阅读说明：本技术 一种改进积分滑模的感应电机模型预测电流控制方法 (Induction machine model prediction current control method for improving integral sliding mode ) 是由 尹忠刚 侯倩茹 张延庆 张瑞峰 于 2020-12-24 设计创作，主要内容包括：本发明公开了一种改进积分滑模的感应电机模型预测电流控制方法,具体包括如下步骤：步骤1,步骤1,在d-q坐标系下,得到感应电机定子电流微分方程,根据d-q轴定子电流微分方程得到相应的电压方程；步骤2,基于步骤1所得的电压方程,定义各参数误差和嵌入给定电压的误差矢量；步骤3,基于电压误差矢量公式确定积分滑模面的构成；步骤4,将参考电压矢量视为传统模型所得的电压分量和扰动分量之和,进而重构代价函数为电压矢量误差的绝对值。本发明解决了目前感应电机在不同工况下运行时发生电机参数不匹配的问题。(The invention discloses a method for controlling the prediction current of an induction machine model with an improved integral sliding mode, which specifically comprises the following steps: step 1, obtaining a stator current differential equation of the induction motor in a d-q coordinate system, and obtaining a corresponding voltage equation according to the stator current differential equation of a d-q axis; step 2, defining error vectors of each parameter and embedded given voltage based on the voltage equation obtained in the step 1; step 3, determining the composition of an integral sliding mode surface based on a voltage error vector formula; and 4, regarding the reference voltage vector as the sum of the voltage component and the disturbance component obtained by the traditional model, and further reconstructing the cost function as the absolute value of the voltage vector error. The invention solves the problem that the parameters of the existing induction motor are not matched when the induction motor operates under different working conditions.)

1. A method for controlling the prediction current of an induction machine model with an improved integral sliding mode is characterized by comprising the following steps: the method specifically comprises the following steps:

step 1, obtaining a stator current differential equation of an induction motor under a d-q coordinate system, then carrying out forward Euler discretization on the stator current differential equation of the induction motor, assuming that the induction motor runs to a stable state, and obtaining a corresponding voltage equation according to the stator current differential equation of a d-q axis;

step 2, defining error vectors of each parameter and embedded given voltage based on the voltage equation obtained in the step 1, and accordingly rewriting the d-q axis voltage vector into the sum of a component obtained by a traditional model and a disturbance component;

step 3, determining the composition of an integral sliding mode surface based on a voltage error vector formula;

and 4, regarding the reference voltage vector as the sum of the voltage component and the disturbance component obtained by the traditional model, and further reconstructing the cost function as the absolute value of the voltage vector error.

2. The method for controlling the predictive current of the improved integral sliding mode induction machine model is characterized in that: the specific process of the step 1 is as follows:

step 1.1, the stator current differential equation of the induction motor is as follows:

wherein u is_sd、u_sq、i_sd、i_sq、ψ_rStator voltage, current and rotor flux in a d-q coordinate system respectively; omega is the rotating speed of the induction motor; omega₁The synchronous rotating speed of the induction motor; r_s、R_rIs a stator-rotor resistor; l is_s、L_rIs stator and rotor inductance, L_mIs mutual inductance; sigma is the leakage coefficient of the motor;is the derivative of the stator current in the d-q coordinate system;

step 1.2, discretizing a stator current differential equation of the induction motor, wherein the formula is as follows:

wherein i_sd(k)、i_sq(k) D-q axis stator current values at the time k; u. of_sd、u_sqIs the d-q axis component of the stator voltage vector; omega₁(k) The synchronous rotating speed of the induction motor at the moment k is obtained; i.e. i_sd(k+1)、i_sq(k +1) is the d-q axis stator current value at the moment of k + 1; t is_sIs the sampling time;

assuming that the induction motor operates to a stable state, taking the stator current at the moment of k +1 as a given value, a given voltage equation can be obtained:

wherein the content of the first and second substances,stator current is given for the d-q axis;ideally a stator voltage value is given for the d-q axis.

3. The method for controlling the predictive current of the improved integral sliding mode induction machine model is characterized in that: the specific process of the step 2 is as follows:

aiming at the condition that the parameters of the induction motor are not matched, the stator current differential equation of the induction motor is rewritten into:

wherein, Δ R_s、ΔR_r、ΔL_r、ΔL_s、ΔL_mRespectively a stator resistance error value, a rotor flux linkage error value, a stator flux linkage error value and a mutual inductance error value;

to suppress the uncertainty of the parameters, the voltage vector is reconstructed as the following equation (5):

wherein u is_d0、u_q0Is a d-q axis voltage vector under an ideal model; u. of_d1，u_q1D-q axis disturbance quantity; u. of_d、u_qIs the d-q axis actual voltage vector.

4. The method for controlling the predictive current of the improved integral sliding mode induction machine model is characterized in that: the specific process of the step 3 is as follows:

step 3.1, according to the design principle of the improved integral sliding mode, the d-q axis sliding mode surface is expressed as follows:

wherein s is_d、s_qIs a d-q axis sliding mode surface; e.g. of the type_d、e_qIs the d-q axis current error amount, i.e.z_d、z_qThe known disturbance variable for the d-q axis is defined as follows:

wherein the content of the first and second substances,the derivative of the known disturbance quantity of the d-q axis; t is t₀Is the initial time; z is a radical of_d(t₀)、z_q(t₀) Is t₀At the moment, the known disturbance quantity value of the d-q axis; i.e. i_sd(t₀)、i_sd(t₀) Is t₀At time, the d-q axis stator current value;is t₀At the moment, the d-q axis gives a stator current value;

step 3.2, in the improved integral sliding mode control, the compensation quantity u_d1eq，u_qleqCalculated from the sliding mode surface, the following formula is defined:

wherein epsilon₁、ε₂、α₁、α₂、δ₁、δ₂Is a positive gain;

in order to solve the problem of high-frequency buffeting of sliding mode control, a low-pass filter is introduced for improvement, compensation quantity is replaced by an average value after passing through the low-pass filter, and the compensation quantity is defined as follows:

wherein the time constant mu is required to ensure the slowly varying component u of the switching function_d1eq、u_q1eqIs not attenuated by the low-pass filter,is the derivative of the disturbance quantity; the time constant mu ensures the disturbance u of the switching function_d1、u_q1Is not attenuated by the low pass filter; u'_d1、u′_q1For controlling the system etcAn amount of effective disturbance;

step 3.3, based on the results obtained in step 3.2, rewriting the formula (5) to the following formula (11):

wherein the content of the first and second substances,is a given voltage vector; u'_d1、u′_q1Is an equivalent disturbance amount in the control system.

5. The method for controlling the predictive current of the improved integral sliding mode induction machine model is characterized in that: the specific process of the step 4 is as follows:

the cost function of the traditional model prediction current control is the sum of absolute values of d-q axis current errors, and since the control target is changed into a voltage vector in step 3, the cost function is reconstructed as shown in the following formula:

wherein the content of the first and second substances,is a given voltage vector; u. of_d，i、u_q，iThe components of 8 basic voltage vectors directly output by the inverter on the d-q axis, i is 0,1, 2.

Technical Field

The invention belongs to the technical field of predictive control of induction machine models, and relates to a predictive current control method of an induction machine model with an improved integral sliding mode.

Background

The induction motor is widely applied to industries such as agricultural production, industrial production, transportation and the like due to the characteristics of simple structure, easy manufacture, low price, reliable operation, firmness, durability and the like. In order to enable the motor to meet the technical requirements of drive control on high dynamic response, accurate speed tracking and excellent stability, a vector control technology of rotor magnetic field orientation is applied. However, in recent years, the development of industrial automation is rapid, new requirements are put on the drive control technology, and the purpose is that the system shows the development trend of 'faster, smaller and more intelligent'. The dynamic response speed of the current loop is a key factor influencing the rapidity of the system, so that model prediction control is provided.

The current inner loop controlled by the vector of the induction motor is controlled by a PI regulator, so that the problems of integral saturation, difficulty in processing system constraint, mutual influence of current control caused by motion coupling and the like exist, and the further improvement of the dynamic response capability of the current loop is limited. The model predictive control is a novel control algorithm based on a controlled object model, the algorithm predicts variables in a control period by depending on a system mathematical model, then expresses expected system output through a cost function, and finally searches for the optimal switching state by utilizing a minimum cost function. Compared with vector control, the current loop has higher response speed, and a modulator link is not needed, so that the current loop structure is simplified. The method can be divided into torque prediction control and current prediction control according to the difference of the prediction quantity, and the latter has the advantages that no weight coefficient is needed in the cost function, and the design of the system is more concise and clearer. The design of model predictive control depends on the design of motor parameters, if external factors and self factors change during the operation of the motor, the motor parameters are not matched, errors exist in a prediction result, and therefore the voltage vector obtained by rolling optimization in a cost function is not an optimal value, and the operation performance of the induction motor is influenced.

Disclosure of Invention

The invention aims to provide a method for controlling the prediction current of an induction machine model with an improved integral sliding mode, which solves the problem that the parameters of the existing induction machine are not matched when the induction machine operates under different working conditions.

The invention adopts the technical scheme that a method for controlling the prediction current of an induction machine model of an improved integral sliding mode specifically comprises the following steps:

step 1, obtaining a stator current differential equation of an induction motor under a d-q coordinate system, then carrying out forward Euler discretization on the stator current differential equation of the induction motor, assuming that the induction motor runs to a stable state, and obtaining a corresponding voltage equation according to the stator current differential equation of a d-q axis;

step 2, defining error vectors of each parameter and embedded given voltage based on the voltage equation obtained in the step 1, and accordingly rewriting the d-q axis voltage vector into the sum of a component obtained by a traditional model and a disturbance component;

step 3, determining the composition of an integral sliding mode surface based on a voltage error vector formula;

and 4, regarding the reference voltage vector as the sum of the voltage component and the disturbance component obtained by the traditional model, and further reconstructing the cost function as the absolute value of the voltage vector error.

The present invention is also characterized in that,

the specific process of the step 1 is as follows:

step 1.1, the stator current differential equation of the induction motor is as follows:

wherein u is_sd、u_sq、i_sd、i_sq、ψ_rStator voltage, current and rotor flux in a d-q coordinate system respectively; omega is the rotating speed of the induction motor; omega₁The synchronous rotating speed of the induction motor; r_s、R_rIs a stator-rotor resistor; l is_s、L_rIs stator and rotor inductance, L_mIs mutual inductance; sigma is the leakage coefficient of the motor;is the derivative of the stator current in the d-q coordinate system;

step 1.2, discretizing a stator current differential equation of the induction motor, wherein the formula is as follows:

wherein i_sd(k)、i_sq(k) D-q axis stator current values at the time k; u. of_sd、u_sqIs the d-q axis component of the stator voltage vector; omega₁(k) The synchronous rotating speed of the induction motor at the moment k is obtained; i.e. i_sd(k+1)、i_sq(k +1) is the d-q axis stator current value at the moment of k + 1; t is_sIs the sampling time;

assuming that the induction motor operates to a stable state, taking the stator current at the moment of k +1 as a given value, a given voltage equation can be obtained:

wherein the content of the first and second substances,stator current is given for the d-q axis;ideally a stator voltage value is given for the d-q axis.

The specific process of step 2 is as follows:

aiming at the condition that the parameters of the induction motor are not matched, the stator current differential equation of the induction motor is rewritten into:

wherein, Δ R_s、ΔR_r、ΔL_r、ΔL_s、ΔL_mAre respectively the stator resistance error valueA rotor resistance error value, a rotor flux linkage error value, a stator flux linkage error value, a mutual inductance error value;

to suppress the uncertainty of the parameters, the voltage vector is reconstructed as the following equation (5):

wherein u is_d0、u_q0Is a d-q axis voltage vector under an ideal model; u. of_d1，u_q1D-q axis disturbance quantity; u. of_d、u_qIs the d-q axis actual voltage vector.

The specific process of the step 3 is as follows:

step 3.1, according to the design principle of the improved integral sliding mode, the d-q axis sliding mode surface is expressed as follows:

wherein s is_d、s_qIs a d-q axis sliding mode surface; e.g. of the type_d、e_qIs the d-q axis current error amount, i.e.z_d、z_qThe known disturbance variable for the d-q axis is defined as follows:

wherein the content of the first and second substances,the derivative of the known disturbance quantity of the d-q axis; t is t₀Is the initial time; z is a radical of_d(t₀)、z_q(t₀) Is t₀At the moment of time, the time of day,the value of the known disturbance quantity of the d-q axis; i.e. i_sd(t₀)、i_sd(t₀) Is t₀At time, the d-q axis stator current value;is t₀At the moment, the d-q axis gives a stator current value;

step 3.2, in the improved integral sliding mode control, the compensation quantity u_d1eq，u_q1eqCalculated from the sliding mode surface, the following formula is defined:

wherein epsilon₁、ε₂、α₁、α₂、δ₁、δ₂Is a positive gain;

in order to solve the problem of high-frequency buffeting of sliding mode control, a low-pass filter is introduced for improvement, compensation quantity is replaced by an average value after passing through the low-pass filter, and the compensation quantity is defined as follows:

wherein the time constant mu is required to ensure the slowly varying component u of the switching function_d1eq、u_q1eqIs not attenuated by the low-pass filter,is the derivative of the disturbance quantity; the time constant mu ensures the disturbance u of the switching function_d1、u_q1Is not attenuated by the low pass filter; u'_d1、u′_q1Is the equivalent disturbance quantity in the control system;

step 3.3, based on the results obtained in step 3.2, rewriting the formula (5) to the following formula (11):

wherein the content of the first and second substances,is a given voltage vector; u'_d1、u′_q1Is an equivalent disturbance amount in the control system.

The specific process of the step 4 is as follows:

the cost function of the traditional model prediction current control is the sum of absolute values of d-q axis current errors, and since the control target is changed into a voltage vector in step 3, the cost function is reconstructed as shown in the following formula:

wherein the content of the first and second substances,is a given voltage vector; u. of_d,i、u_q,iThe components of 8 basic voltage vectors directly output by the inverter on the d-q axis, i is 0,1, 2.

The method has the beneficial effects that the method for controlling the prediction current of the induction machine model based on the integral sliding mode mainly solves the problem that when the parameters of the motor are obviously changed under different operating conditions, the controller can estimate the error in real time and correct the given value so as to ensure that the system has stronger robust performance. In order to further solve the buffeting problem in the sliding mode, the control law is improved, a low-pass filter is introduced, and meanwhile robustness and accuracy of the controller are guaranteed.

Drawings

Fig. 1 is a control block diagram of an integral sliding mode-based induction machine model predictive current control system adopted by the improved integral sliding mode induction machine model predictive current control method of the 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 an induction motor with an improved integral sliding modeThe model prediction current control method adopts an induction machine model prediction current control system based on an integral sliding mode, as shown in fig. 1: mainly comprises two links. One is the rotation speed value omega obtained by the encoder_rWith a given rotational speedThe difference is input to a speed regulator PI, the output of which is used as a given currentPhase current i_a、i_b、i_cObtaining a stator current component i under a two-phase static coordinate system through Clarke transformation after being measured by a current sensor_α、i_β，i_α、i_βThen obtaining a stator current component i under a two-phase rotating coordinate system through Park conversion_d、i_qFor integrating the sliding mode input quantity, the given current is obtained by a voltage equationThe given value of the current and the voltage is used as the input quantity of the integral sliding mode, thereby obtainingSecondly, optimizing control is carried out in the cost function according to the obtained voltage vector to obtain the optimal voltage vector U_i(i ═ 0,1, 2.., 7.) the corresponding optimal switching vector S_a,S_b,S_cAnd controlling the inverter to work so as to control the stable operation of the motor.

The method specifically comprises the following steps:

step 1, obtaining a stator current differential equation of an induction motor under a d-q coordinate system, then carrying out forward Euler discretization on the stator current differential equation of the induction motor, assuming that the induction motor runs to a stable state, and obtaining a corresponding voltage equation according to the stator current differential equation of a d-q axis;

the specific process of the step 1 is as follows:

step 1.1, the stator current differential equation of the induction motor is as follows:

wherein u is_sd、u_sq、i_sd、i_sq、ψ_rStator voltage, current and rotor flux in a d-q coordinate system respectively; omega is the rotating speed of the induction motor; omega₁The synchronous rotating speed of the induction motor; r_s、R_rIs a stator-rotor resistor; l is_s、L_rIs stator and rotor inductance, L_mIs mutual inductance; sigma is the leakage coefficient of the motor;is the derivative of the stator current in the d-q coordinate system;

step 1.2, discretizing a stator current differential equation of the induction motor, wherein the formula is as follows:

wherein i_sd(k)、i_sq(k) D-q axis stator current values at the time k; u. of_sd、u_sqIs the d-q axis component of the stator voltage vector; omega₁(k) The synchronous rotating speed of the induction motor at the moment k is obtained; i.e. i_sd(k+1)、i_sq(k +1) is the d-q axis stator current value at the moment of k + 1; t is_sIs the sampling time;

assuming that the induction motor operates to a stable state, taking the stator current at the moment of k +1 as a given value, a given voltage equation can be obtained:

wherein the content of the first and second substances,stator current is given for the d-q axis;ideally a stator voltage value is given for the d-q axis.

Step 2, defining error vectors of each parameter and embedded given voltage based on the voltage equation obtained in the step 1, and accordingly rewriting the d-q axis voltage vector into the sum of a component obtained by a traditional model and a disturbance component;

the specific process of step 2 is as follows:

aiming at the condition that the parameters of the induction motor are not matched, the stator current differential equation of the induction motor is rewritten into:

wherein, Δ R_s、ΔR_r、ΔL_r、ΔL_s、ΔL_mRespectively a stator resistance error value, a rotor flux linkage error value, a stator flux linkage error value and a mutual inductance error value;

for an indeterminate system, the corresponding control voltage is obtained so that the system can quickly follow the ideal system model. To suppress the uncertainty of the parameters, the voltage vector can be reconstructed as the following equation (5):

wherein u is_d0、u_q0Is a d-q axis voltage vector under an ideal model; u. of_d1，u_q1D-q axis disturbance quantity; u. of_d、u_qIs the d-q axis actual voltage vector.

And 3, the idea of integral sliding mode is focused on realizing robust motion of a global state space, and the design step is to add a discontinuous control term in a control law on the basis of a known nonlinear system and reasonably designed feedback control to counteract unknown dynamic and external disturbance. However, switching in the control inevitably introduces high frequency chattering in practical implementations. In order to solve the main defect of sliding mode control on high-frequency buffeting, an integral sliding mode principle can be utilized to reconstruct a control law, namely a low-pass filter is introduced for improvement.

The specific process of the step 3 is as follows:

step 3.1, according to the design principle of the improved integral sliding mode, the d-q axis sliding mode surface is expressed as follows:

wherein s is_d、s_qIs a d-q axis sliding mode surface; e.g. of the type_d、e_qIs the d-q axis current error amount, i.e.z_d、z_qThe known disturbance variable for the d-q axis is defined as follows:

wherein the content of the first and second substances,the derivative of the known disturbance quantity of the d-q axis; t is t₀Is the initial time; z is a radical of_d(t₀)、z_q(t₀) Is t₀At the moment, the known disturbance quantity value of the d-q axis; i.e. i_sd(t₀)、i_sd(t₀) Is t₀At time, the d-q axis stator current value;is t₀At the moment, the d-q axis gives a stator current value;

step 3.2, switching in sliding mode control inevitably leads to high-frequency buffeting in practical implementation, and the most direct mode for weakening buffeting is to replace a switching function by a saturation function with continuous characteristics, but the switching gain in the boundary of the saturation function is limited, and the thicker the boundary layer, the smaller the switching gain is, so that the robustness and the precision are reduced. In order to solve the main defect that high-frequency buffeting is introduced in sliding mode control, the control law can be reconstructed by utilizing an integral sliding mode principle:

in the improved integral sliding mode control, the compensation quantity u_d1eq，u_q1eqCalculated from the sliding mode surface, the following formula is defined:

wherein epsilon₁、ε₂、α₁、α₂、δ₁、δ₂Is a positive gain.

In order to solve the main defect of sliding mode control of high-frequency buffeting, a low-pass filter is introduced for improvement, compensation quantity is replaced by an average value after passing through the low-pass filter, and the compensation quantity is defined as follows:

wherein the time constant mu is required to ensure the slowly varying component u of the switching function_d1eq、u_q1eqIs not attenuated by the low-pass filter,is the derivative of the disturbance quantity; the time constant mu ensures the disturbance u of the switching function_d1、u_q1Is not attenuated by the low pass filter; u'_d1、u′_q1Is an equivalent disturbance amount in the control system.

Step 3.3, based on the results obtained in step 3.2, rewriting the formula (5) to the following formula (11):

wherein the content of the first and second substances,is a given voltage vector; u'_d1、u′_q1Is an equivalent disturbance amount in the control system.

And 4, regarding the reference voltage vector as the sum of the voltage component and the disturbance component obtained by the traditional model, and further reconstructing the cost function as the absolute value of the voltage vector error.

The specific process of the step 4 is as follows:

the cost function of the traditional model prediction current control is the sum of absolute values of d-q axis current errors, and since the control target is changed into a voltage vector in step 3, the cost function is reconstructed as shown in the following formula:

wherein the content of the first and second substances,is a given voltage vector; u. of_d,i、u_q,iThe components of 8 basic voltage vectors directly output by the inverter on the d-q axis, i is 0,1, 2.

The invention discloses a method for controlling the prediction current of an induction machine model with an improved integral sliding mode, which mainly solves the problem that when the parameters of a motor are obviously changed under different operating conditions, a controller can estimate errors in real time and correct the given parameters so as to ensure that the system has stronger robust performance. In order to further solve the buffeting problem in the sliding mode, the control law is improved, a low-pass filter is introduced, and meanwhile robustness and accuracy of the controller are guaranteed.

Under the condition of meeting the requirement of faster response speed of a current loop, the invention provides the integral sliding mode controller which mainly has the function of improving the robustness of the system under the working condition of parameter mismatching.