps: step 1, establishing a complex vector permanent magnet synchronous motor model, and obtaining an accurate mathematical relation between current and voltage after accurate discretization; step 2, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model, and carrying out digital delay compensation on the active disturbance rejection controller; and 3, designing a feedback gain matrix of the discrete domain extended state observer which ensures stable operation in a full-speed range according to the pole allocation. The invention solves the problem that the traditional active disturbance rejection control has low control precision and even is out of control under the high-speed low-carrier ratio.)

1. A novel PMSM accurate discrete active-disturbance-rejection control method under a low carrier ratio is characterized in that: the method specifically comprises the following steps:

step 1, establishing a complex vector permanent magnet synchronous motor model, and obtaining an accurate mathematical relation between current and voltage after accurate discretization;

step 2, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model, and carrying out digital delay compensation on the active disturbance rejection controller;

and 3, designing a feedback gain matrix of the discrete domain extended state observer which ensures stable operation in a full-speed range according to the pole allocation.

2. The novel PMSM accurate discrete active-disturbance-rejection control method according to claim 1, wherein: the specific process of the step 1 is as follows:

step 1.1, establishing a continuous domain complex vector PMSM model under a rotating coordinate system;

the complex vector PMSM model is concretely as follows:

in the formula (1), u_d、u_q、i_d、i_qRespectively a d-q axis voltage and a d-q axis current under a two-phase rotating d-q coordinate system; r_s、Ψ_f、L_s、ω_eStator resistance, permanent magnet flux linkage, inductance, and electrical angular velocity, respectively; p is a differential operator;

the formula (1) is used in the form of a complex vector x_dq＝x_d+jx_qExpressed as shown in the following equation (2):

in the formula (2), u_dqAnd i_dqThe method is characterized in that the method is respectively in a complex vector form of stator voltage and stator current under a d-q coordinate system, and j is an imaginary number unit;

and step 1.2, accurately discretizing the complex vector PMSM model established in the step 1.1.

3. The novel PMSM accurate discrete active-disturbance-rejection control method under low carrier ratio as claimed in claim 2, wherein: the specific process of the step 1.2 is as follows:

writing the complex vector model (2) of PMSM in the continuous domain in the form of a differential equation, as shown in equation (3) below:

in the formula (3), the initial condition is time t₀Current i at time_dq(t₀) Obtaining the current response i at the time t_dq(t), expanding the counter electromotive force e_dqAnd voltage u_dqIs time-varying and requires a pair of e in order to simplify the integration operation in equation (3)_dqAnd u_dqThe following two assumptions are made:

A) suppose that between two sampling intervals kT to (k +1) T, the rotational speed ω of the motor_eRemains unchanged, so the extended back emf is also constant during this time:

B) assuming a voltage value u in a continuous domain under an alpha-beta shafting_αβ(t) and sampled voltage value u at time kT_αβ(kT) equal, i.e.:

e_dq(t)＝e_dq(kT) (4)；

secondly, assume the voltage value u in the continuous domain under the alpha-beta shafting_αβ(t) and sampled voltage value u at time kT_αβ(kT) equal, i.e.:

u_αβ(t)＝u_αβ(kT) (5)；

and then obtaining the following results according to coordinate transformation:

u_dq(kT)＝e^-jθ(kT)u_αβ(kT) (6)；

a complex vector equation of the voltage in the d-q axis system can be obtained according to the equations (5) and (6), and the conversion from the continuous domain to the discrete domain is shown in the following equation (7):

assuming a rotation speed omega within a sampling interval_eKeeping unchanged, the step (7) can be further simplified into the following steps:

substituting equations (4) and (8) into equation (3) and solving the differential equation directly can obtain:

obtaining a discretized model of the electrical machine by solving equation (9), where the variable t is in the continuous domain₀And T is replaced by kT and (k +1) T, respectively, in the discrete domain, as shown in equation (10) below:

converting equation (10) into a state space form as shown in equation (11):

wherein:

4. the novel PMSM accurate discrete active-disturbance-rejection control method under low carrier ratio as claimed in claim 3, wherein: the specific process of the step 2 is as follows:

step 2.1, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model, specifically:

considering that the disturbance can be caused to the motor operation process by the disturbance, the d-axis model in the formula (11) is rewritten, as shown in the following formula (12):

in formula (12), f_d0(k) Is a disturbance term that can be modeled and,is the amount of coupling of the q-axis to the d-axis, A₁₁、B₁₁Is the first row and column, A, of the matrix A, B₁₂、B₁₂Is the first row and second column, C, of the matrix A, B₁(k) Is the first row of the matrix C, d₁(k) Is a disturbance for which the non-linear factor of the inverter is unknown;

establishing a linear Extended State Observer (ESO) from the model (12) to measure the total disturbanceAs a new state quantity, in order to avoid delay problem of two inputs of ESO, the output u of the current controller is used_d(k) After digital delay compensationAs an input of the ESO, the following formula (13) shows:

wherein:

the disturbance compensation link is designed as follows:

in observing disturbancesEqual to the actual disturbanceWhen the observation error is ignored, the system is changed into an integral series standard system as shown in the following formula (15):

by the I-type system of equation (15), the linear state error feedback control rate LSEF is designed to be proportional, that is, the control of the current loop is realized, as shown in equation (16):

step 2.2, performing delay compensation according to the discrete linear active disturbance rejection controller of disturbance compensation, specifically:

the delay compensation is performed by equation (14), as shown in equation (17):

wherein the content of the first and second substances,

from equation (17), the discrete active disturbance rejection controller output u of the current loop_dMeridian passageThrough K (omega)_eT) amplitude compensation, 1.5 omega_eCompensation of T phase to obtain

5. The novel PMSM accurate discrete active-disturbance-rejection control method under low carrier ratio as claimed in claim 4, wherein: the specific process of the step 3 is as follows:

step 3.1, designing a linear Extended State Observer (ESO) according to the formula (13), wherein the discrete domain characteristic polynomial is expressed as the following formula (18):

the observer characteristic polynomial p (z) collocated by the poles in the discrete domain is shown in equation (19) below:

P(z)＝(z-p₁)(z-p₂) (19)；

from the equations (18) and (19), the feedback gain l of the linear extended state observer ESO₁,l₂As shown in the following equation (20):

step 3.2, designing a pole of the ESO of the discrete domain linear extended state observer by using a pole allocation criterion in the continuous domain, specifically:

solving a characteristic polynomial in the continuous domainRoot of (1) and order

Then using z ═ e^sTMapping the poles (21) of the characteristic polynomial in the continuous domain to the discrete domain to obtain discrete domain poles p₁And p₂。

Technical Field

The invention belongs to the technical field of control of high-performance permanent magnet synchronous motors, and relates to a novel PMSM (permanent magnet synchronous motor) accurate discrete active-disturbance-rejection control method under a low carrier ratio.

Background

Permanent Magnet Synchronous Motors (PMSM) are widely used in many transmission fields such as rail transit, industrial control and household appliances due to their characteristics of high efficiency, high power density, easy field weakening and speed expansion. In a high-power traction transmission system, in order to reduce the switching loss of a power device, the switching frequency of an inverter is only hundreds of hertz; in the ultra-high speed and multi-pole logarithmic motor control system, the running frequency can reach over 500 Hz. The above conditions make the inverter switch frequency (f)_PWM) With the motor operating frequency (f)_e) Ratio of (carrier ratio f)_ratio＝f_PWM/f_e) The current loop is controlled out of control due to amplitude limiting protection, so that the low carrier ratio control strategy of the permanent magnet synchronous motor becomes a research hotspot. Under the condition of low carrier ratio, the dynamic performance of the motor is limited due to the influence of current loop coupling effect. Meanwhile, the design of the current loop controller needs to consider the influence of a delay and discretization mode on the control precision. Therefore, a suitable discrete current controller approach is critical to achieving system stability and dynamic performance at low carrier ratios. Generally, a method that a current controller is designed in a continuous domain and then is dispersed is widely applied, the control effect is good when the carrier ratio is high, but the accuracy of the method depends on a discretization method, and as the carrier ratio is reduced, a larger digital control delay and a discretization truncation error are generated, so that the effectiveness of the current controller is reduced. Therefore, the current controller of the permanent magnet synchronous motor with a low carrier ratio needs to be studied deeply.

At present, the PID control is the most commonly used controller for the current loop, but the performance is limited when there is model mismatch and external interference. Teaching korean proposes auto-disturbance rejection control (ADRC), which combines the internal parameter variation and the uncertain external disturbance as total disturbance, designs an extended state observer to estimate and eliminate the total disturbance in real time, and simplifies the controlled object into a standard series integral type, so that the design of the control system becomes simple. Because of the advantages of strong anti-interference capability, good dynamic performance, low sensitivity to parameter change and the like, the ADRC is widely applied to permanent magnet synchronous motor controllers. In recent years, as a permanent magnet synchronous motor is widely applied to high-power and high-speed occasions, the problems of ADRC performance reduction caused by reduction of a carrier ratio, large digital delay, large Euler dispersion error, heavy coupling and the like occur, and finally ADRC divergence may be caused.

Disclosure of Invention

The invention aims to provide a novel PMSM (permanent magnet synchronous motor) accurate discrete active-disturbance-rejection control method under a low carrier ratio, and solves the problem that the traditional active-disturbance-rejection control under the high-speed low carrier ratio has low control precision and even is out of control.

The technical scheme adopted by the invention is that a novel PMSM accurate discrete active-disturbance-rejection control method under a low carrier ratio specifically comprises the following steps:

step 1, establishing a complex vector permanent magnet synchronous motor model, and obtaining an accurate mathematical relation between current and voltage after accurate discretization;

step 2, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model, and carrying out digital delay compensation on the active disturbance rejection controller;

and 3, designing a feedback gain matrix of the discrete domain extended state observer which ensures stable operation in a full-speed range according to the pole allocation.

The present invention is also characterized in that,

the specific process of the step 1 is as follows:

step 1.1, establishing a continuous domain complex vector PMSM model under a rotating coordinate system;

the complex vector PMSM model is concretely as follows:

in the formula (1), u_d、u_q、i_d、i_qRespectively a d-q axis voltage and a d-q axis current under a two-phase rotating d-q coordinate system; r_s、Ψ_f、L_s、ω_eRespectively a stator resistor, a permanent magnet flux linkage,Inductance and electrical angular velocity; p is a differential operator;

the formula (1) is used in the form of a complex vector x_dq＝x_d+jx_qExpressed as shown in the following equation (2):

in the formula (2), u_dqAnd i_dqThe method is characterized in that the method is respectively in a complex vector form of stator voltage and stator current under a d-q coordinate system, and j is an imaginary number unit;

and step 1.2, accurately discretizing the complex vector PMSM model established in the step 1.1.

The specific process of the step 1.2 is as follows:

writing the complex vector model (2) of PMSM in the continuous domain in the form of a differential equation, as shown in equation (3) below:

in the formula (3), the initial condition is time t₀Current i at time_dq(t₀) Obtaining the current response i at the time t_dq(t), expanding the counter electromotive force e_dqAnd voltage u_dqIs time-varying and requires a pair of e in order to simplify the integration operation in equation (3)_dqAnd u_dqThe following two assumptions are made:

A) suppose that between two sampling intervals kT to (k +1) T, the rotational speed ω of the motor_eRemains unchanged, so the extended back emf is also constant during this time:

B) assuming a voltage value u in a continuous domain under an alpha-beta shafting_αβ(t) and sampled voltage value u at time kT_αβ(kT) equal, i.e.:

e_dq(t)＝e_dq(kT) (4)；

secondly, assume the voltage value u in the continuous domain under the alpha-beta shafting_αβ(t) and sampled voltage value u at time kT_αβ(kT) equal, i.e.:

u_αβ(t)＝u_αβ(kT) (5)；

and then obtaining the following results according to coordinate transformation:

u_dq(kT)＝e^-jθ(kT)u_αβ(kT) (6)；

a complex vector equation of the voltage in the d-q axis system can be obtained according to the equations (5) and (6), and the conversion from the continuous domain to the discrete domain is shown in the following equation (7):

assuming a rotation speed omega within a sampling interval_eKeeping unchanged, the step (7) can be further simplified into the following steps:

substituting equations (4) and (8) into equation (3) and solving the differential equation directly can obtain:

obtaining a discretized model of the electrical machine by solving equation (9), where the variable t is in the continuous domain₀And T is replaced by kT and (k +1) T, respectively, in the discrete domain, as shown in equation (10) below:

converting equation (10) into a state space form as shown in equation (11):

wherein:

the specific process of the step 2 is as follows:

step 2.1, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model, specifically:

considering that the disturbance can be caused to the motor operation process by the disturbance, the d-axis model in the formula (11) is rewritten, as shown in the following formula (12):

in formula (12), f_d0(k) Is a disturbance term that can be modeled and,is the amount of coupling of the q-axis to the d-axis, A₁₁、B₁₁Is the first row and column, A, of the matrix A, B₁₂、B₁₂Is the first row and second column, C, of the matrix A, B₁(k) Is the first row of the matrix C, d₁(k) Is a disturbance for which the non-linear factor of the inverter is unknown;

establishing a linear Extended State Observer (ESO) from the model (12) to measure the total disturbanceAs a new state quantity, in order to avoid delay problem of two inputs of ESO, the output u of the current controller is used_d(k) After digital delay compensationAs an input of the ESO, the following formula (13) shows:

wherein:

the disturbance compensation link is designed as follows:

in observing disturbancesEqual to the actual disturbanceWhen the observation error is ignored, the system is changed into an integral series standard system as shown in the following formula (15):

by the I-type system of equation (15), the linear state error feedback control rate LSEF is designed to be proportional, that is, the control of the current loop is realized, as shown in equation (16):

step 2.2, performing delay compensation according to the discrete linear active disturbance rejection controller of disturbance compensation, specifically:

the delay compensation is performed by equation (14), as shown in equation (17):

wherein the content of the first and second substances,

from the formula (17), the current loop is discreteOutput u of active disturbance rejection controller_dGo through K (omega)_eT) amplitude compensation, 1.5 omega_eCompensation of T phase to obtain

The specific process of the step 3 is as follows:

step 3.1, designing a linear Extended State Observer (ESO) according to the formula (13), wherein the discrete domain characteristic polynomial is expressed as the following formula (18):

the observer characteristic polynomial p (z) collocated by the poles in the discrete domain is shown in equation (19) below:

P(z)＝(z-p₁)(z-p₂) (19)；

from the equations (18) and (19), the feedback gain l of the linear extended state observer ESO₁,l₂As shown in the following equation (20):

step 3.2, designing a pole of the ESO of the discrete domain linear extended state observer by using a pole allocation criterion in the continuous domain, specifically:

solving a characteristic polynomial in the continuous domainRoot of (1) and order

Then using z ═ e^sTMapping the poles (21) of the characteristic polynomial in the continuous domain to the discrete domainTo obtain the discrete domain pole p₁And p₂。

Compared with the traditional linear active-disturbance-rejection controller, the novel PMSM accurate discrete active-disturbance-rejection control method under the low carrier ratio has the advantages that a complex vector permanent magnet synchronous motor model is provided, accurate discrete mathematical relation between given voltage and detected current is obtained after accurate discretization, linear active-disturbance-rejection control is designed in a discrete domain, truncation errors caused by designing a continuous domain and then Euler discretization are fundamentally avoided, disturbance compensation is carried out on known disturbance capable of modeling in order to reduce the burden of a linear extended state observer, and a feedback gain matrix of an ESO (active-disturbance-rejection rate) in the discrete domain is designed on the basis of deep research on the configuration of an active-disturbance-rejection control pole in the continuous domain, so that the stability and the dynamic performance of the PMSM under the high-speed low carrier ratio are improved.

Drawings

FIG. 1 is a vector system diagram of a novel PMSM accurate discrete active-disturbance-rejection control method under a low carrier ratio of the present invention;

fig. 2 is a block diagram of a quasi-discrete ADRC current controller used in a novel PMSM precise discrete active disturbance rejection control method under a low carrier ratio according to the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The invention relates to a novel PMSM (permanent magnet synchronous machine) accurate discrete active-disturbance-rejection control method under a low carrier ratio, wherein a block diagram of a permanent magnet synchronous motor quasi-discrete linear active-disturbance-rejection control vector system under an adopted high-speed low carrier ratio is shown in figure 1, and the method specifically comprises the following steps:

step 1, establishing a complex vector permanent magnet synchronous motor model, and obtaining an accurate mathematical relation between current and voltage after accurate discretization, wherein the method specifically comprises the following steps:

step 1.1, establishing a continuous domain complex vector PMSM model under a rotating coordinate system;

the complex vector PMSM model is concretely as follows:

in the formula (1), u_d、u_q、i_d、i_qD-q axis voltage and d-q axis current under a two-phase rotation (d-q) coordinate system respectively; r_s、Ψ_f、L_s、ω_eStator resistance, permanent magnet flux linkage, inductance, and electrical angular velocity, respectively; p is a differential operator.

The formula (1) is used in the form of a complex vector x_dq＝x_d+jx_qIt is shown that,

in the formula (2), u_dqAnd i_dqThe stator voltage and the stator current are respectively in complex vector form in d-q coordinate system, and j is an imaginary unit.

Step 1.2, accurately discretizing the complex vector PMSM model;

the complex vector model (2) of PMSM in the continuous domain is first written in the form of a differential equation:

in the formula (3), the initial condition is time t₀Current i at time_dq(t₀) Obtaining the current response i at the time t_dq(t), expanding the counter electromotive force e_dqAnd voltage u_dqIs time-varying. To simplify the integral operation of the above equation, e needs to be the same_dqAnd u_dqThe following two assumptions are made. Firstly, the rotation speed omega of the motor is assumed to be between two sampling intervals kT and (k +1) T_eRemains unchanged, so the extended back emf is also constant during this period:

e_dq(t)＝e_dq(kT) (4)；

secondly, assume the voltage value u in the continuous domain under the alpha-beta shafting_αβ(t) and sampled voltage value u at time kT_αβ(kT) equal, i.e.:

u_αβ(t)＝u_αβ(kT) (5)；

and then obtaining the following results according to coordinate transformation:

u_dq(kT)＝e^-jθ(kT)u_αβ(kT) (6)；

according to the complex vector equation of the voltage in the d-q axis system obtained in the steps (5) and (6), the conversion from the continuous domain to the discrete domain is realized:

since the sampling interval is short, it is assumed that the rotation speed ω is within the sampling interval_eKeeping unchanged, the step (7) can be further simplified into the following steps:

substituting equations (4) and (8) into equation (3) and solving the differential equation directly can obtain:

the discretization model of the motor can be obtained by solving equation (9), wherein the variable t in the continuous domain₀And T may be replaced by kT and (k +1) T respectively in the discrete domain,

equation (10) is transformed into a state space form to facilitate the design of ADRC.

Wherein:

step 2, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate discrete domain complex vector PMSM model; then carrying out digital delay compensation on the active disturbance rejection controller; taking the d-axis auto-disturbance rejection design as an example, the q-axis is designed like this. The method specifically comprises the following steps:

step 2.1, designing a discrete linear active disturbance rejection controller with disturbance compensation according to the accurate mathematical model in the step 1, wherein the block diagram of the discrete linear active disturbance rejection controller is shown in fig. 2;

step 2.1, designing a discrete linear active disturbance rejection controller with disturbance compensation according to an accurate discrete domain complex vector PMSM model;

an accurate discrete mathematical relation between a given voltage and a detected current is obtained in the formula (11), and the linear active disturbance rejection control is designed in a discrete domain, so that a truncation error caused by continuous domain design and Euler discretization is avoided, and meanwhile, in order to reduce the burden of a linear extended state observer, the known disturbance which can be modeled is adopted for disturbance compensation.

Considering that the disturbance can be caused to the motor operation process by the disturbance, the d-axis model in the equation (11) is rewritten as:

in formula (12), f_d0(k) Is a disturbance term that can be modeled and,is the amount of coupling of the q-axis to the d-axis, A₁₁、B₁₁Is the first row and column, A, of the matrix A, B₁₂、B₁₂Is the first row and second column, C, of the matrix A, B₁(k) Is the first row of the matrix C, d₁(k) Is an unknown disturbance such as a nonlinear factor of the inverter.

Building a linear Extended State Observer (ESO) from the model (12) to sum the disturbancesAs a new state quantity, in order to avoid delay problem of two inputs of ESO, the output u of the current controller is used_d(k) After digital delay compensationAs input to the ESO.

Wherein:

the disturbance compensation procedure is designed as

In observing disturbancesEqual to the actual disturbanceWhen the system is used, the observation error is negligible, and the system is converted into an integral series standard system:

by the I-type system of equation (15), the linear state error feedback control rate (LSEF) can be designed as a proportional type, i.e. the control of the current loop can be realized:

2.2, performing digital delay compensation according to the discrete linear active disturbance rejection controller with disturbance compensation;

output u of active disturbance rejection control when motor is in high speed and low carrier ratio_dShould be at theta_eActing on the ac machine, now at theta_e+ω_eT to theta_e+2ω_eT acts on the motor in the process, u_dWith amplitude and phase errors, input u of ESO_d,i_dTiming and amplitude mismatches result in significant degradation of current controller performance.

Delay compensation is performed by equation (14):

wherein:

from equation (17), the discrete active disturbance rejection controller output u of the current loop_dGo through K (omega)_eT) amplitude compensation, 1.5 omega_eCompensation of T phase to obtain

Step 3 comprises the following specific calculation steps:

step 3.1, in order to ensure that the ESO stably runs in a full speed range, pole allocation needs to be carried out on a discrete domain z plane, and then a feedback gain matrix L is calculated through characteristic polynomial coefficients;

an ESO designed according to equation (13), the discrete domain signature polynomial may be expressed as:

the observer characteristic polynomial, in the discrete domain, configured by poles, is:

P(z)＝(z-p₁)(z-p₂) (19)；

by comparing the formula (18) and the formula (19), the feedback gain l of ESO can be obtained₁,l₂。

Step 3.2, designing a pole of the ESO of the discrete domain by using a pole allocation criterion in the continuous domain;

solving a characteristic polynomial in the continuous domainRoot of (1) and order

Then using z ═ e^sTMapping the poles (21) of the characteristic polynomial in the continuous domain to the discrete domain to obtain discrete domain poles p₁And p₂。

Closed loop pole p calculated by equation (22)₁,p₂Taken into the ESO feedback gain matrix L (i.e., equation (20)), the ESO can operate stably over the full speed range.