阅读说明：本技术 直线感应电机多步长有限集模型预测控制方法及系统 (Linear induction motor multi-step finite set model prediction control method and system ) 是由 徐伟 邹剑桥 董定昊 刘毅 于 2020-01-17 设计创作，主要内容包括：本发明公开了一种直线感应电机多步长有限集模型预测控制方法,属于直线感应电机控制技术领域。方法具体为：采集直线感应电机在三相坐标系下的初级相电流；依据电流值迭代求解多步长的参考电压矢量序列；在每一个预测步长内,只保留两个与参考电压矢量最近的两个非零电压矢量及一个零电压矢量；最后通过在线动态和成本函数值做比较,将较大成本函数值的电压矢量序列进一步排除掉。本发明将多步长有限集模型预测控制方法运用到直线感应电机,提高直线感应电机的运行性能,尤其是在低开关频率的应用场合。并对该控制方法进行了简化,减小该方法执行所需的硬件成本,使得该方法能够在实际系统当中得到应用。(The invention discloses a multi-step finite set model prediction control method for a linear induction motor, and belongs to the technical field of control of linear induction motors. The method comprises the following specific steps: acquiring primary phase current of a linear induction motor under a three-phase coordinate system; iteratively solving a multi-step reference voltage vector sequence according to the current value; only two non-zero voltage vectors and one zero voltage vector which are closest to the reference voltage vector are reserved in each prediction step; finally, the voltage vector sequence with larger cost function value is further eliminated by comparing the online dynamic state with the cost function value. The method applies the multi-step length finite set model prediction control method to the linear induction motor, improves the running performance of the linear induction motor, and is particularly applied to low switching frequency. The control method is simplified, and the hardware cost required by the method is reduced, so that the method can be applied to an actual system.)

1. A linear induction motor multi-step finite set model prediction control method is characterized by comprising the following steps:

(1) at the current moment k, collecting primary phase current of the linear induction motor in a three-phase coordinate system

(2) According to the current vector value at the k timePredicting current vector value at time k +1

(3) Vector value of currentAs an initial value, the reference voltage vector at time k + i is iteratively calculated

wherein the content of the first and second substances,V₁ ^k+i-1the voltage vector selected for time k + i-1,λ is a weight coefficient;

a and b areThe coefficients of which are such that,

T_sin order to be the sampling period of time,for the reference current command, j denotes the imaginary part; r represents resistance; psi represents the motor flux linkage, subscripts 1 and 2 represent the motor primary and secondary variables, respectively; omega₂Represents the secondary angular velocity, L_lRepresenting the leakage inductance of the motor; l is_rIs a secondary inductance, L_sIs a primary inductance, L_mIs mutual inductance.

2. The linear induction motor multi-step finite set model predictive control method of claim 1, further comprising the steps of:

(4) dividing the output voltage range of the inverter into six sectors equally, respectively determining the output voltage range as the 1 st to the sixth sectors in a counterclockwise manner, and judging V one by one_k+1,…,V_k+NConverting the reference voltage vector angle of each sector into a first sector by the sector to which the reference voltage vector of the moment belongs;

(5) according to reference voltage vector converted into first sector

(6) output voltage sequence to be selected from inverter with minimum cost function value as targetFinding the optimal voltage vector sequence.

3. A method according to claim 1 or 2, characterized by angle-converting the reference voltage vector of each sector into the first sector by an angle conversion formula:

wherein: and n is the sector number of the reference voltage vector.

4. A method according to claim 1 or 2, wherein the cost function value is expressed as:

wherein:

5. The linear induction motor multi-step finite set model predictive control system is characterized by comprising the following modules:

a sampling module for collecting the primary phase current of the linear induction motor in a three-phase coordinate system at the current moment k

A current conversion module for converting the current vector value according to the k timePredicting current vector value at time k +1

A reference voltage vector prediction module for predicting the current vector valueAs an initial value, the reference voltage vector at time k + i is iteratively calculatedPredicting time i is 1, …, N, N is total predicting step number;

wherein the content of the first and second substances,

a and b are coefficients for the number of,

T_sin order to be the sampling period of time,for the reference current command, j denotes the imaginary part; r represents resistance; psi represents the motor flux linkage, subscripts 1 and 2 represent the motor primary and secondary variables, respectively; omega₂Represents the secondary angular velocity, L_lRepresenting the leakage inductance of the motor; l is_rIs a secondary inductance, L_sIs a primary inductance, L_mIs mutual inductance.

6. The system of claim 5, further comprising the following modules:

a sector processing module for dividing the output voltage range of the inverter into six sectors, determining the six sectors as the 1 st to the sixth sector counterclockwise respectively, and judging V one by one_k+1,…,V_k+NConverting the reference voltage vector angle of each sector into a first sector by the sector to which the reference voltage vector of the moment belongs;

a screening sorting module for sorting the reference voltage vector according to the converted reference voltage vectorScreening and sorting to obtain inverter candidate output voltage sequenceWherein:V_dcis a dc bus voltage; v₀Zero voltage vector, V, output by inverter_n,V_n+1，V_n-1A non-zero voltage vector output for the inverter;

an optimization module for selecting the output voltage sequence from the inverter with the minimum cost function value as the target

7. The system of claim 5 or 6, wherein the sector processing module angle-converts the reference voltage vector for each sector into the first sector by an angle conversion formula, the angle conversion formula being:

wherein: and n is the sector number of the reference voltage vector.

8. The system according to claim 5 or 6, wherein the cost function value in the optimizing module is expressed as:wherein:

Technical Field

The invention belongs to the technical field of linear induction motor control, and particularly relates to a multi-step length finite set model prediction control method and system.

Background

The electromagnetic structure of the linear induction motor is derived from a rotary induction motor, and the circular stator is cut open and flattened along the radial direction to form a straight line, so that the linear induction motor can generate linear motion without an intermediate transmission conversion device. However, due to the open structure at both ends of the linear motor, which causes the side effect, the flux linkage is attenuated under the condition that the motor operates at a high speed, and thus the motor is difficult to generate a high thrust at a high speed.

Because the parameter transformation of the linear motor is severe, the parameter transformation can be changed along with the operation condition of the motor. Conventional control strategies, such as: vector control and direct thrust control strategies cannot well consider the change of motor parameters, so that a good control effect is difficult to obtain. The model prediction control algorithm can be combined with an equivalent circuit model of the linear induction motor proposed by a scholars, the influence of parameter change caused by the side end effect is fully considered, and the running performance of the motor is further improved.

In high power situations, linear induction motor drive systems, such as: the linear subway has low switching frequency, which is usually only about several hundred hertz. In order to obtain a smaller current distortion coefficient under a low switching frequency, a multi-step length finite set model prediction control method can be adopted, and the relation between the switching frequency and the current quality is optimized in a step length changing mode. However, by increasing the number of prediction steps, the number of the voltage sequences to be selected increases exponentially, so that the calculation amount of the algorithm is heavy. Therefore, a simplified method is required to reduce the calculation amount of the multi-step predictive control algorithm, so that the algorithm can be really applied to the actual control system.

Disclosure of Invention

Aiming at the defects or improvement requirements in the prior art, the invention provides a linear induction motor multi-step finite set model prediction control method which can compensate the influence caused by the side effect, can reasonably arrange a voltage vector switching sequence in a prediction range and obtain a smaller current distortion coefficient under a lower switching frequency.

In order to achieve the purpose, the invention adopts the following technical scheme:

a multi-step finite set model prediction control method for a linear induction motor comprises the following steps:

(1) at the current moment k, collecting primary phase current of the linear induction motor in a three-phase coordinate systemAnd converting the current vector into αβ coordinate system to obtain current vector value

(2) According to the current vector value at the k time

Predicting current vector value at time k +1

(3) Vector value of currentAs an initial value, the reference voltage vector at time k + i is iteratively calculated

Predicting time i is 1, …, N, N is total predicting step number;

wherein the content of the first and second substances,

the voltage vector selected for time k + i-1,

λ is a weight coefficient;

a and b are coefficients for the number of,

T_sin order to be the sampling period of time,for the reference current command, j denotes the imaginary part; r represents resistance; psi represents the motor flux linkage, subscripts 1 and 2 represent the motor primary and secondary variables, respectively; omega₂Represents the secondary angular velocity, L_lRepresenting the leakage inductance of the motor; l is_rIs a secondary inductance, L_sIs a primary inductance, L_mIs mutual inductance.

Further, the method also comprises the following steps:

(4) dividing the output voltage range of the inverter into six sectors equally, respectively determining the output voltage range as the 1 st to the sixth sectors in a counterclockwise manner, and judging V one by one_k+1,…,V_k+NConverting the reference voltage vector angle of each sector into a first sector by the sector to which the reference voltage vector of the moment belongs;

(5) according to reference voltage vector converted into first sectorScreening and sorting to obtain inverter candidate output voltage sequence

Wherein:V_dcis a dc bus voltage; v₀Zero voltage vector, V, output by inverter_n,V_n+1，V_n-1A non-zero voltage vector output for the inverter;

(6) output voltage sequence to be selected from inverter with minimum cost function value as target

Finding the optimal voltage vector sequence.

Further, the reference voltage vector angle of each sector is converted into the first sector by an angle conversion formula, wherein the angle conversion formula is as follows:

wherein: and n is the sector number of the reference voltage vector.

Further, the cost function value is expressed as:

wherein:

representing the reference voltage vector at time k + i.

A linear induction motor multi-step finite set model predictive control system comprises the following modules:

a sampling module for collecting the primary phase current of the linear induction motor in a three-phase coordinate system at the current moment k

And converting the current vector into αβ coordinate system to obtain current vector value

A current conversion module for converting the current vector value according to the k time

Predicting current vector value at time k +1

A reference voltage vector prediction module for predicting the current vector valueAs an initial value, the reference voltage vector at time k + i is iteratively calculated

Predicting time i is 1, …, N, N is total predicting step number;

wherein the content of the first and second substances,

the voltage vector selected for time k + i-1,

λ is a weight coefficient;

a and b are coefficients for the number of,

T_sin order to be the sampling period of time,

for the reference current command, j denotes the imaginary part; r represents resistance; psi represents the motor flux linkage, subscripts 1 and 2 represent the motor primary and secondary variables, respectively; omega₂Represents the secondary angular velocity, L_lRepresenting the leakage inductance of the motor; l is_rIs a secondary inductance, L_sIs a primary inductance, L_mIs mutual inductance.

Further, the method also comprises the following modules:

a sector processing module for dividing the output voltage range of the inverter into six sectors, determining the six sectors as the 1 st to the sixth sector counterclockwise respectively, and judging V one by one_k+1,…,V_k+NConverting the reference voltage vector angle of each sector into a first sector by the sector to which the reference voltage vector of the moment belongs;

a screening sorting module for sorting the reference voltage vector according to the converted reference voltage vectorScreening and sorting to obtain inverter candidate output voltage sequence

Wherein:V_dcis a dc bus voltage; v₀Zero voltage vector, V, output by inverter_n,V_n+1，V_n-1A non-zero voltage vector output for the inverter;

an optimization module for selecting the output voltage sequence from the inverter with the minimum cost function value as the targetFinding the optimal voltage vector sequence.

Further, the sector processing module angle-converts the reference voltage vector of each sector into the first sector by an angle conversion formula, wherein the angle conversion formula is as follows:

wherein: and n is the sector number of the reference voltage vector.

Further, the cost function value in the optimizing module is expressed as:

wherein:

generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

1. the method adopts multi-step finite set model prediction control, combines a motor equivalent circuit model, compensates the influence caused by the side effect, simultaneously can reasonably arrange a voltage vector switching sequence in a prediction range, and obtains a smaller current distortion coefficient under a lower switching frequency;

2. furthermore, the multi-step length finite set prediction control algorithm is simplified, and the screened voltage vector sequence can be obtained by judging the sector of each reference voltage vector in the reference voltage sequence. In order to avoid analyzing possible situations of other sectors, the reference voltage vector can be converted into the first sector, so that the hardware cost required by the algorithm is reduced, and the method can be widely applied to practical drive control systems.

3. In each prediction step, only two non-zero voltage vectors and one zero voltage vector which are closest to the reference voltage vector are reserved, namely only 3 voltage vectors are evaluated in each prediction step, and in the last prediction step, only the voltage vector which is closest to the reference voltage vector is selected to minimize the cost function, and after the irrelevant voltage vector sequence is eliminated, the number of the voltage vectors which need to be evaluated is reduced to N × 3^N-1And (4) respectively.

In general, the multi-step length finite set model predictive control algorithm is applied to the linear induction motor, so that the running performance of the linear induction motor is improved, and the linear induction motor is particularly applied to low switching frequency. In order to reduce the calculation amount of the algorithm, the control method is simplified, and the hardware cost required by the execution of the method is reduced, so that the method can be applied to an actual system.

Drawings

FIG. 1 is a schematic diagram of a linear induction motor construction;

FIG. 2 is a sector division area of a single-step finite set model predictive control method;

FIG. 3 is a multi-step length finite set model predictive control selection voltage vector process;

FIG. 4 is a sector division area of a multi-step length finite set model predictive control method;

fig. 5 is a flow chart of a control method of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

Firstly, establishing a mathematical model of a linear induction motor under an alpha beta coordinate system

In order to compensate the side effect generated in the operation process of the linear induction motor, the side effect influence factor is introduced:

wherein: d is the primary length of the motor; v is the motor linear velocity; r₂Is a motor secondary resistance; l is_l2Is a motor secondary inductor; l is_mIs the mutual inductance when the motor is at rest.

According to the structural schematic diagram of the linear induction motor shown in fig. 1, the motor voltage equation can be obtained as follows:

the motor flux linkage equation is as follows:

where subscripts 1 and 2 represent motor primary and secondary variables, respectively, subscripts α and β represent motor α and β axis variables, respectively, and ω is₂Represents the secondary angular velocity; u represents a voltage; i represents a current; r represents resistance; psi represents the motor flux linkage; l is_lRepresenting the leakage inductance of the motor;

selecting a state variable [ i ]_α1,i_β1,ψ_α2,ψ_β2]Combining the motor voltage and the flux linkage equation, the following can be obtained:

wherein: l is_r＝L_l2+L_m[1-f(Q)]；L_s＝L_l1+L_m[1-f(Q)]；L_m＝L_m[1-f(Q)]。

Further, expression (4) is expressed in vector form, and may be expressed as:

wherein: i is₁＝i_α1+ji_β1；V₁＝u_α1+ju_β1；ψ₂＝ψ_α2+jψ_β2。

Discretizing the formula (5) by using a first-order Euler discretization method to obtain:

wherein: t is_sTo sampleAnd (4) period.

Second, single step length finite set model prediction control method simplification

At the current time k, the current at the time needs to be sampled, and in order to compensate for the control delay caused by calculation, the predicted current at the time k +1 needs to be obtained by predicting according to equation (6) to compensate for the calculation delay.

The cost function can be expressed as:

wherein:setting a current vector value; k is a radical of_swThe current tracking error and the switching frequency penalty term are balanced by a weight coefficient.

For a two-level inverter, the conventional search method needs to bring 7 different voltage vectors into the formula (6) for prediction, the obtained predicted values are respectively brought into the formula (7) for evaluation, and the voltage vector with the minimum cost function value is selected as the optimal voltage vector. Therefore, this search method requires a large amount of computation time to solve the optimal control amount.

To simplify the computation in the case of single-step prediction, the cost function can be rewritten by substituting equation (6) into equation (7):

wherein:

due to the fact that

The constant term is a constant term which changes along with time and does not change along with the difference of the voltage vector to be selected. Thus, the cost function can be simplified to:

from equation (11), the optimum voltage vector that minimizes the cost function value is separated from the reference voltage vectorThe closest distance. Therefore, in order to compare the distances between the two, the sectors may be divided as shown in fig. 2, and the candidate voltage vector of the same sector is selected as the optimal voltage vector by determining the sector to which the reference voltage belongs.

Three, multi-step length finite set model prediction control method simplification

Therefore, when the prediction step size is N steps, for the two-level inverter, the number of the candidate voltage vectors to be evaluated and compared is increased from the original 7 to N × 7^NAnd (4) respectively. The number of the candidate voltage vectors is increased exponentially, so that the calculation amount of the multi-step predictive control algorithm is heavy, and the online calculation amount of the algorithm is further reduced by reducing the number of the candidate voltage vectors.

When the predicted step size is N steps, a cost function expression of the multi-step finite set model predictive control algorithm can be written according to equation (8), and can be represented as:

for simplicity, it is assumed that the secondary flux linkage and angular velocity remain unchanged within the prediction step, while the current vector reference value also remains unchanged, i.e.:at this time, by substituting equation (6) into equation (9), a recursive expression between reference voltage vectors at different prediction steps can be obtained, which can be expressed as:

to further simplify equation (12), the following equation is derived, expressed as:

by iteratively using equations (6), (13), and (14), equation (12) can be rewritten as:

the recursion relational expression of each variable in the above formula is as follows:

due to the fact that

Only changes along with time, and the value cannot change due to different voltage vector sequences. The value of the cost function is therefore only related to the first term, i.e. the sequence of candidate voltage vectors

With reference voltage vector sequence

The cost function can be simplified to:

as shown in FIG. 3, only two non-zero voltage vectors and one zero voltage vector which are nearest to the reference voltage vector are reserved in each prediction step, namely only 3 voltage vectors are evaluated in each prediction step, and only the voltage vector nearest to the reference voltage vector is selected in the last prediction step to minimize the cost function^N-1And (4) respectively.

The screened voltage vector sequence can be obtained by determining the sector of each reference voltage vector in the reference voltage sequence, the sector division being as shown in fig. 4. To avoid analyzing other possible sectors, the reference voltage vector can be converted into the first sector by the following expression:

wherein: n is the sector of the reference voltage vector.

Reference voltage vector processed by equation (26)The 3 screened voltage vectors can be further sorted as follows:

wherein:

V_dcis the dc bus voltage. If n is 1, V_n-1Is a V₆If n is 6, V_n+1Is a V₁。

Therefore, only the first voltage vector in equation (27), i.e., S, needs to be selected in the last prediction step_N(1). However, in other prediction steps, each voltage vector needs to be compared and evaluated according to the ranking sequence of the formula (27), namely S_i(1,2,3). By evaluating in this order, the cost function value can be made small at the beginning, the probability of becoming the optimum voltage vector sequence is large, and the probability of becoming the optimum voltage vector sequence becomes smaller as the search goes backward. On the basis, the calculated cost function value is compared with the current optimal cost function value in each prediction step, if the cost function value is larger than the optimal value, the voltage vector sequence can be abandoned, and the next voltage vector sequence is selected for evaluation. This process can dynamically remove some voltage vectors online, further reducing the computational load.

Fourthly, an execution flow chart of a final simplified algorithm is shown in fig. 5, and the linear induction motor multi-step finite set model prediction control method comprises the following steps:

(1) at the current moment k, collecting primary phase current of the linear induction motor in a three-phase coordinate system

And converting the current vector into αβ coordinate system to obtain current vector value

(2) According to the current vector value at the k timePredicting current vector value at time k +1

(3) Vector value of current

As an initial value, the reference voltage vector at time k + i is iteratively calculatedPredicting time i is 1, …, N, N is total predicting step number;

wherein the content of the first and second substances,

the voltage vector selected for time k + i-1,λ is a weight coefficient;

a and b are coefficients for the number of,

T_sin order to be the sampling period of time,for the reference current command, j denotes the imaginary part; r represents resistance; psi represents the motor flux linkage, subscripts 1 and 2 represent the motor primary and secondary variables, respectively; omega₂Represents the secondary angular velocity, L_lRepresenting the leakage inductance of the motor; l is_rIs a secondary inductance, L_sIs a primary inductance, L_mIs mutual inductance.

In a preferred mode, the control method is simplified through subsequent steps, hardware cost required for execution of the method is reduced, and the algorithm can be applied to an actual system.

(4) Dividing the output voltage range of the inverter into six sectors equally, respectively determining the output voltage range as the 1 st to the sixth sectors in a counterclockwise manner, and judging V one by one_k+1,…,V_k+NConverting the reference voltage vector angle of each sector into a first sector by the sector to which the reference voltage vector of the moment belongs;

(5) according to reference voltage vector converted into first sector

Screening and sorting to obtain inverter candidate output voltage sequenceWherein:

V_dcis a dc bus voltage; v₀Zero voltage vector, V, output by inverter_n,V_n+1，V_n-1A non-zero voltage vector output for the inverter;

(6) with the aim of minimizing the value of the cost function, fromInverter standby output voltage sequence

Finding the optimal voltage vector sequence.

More specifically, the reference voltage vector angle of each sector is converted into the first sector by an angle conversion formula:

wherein: and n is the sector number of the reference voltage vector.

More specifically, the cost function value is expressed as:

wherein:

representing the reference voltage vector at time k + i.

The method applies the multi-step length finite set model prediction control method to the linear induction motor, improves the running performance of the linear induction motor, and is particularly applied to low switching frequency. The control method is simplified, and the hardware cost required by the method is reduced, so that the method can be applied to an actual system.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.