CN109660160B - Switching duty ratio prediction torque control method - Google Patents

Switching duty ratio prediction torque control method Download PDF

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CN109660160B
CN109660160B CN201811140546.1A CN201811140546A CN109660160B CN 109660160 B CN109660160 B CN 109660160B CN 201811140546 A CN201811140546 A CN 201811140546A CN 109660160 B CN109660160 B CN 109660160B
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phase
duty ratio
flux linkage
stator
switching duty
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CN109660160A (en
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夏长亮
李晨
阎彦
史婷娜
王志强
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Tianjin University
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Tianjin University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Abstract

A switching duty cycle predicted torque control method: establishing a prediction model in the permanent magnet synchronous motor system by taking the three-phase switching duty ratio as a control variable according to the relation between the three-phase switching duty ratio of an inverter in the permanent magnet synchronous motor system and electromagnetic torque and stator flux linkage; the method comprises the steps that a discrete three-phase switch duty ratio group is brought into a control set, and a new three-phase discrete switch duty ratio group control set is established; the method comprises the steps of taking the square of the error of the electromagnetic torque and the stator flux linkage at the end of each control period as an evaluation index, constructing an evaluation function, and evaluating the error of the electromagnetic torque and the stator flux linkage at the end of each control period, wherein the electromagnetic torque and the error correspond to different three-phase discrete switch duty ratio groups in a newly-built three-phase discrete switch duty ratio group control set; and outputting the three-phase switching signals corresponding to the minimum three-phase discrete switching duty ratio group in the evaluation result to the three-phase inverter. According to the method, the three-phase switch state corresponding to the optimal three-phase switch duty ratio is directly output to the inverter according to the screening result of the evaluation function.

Description

Switching duty ratio prediction torque control method
Technical Field
The invention relates to a control method of a permanent magnet synchronous motor. And more particularly, to a switching duty ratio predictive torque control method that takes into account the operating performance of a motor in the case of predictive torque control.
Background
The permanent magnet synchronous motor has the advantages of simple structure, high power density, wide speed regulation range and the like, so the permanent magnet synchronous motor is widely researched and applied in the fields of elevator dragging, numerical control machine tools, railway traction systems and the like. The predicted torque control has the advantages of flexible implementation method, easy implementation in a multivariable system, high dynamic response speed and the like, and the predicted torque control is paid more and more attention with the continuous development of microprocessor technology and is widely researched in a permanent magnet synchronous motor system.
In a two-level voltage source inverter fed permanent magnet synchronous motor system, the control variables in the control set of the limited control set predictive torque control method are 8 basic voltage vectors: 6 effective voltage vectors with fixed amplitude and phase angle and 2 zero vectors. Since the limited control set predicted torque control method selects only one optimal voltage vector from the control set to output to the inverter in each control period, the limited control set predicted torque control has low control freedom, and the electromagnetic torque is difficult to realize high-precision control, resulting in large torque fluctuation. In order to reduce steady-state torque fluctuation of the limited control set predicted torque control, the existing method improves the control precision of electromagnetic torque and stator flux linkage by expanding control variables in the control set, and reduces the torque fluctuation. Various types of predictive torque control methods improve the control accuracy of electromagnetic torque and stator flux linkage by enriching the control variables in the control set or applying multiple basic voltage vectors in one control cycle, but more control quantities also mean higher computational complexity. With the continuous development of power electronic device technology, such as the continuous maturation and popularization of SiC power switching device technology, the allowable switching frequency of the power switching device is continuously increased. In order to meet the demand for obtaining a higher switching frequency, it is necessary to complete the execution of the control method in a longer time, thereby increasing the control frequency of the digital control circuit. It is therefore becoming more meaningful to find a control method that has good control performance and is less complex in the method.
Disclosure of Invention
The invention aims to solve the technical problem of providing a switching duty ratio predictive torque control method which can reduce the computational complexity of predictive control on the basis of obtaining good torque and flux linkage stable state performance of a permanent magnet synchronous motor.
The technical scheme adopted by the invention is as follows: a switching duty cycle predicted torque control method includes the steps of:
1) establishing a prediction model in the permanent magnet synchronous motor system by taking the three-phase switching duty ratio as a control variable according to the relation between the three-phase switching duty ratio of an inverter in the permanent magnet synchronous motor system and electromagnetic torque and stator flux linkage;
2) the method comprises the steps that a discrete three-phase switch duty ratio group is brought into a control set, and a new three-phase discrete switch duty ratio group control set is established;
3) the method comprises the steps of taking the square of the error of the electromagnetic torque and the stator flux linkage at the end of each control period as an evaluation index, constructing an evaluation function, and evaluating the error of the electromagnetic torque and the stator flux linkage at the end of each control period, wherein the electromagnetic torque and the error correspond to different three-phase discrete switch duty ratio groups in a newly-built three-phase discrete switch duty ratio group control set;
4) and outputting the three-phase switching signals corresponding to the minimum three-phase discrete switching duty ratio group in the evaluation result to the three-phase inverter.
The prediction model in the step 2) is as follows:
Figure BDA0001815702980000021
Figure BDA0001815702980000022
in the formula, | ψs(k +1) | and Te(k +1) represents the stator flux linkage amplitude and the electromagnetic torque at (k +1) T respectivelysA predicted value of the time; phis(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsAn observed value of a time; rsRepresenting the stator resistance; i.e. isxA component of the stator current vector on the x-axis; vdcRepresents a dc-side bus voltage; omegarRepresenting a rotor flux linkage vector rotation angular velocity; psifRepresents a permanent magnet flux linkage; t issRepresents a control period;
Figure BDA0001815702980000023
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npRepresenting the pole pair number of the PMSM, and delta representing the load angle, i.e. the stator flux linkage vector angle thetasFlux linkage vector angle with rotorDegree thetarThe difference between them; dA、dBAnd dCRepresenting the three-phase switching duty cycle.
The new three-phase discrete switch duty cycle group control set of step 1) is as follows:
Figure BDA0001815702980000024
wherein S denotes a sector number, and S is 1,2, or 3; lxAnd lyReference symbols, l, representing the discrete SDR of each phase respectivelyx＝0，1,2,…, N， l y0,1,2, …, N; when S is 1, x is A, y is B, and Z is C; when S is 2, x is A, y is C, and Z is B; when S is 3, x is B, y is C, and Z is A.
The evaluation function in the step 3) is as follows:
Figure BDA0001815702980000025
in the formula (d)A、dB、dCA, B, C three-phase switch duty cycles respectively; lambda represents a weight factor for specifying the importance of the stator flux linkage term in the evaluation function; e.g. of the typeT0＝Te *-Te(k)+Kωr|ψs(k)|TsWherein, Te *Indicating the desired value, | ψ, of the electromagnetic torques(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsObserved value of time, ωrRepresenting the rotor flux linkage vector rotation angular velocity, TsIt is indicated that the control period is,
Figure BDA0001815702980000026
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npRepresenting the pole pair number of the PMSM, and delta representing the load angle, i.e. the stator flux linkage vector angle thetasVector angle theta with rotor flux linkagerThe difference between them; e.g. of the typeψ0＝|ψs *|-|ψs(k)|+RsisxTsWherein ψs *Representing the expected value, R, of the stator flux linkage vectorsRepresents a stator resistance; i.e. isxA component of the stator current vector on the x-axis; gamma rayT＝2KVdcTs/3 wherein VdcRepresents a dc-side bus voltage; gamma rayψ＝2VdcTs/3。
After the step 2) is finished, a newly-built three-phase discrete switch duty ratio group is removed in advance by utilizing a dead beat technology, the three-phase discrete switch duty ratio group which does not have the capability of optimizing the control performance is controlled and concentrated, the number of the three-phase discrete switch duty ratio groups to be evaluated is reduced to 4, and then the step 3) is carried out.
The number of the three-phase discrete switch duty ratio groups to be evaluated is reduced to 4, the predicted values of the electromagnetic torque and the stator flux linkage in the prediction model in the step 1) are replaced by the predicted values of the electromagnetic torque and the stator flux linkage, and d is solved respectivelyAIs zero, dBIs zero and dCThree groups of three-phase switch duty cycles d at zeroA、dBAnd dCWherein the three-phase switching duty cycle dA、dBAnd dCThe group of three-phase switching duty ratios with the values of more than or equal to zero are reference three-phase switching duty ratios meeting the dead beat principle; comparing each three-phase discrete switch duty cycle group in the new three-phase discrete switch duty cycle group control set in the step 1) with a reference three-phase switch duty cycle, taking 4 three-phase discrete switch duty cycle groups closest to the reference three-phase switch duty cycle as groups to be evaluated, and entering the step 3) for evaluation.
The method for controlling the predicted torque of the switching duty ratio has the following beneficial effects:
1. the method of the invention does not use the stator voltage vector as a control variable any more, but directly uses the three-phase discrete three-phase switch duty ratio group as the control variable. Compared with the traditional predicted torque control method, the method has the advantages that the processes of vector synthesis and calculation of the corresponding three-phase switch duty ratio are omitted, and the three-phase switch state corresponding to the optimal three-phase switch duty ratio can be directly output to the inverter according to the screening result of the evaluation function.
2. In order to avoid exhausting all three-phase discrete switch duty ratio groups and increase unnecessary calculation burden, the invention adopts the electromagnetic torque and stator flux linkage dead beat technology, and the three-phase discrete switch duty ratio groups without optimized performance are eliminated in advance in each control period, thereby further reducing the calculation burden of the method.
3. Because the discretization results of the duty ratios of the switches of all phases are the same, the discretization results of the three-phase discretization switch duty ratio groups do not need to be stored in a complex multi-dimensional table, and only need to be stored in a simplified one-dimensional table of N +1, so that the occupation of the storage space of the digital controller by the discretization results is reduced.
Drawings
FIG. 1 is a flow chart of a switching duty cycle predictive torque control method of the present invention;
FIG. 2 is a topology diagram of a two-level voltage source inverter fed PMSM system;
FIG. 3 is a two-level voltage source inverter voltage vector diagram;
FIG. 4a is a switching sequence diagram of the resultant voltage vector in sector 1 of a control cycle;
FIG. 4b is a switching sequence diagram of the resultant voltage vector in sector 2 of a control cycle;
FIG. 4c is a switching sequence diagram of the resultant voltage vector in sector 3 of a control cycle;
FIG. 5 is a schematic diagram of three-phase discrete switching duty cycles;
FIG. 6 is a control block diagram of a three-phase switching duty cycle predicted torque control method;
FIG. 7a is a transient waveform diagram of the proposed switching duty cycle predicted torque control method and classical finite control set predicted torque control at a sudden change in rotational speed;
FIG. 7b is a waveform of the transient state of the proposed switching duty cycle predicted torque control method and classical finite control set predicted torque control at the time of a torque jump;
FIG. 8a is a steady state waveform of electromagnetic torque, stator flux linkage, a-phase stator current for a classical finite control set predictive torque control;
FIG. 8b is a steady state waveform of electromagnetic torque, stator flux, a-phase stator current for the extended control set predicted torque control;
FIG. 8c is a steady state waveform of the electromagnetic torque, stator flux, a-phase stator current of the switching duty cycle predicted torque control;
FIG. 8d is the torque ripple σ for 3 methodsTStator flux linkage fluctuation sigmaψStator current total harmonic distortion iTHDAnd average switching frequency favThe experimental statistics of (3);
FIG. 9a is N-5 and TsThe switching duty ratio predicts the steady-state waveform of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the torque control method when the time is 200 mus;
FIG. 9b is N-10 and TsThe switching duty ratio predicts the steady-state waveform of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the torque control method when the time is 200 mus;
FIG. 9c is N-20 and TsThe switching duty ratio predicts the steady-state waveform of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the torque control method when the time is 200 mus;
fig. 9d shows the torque ripple σ of the switching duty ratio predicted torque control method when the values are taken when N is 5, N is 10, and N is 20TStator flux linkage fluctuation sigmaψStator current total harmonic distortion iTHDAnd average switching frequency favThe experimental statistics of (3);
FIG. 10a is TsThe switching duty ratio of the torque control method is predicted when the switching duty ratio is 65 mus and N is 15, and the steady-state waveforms of the electromagnetic torque, the stator flux linkage and the a-phase stator current are obtained;
FIG. 10b is TsThe switching duty ratio predicts the steady-state waveform of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the torque control method when 333 mus and N is 15;
FIG. 10c is Ts65 μ s and TsTorque fluctuation sigma of switching duty ratio prediction torque control method when 333 mu s is takenTStator flux linkage fluctuation sigmaψStator current total harmonic distortion iTHDAnd average switching frequency favThe experimental statistics of (3);
FIG. 11a is Ld(Lq) Changing the steady-state waveforms of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the original 0.8-time switching duty ratio prediction torque control method;
FIG. 11b is Ld(Lq) Changing the steady-state waveforms of the electromagnetic torque, the stator flux linkage and the a-phase stator current of the original 1.2-time switching duty ratio prediction torque control method;
FIG. 11c is Ld(Lq) Torque fluctuation sigma of switching duty ratio prediction torque control method in different changesTStator flux linkage fluctuation sigmaψStator current total harmonic distortion iTHDAnd average switching frequency favThe experimental statistics of (2).
Detailed Description
A switching duty ratio predicted torque control method according to the present invention will be described in detail with reference to the following embodiments and the accompanying drawings.
As shown in fig. 1, the switching duty ratio prediction torque control method of the present invention includes the following steps:
1) establishing a prediction model in the permanent magnet synchronous motor system by taking the three-phase switching duty ratio as a control variable according to the relation between the three-phase switching duty ratio of an inverter in the permanent magnet synchronous motor system and electromagnetic torque and stator flux linkage; the prediction model is as follows:
Figure BDA0001815702980000041
Figure BDA0001815702980000042
in the formula, | ψs(k +1) | and Te(k +1) represents the stator flux linkage amplitude and the electromagnetic torque at (k +1) T respectivelysA predicted value of the time; phis(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsAn observed value of a time; rsRepresenting the stator resistance; i.e. isxStator current vectorThe component of the quantity on the x-axis; vdcRepresents a dc-side bus voltage; omegarRepresenting a rotor flux linkage vector rotation angular velocity; psifRepresents a permanent magnet flux linkage; t issRepresents a control period;
Figure BDA0001815702980000043
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npRepresenting the pole pair number of the PMSM, and delta representing the load angle, i.e. the stator flux linkage vector angle thetasAngle theta with rotor flux linkage vectorrThe difference between them; dA、dBAnd dCRepresenting the three-phase switching duty cycle. .
2) The method comprises the steps that a discrete three-phase switch duty ratio group is brought into a control set, and a new three-phase discrete switch duty ratio group control set is established; the new three-phase discrete switch duty ratio group control set is as follows:
Figure BDA0001815702980000044
wherein S denotes a sector number, and S is 1,2, or 3; lxAnd lyReference symbols, l, representing the duty cycle of the discrete switches of each phase, respectivelyx＝0， 1,2,…,N， l y0,1,2, …, N; when S is 1, x is A, y is B, and Z is C; when S is 2, x is A, y is C, and Z is B; when S is 3, x is B, y is C, and Z is A.
3) The method comprises the steps of taking the square of the error of the electromagnetic torque and the stator flux linkage at the end of each control period as an evaluation index, constructing an evaluation function, and evaluating the error of the electromagnetic torque and the stator flux linkage at the end of each control period, wherein the electromagnetic torque and the error correspond to different three-phase discrete switch duty ratio groups in a newly-built three-phase discrete switch duty ratio group control set; the evaluation function is as follows:
Figure BDA0001815702980000051
in the formula (d)A、dB、dCA, B, C three-phase switch duty cycles respectively; lambda represents a weight factor for specifying the importance of the stator flux linkage term in the evaluation function; e.g. of the typeT0＝Te *-Te(k)+Kωr|ψs(k)|TsWherein, Te *Indicating the desired value, | ψ, of the electromagnetic torques(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsObserved value of time, ωrRepresenting the rotor flux linkage vector rotation angular velocity, TsIt is indicated that the control period is,
Figure BDA0001815702980000052
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npRepresenting the pole pair number of the PMSM, and delta representing the load angle, i.e. the stator flux linkage vector angle thetasVector angle theta with rotor flux linkagerThe difference between them; e.g. of the typeψ0＝|ψs *|-|ψs(k)|+RsisxTsWherein ψs *Representing the expected value, R, of the stator flux linkage vectorsRepresents a stator resistance; i.e. isxA component of the stator current vector on the x-axis; gamma rayT＝2KVdcTs/3 wherein VdcRepresents a dc-side bus voltage; gamma rayψ＝2VdcTs/3。
4) And outputting the three-phase switching signals corresponding to the minimum three-phase discrete switching duty ratio group in the evaluation result to the three-phase inverter.
After the step 2) is finished, in order to avoid unnecessary calculation burden, a newly-built three-phase discrete switch duty ratio group which is not provided with the optimized control performance capability in a control set can be removed in advance by utilizing a dead beat technology, the number of the three-phase discrete switch duty ratio groups to be evaluated is reduced to 4, and then the step 3 is carried out).
The number of the three-phase discrete switch duty ratio groups to be evaluated is reduced to 4, the electromagnetic torque and the stator magnetic linkage expected values in the step 1) of the prediction model are replaced by the electromagnetic torque and the stator magnetic linkage expected valuesThe predicted values of the chains are respectively solved to obtain dAIs zero, dBIs zero and dCThree groups of three-phase switch duty cycles d at zeroA、dBAnd dCWherein the three-phase switching duty cycle dA、dBAnd dCThe group of three-phase switching duty ratios with the values of more than or equal to zero are reference three-phase switching duty ratios meeting the dead beat principle; comparing each three-phase discrete switch duty cycle group in the new three-phase discrete switch duty cycle group control set in the step 1) with a reference three-phase switch duty cycle, taking 4 three-phase discrete switch duty cycle groups closest to the reference three-phase switch duty cycle as groups to be evaluated, and entering the step 3) for evaluation.
The invention brings the three-phase discrete switch duty ratio groups into the control set through the steps 1) to 4), establishes a novel three-phase discrete switch duty ratio group control set, takes the square of the error of the electromagnetic torque and the stator flux linkage at the end of each control period as an evaluation index, constructs an evaluation function, evaluates the errors of the electromagnetic torque and the stator flux linkage at the end of each control period when different three-phase discrete switch duty ratio groups are selected, finally rejects the three-phase discrete switch duty ratio groups without the capability of optimizing the control performance in advance by using an error shooting technology, reduces the number of the three-phase discrete switch duty ratio groups to be evaluated to 4, and avoids unnecessary calculation burden. According to the method, on the basis of ensuring that the permanent magnet synchronous motor system has good dynamic performance, the torque fluctuation and the stator flux linkage fluctuation are reduced, meanwhile, the calculation complexity of the prediction control method is greatly reduced, and various requirements in practical application are met.
The method of the present invention is further described below with reference to fig. 2 to 6, and the specific calculation formulas:
firstly, establishing a mathematical model of a permanent magnet synchronous motor:
in fig. 2, since the switching states of the upper and lower arm IGBTs are complementary, S is usedA、SBAnd SCThe switching patterns of the upper and lower arm IGBTs of the three phases (A, B and C) of the two-level voltage source inverter are shown, respectively. "Sx＝1”The upper bridge arm IGBT is in an on state, the lower bridge arm IGBT is in an off state, and SxThe term "0" denotes that the upper arm IGBT is in an off state and the lower arm IGBT is in an on state, where x is a, B, and C.
The 2L-VSI has 8 switch groups in total, the phase voltages corresponding to the 8 switch groups are converted into a space vector form, and 8 basic voltage vectors can be obtained, namely 6 effective voltage vectors with fixed amplitude values and space phase angles and 2 zero vectors: v1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101) And V0(000)、V7(111) As shown in fig. 3.
By a voltage vector V1For example, 100 indicates that the upper arm of the phase a is on, the lower arm is off, the upper arms of the phase B and the phase C are off, the lower arm is on, and the meanings of the other 5 effective voltage space vectors are analogized, which is not described in detail in the embodiments of the present invention. Wherein the effective voltage vector V1～V6The subscripts of (a) are the voltage vector hexagons in figure 3 numbered in the counterclockwise direction.
The voltage space vector can be expressed as follows:
Figure RE-GDA0001945099850000061
in formula (1), VnRepresents the basic voltage vector, n is 0,1, …, 7; vdcThe dc-side bus voltage is shown.
In a PMSM system, a two-phase rotating coordinate system oriented with a stator flux linkage vector is established, where the stator flux linkage vector ψsThe coordinate axis in the same direction is an x axis, and the coordinate axis 90 degrees ahead of the stator flux linkage vector is a y axis. Then the stator voltage equations of PMSM on the x and y axes are respectively expressed as follows:
Figure BDA0001815702980000062
in the formula (2), Vsx、Vsy、isxAnd isyRespectively representing the components of the stator voltage vector and the stator current vector on x and y axes; rsRepresenting the stator resistance; omegasA rotation angular velocity representing a stator flux linkage vector; psisRepresenting the stator flux linkage vector.
Neglecting the effect of stator resistance, the rate of change of electromagnetic torque can be expressed as follows:
Figure BDA0001815702980000063
in the formula (3), ω isrRepresenting a rotor flux linkage vector rotation angular velocity; psifRepresents a permanent magnet flux linkage; l isdAnd LqRespectively representing d-axis and q-axis stator inductances; n ispRepresenting the number of pole pairs of the PMSM; delta denotes the load angle, i.e. the stator flux linkage vector angle thetasAngle theta with rotor flux linkage vectorrThe difference between them.
K and ω in the formula (3) considering that the control period is sufficiently shortr|ψs(k) L may be regarded as a constant within one control period. Therefore, the stator flux linkage amplitude and the electromagnetic torque are at (k +1) TsThe predicted value of the time can be expressed as follows according to the formula:
|ψs(k+1)|＝|ψs(k)|+(Vsx-Rsisx)Ts (4)
Te(k+1)＝Te(k)-Kωr|ψs(k)|Ts+KVsyTs (5)
in the formulae (4) and (5), | ψs(k +1) | and Te(k +1) represents the stator flux linkage amplitude and the electromagnetic torque at (k +1) T respectivelysA predicted value of the time; phis(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsAn observed value of a time; t issIndicating a control period.
Establishing a prediction model taking the duty ratio of the three-phase switch as a control variable in the permanent magnet synchronous motor system:
the voltage vector is taken as the control different from the traditional predicted torque controlMaking variable quantity, the invention directly combines dA、dBAnd dC(dA、dBAnd dCRespectively representing S in each control periodA、SBAnd SCThe time of 1, which is a proportion of the entire control period, i.e., the three-phase switching duty ratio, as shown in fig. 4) is included as a control variable in the control set. As can be seen from fig. 4, the resultant stator voltage vector VsIn the process of (2), one-phase switching signal is always 0. The voltage vector plane is therefore divided into 3 sectors (S ═ 1,2,3) according to the law in the switching sequence diagram in fig. 4, the division result being shown in fig. 3. V1、V3And V5Located at the boundary of three sectors, and three coordinate axes A, B and C are sequentially established along the directions of the three voltage vectors, so that three vectors e in the formula (1)j0、 ej2 π/3、ej4π/3Located on three coordinate axes in sequence.
As shown in fig. 3, the voltage vector V falling in sector 1sCan be seen as the vector e falling on the coordinate axes A and Bj0And ej2 π/3By synthesis, the same vector falling in sector 2 or sector 3 can be represented by ej0And ej4π/3Or ej2π/3And ej4π/3And (4) synthesizing. Thus V in 3 sectorssThe synthetic expressions of (a) are collectively expressed as follows:
Figure BDA0001815702980000071
in the formula (6), the reaction mixture is,
Figure BDA0001815702980000072
and
Figure BDA0001815702980000073
respectively corresponding to basic voltage vectors V1、V3And V5. At application of vector V1When only the A-phase switching state is 1 and the other two-phase switching state is 0, V is similarly applied3And V5Only the B phase and the C phase are switched to the state of 1, so that V1、V3、V5The action time of (d) is the same as the time when the switching state of the A phase, the B phase, and the C phase is 1, in other words, the vector e in the formula (6)j0、ej2π/3And ej4π/3The duty ratio of the phase D is respectively consistent with the duty ratios of the phase A, the phase B and the phase C, and d can be respectively usedA、dBAnd dCAnd (4) showing. When V issRespectively corresponding to d in sectors 1,2 and 3C、dB、dAIs always 0.
As can be seen by comparing formula (1) with formula (6), formula (1) is a special case of formula (6), i.e. when d isA、dBAnd dCWhen the value of (1) is only 0 or 1, the resultant voltage vector is the basic voltage vector. When d isA、dBAnd dCWhen the value is arbitrarily selected between 0 and 1, the formula (6) represents a voltage vector of an arbitrary amplitude and angle. V in each sectorsThe components on the coordinate axes of alpha and beta can be respectively and directly represented by the three-phase switching duty ratio as follows:
Figure BDA0001815702980000074
Figure BDA0001815702980000075
when equations (7) and (8) are subjected to coordinate transformation and transformed into an x-y coordinate system, VsThe components on the x and y axes can be expressed as follows
Figure BDA0001815702980000076
Figure BDA0001815702980000077
The formula (9) and the formula (10) are respectively substituted into the formula (4) and the formula (5), and the predicted expressions of the stator flux linkage amplitude and the electromagnetic torque are respectively obtained
Figure BDA0001815702980000081
Figure BDA0001815702980000082
In summary, in the prediction model of the permanent magnet synchronous motor, the voltage vector in the prediction equation of the electromagnetic torque and the stator flux linkage can be replaced by the three-phase switching duty ratio. If the three-phase switching duty ratio is used as a control variable, compared with the traditional prediction torque control method, the processes of selecting and synthesizing the optimal voltage vector and calculating the corresponding three-phase switching duty ratio can be omitted, and therefore the complexity of the prediction method can be further reduced.
Thirdly, establishing a new three-phase discrete switch duty ratio group control set:
first, the three-phase switching duty ratios are discretized, A, B, C the switching duty ratios of each phase are equally divided into N, and the division result is shown in fig. 5, where the real points on the three coordinate axes A, B and C in the figure represent the discretized switching duty ratios of each phase. As can be seen from fig. 4, the switching duty ratio of one phase in each divided sector is constant to zero, so the switching duty ratio to be calculated in each sector is only two phases. Accordingly, the present invention combines three-phase discrete switching duty cycles (as shown in fig. 5, the intersection point of each dotted line in the figure represents a group of any discrete switching duty cycle, and essentially, each three-phase switching duty cycle group corresponds to one discrete virtual voltage vector) and establishes a control set as shown in the following formula:
Figure BDA0001815702980000083
in (13), S denotes a sector number, and S is 1,2, or 3; lxAnd lyReference symbols, l, representing the duty cycle of the discrete switches of each phase, respectivelyx＝0，1,2,…,N， l y0,1,2, …, N; when S is 1, x is A, y is B, and Z is C; when the S is equal to 2, the S is not more than 2,x is A, y is C, and Z is B; when S is 3, x is B, y is C, and Z is A.
And establishing a quantization result table of the three-phase discrete switch duty ratio group according to different values of N. Corresponds to dA、dBAnd dCIn the case of 0, 3N × (N +1) two-dimensional tables need to be established, and the number of three-phase discrete switching duty cycle groups obtained by integrating the three tables is N × (N +1) × 3+ 1. However, since the switching duty ratios of each phase are equally divided into N, and the quantization results of the switching duty ratios of each phase are the same (as shown by the solid dots on the three coordinate axes A, B and C in fig. 5), the discrete quantization results of the three-phase discrete switching duty ratio set can be simplified into a one-dimensional table with N +1 elements, which is expressed in a one-dimensional array manner as: dxyz＝[0,1/N,2/N,…,1]And the numerical value corresponding to the duty ratio of each phase of switch is sequentially called from the array every time, so that the occupation of the storage space of the digital controller by the numerical value is reduced. In addition, the discrete three-phase switch duty ratio groups generated by the present invention are uniformly distributed within and on the boundaries of the voltage vector hexagons (as shown in fig. 5), thereby making full use of the voltage vector hexagons.
Fourthly, constructing an evaluation function:
in the traditional predictive torque control method, control variables in control concentration are stator voltage vectors, and the action effects of different voltage vectors on control targets such as electromagnetic torque, stator flux linkage and the like are evaluated through an evaluation function, so that the optimal voltage vector is selected. And finally, calculating the duty ratio of the three-phase signal according to the selected voltage vector and finally outputting a three-phase switching signal. The optimal voltage vector can be obtained by evaluating the following evaluation functions:
Figure BDA0001815702980000091
in the formula (d)A、dB、dCA, B, C three-phase switch duty cycles respectively; lambda represents a weight factor for specifying the importance of the stator flux linkage term in the evaluation function; e.g. of the typeT0＝Te *-Te(k)+Kωr|ψs(k)|T；eψ0＝|ψs *|-|ψs(k)|+RsisxTs；γT＝2KVdcTs/3； γψ＝2VdcTs/3。
Fifthly, calculating a reference three-phase switching duty ratio meeting the dead beat principle:
when the number N of the discretized three-phase switch duty ratios is large, if all the discretized switch duty ratio groups are evaluated in an exhaustion mode, a large number of discretized switch duty ratio groups without optimized control performance can cause more redundant calculation amount. In order to further reduce the calculation amount, the invention adopts a dead beat technology to further reduce the number of the alternative discrete switch duty cycle groups.
According to the principle of dead beat control of electromagnetic torque and stator flux linkage amplitude, respectively using Te *And | ψs *I replaces T in the formulas (11) and (12)e(k +1) and | ψsAfter (k +1) | is completed, the three-phase switch duty ratio reference value (d) meeting the dead-beat control principle is solved by simultaneous two formulasA ref, dB ref,dC ref). Because the duty ratio of one phase of switch is constantly 0 in each sector, only the duty ratio of the other two phases of switches needs to be calculated, so that the method searches d meeting the dead beat principle in three sectors in sequenceA ref、dB ref、dC ref. In each sector there is a set of expressions for calculating the three-phase switching duty cycle reference, as shown in table 1. When any one-phase switching duty ratio reference value calculated in one sector is smaller than 0, it is described that the resultant vector corresponding to the three-phase switching duty ratio reference value is not in the sector (as shown in an example in the sector 1 in fig. 3), and it is necessary to find the three-phase switching duty ratio reference value in another sector.
TABLE 1
Figure BDA0001815702980000092
Sixthly, the implementation of the permanent magnet synchronous motor system switching duty ratio prediction torque control method:
a control block diagram of the three-phase switching duty ratio predicted torque control method is shown in fig. 6.
And calculating the three-phase reference switch duty ratio meeting the dead-beat principle at the next moment according to the three-phase stator current, the electromagnetic torque and the stator flux linkage which are measured and estimated at the current moment and the table 1, and taking 4 groups of three-phase discrete switch duty ratio groups closest to the three-phase reference switch duty ratio as alternative groups after obtaining the three-phase reference switch duty ratio meeting the dead-beat principle of the electromagnetic torque and the stator flux linkage. Taking sector 1 as an example, in fig. 5, 'o' indicates a reference value (d) of the three-phase switching duty ratioA ref,dB ref,dc ref) The 4 groups of three-phase discrete switching duty cycle groups closest thereto are then selected as the alternative groups, denoted by 'Δ'. And finally, evaluating the 4 alternative groups by utilizing an evaluation function and selecting an optimal three-phase discrete switch duty ratio group from the 4 alternative groups.
Equation (14) uses the electromagnetic torque and the stator flux linkage error at the end of each control cycle as evaluation criteria, and the order of the action of the different voltage vectors has no effect on the result at the end of the control cycle. Therefore, after the optimal three-phase switching duty ratio is selected, the switching sequence shown in fig. 5 can be directly generated according to the volt-second balance principle without a voltage synthesis process and output to the inverter.
The specific implementation flow of the switching duty ratio predicted torque control method is shown in fig. 6. .
In conclusion, the motor can run more stably through the steps; meanwhile, the current distortion rate of the motor stator can be reduced, and the motor loss caused by current harmonics in the motor running process is reduced; the complexity of the control method is reduced, so that the time required by the program of the numerical control execution method is reduced; finally, the discrete quantization result of the three-phase discrete switch duty ratio group can be simplified into a one-dimensional table with N +1 elements, so that the occupation of the storage space of the digital controller is reduced, and various requirements in practical application are met.
The feasibility of the method of the present invention is verified below with reference to the specific experimental data and fig. 7 to 11.
In order to verify the feasibility and the effectiveness of the switching duty ratio prediction torque control method, experimental verification is carried out in a 6.0kW permanent magnet synchronous motor system. The motor parameters are shown in table 2. In the experimental test platform, a Digital Signal Processor (DSP) TMS320F28335 performed the implementation of the method and the load was provided by an induction motor, which was controlled by S120 manufactured by siemens. Using standard deviation sigma of electromagnetic torque and stator flux linkage respectivelyTAnd σψThe respective fluctuation amounts were evaluated. The calculation formula is uniformly expressed as follows:
Figure BDA0001815702980000101
in equation (15), n represents the number of sampling points, and n is 4 × 5 in the present invention6+1；
Figure BDA0001815702980000102
T or ψ.
TABLE 2
Figure BDA0001815702980000103
First, transient performance verification
Fig. 7 shows transient performance experimental waveforms of the limited control set predicted torque control method and the proposed switching duty ratio predicted torque control method, where the limited control set predicted torque control method means the limited control set predicted torque control method and the switching duty ratio predicted torque control means the switching duty ratio predicted torque control method. In the experiment, the PI parameter settings of the speed loops were the same for both methods. In the transient experiment process, the initial rotating speed of the motor is 100r/min, the load is 50Nm, then the given rotating speed of the motor is suddenly changed to 200r/min, and finally the load of the motor is suddenly changed to 100 Nm. Wherein, fig. 7a is a transient waveform of the limited control set predicted torque control method and the switching duty ratio predicted torque control when the rotation speed is suddenly changed from 100r/min to 200r/min when the load torque is 50Nm, and fig. 7b is a transient waveform of the limited control set predicted torque control method and the switching duty ratio predicted torque control when the load torque is suddenly changed from 50Nm to 100Nm when the rotation speed is 200 Nm. Fig. 7 demonstrates that the proposed switching duty cycle predicted torque control method has the same transient response performance as the limited control set predicted torque control method.
Second, comparison with the Steady State Performance of the conventional predicted Torque control method
Experiments compare the steady state performance of the switching duty cycle predicted torque control method with the classical finite control set predicted torque control method and the extended control set predicted torque control method based on the discrete SVPWM technique. Wherein, N is 15 in the switching duty ratio prediction torque control method. For the control method of the extended control set prediction torque, according to the discrete SVPWM principle, the voltage vector plane is equally divided into N according to the amplitudemIs divided into N equal parts according to phase angleaIf all the synthesized virtual voltage vectors and the total number of the basic voltage vectors are Nm×Na+1 (with zero vector V)0And V7As the same vector). In order to make the number of the generated virtual voltage vectors the same as the number of the three-phase discrete switching duty ratio groups, N in the torque control method is predicted by the expanded control setmIs set to 15, NaIs set to 48.
In the steady state experiment, the operation condition of the motor is as follows: the rotational speed is 250r/min and the load torque is 150 Nm. Average switching frequency (f) for 3 methodsav) On the same level, the classic single vector finite control set predicts the control period (T) of the torque control methods) Is 50 mus, fav3.58 kHz; extended control set predicted torque control method TsIs 200 mus, fav3.31 kHz; t of the proposed switching duty cycle predicted torque control methodsIs 200 mus, fav＝3.21kHz。
FIG. 8 shows steady-state waveforms of electromagnetic torque, stator flux linkage, and a-phase stator current corresponding to the 3 methods, and FIGS. 8a and 8b8b and 8c are steady-state waveforms of a classical finite control set predicted torque control method, an extended control set predicted torque control method and a switching duty ratio predicted torque control method, respectively; torque fluctuation σ of 3 methodsTStator flux linkage fluctuation sigmaψStator current total harmonic distortion iTHDAnd average switching frequency favThe statistics are in fig. 8 d. Comparing the steady state waveforms of the 3 methods and the experimental results, it can be seen that the steady state performance of the remaining 2 improved methods is significantly improved compared to the classical finite control set prediction torque control method. The extended control set predicted torque control method is equivalent to the switching duty ratio predicted torque control method in steady state performance.
Third, different methods perform time comparison
The execution times of the above 3 methods are given below. The method for controlling the predicted torque of the extended control set is simplified by adopting a dead-beat technology. In the experiment, the working frequency of the MCU is 150MHz, and the statistical time does not include the execution time of an AD sampling program, a speed measuring program and a flux linkage observer program. It can be concluded that the switching duty ratio predicted torque control method has the shortest execution time, 1.904 mus less than the classical finite control set predicted torque control method, and the extended control set predicted torque control method has the longest execution time (52.688 mus), which is much higher than the switching duty ratio predicted torque control method. The comparison result shows that the execution time of the method is greatly reduced on the basis of ensuring good transient and steady-state control performance, and the method is efficient.
Fourthly, N, TsAnd Ld(Lq) Effect on control Performance of a switching Duty ratio predicted Torque control method
FIGS. 9-11 show the number of discrete switch duty cycles N and the control period TsAnd a stator inductance Ld(Lq) And (3) predicting the influence of the torque and the stator flux linkage control performance of the torque control method on the switching duty ratio. In the experiment, the rotating speed of the motor is 250 r/min; the load torques were 150 Nm. Fig. 9 shows the effect of different values of N on torque and stator flux linkage control performance, where N is 5 and N is 5 in fig. 9a to 9cElectromagnetic torque, stator flux linkage, steady state waveform of a-phase stator current of the motor at 10 and N-20, and statistical results of the experiment in fig. 9 d. From 9d, it can be seen that the control performance of the motor is better and better as N increases, but the experimental result comparing fig. 9 and fig. 8c shows that the control performance of the motor when N is 20 is not significantly improved compared with that when N is 15. Therefore, the value of N does not need to be too large, and the overlarge value of N can not generate obvious improvement effect on the control performance of the motor.
FIG. 10 shows the difference TsThe effect on motor control performance and the experimental results are summarized in fig. 10 c. As can be seen by comparing the results in FIG. 10c, with TsThe average switching frequency of the inverter is increased, so that the electromagnetic torque, the stator flux ripple and the ITHDWill gradually decrease, which means that the electromagnetic torque fluctuation of the system output will gradually decrease and the harmonic distortion degree of the current will gradually decrease. Compared with a classical finite control set prediction torque control method, the complexity of the method is low, the execution time of the method is short, so that the control period of the method can be further reduced to be low enough according to the improvement of performance requirements, and the switching frequency of an inverter is improved to improve the control performance of the PMSM system.
FIG. 11 shows Ld(Lq) The effect of the change on the performance of the motor, and Ld(Lq) The results of the experiment after the change are statistically shown in FIG. 11 c. L in FIG. 11adAnd LqAt the dotted line, L in FIG. 11b, becomes 0.8 times the original value at the same timedAnd LqAt the dotted line it also becomes 1.2 times the original. By L in FIG. 11d(Lq) The steady state test waveform before and after the change and the test result in FIG. 11c show that at LdAnd LqAfter the motor is changed to be 0.8 times or 1.2 times of the original motor, the control performance of the motor is not greatly changed, which shows that the method has certain parameter disturbance resistance.
The invention has no limitation to the types of other devices except for the specific description of the types of the devices, as long as the devices can complete the functions.
Those skilled in the art will appreciate that the drawings are only schematic representations, and the numbers of the above-mentioned embodiments of the present invention are only for the purpose of description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A switching duty ratio predicted torque control method is characterized by comprising the following steps:
1) establishing a prediction model in the permanent magnet synchronous motor system by taking the three-phase switching duty ratio as a control variable according to the relation between the three-phase switching duty ratio of an inverter in the permanent magnet synchronous motor system and electromagnetic torque and stator flux linkage; the prediction model is as follows:
Figure FDA0003434878320000011
Figure FDA0003434878320000012
in the formula, | ψs(k +1) | and Te(k +1) represents the stator flux linkage amplitude and the electromagnetic torque at (k +1) T respectivelysA predicted value of the time; phis(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsAn observed value of a time; rsRepresenting the stator resistance; i.e. isxA component of the stator current vector on the x-axis; vdcRepresents a dc-side bus voltage; omegarRepresenting a rotor flux linkage vector rotation angular velocity; psifRepresents a permanent magnet flux linkage; t issRepresents a control period;
Figure FDA0003434878320000013
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npExpressing the pole pair number of the permanent magnet synchronous motor, and delta expressing the load angle, namely the stator flux linkage vector angle thetasAngle theta with rotor flux linkage vectorrThe difference between them; dA、dBAnd dCRepresenting the three-phase switching duty cycle;
2) the method comprises the steps that a discrete three-phase switch duty ratio group is brought into a control set, and a new three-phase discrete switch duty ratio group control set is established;
3) the method comprises the steps of taking the square of the error of the electromagnetic torque and the stator flux linkage at the end of each control period as an evaluation index, constructing an evaluation function, and evaluating the error of the electromagnetic torque and the stator flux linkage at the end of each control period, wherein the electromagnetic torque and the error correspond to different three-phase discrete switch duty ratio groups in a newly-built three-phase discrete switch duty ratio group control set;
4) and outputting the three-phase switching signals corresponding to the minimum three-phase discrete switching duty ratio group in the evaluation result to the three-phase inverter.
2. The switching duty cycle predictive torque control method of claim 1 wherein the new three-phase discrete switching duty cycle group control set of step 2) is as follows:
Figure FDA0003434878320000014
wherein S denotes a sector number, and S is 1,2, or 3; lxAnd lyReference symbols, l, representing the duty cycle of the discrete switches of each phase, respectivelyx＝0，1,2,…,N，ly＝0,1,2,…,N；dxRepresenting the x-phase switching duty cycle, dyRepresenting the switching duty of the y phase, dzRepresents the z-phase switching duty cycle; when S is 1, x is A, y is B, and Z is C; when S is 2, x is A, y is C, and Z is B; when S is 3, x is B, y is C, and Z is A.
3. The switching duty ratio predicted torque control method according to claim 1, wherein the evaluation function of step 3) is:
Figure FDA0003434878320000015
in the formula (d)A、dB、dCA, B, C three-phase switch duty cycles respectively; lambda represents a weight factor for specifying the importance of the stator flux linkage term in the evaluation function; e.g. of the typeT0＝Te *-Te(k)+Kωr|ψs(k)|TsWherein, Te *Indicating the desired value, | ψ, of the electromagnetic torques(k) I and Te(k) Respectively representing the amplitude of stator flux linkage and the electromagnetic torque at kTsObserved value of time, ωrRepresenting the rotor flux linkage vector rotation angular velocity, TsIt is indicated that the control period is,
Figure FDA0003434878320000021
wherein L isdAnd LqRespectively representing d and q axis stator inductances, npExpressing the pole pair number of the permanent magnet synchronous motor, and delta expressing the load angle, namely the stator flux linkage vector angle thetasAngle theta with rotor flux linkage vectorrThe difference between them; e.g. of the typeψ0＝|ψs *|-|ψs(k)|+RsisxTsWherein ψs *Representing the expected value, R, of the stator flux linkage vectorsRepresenting the stator resistance; i.e. isxA component of the stator current vector on the x-axis; gamma rayT＝2KVdcTs/3 wherein VdcRepresents a dc-side bus voltage; gamma rayψ＝2VdcTs/3。
4. The method for controlling the torque through the prediction of the switching duty ratio according to claim 1, wherein after the step 2) is completed, a newly-built three-phase discrete switching duty ratio group control set without the capability of optimizing the control performance is removed in advance by using a dead-beat technology, the number of the three-phase discrete switching duty ratio groups to be evaluated is reduced to 4, and then the step 3 is performed).
5. The method for controlling the torque according to claim 4, wherein the step of reducing the number of the three-phase discrete switch duty cycle groups to be evaluated to 4 is to replace the predicted values of the electromagnetic torque and the stator flux linkage in the prediction model in the step 1) with the expected values of the electromagnetic torque and the stator flux linkage, and respectively solve the dAIs zero, dBIs zero and dCThree groups of three-phase switch duty cycles d at zeroA、dBAnd dCWherein the three-phase switching duty cycle dA、dBAnd dCThe group of three-phase switching duty ratios with the values of more than or equal to zero are reference three-phase switching duty ratios meeting the dead beat principle; comparing each three-phase discrete switch duty cycle group in the new three-phase discrete switch duty cycle group control set in the step 2) with a reference three-phase switch duty cycle, taking 4 three-phase discrete switch duty cycle groups closest to the reference three-phase switch duty cycle as groups to be evaluated, and entering the step 3) for evaluation.
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