Permanent magnet synchronous motor full-speed domain model prediction flux linkage control method
阅读说明：本技术 一种永磁同步电机全速域模型预测磁链控制方法 (Permanent magnet synchronous motor full-speed domain model prediction flux linkage control method ) 是由 於锋 霍闯 茅靖峰 李凯凯 于 2019-11-18 设计创作，主要内容包括：本发明公开了一种永磁同步电机全速域模型预测磁链控制方法,首先通过转速外环PI控制器获得参考转矩T<Sub>e</Sub><Sup>ref</Sup>；再获取永磁同步电机的电角度θ<Sub>r</Sub>和电角速度ω<Sub>r</Sub>,并获取k时刻的三相定子电流,经坐标变换后得到k时刻定子电流的d-q轴分量；然后,结合磁链方程和负载角进行磁链计算,得到(k+1)时刻磁链预测值及磁链参考值；进而,利用(k+1)时刻磁链预测值和参考值构建全速域价值函数,并通过最小化全速域价值函数获得逆变器最优电压矢量；最后根据q轴磁链无差拍思想计算占空比,分配最优电压矢量与零矢量作用于逆变器的时间。本发明可有效降低电流与转矩脉动,同时兼具良好的动稳态性能,在恒转矩区和恒功率区均能适用。(The invention discloses a permanent magnet synchronous motor full-speed domain model prediction flux linkage control method which includes the steps of firstly obtaining reference torque T through a rotating speed outer ring PI controller e ref (ii) a Then obtaining the electrical angle theta of the permanent magnet synchronous motor r And electrical angular velocity ω r Obtaining three-phase stator current at the moment k, and obtaining d-q axis components of the stator current at the moment k after coordinate transformation; then, calculating flux linkage by combining a flux linkage equation and a load angle to obtain a flux linkage predicted value and a flux linkage reference value at the (k +1) moment; further, a full-speed domain cost function is constructed by using the predicted value of the flux linkage at the (k +1) moment and the reference value, and the optimal voltage vector of the inverter is obtained by minimizing the full-speed domain cost function; finally, duty ratio is calculated according to the q-axis flux linkage dead-beat idea, and time of acting the optimal voltage vector and the zero vector on the inverter is distributed. The invention can effectively reduce current and torque pulsation, has good dynamic and steady performance, and is applicable to a constant torque area and a constant power area.)
1. A permanent magnet synchronous motor full-speed domain model prediction flux linkage control method is characterized by comprising the following steps: the system comprises a rotating speed outer-loop PI controller (1), a model prediction flux linkage control module (2), a full-speed domain value function module (3), a duty ratio calculation module (4), an inverter (5), a coordinate transformation module (6), a permanent magnet synchronous motor (7) and an encoder (8); firstly, a reference torque T is obtained through a rotating speed outer ring PI controller e ref(ii) a Then obtaining the electrical angle theta of the permanent magnet synchronous motor from the motor encoder rAnd electrical angular velocity ω rAnd acquiring three-phase stator current i at the time k by using a current sensor a，i bAnd i cObtaining d-q axis component i of stator current at the moment k after coordinate transformation dAnd i q(ii) a Then, flux linkage calculation is carried out by combining a flux linkage equation and a load angle to obtain a predicted value psi of flux linkage at the (k +1) moment sd(k+1)、ψ sq(k +1) and flux linkage reference value psi sd ref(k+1)、ψ sq ref(k + 1); further, a full-speed domain cost function is constructed by using the flux linkage predicted value and the flux linkage reference value at the (k +1) moment, and an optimal voltage vector of the inverter is obtained by minimizing the full-speed domain cost function; and finally, calculating the duty ratio according to the q-axis flux linkage dead-beat concept, and distributing the time of the optimal voltage vector and the zero vector acting on the inverter.
2. The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method according to claim 1, characterized in that: the reference torque T e refThe acquisition method comprises the following steps: the difference e between the reference speed and the actual speed of the motor is calculated nInputting a rotating speed PI controller, and obtaining a reference torque T according to a formula (1) e ref；
In the formula, k pAnd k iProportional gain and integral gain of the rotating speed PI controller are respectively shown, and s represents a complex variable.
3. The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method according to claim 1, characterized in that: the electrical angle theta rElectrical angular velocity omega rAnd d-q axis component i of stator current at time k d，i qThe acquisition method comprises the following steps: obtaining the electrical angle theta of the permanent magnet synchronous motor from the encoder rThen, the electrical angle theta is obtained through the formula (2) rWith respect to the differentiation of time, an electrical angular velocity ω is obtained r(ii) a Measuring k-time three-phase stator current i of permanent magnet synchronous motor by using current sensor a，i bAnd i cObtaining d-q axis component i of stator current at the moment k after coordinate transformation dAnd i q；
4. According to claimThe permanent magnet synchronous motor full-speed domain model prediction flux linkage control method of claim 1, is characterized in that: calculating a predicted value psi of flux linkage at time (k +1) sd(k+1)、ψ sqReference value ψ of flux linkage at time (k +1) and (k +1) sd ref(k+1)、ψ sq refThe method of (k +1) is: the obtained d-q axis current component i dAnd i qAngular velocity ω of rotor rAnd rotor electrical angle theta rInputting a model prediction flux linkage control module, obtaining a prediction current model at the moment (k +1) according to a formula (3), and then obtaining a predicted flux linkage value psi at the moment (k +1) according to a formula (4) sd(k+1)、ψ sq(k + 1); obtaining the load angle delta and the electromagnetic torque T according to the formula (5) eAnd the load angle delta is derived according to the formula (6) to obtain the load angle increment delta of the formula (7), and the reference value delta of the load angle delta at the moment of (k +1) is obtained according to the formula (8) refThe reference value ψ of the flux linkage at the time (k +1) is obtained according to the formula (9) sd ref(k+1)、ψ sq ref(k+1)；
δ ref＝△δ+δ (8)
In the formula (I), the compound is shown in the specification,
5. The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method according to any one of claims 1-4, characterized in that: constructing a full-speed domain cost function comprises constructing a cost function of a low-medium speed region control target and a cost function of a high-speed region control target in a full-speed domain cost function module (3);
the method for constructing the low and medium speed region control target comprises the following steps: obtaining a flux linkage error function g of the low and medium speed region at the time of (k +1) according to the formula (10) F(ii) a When the permanent magnet synchronous motor operates in the mode of maximum torque current ratio, a convergence function g of a low-medium speed region at the moment of (k +1) is obtained according to a formula (11) MTPA(ii) a Obtaining a flux linkage limiting condition function g of the low and medium speed region at the moment (k +1) according to the formula (12) FMAX(ii) a Obtaining the direction selection function g of the low and medium speed regions at the moment (k +1) according to the formula (13) dir；
The method for constructing the high-speed area control target comprises the following steps: calculating a flux linkage error function g 'of the high-speed region at the moment (k + 1)' FFlux linkage error function g 'of high speed region' FFlux linkage error function g of low and medium speed region FThe consistency is achieved; neglecting the stator resistance voltage drop when the permanent magnet synchronous motor operates stably at high speed to obtain a formula (14), and obtaining a high-speed area convergence function g at the moment of (k +1) according to the formula (15) FW(ii) a Calculating a high-speed region flux linkage limitation condition function g 'at the moment of (k + 1)' FMAXHigh speed region flux linkage constraint function g' FMAXFlux linkage limiting condition function g of low and medium speed regions FMAXThe consistency is achieved; when the permanent magnet synchronous motor operates above the basic speed, the voltage limiting condition function g of the high-speed area at the moment of (k +1) is obtained according to the formula (16) under the constraint of the maximum output voltage of the inverter umax(ii) a Obtaining a high-speed region stable operation function g at the moment (k +1) according to the formula (17) stab；
In the formula u sIs the stator voltage; u. of smaxIs the maximum output voltage of the inverter; v dcIs a dc bus voltage; lambda [ alpha ] mVoltage coefficient, η voltage limit condition intermediate variable, and ζ motor high speed stable operation condition intermediate variable.
6. The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method according to claim 5, characterized in that: the method for obtaining the optimal voltage vector of the inverter by minimizing the full-speed domain cost function comprises the following steps: obtaining a full-speed domain cost function according to the formula (18), respectively substituting eight basic voltage vectors into the cost function, and outputting a switch state S which enables the cost function to be minimum abcFeeding the inverter;
g(min)＝g F+g c+g L(18)
definition of ω cFor the corresponding electrical angular velocity when the permanent magnet synchronous motor is operated at the base speed, when omega r<ω cWhen g is c＝g MTPAAnd g is L＝g FMAX+g dir(ii) a When ω is r>ω cWhen g is c＝g FWAnd g is L＝g FMAX+g umax+g stab。
7. The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method according to claim 6, characterized in that: the duty ratio calculation method comprises the following steps: the q-axis flux linkage obtained according to the formula (19) reaches the given value psi at the moment of (k +1) under the combined action of the optimal voltage vector and the zero voltage vector sq ref(ii) a Combining a stator flux linkage equation and a voltage equation, and obtaining the slope S of the q-axis flux linkage when the zero vector acts according to the formula (20) 0The slope S of the q-axis flux linkage at the time of the optimum voltage vector action is obtained from the equation (21) optObtaining the optimum voltage vector action time t according to the equation (22) opt：
In the formula, # sqRepresenting flux linkage, ψ, in the q-axis component sq(k) Is the flux linkage on the q-axis component at time k; s 0Is the slope of the q-axis flux linkage when zero vector is applied; s optIs the slope of the q-axis flux linkage when the optimal voltage vector acts; t is t optIs the optimal voltage vector action time; u. of q k| soptRepresenting the q-axis voltage under the optimal vector at time k.
Technical Field
The invention relates to a permanent magnet synchronous motor full-speed domain model prediction flux linkage control method, and belongs to the field of motor driving and control.
Background
A Permanent Magnet Synchronous Motor (PMSM) has the advantages of small loss, low temperature rise, high power factor, high starting torque, short starting time, high overload capability and the like. The conventional control method for the permanent magnet synchronous motor mainly includes Vector Control (VC) and Direct Torque Control (DTC). VC is a linear control method for independently controlling flux linkage and torque by controlling exciting current and torque current. However, coordinate transformation is complex, a current regulator is usually PI control, and the PI control has inertia link and hysteresis, so that the dynamic performance of the system is poor. The DTC adopts a hysteresis controller and an offline switching meter, simplifies the system structure, but has large switching frequency change, and causes poor performance when the motor runs at low speed. As microprocessor performance has improved, Model Predictive Control (MPC) has gained widespread attention. MPC uses mathematical model to predict the change trend of system variable at next time to select the corresponding optimal control action at current time for rolling optimization, thereby accurately controlling the control target. Therefore, a novel model prediction control method derived from the DTC is provided, and the principle of the method is similar to that of the DTC, namely, the torque and the flux linkage are directly predicted through a prediction model of a system, and an optimal voltage vector is selected through a corresponding cost function. The algorithm has the advantages of simple structure, quick dynamic response and the like, but the weight coefficient design process is complex.
Aiming at the problem of complex weight coefficient design, the model prediction flux linkage control converts the control on the stator flux linkage amplitude and the electromagnetic torque into the control on the equivalent stator flux linkage vector by deeply deducing the analytic relation between the flux linkage and the torque, thereby eliminating the complicated weight coefficient design in the traditional method, and the algorithm is simple and is easy to realize. Since the MPC strategy has a good application prospect in the field of PMSM driving, in recent years, many scholars are dedicated to research and improvement of MPC in a full-speed motor domain operation state. When the motor runs below the basic speed, namely in a constant torque area, the Maximum torque current ratio (MTPA) is adopted for control, so that the reluctance torque can be effectively utilized, and the system efficiency of the motor is improved. When the motor operates above the basic speed, namely in a constant power area, Flux Weakening Control (FWC) is adopted, so that the operating speed range of the PMSM can be widened. In addition, the current and torque ripple can be effectively reduced by adopting the double-vector model predictive control of duty ratio control.
The invention patent 201810417636.4, entitled model-based torque prediction control method for a permanent magnet synchronous motor considering switching frequency optimization, discloses a method and device for model-based torque prediction control when the permanent magnet synchronous motor operates in a constant torque region and a constant power region. The method utilizes a prediction model to predict the d-q component i of the stator current at the (k +1) moment on line d k+1，i q k+1And electromagnetic torque T e k+1Constructing a full-speed domain cost function by combining a plurality of control targets; and finally, the optimal voltage vector of the inverter is obtained by minimizing the full-speed domain cost function, so that the switching frequency of the inverter is reduced, and a better system control effect is obtained. However, the patent does not consider the problem of complicated weight coefficient design in the full-speed domain cost function, and also does not consider the problem of large current and torque ripple in model prediction torque control.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the prior art, the permanent magnet synchronous motor full-speed domain model prediction flux linkage control method is provided, good dynamic and steady-state performance can be obtained while weight coefficients are eliminated, current and torque pulsation are effectively reduced, and the method is suitable for a constant torque area and a constant power area.
The technical scheme is as follows: a permanent magnet synchronous motor full-speed domain model prediction flux linkage control method comprises the following steps: firstly, a reference torque T is obtained through a rotating speed outer ring PI controller e ref(ii) a Then obtaining the electrical angle theta of the permanent magnet synchronous motor from the motor encoder rAnd electrical angular velocity ω rAnd acquiring three-phase stator current i at the time k by using a current sensor a，i bAnd i cObtaining d-q axis component i of stator current at the moment k after coordinate transformation dAnd i q(ii) a Then, the magnetic linkage equation and the load angle are combinedCalculating the line flux linkage to obtain a predicted value psi of the flux linkage at the (k +1) moment sd(k+1)、ψ sq(k +1) and flux linkage reference value psi sd ref(k+1)、ψ sq ref(k + 1); further, a full-speed domain cost function is constructed by using the flux linkage predicted value and the flux linkage reference value at the (k +1) moment, and an optimal voltage vector of the inverter is obtained by minimizing the full-speed domain cost function; and finally, calculating the duty ratio according to the q-axis flux linkage dead-beat concept, and distributing the time of the optimal voltage vector and the zero vector acting on the inverter.
Further, the reference torque T e refThe acquisition method comprises the following steps: the difference e between the reference speed and the actual speed of the motor is calculated nInputting a rotating speed PI controller, and obtaining a reference torque T according to a formula (1) e ref；
In the formula, k pAnd k iProportional gain and integral gain of the rotating speed PI controller are respectively shown, and s represents a complex variable.
Further, the electrical angle θ rElectrical angular velocity omega rAnd d-q axis component i of stator current at time k d，i qThe acquisition method comprises the following steps: obtaining the electrical angle theta of the permanent magnet synchronous motor from the encoder rThen, the electrical angle theta is obtained through the formula (2) rWith respect to the differentiation of time, an electrical angular velocity ω is obtained r(ii) a Measuring k-time three-phase stator current i of permanent magnet synchronous motor by using current sensor a，i bAnd i cObtaining d-q axis component i of stator current at the moment k after coordinate transformation dAnd i q；
Further, a predicted value psi of flux linkage at the time (k +1) is calculated sd(k+1)、ψ sqReference value ψ of flux linkage at time (k +1) and (k +1) sd ref(k+1)、ψ sq refThe method of (k +1) is: the obtained d-qAxial current component i dAnd i qAngular velocity ω of rotor rAnd rotor electrical angle theta rInputting a model prediction flux linkage control module, obtaining a prediction current model at the moment (k +1) according to a formula (3), and then obtaining a predicted flux linkage value psi at the moment (k +1) according to a formula (4) sd(k+1)、ψ sq(k + 1); obtaining the load angle delta and the electromagnetic torque T according to the formula (5) eAnd the load angle delta is derived according to the formula (6) to obtain the load angle increment delta of the formula (7), and the reference value delta of the load angle delta at the moment of (k +1) is obtained according to the formula (8) refThe reference value ψ of the flux linkage at the time (k +1) is obtained according to the formula (9) sd ref(k+1)、ψ sq ref(k+1)；
δ ref＝△δ+δ (8)
In the formula i d k+1、i q k+1The predicted value of the current at the moment (k + 1); r sIs a stator phase resistance; l is d、L qThe inductor is a direct axis inductor and a quadrature axis inductor; t is the sampling period of the system; u. of d k、u q kThe voltage of the stator voltage on the d-q axis component at the moment k; psi fIs a rotor permanent magnet flux linkage; n is pIs the number of pole pairs; psi sFor the resultant flux linkage psi on the d-q axis component at time k s(k) The amplitude of (d); psi sd ref(k+1)、ψ sq ref(k +1) is a flux linkage reference value of the stator flux linkage on the d-q axis component at the moment (k + 1); delta T eIs the electromagnetic torque increment; delta refIs the reference value of the load angle at the moment (k + 1).
Further, constructing a full-speed domain cost function comprises constructing a cost function of the low-medium speed region control target and a cost function of the high-speed region control target in a full-speed domain cost function module;
the method for constructing the low and medium speed region control target comprises the following steps: obtaining a flux linkage error function g of the low and medium speed region at the time of (k +1) according to the formula (10) F(ii) a When the permanent magnet synchronous motor operates in the mode of maximum torque current ratio, a convergence function g of a low-medium speed region at the moment of (k +1) is obtained according to a formula (11) MTPA(ii) a Obtaining a flux linkage limiting condition function g of the low and medium speed region at the moment (k +1) according to the formula (12) FMAX(ii) a Obtaining the direction selection function g of the low and medium speed regions at the moment (k +1) according to the formula (13) dir；
The method for constructing the high-speed area control target comprises the following steps: calculating a flux linkage error function g 'of the high-speed region at the moment (k + 1)' FFlux linkage error function g 'of high speed region' FFlux linkage error function g of low and medium speed region FThe consistency is achieved; neglecting the stator resistance voltage drop when the permanent magnet synchronous motor operates stably at high speed to obtain a formula (14), and obtaining a high-speed area convergence function g at the moment of (k +1) according to the formula (15) FW(ii) a Calculating a high-speed region flux linkage limitation condition function g 'at the moment of (k + 1)' FMAXHigh speed region flux linkage constraint function g' FMAXFlux linkage limiting condition function g of low and medium speed regions FMAXThe consistency is achieved; when the permanent magnet synchronous motor operates above the basic speed, the voltage limiting condition function g of the high-speed area at the moment of (k +1) is obtained according to the formula (16) under the constraint of the maximum output voltage of the inverter umax(ii) a Obtaining a high-speed region stable operation function g at the moment (k +1) according to the formula (17) stab；
In the formula u sIs the stator voltage; u. of smaxIs the maximum output voltage of the inverter; v dcIs a dc bus voltage; lambda [ alpha ] mVoltage coefficient, η voltage limit condition intermediate variable, and ζ motor high speed stable operation condition intermediate variable.
Further, the step of obtaining the optimal voltage vector of the inverter by minimizing the full-speed domain cost function comprises the following steps: obtaining a full-speed domain cost function according to the formula (18), respectively substituting eight basic voltage vectors into the cost function, and outputting a switch state S which enables the cost function to be minimum abcFeeding the inverter;
g(min)＝g F+g c+g L(18)
definition of ω cIs a permanent magnetThe corresponding electrical angular velocity when the step motor runs at the basic speed is omega r<ω cWhen g is c＝g MTPAAnd g is L＝g FMAX+g dir(ii) a When ω is r>ω cWhen g is c＝g FWAnd g is L＝g FMAX+g umax+g stab。
Further, the duty ratio calculation method comprises: the q-axis flux linkage obtained according to the formula (19) reaches the given value psi at the moment of (k +1) under the combined action of the optimal voltage vector and the zero voltage vector sq ref(ii) a Combining a stator flux linkage equation and a voltage equation, and obtaining the slope S of the q-axis flux linkage when the zero vector acts according to the formula (20) 0The slope S of the q-axis flux linkage at the time of the optimum voltage vector action is obtained from the equation (21) optObtaining the optimum voltage vector action time t according to the equation (22) opt；
In the formula, # sqRepresenting flux linkage, ψ, in the q-axis component sq(k) Is the flux linkage on the q-axis component at time k; s 0Is the slope of the q-axis flux linkage when zero vector is applied; s optIs the slope of the q-axis flux linkage when the optimal voltage vector acts; t is t optIs the optimal voltage vector action time; u. of q k| soptRepresenting the q-axis voltage under the optimal vector at time k.
Has the advantages that: compared with the prior art, the method is based on the model prediction flux linkage control principle, double-vector model prediction control based on duty ratio control is introduced into the MPFC, a full-speed domain cost function of a plurality of control targets including flux linkage control, MTPA optimization, flux linkage limitation, voltage limitation and the like is constructed, the optimal voltage vector acting on the inverter is obtained through the cost function, and after zero vector action is added, not only can good dynamic and steady-state performance be obtained, but also current and torque ripple are effectively reduced, and the method is suitable for a constant torque area and a constant power area.
Drawings
FIG. 1 is a schematic diagram of a permanent magnet synchronous motor full-speed domain model prediction flux linkage control method provided by the invention;
FIG. 2 is a flowchart of a permanent magnet synchronous motor full-speed domain model predictive flux linkage control method provided by the invention;
FIG. 3 is a simulation result of the permanent magnet synchronous motor full-speed domain model predicting the working condition below the flux linkage control base speed; FIG. 3(a) is a simulation result of a single vector model predicting a steady state below a flux control base speed, and FIG. 3(b) is a simulation result of a dual vector model predicting a steady state below a flux control base speed;
FIG. 4 is a simulation result of the condition below the basic speed of the permanent magnet synchronous motor full-speed domain model prediction flux linkage control method; FIG. 4(a) is a simulation result of a sudden change in rotation speed when the single vector model predicts that the flux linkage control is equal to or less than the basic speed, and FIG. 4(b) is a simulation result of a sudden change in rotation speed when the double vector model predicts that the flux linkage control is equal to or less than the basic speed;
FIG. 5 shows a simulation result of the full-speed domain condition of model predictive flux linkage control.
Detailed Description
The invention is further explained below with reference to the drawings.
A schematic diagram of a full-speed domain model prediction flux linkage control method of a permanent magnet synchronous motor is shown in fig. 1, and the full-speed domain model prediction flux linkage control method comprises a rotating
Firstly, a reference torque T is obtained through a rotating speed outer ring PI controller e ref(ii) a Then obtaining the electrical angle theta of the permanent magnet synchronous motor from the motor encoder rAnd electricityAngular velocity omega rAnd acquiring three-phase stator current i at the time k by using a current sensor a，i bAnd i cObtaining d-q axis component i of stator current at the moment k after coordinate transformation dAnd i q(ii) a Then, flux linkage calculation is carried out by combining a flux linkage equation and a load angle to obtain a predicted value psi of flux linkage at the (k +1) moment sd(k+1)、ψ sq(k +1) and flux linkage reference value psi sd ref(k+1)、ψ sq ref(k + 1); further, a full-speed domain cost function is constructed by using the flux linkage predicted value and the flux linkage reference value at the (k +1) moment, and an optimal voltage vector of the inverter is obtained by minimizing the full-speed domain cost function; and finally, calculating the duty ratio according to the q-axis flux linkage dead-beat concept, and distributing the time of the optimal voltage vector and the zero vector acting on the inverter.
The method specifically comprises the following steps:
(1) calculating a given torque T
e ref: the difference e between the reference speed and the actual speed of the motor is calculated
nInputting the rotation
In the formula, k pAnd k iProportional gain and integral gain of the rotating speed PI controller are respectively shown, and s represents a complex variable.
(2) Calculating the electrical angle theta rElectrical angular velocity omega rAnd d-q component i of stator current at time k dAnd i q: obtaining the electrical angle theta of the motor from the encoder rThen, the electrical angle theta is obtained through the formula (2) rWith respect to the differentiation of time, an electrical angular velocity ω is obtained r(ii) a Three-phase stator current i at motor k moment is measured again a，i bAnd i cObtaining i through a coordinate transformation module dAnd i q；
(3) Calculating the (k +1) time flux linkagePredicted value psi sd(k+1)、ψ sqReference value ψ of flux linkage at time (k +1) and (k +1) sd ref(k+1)、ψ sq refThe method of (k +1) is: the obtained d-q axis current component i dAnd i qAngular velocity ω of rotor rAnd rotor electrical angle theta rInputting a model prediction flux linkage control module 2, obtaining a prediction current model at the moment (k +1) according to a formula (3), and then obtaining a predicted flux linkage value psi at the moment (k +1) according to a formula (4) sd(k+1)、ψ sq(k + 1). Obtaining the load angle delta and the electromagnetic torque T according to the formula (5) eAnd the load angle delta is derived according to the formula (6) to obtain the load angle increment delta of the formula (7), and the reference value delta of the load angle delta at the moment of (k +1) is obtained according to the formula (8) refThe reference value ψ of the flux linkage at the time (k +1) is obtained according to the formula (9) sd ref(k+1)、ψ sq ref(k+1)；
δ ref＝△δ+δ (8)
In the formula i d k+1、i q k+1The predicted value of the current at the moment (k + 1); r sIs a stator phase resistance; l is d、L qThe inductor is a direct axis inductor and a quadrature axis inductor; t is the sampling period of the system; u. of d k、u q kThe voltage of the stator voltage on the d-q axis component at the moment k; psi fIs a rotor permanent magnet flux linkage; n is pIs the number of pole pairs; psi sFor the resultant flux linkage psi on the d-q axis component at time k s(k) The amplitude of (d); psi sd ref(k+1)、ψ sq ref(k +1) is a flux linkage reference value of the stator flux linkage on the d-q axis component at the moment (k + 1); delta T eIs the electromagnetic torque increment; delta refIs the reference value of the load angle at the moment (k + 1).
(4) Full-speed domain cost functions are constructed in full-speed domain cost function module 3, including cost functions of low and medium speed region control targets and cost functions of high-speed region control targets.
The method for constructing the low and medium speed region control target comprises the following steps: obtaining a flux linkage error function g of the low and medium speed region at the time of (k +1) according to the formula (10) F(ii) a When the permanent magnet synchronous motor operates in the mode of maximum torque current ratio, a convergence function g of a low-medium speed region at the moment of (k +1) is obtained according to a formula (11) MTPA(ii) a Obtaining a flux linkage limiting condition function g of the low and medium speed region at the moment (k +1) according to the formula (12) FMAX(ii) a Obtaining the direction selection function g of the low and medium speed regions at the moment (k +1) according to the formula (13) dir；
Price for building high speed zone control targetsThe value function includes: calculating a flux linkage error function g 'of the high-speed region at the moment (k + 1)' FFlux linkage error function g 'of high speed region' FFlux linkage error function g of low and medium speed region FThe consistency is achieved; neglecting the stator resistance voltage drop when the permanent magnet synchronous motor operates stably at high speed to obtain a formula (14), and obtaining a high-speed area convergence function g at the moment of (k +1) according to the formula (15) FW(ii) a Calculating a high-speed region flux linkage limitation condition function g 'at the moment of (k + 1)' FMAXHigh speed region flux linkage constraint function g' FMAXFlux linkage limiting condition function g of low and medium speed regions FMAXThe consistency is achieved; when the permanent magnet synchronous motor operates above the basic speed, the voltage limiting condition function g of the high-speed area at the moment of (k +1) is obtained according to the formula (16) under the constraint of the maximum output voltage of the inverter umax(ii) a Obtaining a high-speed region stable operation function g at the moment (k +1) according to the formula (17) stab；
In the formula u sIs the stator voltage; u. of smaxIs the maximum output voltage of the inverter; v dcIs a dc bus voltage; lambda [ alpha ] mVoltage coefficient, η voltage limit condition intermediate variable, and ζ motor high speed stable operation condition intermediate variable.
(5) Designing a value function: obtaining a value function of the full-speed-domain permanent magnet synchronous motor according to the formula (18), respectively substituting eight basic voltage vectors in the table 1 into the value function, and outputting a switching state S enabling the value function to be minimum abcFeeding the inverter;
g(min)＝g F+g c+g L(18)
TABLE 1 basic Voltage vector Table
Definition of ω cFor the corresponding electrical angular velocity when the permanent magnet synchronous motor is operated at the base speed, when omega r<ω cWhen g is c＝g MTPAAnd g is L＝g FMAX+g dir(ii) a When ω is r>ω cWhen g is c＝g FWAnd g is L＝g FMAX+g umax+g stab。
(6) Calculating the duty ratio: the q-axis flux linkage obtained according to the formula (19) reaches the given value psi at the moment of (k +1) under the combined action of the optimal voltage vector and the zero voltage vector sq ref(ii) a Combining a stator flux linkage equation and a voltage equation, and obtaining the slope S of the q-axis flux linkage when the zero vector acts according to the formula (20) 0The slope S of the q-axis flux linkage at the time of the optimum voltage vector action is obtained from the equation (21) optObtaining the optimum voltage vector action time t according to the equation (22) opt；
In the formula, # sqRepresenting flux linkage, ψ, in the q-axis component sq(k) Is the flux linkage on the q-axis component at time k; s 0Is the slope of the q-axis flux linkage when zero vector is applied; s optIs the q-axis flux linkage when the optimal voltage vector actsThe slope of (a); t is t optIs the optimal voltage vector action time; u. of q k| soptRepresenting the q-axis voltage under the optimal vector at time k.
The permanent magnet synchronous motor full-speed domain model prediction flux linkage control method is shown in a flow chart of fig. 2, and firstly, a stator current d-q axis component i at the moment k is obtained dAnd i qElectric angle of rotor theta rAngular velocity ω of rotor rAnd a reference torque T e ref(ii) a And then predicting a flux linkage predicted value and a flux linkage reference value at the (k +1) moment, and predicting and constructing a flux linkage error function g at the (k +1) moment by utilizing three control requirements of a maximum torque-current ratio control or weak magnetic control strategy based on model prediction flux linkage control FZone convergence function g cAnd a constraint function g L(ii) a Then, according to the rotating speed, selecting a value function of an MTPA (maximum Transmission Power Amplifier) area or a weak magnetic area and carrying out online rolling optimization to obtain an optimal voltage vector of the inverter; and finally, calculating the duty ratio by using the q-axis flux linkage dead beat, and distributing the time of the optimal voltage vector and the zero vector acting on the inverter.
FIG. 3 is a comparison of steady-state simulation results of model prediction flux linkage control of the single-double vector permanent magnet synchronous motor below the base speed. The simulation working condition is set as follows: the motor is given with the rotating speed of 400r/min and the electromagnetic torque of 4 N.m. At this time, the torque ripple of the single vector model prediction flux linkage control in fig. 3(a) is 33%, and the torque ripple of the double vector model prediction flux linkage control in fig. 3(b) is only 20%; comparing the current THD of the two schemes, the single vector model predicted flux linkage control current THD was 17.49%, while the dual vector model predicted flux linkage control current THD was only 7.96%. FIG. 4 is a comparison of simulation results of single and double vector permanent magnet synchronous motor model prediction flux linkage control when the rotation speed is suddenly changed below the base speed. Given a load of 4N · m, the initial rotational speed is 200r/min, and the rotational speed is abruptly changed to 400r/min at t ═ 0.6 s. For sudden change of the rotating speed, the two schemes can both rapidly respond, the rotating speed overshoot does not exceed 3%, and the current waveform can also keep good sine degree. The simulation results of the two schemes are compared to see that the dynamic performances of the single-double vector MPFC are basically consistent.
FIG. 5 shows the prediction of PMSM model under full-speed region conditionAnd controlling a simulation result by a chain, wherein the simulation working condition is set as follows: the motor is started from no load to the basic speed of 600r/min, then the flux weakening control is adopted, the rotating speed of the motor reaches 1800r/min, and the rotating speed is suddenly reduced to 0r/min when t is 0.4 s. FIG. 5(a) shows a stator current i sAnd d-q axis component i d、i qA waveform diagram; FIG. 5(b) is a motor speed diagram; FIG. 5(c) is a three-phase current waveform diagram when the motor is operating in the full speed domain; fig. 5(d) is a waveform diagram of electromagnetic torque of the motor. In the starting stage of the motor, in order to enable the motor to quickly reach a rotating speed set value 1800r/min, the three-phase current reaches a maximum value 10A, the torque reaches a maximum value 9N · m, the motor reaches the set rotating speed 1800r/min after being started for 5ms, the three-phase current value is 4A, the torque is 0N · m, when the rotating speed suddenly drops to 0r/min when the set rotating speed is t being 0.4s, the rotating speed of the motor becomes 0r/min after 10ms, and at the moment, the three-phase current and the torque respond quickly and reach the maximum value again.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.