阅读说明：本技术 基于最优参考磁链的直线电机模型预测控制方法及系统 (Linear motor model prediction control method and system based on optimal reference flux linkage ) 是由 徐伟 唐一融 董定昊 于 2021-07-26 设计创作，主要内容包括：本发明公开了一种基于最优参考磁链的直线电机模型预测控制方法及系统。该方法应用于直线感应电机领域,包括：获取实时采集的直线感应电机的状态参数,根据状态参数通过预先构建的磁链观测器观测电机当前的磁链；根据状态参数判断直线感应电机的运行区域,根据运行区域和电机当前的磁链计算对应的最优参考磁链矢量,运行区域包括MTPA、恒功率和MTPV运行区；根据电机当前的磁链和最优参考磁链矢量确定最优电压矢量组合；根据最优电压矢量组合计算最优占空比,根据最优占空比控制逆变器中的三相桥臂脉冲序列。本发明将全部控制目标包含在最优参考磁链矢量中,可省略价值函数中因为不同量纲控制量而引入的权重系数,进而省去复杂的权重系数整定过程。(The invention discloses a linear motor model prediction control method and system based on optimal reference flux linkage. The method is applied to the field of linear induction motors and comprises the following steps: acquiring real-time acquired state parameters of the linear induction motor, and observing the current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameters; judging the operation area of the linear induction motor according to the state parameters, and calculating a corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA (maximum power transformer), a constant power transformer and an MTPV (maximum power transformer) operation area; determining an optimal voltage vector combination according to the current flux linkage and the optimal reference flux linkage vector of the motor; and calculating the optimal duty ratio according to the optimal voltage vector combination, and controlling a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio. According to the invention, all control targets are contained in the optimal reference flux linkage vector, so that the weight coefficient introduced by different dimension control quantities in the cost function can be omitted, and further, the complicated weight coefficient setting process is omitted.)

1. A linear motor model prediction control method based on optimal reference flux linkage is applied to the field of linear induction motors and is characterized by comprising the following steps:

acquiring state parameters of a linear induction motor collected in real time, and observing the current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameters, wherein the state parameters comprise phase current and speed parameters, and the flux linkage comprises a primary flux linkage and a secondary flux linkage;

judging the operation area of the linear induction motor according to the state parameters, and calculating a corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA operation area, a constant power operation area and an MTPV operation area;

determining an optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector;

and calculating an optimal duty ratio according to the optimal voltage vector combination, and controlling a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio to realize the control of the linear induction motor.

2. The optimal reference flux linkage-based linear motor model predictive control method according to claim 1, wherein a critical speed ω for switching from the MTPA operation region to the constant power operation region_IComprises the following steps:

critical speed ω for switching from the constant power operating zone to the MTPV operating zone_IIComprises the following steps:

wherein the content of the first and second substances,for the maximum voltage, u, that the inverter can output in the linear modulation region_dcIs a dc bus voltage; rho is a correction coefficient when the resistance voltage drop and other non-ideal factors are ignored, and rho epsilon is (0.8, 1); i is_mIs the maximum phase current amplitude;is the magnetic leakage coefficient, L₁Is a primary inductance, L₂Is a secondary inductance, L_meqThe equivalent excitation inductance after considering the side end effect is obtained.

3. The optimal reference flux linkage based linear motor model prediction control method according to claim 2, wherein the optimal reference flux linkage vector is an optimal reference primary flux linkage vector, the optimal reference primary flux linkage vector comprises an optimal reference primary flux linkage amplitude and an optimal reference primary flux linkage phase angle, and the optimal reference primary flux linkage amplitude is:

the optimal reference primary flux linkage phase angle is:

wherein the content of the first and second substances,respectively alpha-beta components of the optimal reference primary flux linkage; psi₁、ψ₂Primary and secondary flux linkage vectors respectively;tau is the pole pitch of the motor;is a thrust reference value; f_ratedRated thrust; psi_ratedIs a nominal primary flux linkage.

4. The optimal reference flux linkage based linear motor model predictive control method of claim 3, wherein the step of determining an optimal voltage vector combination based on the current flux linkage and the optimal reference flux linkage vector of the motor comprises:

and calculating a reference voltage vector according to the primary flux linkage and the optimal reference primary flux linkage vector, and determining an optimal voltage vector combination according to the reference voltage vector.

5. The optimal reference flux linkage based linear motor model predictive control method of claim 4, wherein the step of calculating a reference voltage vector from the primary flux linkage and the optimal reference primary flux linkage vector comprises:

introducing a cost function of

When the cost function is zero, no tracking error is generated when the reference voltage vector acts, and the alpha-beta component of the obtained reference voltage vector is as follows:

wherein k +1 is a motor state variable at the moment of k + 1; r₁Represents the primary resistance; t is_sIs a control period; i.e. i_1α、i_1βRespectively, the alpha-beta components of the primary current; psi_1α、ψ_1βRespectively, the alpha-beta components of the primary flux linkage;respectively, are alpha-beta components of the reference voltage vector.

6. The optimal reference flux linkage based linear motor model predictive control method of claim 5, wherein the step of determining an optimal voltage vector combination from the reference voltage vectors comprises:

and selecting the optimal voltage vector combination with the shortest distance to the reference voltage vector based on the error-free tracking principle of the reference voltage vector.

7. The optimal reference flux linkage based linear motor model predictive control method according to claim 6, wherein the optimal duty cycle is:

wherein the content of the first and second substances,u^*is a reference voltage vector; | V | | is the modular length of vector V; (u)_i,u_j) Is the optimal voltage vector combination.

8. The optimal reference flux linkage based linear motor model prediction control method according to claim 1, wherein after the step of observing the current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameter, the method further comprises:

and compensating the controller delay according to the current flux linkage of the motor and by combining a mathematical model of the linear induction motor.

9. The optimal reference flux linkage based linear motor model predictive control method according to claim 8, wherein the linear induction motor mathematical model is:

wherein u is₁＝u_1d+ju_1qAnd u₂＝u_2d+ju_2qPrimary and secondary voltage vectors, respectively; i.e. i₁＝i_1d+ji_1qAnd i₂＝i_2d+ji_2qPrimary and secondary current vectors; psi₁＝ψ_1d+jψ_1qAnd psi₂＝ψ_2d+jψ_2qPrimary and secondary flux linkage vectors; l is₁＝L_meq+L_l1And L₂＝L_meq+L_l2Primary and secondary inductors; r₁And R₂Primary and secondary resistances; omega₁Is the synchronous angular velocity; omega₂Is the secondary angular velocity; f_eIs electromagnetic thrust; tau is the pole pitch of the motor; l is_meqTo take into account the equivalent excitation inductance after the side effect, L_meq＝L_m(1-f(Q))；

Based on the linear induction motor mathematical model, the constructed flux linkage observer is as follows:

wherein k and k-1 are motor state variables at the moment of k and k-1 respectively; the superscript "" is the observed quantity,is the magnetic flux leakage coefficient; t is_sIs a control cycle.

10. A linear induction motor model predictive control system based on an optimal reference flux linkage is characterized by comprising:

the system comprises an observation module, a flux linkage observer and a control module, wherein the observation module is used for acquiring real-time acquired state parameters of the linear induction motor and observing the current flux linkage of the motor through the flux linkage observer which is constructed in advance according to the state parameters, the state parameters comprise phase current and speed parameters, and the flux linkage comprises a primary flux linkage and a secondary flux linkage;

the optimal reference flux linkage vector determining module is used for judging an operation area of the linear induction motor according to the state parameters, and calculating a corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA operation area, a constant power operation area and an MTPV operation area;

the optimal voltage vector combination determining module is used for determining an optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector;

and the pulse sequence control module is used for calculating the optimal duty ratio according to the optimal voltage vector combination, controlling a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio and realizing the control of the linear induction motor.

Technical Field

The invention belongs to the technical field of linear motor control, and particularly relates to a linear motor model prediction control method and system based on optimal reference flux linkage.

Background

The linear induction motor does not need a transmission mechanism such as a gear box and the like, can directly generate linear motion, and has wide application prospect in urban rail traffic driving systems such as subway, light rail and the like. Compared with a rotary induction motor driven rail traffic system, the linear induction motor driven system has the advantages of stronger climbing capability, smaller turning radius and smaller sectional area. However, the side-end effect of the linear induction motor is generated due to the structural particularity, so that the mutual inductance change is severe in the operation of the motor, and the influence caused by the side-end effect cannot be well considered in the traditional control strategies such as vector control and direct torque control, so that the operation performance of the motor is not ideal. The model prediction control selects the optimal voltage vector to act on the inverter by adopting a value function online optimization mode, so that the influence of the side end effect of the linear induction motor can be effectively coped with, and the model prediction control has higher response speed and robustness.

The efficiency of the linear induction motor is 5% -15% lower than that of the rotary induction motor due to the large air gap and the edge effect, and the output thrust of the motor is seriously attenuated particularly at high speed due to the edge effect. MTPA is the control of the maximum thrust-current ratio, the same thrust output can be realized by using smaller current, the copper consumption of the motor and the switching loss of the inverter are reduced, and the running efficiency of the motor and a control system is further improved. MTPV is the control of the maximum thrust-voltage ratio, can output larger thrust under the same voltage, and is beneficial to compensating thrust attenuation brought by the edge effect when the linear induction motor operates in a high-speed weak magnetic region. However, when the MTPA and the MTPV are introduced as control targets to model predictive control to improve the motor performance, the existing methods need to additionally introduce weight coefficients in the cost function to adjust the control targets with different dimensions, thereby bringing about a complicated weight coefficient setting problem.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide a linear motor model prediction control method and system based on optimal reference flux linkage, so as to solve the problem of complex weight system setting caused by the fact that a plurality of control quantities are adopted as control targets in the traditional model prediction method.

In order to achieve the above object, in a first aspect, the present invention provides a linear motor model prediction control method based on an optimal reference flux linkage, which is applied in the field of linear induction motors, and includes the following steps:

acquiring state parameters of a linear induction motor collected in real time, and observing the current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameters, wherein the state parameters comprise phase current and speed parameters, and the flux linkage comprises a primary flux linkage and a secondary flux linkage;

judging the operation area of the linear induction motor according to the state parameters, and calculating a corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA operation area, a constant power operation area and an MTPV operation area;

determining an optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector;

and calculating an optimal duty ratio according to the optimal voltage vector combination, and controlling a three-phase bridge arm pulse sequence in an inverter according to the optimal duty ratio to realize the control of the linear induction motor.

In one embodiment, the critical speed ω for switching from the MTPA operating region to the constant power operating region_IComprises the following steps:

critical speed ω for switching from the constant power operating zone to the MTPV operating zone_IIComprises the following steps:

wherein the content of the first and second substances,for the maximum voltage, u, that the inverter can output in the linear modulation region_dcIs a dc bus voltage; rho is a correction coefficient when the resistance voltage drop and other non-ideal factors are ignored, and rho epsilon is (0.8, 1); i is_mIs the maximum phase current amplitude;is the magnetic leakage coefficient, L₁Is a primary inductance, L₂Is a secondary inductor, L_meqThe equivalent excitation inductance after considering the side end effect is obtained.

In one embodiment, the optimal reference flux linkage vector is an optimal reference primary flux linkage vector, the optimal reference primary flux linkage vector includes an optimal reference primary flux linkage amplitude and an optimal reference primary flux linkage phase angle, and the optimal reference primary flux linkage amplitude is:

the optimal reference primary flux linkage phase angle is:

wherein the content of the first and second substances,respectively alpha-beta components of the optimal reference primary flux linkage; psi₁、ψ₂Primary and secondary flux linkage vectors respectively;tau is the electrode distance of the motor;is a thrust reference value; f_ratedRated thrust; psi_ratedIs a nominal primary flux linkage.

In one embodiment, the step of determining an optimal voltage vector combination according to the current flux linkage and the optimal reference flux linkage vector of the motor includes:

and calculating a reference voltage vector according to the primary flux linkage and the optimal reference primary flux linkage vector, and determining an optimal voltage vector combination according to the reference voltage vector.

In one embodiment, the step of calculating a reference voltage vector based on the primary flux linkage and the optimal reference primary flux linkage vector comprises:

introducing a cost function of

When the cost function is zero, no tracking error is generated when the reference voltage vector acts, and the alpha-beta component of the reference voltage vector is obtained as follows:

wherein k +1 is a motor state variable at the moment of k + 1; r₁Represents the primary resistance; t is_sTo control the cycle; i.e. i_1α、i_1βRespectively, the alpha-beta components of the primary current; psi_1α、ψ_1βRespectively, the alpha-beta components of the primary flux linkage;respectively, are alpha-beta components of the reference voltage vector.

In one embodiment, the step of determining an optimal voltage vector combination from the reference voltage vectors comprises:

and selecting the optimal voltage vector combination with the shortest distance to the reference voltage vector based on the error-free tracking principle of the reference voltage vector.

In one embodiment, the optimal duty cycle is:

wherein the content of the first and second substances,u^*is a reference voltage vector; | V | | is the modular length of vector V; (u)_i,u_j) Is the optimal voltage vector combination.

In one embodiment, after the step of observing the current flux linkage of the motor by a flux linkage observer constructed in advance according to the state parameters, the method further comprises the following steps:

and compensating the controller delay according to the current flux linkage of the motor and by combining a mathematical model of the linear induction motor.

In one embodiment, the mathematical model of the linear induction motor is:

wherein u is₁＝u_1d+ju_1qAnd u₂＝u_2d+ju_2qPrimary and secondary voltage vectors, respectively; i.e. i₁＝i_1d +ji_1qAnd i₂＝i_2d+ji_2qPrimary and secondary current vectors; psi₁＝ψ_1d+jψ_1qAnd psi₂＝ψ_2d+jψ_2qPrimary and secondary flux linkage vectors; l is₁＝L_meq+L_l1And L₂＝L_meq+L_l2Primary and secondary inductors; r₁And R₂Primary and secondary resistances; omega₁Is the synchronous angular velocity; omega₂Is the secondary angular velocity; f_eIs electromagnetic thrust; tau is the pole pitch of the motor; l is_meqTo take into account the equivalent excitation inductance after the side effect, L_meq＝L_m(1-f(Q))；

Based on the linear induction motor mathematical model, the constructed flux linkage observer is as follows:

wherein k and k-1 are motor state variables at the moment of k and k-1 respectively; the superscript ^ is an observed quantity,is the magnetic flux leakage coefficient; t is_sIs a control cycle.

In a second aspect, the present invention provides a linear induction motor model predictive control system based on an optimal reference flux linkage, including:

the system comprises an observation module, a flux linkage observer and a control module, wherein the observation module is used for acquiring real-time acquired state parameters of the linear induction motor and observing the current flux linkage of the motor through the flux linkage observer which is constructed in advance according to the state parameters, the state parameters comprise phase current and speed parameters, and the flux linkage comprises a primary flux linkage and a secondary flux linkage;

the optimal reference flux linkage vector determining module is used for judging the operation area of the linear induction motor according to the state parameters and calculating a corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA operation area, a constant power operation area and an MTPV operation area;

the optimal voltage vector combination determining module is used for determining an optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector;

and the pulse sequence control module is used for calculating the optimal duty ratio according to the optimal voltage vector combination, controlling a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio and realizing the control of the linear induction motor.

Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:

(1) according to the linear motor model prediction control method and system based on the optimal reference flux linkage, all control targets are contained in the optimal reference flux linkage vector under the condition that the MTPA operation area condition, the constant power operation area condition and the MTPV operation area condition are introduced, so that the weight coefficients introduced due to different dimension control quantities in the value function can be effectively omitted, and further, the complicated weight coefficient setting process is omitted.

(2) The linear motor model predictive control method and system based on the optimal reference flux linkage provided by the invention aim at the problems of larger thrust and flux linkage fluctuation existing in the traditional single vector model predictive control, and the method adopts a mode of combining two voltage vectors in each control period, so that the control performance of an algorithm can be further improved, and the thrust and flux linkage fluctuation can be reduced; meanwhile, the searching process of the optimal voltage vector is converted into the judgment of the distance, so that the optimizing process can be further simplified, and the calculation burden is reduced.

Drawings

FIG. 1 is a flowchart of a linear motor model predictive control method based on optimal reference flux linkage according to an embodiment of the present invention;

FIG. 2 is a flowchart of a linear motor model prediction control method based on an optimal reference flux linkage according to another embodiment of the present invention;

FIG. 3 is a T-shaped equivalent circuit diagram of the linear induction motor provided by the present invention;

FIG. 4 is a schematic diagram of the motor trajectory in the d-q plane provided by the present invention;

FIG. 5 is a schematic diagram of voltage vector combination selection and optimal duty cycle calculation provided by the present invention;

FIG. 6 is an overall control block diagram of the linear motor model predictive control method provided by the present invention;

fig. 7 is an architecture diagram of a linear motor model predictive control system provided by 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.

The invention provides a linear motor model prediction control method based on an optimal reference flux linkage, which aims to solve the problem of complex weight coefficient setting caused by the fact that a plurality of weight coefficients are additionally introduced into a value function to adjust control targets of different dimensions by taking a plurality of control quantities as control targets in the traditional model prediction control method.

According to the control method provided by the invention, under the condition of introducing the MTPA operation area condition, the constant power operation area condition and the MTPV operation area condition, all control targets are contained in the optimal reference flux linkage vector, the weight coefficients introduced by different dimension control quantities in the cost function are omitted, and the complicated weight coefficient setting process is further omitted.

Fig. 1 is a flowchart of a linear motor model predictive control method based on an optimal reference flux linkage according to an embodiment of the present invention, which is mainly applied to the field of linear induction motors, as shown in fig. 1, including step S10, step S20, step S30, and step S40, and is detailed as follows:

and step S10, acquiring real-time acquired state parameters of the linear induction motor, and observing the current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameters, wherein the state parameters comprise phase current and speed parameters, and the flux linkage comprises a primary flux linkage and a secondary flux linkage.

And step S20, judging the operation area of the linear induction motor according to the state parameters, and calculating the corresponding optimal reference flux linkage vector according to the operation area and the current flux linkage of the motor, wherein the operation area comprises an MTPA operation area, a constant power operation area and an MTPV operation area.

And step S30, determining the optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector.

And step S40, calculating the optimal duty ratio according to the optimal voltage vector combination, and controlling a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio to realize the control of the linear induction motor.

In a specific embodiment, as shown in fig. 2, fig. 2 is a technical flowchart of a linear motor model predictive control method based on an optimal reference flux linkage according to another embodiment of the present invention, including the following steps:

s1, respectively sampling motor phase current and speed parameters by using a current sensor and a speed sensor; and calculating primary and secondary flux linkages according to the sampling result based on a flux linkage observer, and compensating the time delay of the controller by combining a motor mathematical model.

Specifically, a T-shaped equivalent circuit of a linear induction motor is shown in fig. 3, and compared with a rotary induction motor, due to a primary core breaking structure, an edge effect is generated, so that the excitation inductance changes during the operation of the motor. To quantitatively describe this mutual inductance variation, a function f (q) is defined:

wherein Q ═ lR₂/v₂(L_m+L_l2) L is the primary length of the motor, v₂Is the linear speed of the motor, R₂Is the secondary resistance of the motor, L_l2Is a secondary inductance of the motor, L_mThe excitation inductance is used when the motor is static.

According to the equivalent circuit shown in fig. 3, the mathematical model of the linear induction motor can be expressed as:

wherein u is₁＝u_1d+ju_1qAnd u₂＝u_2d+ju_2qPrimary and secondary voltage vectors, respectively; i.e. i₁＝i_1d +ji_1qAnd i₂＝i_2d+ji_2qPrimary and secondary current vectors; psi₁＝ψ_1d+jψ_1qAnd psi₂＝ψ_2d+jψ_2qPrimary and secondary flux linkage vectors; l is₁＝L_meq+L_l1And L₂＝L_meq+L_l2Primary and secondary inductors; r₁And R₂Primary and secondary resistances; omega₁Is the synchronous angular velocity; omega₂Is the secondary angular velocity; f_eIs electromagnetic thrust; tau is the pole pitch of the motor; l is_meqTo consider the equivalent excitation inductance after the side-end effect, it can be expressed as:

L_meq＝L_m(1-f(Q)) (3)

based on the mathematical model in equation (2), a flux linkage observer can be constructed:

wherein k and k-1 represent motor state variables at the moment of k and k-1 respectively; superscript ^ means appearance measurement;is the magnetic flux leakage coefficient; t is_sIs a control cycle. Based on equation (4), the current flux linkage observed quantity can be obtained according to the sampling current and the state quantity at the previous moment.

Further, for the delay caused by the calculation time of the actual control system, the influence of the delay needs to be compensated by further combining with the motor mathematical model prediction, so that the control precision of the controller is improved. Predicting the k +1 moment according to the sampling and observation value of the current k moment, wherein the prediction expression is as follows:

wherein λ is 1/σ L₁L₂，u_optThe optimal voltage vector determined for the last moment.

And S2, judging the operation area according to the motor speed, and adopting the corresponding optimal reference flux linkage vector at different speeds.

Specifically, firstly, the corresponding optimal reference flux linkage vector amplitude expression of the motor in different operation areas is deduced. When the motor adopts the orientation of the secondary magnetic field to realize decoupling control, the secondary flux linkage of the motor meets the following conditions:

substituting formula (6) for formula (2), satisfying in a steady state:

the secondary flux linkage and the electromagnetic thrust in equation (2) can be further simplified as follows:

as can be seen from equation (8), the constant thrust curve of the motor is hyperbolic in the d-q plane. For a certain constant thrust, there is a set of (i)_d,i_q) The magnitude of the phase current is minimized and maximum thrust to current ratio, MTPA operation, is achieved, as shown in fig. 4. When the motor speed is lower, the output thrust is mainly limited by the current, and solving the MTPA condition can be equivalent to:

wherein, I_mIs the motor phase current amplitude; when it is satisfied withIn this case, the maximum thrust can be output under this constraint condition, and at this time, the primary flux linkage amplitude of the motor can be expressed as:

when the MTPA condition is satisfied, the electromagnetic thrust can also be expressed as:

according to the formulas (10) and (11), the primary flux linkage amplitude of the motor and the electromagnetic thrust have a definite relation when the MTPA condition is met, and the reference value of the electromagnetic thrust is output by the rotating speed loop regulatorThe primary flux linkage amplitude that satisfies the MTPA condition can then be expressed as:

the motor is also limited in operation by the inverter output voltage, and as speed increases, voltage constraints become a significant factor in the operation of the motor. Ignoring the resistive drop and dynamic factors at high speed, the primary terminal voltage in equation (2) can be expressed as:

the terminal voltage needs to satisfy the limitation of the inverter output voltage, that is:

wherein the content of the first and second substances,the maximum voltage which can be output by the inverter in the linear modulation region is obtained; u. of_dcIs a dc bus voltage; ρ is the correction coefficient in equation (13) neglecting the resistance drop and other non-idealities, ρ ∈ (0.8, 1). Equation (14) indicates that the voltage limit in the d-q plane is an ellipse and that the voltage limit circle is continuously decreasing with increasing speed.

As shown in fig. 4, for further increases in motor speed, the motor will leave the MTPA trajectory. And then, the motor enters a constant-power operation interval and is limited by a current limit circle and a voltage limit circle, and the working point of the motor is positioned on the intersection point of the current limit circle and the voltage limit circle. In the constant-power operation interval, the primary flux linkage and the thrust force change according to the following rules:

wherein psi_1ratedIs a rated primary flux linkage; v. of_ratedIs a rated speed; f_ratedRated thrust; f_m1The maximum thrust that can be generated when operating in the constant power region. The thrust reference value of the constant power region may be set as:

wherein the content of the first and second substances,the output of the PI controller is used for the speed loop. According to the flux linkage and thrust relation expressed by equation (15) and the thrust reference value expression given by equation (16), the primary flux linkage reference value can be expressed as:

as the motor speed increases further, the voltage limit circle, which becomes the dominant factor limiting the motor thrust output, decreases further, and in order to generate as much thrust output as possible at the same inverter output voltage, MPTV control is used and the reference value of the primary flux linkage is derived therefrom. Solving for the MTPV condition can be equivalent to:

when it is satisfied withIt is possible to output the maximum thrust under this constraint. At this time, the motor primary flux linkage amplitude can be expressed as:

the electromagnetic thrust can be expressed as:

the maximum thrust F that the motor can output in the interval_m2Can be expressed as:

therefore, the thrust reference value for the MTPV operating zone may be set to:

outputting a reference value of the electromagnetic thrust at the speed ring regulator according to the relationship between the flux linkage and the thrust represented by the expressions (19) and (20) and the thrust reference value expression given by the expression (22)The primary flux linkage amplitude that satisfies the MTPV condition can then be expressed as:

further, in order to eliminate the weight coefficient introduced by respectively controlling the flux linkage and the thrust in the model predictive control, an optimal reference flux linkage phase angle is deduced according to the relation between the flux linkage and the thrust, a control target is converted into the control on the optimal primary flux linkage vector, the weight coefficient is eliminated, and the control execution process is simplified.

The thrust of a linear induction motor can be further represented by the primary flux linkage and the secondary flux linkage as:

control of thrust can be converted to control of flux linkage phase angle by (24). Equation (24) is determined by the electromagnetic relationship inherent to the motor, regardless of the motor operating state. Thus, assuming that the primary flux linkage and thrust in (24) are represented by reference values, it can be deduced that the phase angle of the primary reference flux linkage satisfies:

further, it is necessary to determine the speed critical conditions under which the motor switches in the respective zones. As shown in fig. 3, the reason for switching the motor from the MTPA to the constant power region is that the motor speed continuously increases and the voltage limit circle continuously decreases, so that the motor cannot run on the MTPA track, and the critical condition is that the MTPA track and the voltage limit circle start to intersect. At the moment, the primary current of the motor meets the following conditions:

the critical angular velocity omega can be deduced after being substituted into the voltage limit circle_I：

When ω is₁>ω_IWhen the motor is in operation in a constant power area.

As shown in fig. 4, the reason for switching the motor from the constant torque region to the MTPV is that the motor speed is continuously increased, the voltage limit circle is reduced to have no intersection with the current limit circle, and the motor enters the MPTV control state and outputs as much torque as possible at the same voltage. The critical condition is that the MTPV trace and the voltage limit circle begin to intersect. The primary current of the motor at this time satisfies:

the critical angular velocity omega can be deduced after being substituted into the voltage limit circle_II：

When ω is₁>ω_IIAt that time, the motor enters MTPV operation. The speed v of the motor is obtained by sampling at a speed sensor₂Then, the synchronous angular velocity ω for determination₁Can be expressed as:

in summary, the optimal reference flux linkage vector can be expressed as:

wherein the content of the first and second substances,in order to ensure the proper operation of the motor,is limited to a minimum value of psi_1m，ψ_1mThe minimum primary flux linkage that can maintain the operation of the motor.The expression is shown in formula (25).

The cost function in model predictive control can be designed as:

and S3, solving a reference voltage vector according to the optimal reference flux linkage vector, and determining an optimal voltage vector combination according to the position of the reference voltage vector.

Specifically, in the conventional solution process of dual-vector model predictive control, 49 possible voltage vector combinations need to be compared and evaluated one by one, and in order to reduce the calculated amount, a reference voltage vector is derived and used for guiding the search process. Let the cost function in (32) be 0, that is, no tracking error is generated when the reference voltage vector acts, and we can obtain:

wherein:andrespectively, are alpha-beta components of the reference voltage vector. Further, the α - β component of the reference voltage vector may be expressed as:

based on the principle of error-free tracking of the reference voltage vector, the distance between the selected optimal voltage vector and the reference voltage vector is the shortest, and the cost function can be rewritten as follows:

J＝||u^*-u|| (35)

wherein | V | is the modular length of vector V,u is the optimum obtained by synthesisVoltage vector. Equation (35) has converted the finding process of the optimum voltage vector into the judgment of the distance.

Furthermore, in order to conveniently judge the distance relationship between the vectors, the output voltage range of the inverter is divided into 6 large sectors I-VI. The selection method is specifically described by taking an example in which the reference voltage vector is located in the I-th sector. When the reference voltage vector falls at the position shown in fig. 5(a) in the I-th sector, the voltage vector combinations in other sectors can be excluded, and the candidate voltage vector combination includes (u)₁,u₀)，(u₂, u₇) And (u)₁,u₂). The shortest distance between the combination of different voltage vectors and the reference voltage vector is the vertical distance, and is respectively marked as d₁，d₂And d₃As shown in fig. 5 (b). When the reference voltage vector is located in sector I-R₁And the distance between the three satisfies the following conditions:

d₂<d₁<d₃ (36)

thus, the optimum voltage vector combination at this time is (u)₂,u₇). When the reference voltage vector is located at the midpoint of the three bisectors of the triangle formed by sector I, there is d₁＝d₂＝d₃And therefore the bisector of the angle may be taken as the dividing boundary. When the reference voltage vector is located in other sectors, a transformation may be performed:

where n is the sector in which the reference voltage vector is located. After being transformed to sector I by equation (37), the sector I is judged by the method described above. The optimum voltage vector combinations for the different cases are shown in table 1. According to the table 1, the optimal voltage vector combination can be directly selected only by judging which region the reference voltage vector belongs to, and the calculation amount is reduced without comparing one by one.

TABLE 1 optimal Voltage vector combinations under different conditions

And S4, calculating the optimal duty ratio and distributing the three-phase bridge arm pulse sequence to act on the inverter to realize the control of the linear induction motor.

Specifically, after determining the optimal voltage vector combination, it is necessary to further determine the respective acting time of the two voltage vectors, i.e. the optimal duty cycle. For optimal voltage vector combination (u)_i,u_j) When the optimum duty ratio is d_optThe synthesized voltage vector may be expressed as:

u_opt＝d_optu_i+(1-d_opt)u_j (38)

in the cost function represented by formula (35):

J＝||u^*-u_opt||＝||(u^*-u_j)-d_opt(u_i-u_j)|| (39)

formula (39) can be understood as (u)^*-u_j) And d (u)_i-u_j) D may be adjusted so that this distance is the shortest, i.e. the value of the cost function is the smallest, when d equals d_opt. As shown in FIG. 5(c), (u) is^*-u_j) To (u)_i-u_j) Projection, obtaining the optimal duty ratio when the distance is shortest:

where, represents the dot product between the two voltage vectors. And further, distributing three-phase bridge arm pulses to act on the inverter according to the selected optimal voltage vector combination and the optimal duty ratio. Specifically, the overall control block diagram of the present embodiment is shown in fig. 6.

Fig. 7 is an architecture diagram of a linear induction motor model predictive control system based on an optimal reference flux linkage according to the present invention, which includes an observation module 100, an optimal reference flux linkage vector determination module 200, an optimal voltage vector combination determination module 300, and a pulse sequence control module 400, wherein,

the observation module 100 is configured to acquire state parameters of the linear induction motor collected in real time, and observe a current flux linkage of the motor through a flux linkage observer constructed in advance according to the state parameters, where the state parameters include phase current and speed parameters, and the flux linkage includes a primary flux linkage and a secondary flux linkage.

And the optimal reference flux linkage vector determining module 200 is configured to determine an operation area of the linear induction motor according to the state parameter, and calculate a corresponding optimal reference flux linkage vector according to the operation area and a current flux linkage of the motor, where the operation area includes an MTPA operation area, a constant power operation area, and an MTPV operation area.

And an optimal voltage vector combination determining module 300, configured to determine an optimal voltage vector combination according to the current flux linkage of the motor and the optimal reference flux linkage vector.

And the pulse sequence control module 400 is configured to calculate an optimal duty ratio according to the optimal voltage vector combination, and control a three-phase bridge arm pulse sequence in the inverter according to the optimal duty ratio, so as to control the linear induction motor.

Specifically, the functions of the modules in the linear induction model predictive control system for optimal reference flux linkage provided by the present invention can be referred to the detailed description of the above method embodiments, and are not repeated herein.

Compared with the traditional motor model prediction control method, the method has the following beneficial effects:

1. aiming at the problems of low efficiency and serious attenuation of output thrust at high speed in the operation of a linear induction motor, the invention provides an optimal reference flux linkage vector in control, and MTPA and MPTV operation of the motor is realized by adjusting the primary flux linkage level in the operation;

2. according to the model prediction control method and system based on the optimal reference flux linkage, all control targets are contained in the optimal reference flux linkage vector under the condition that MTPA (maximum Transmission Power) operation condition, constant power operation condition and MPTV (Multi-Point TV) operation condition are introduced, so that weight coefficients introduced due to different dimension control quantities in a cost function can be effectively omitted, and a complex weight coefficient setting process is omitted; meanwhile, the reference voltage vector derived based on the optimal reference flux linkage vector provided by the invention can be well combined with a dual-vector modulation strategy and guide the selection process of the voltage vector, and the thrust and flux linkage fluctuation in the operation of the motor are reduced under the condition that the program complexity is not obviously increased.

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.