CN110445438B

CN110445438B - Permanent magnet synchronous motor prediction flux linkage control method based on extended control set

Info

Publication number: CN110445438B
Application number: CN201910579131.2A
Authority: CN
Inventors: 宋战锋; 王亚琦
Original assignee: Tianjin University
Current assignee: Firefly technology development (Tianjin) Co.,Ltd.
Priority date: 2019-06-28
Filing date: 2019-06-28
Publication date: 2020-11-10
Anticipated expiration: 2039-06-28
Also published as: CN110445438A

Abstract

The invention discloses a permanent magnet synchronous motor prediction flux linkage control method based on an extended control set, which comprises the following steps: carrying out mathematical modeling on the permanent magnet synchronous motor; aiming at a stator voltage vector in a mathematical model, acquiring a virtual voltage vector of which an end point is positioned on the boundary of a space voltage vector hexagonal plane, and forming an expansion control set together with a basic voltage vector; acquiring a prediction flux linkage control model based on an extended control set, adopting a stator flux linkage vector as a control variable, and constructing a cost function according to the influence of different control sets on a stator flux linkage track in a sampling period, wherein the cost function quantifies the average value of a reference track and an actual track error of the stator flux linkage in the sampling period, which are calculated by an integral method; determining an optimal sector through optimal solution of a cost function, searching an optimal extension voltage vector in the optimal sector, and performing amplitude optimization on the optimal extension voltage vector.

Description

Permanent magnet synchronous motor prediction flux linkage control method based on extended control set

Technical Field

The invention relates to the field of motor systems and control, in particular to a permanent magnet synchronous motor prediction flux linkage control method based on an extended control set.

Background

Permanent Magnet Synchronous Motors (PMSM) have the characteristics of high power density, high energy efficiency, compact structure, high torque-to-current ratio and the like, and have attracted extensive attention in motion control systems. In the past decades, its control algorithms have been extensively studied. Model predictive control strategies are not reduced from the first application of model predictive control strategies in the fields of power electronics and motor driving for more than twenty years ago to the present day. Due to its obvious advantages of simple implementation, fast dynamic response, and high flexibility of combining multiple control targets with various constraints, model predictive control, particularly its finite set of predictive control branches, has proven to be a fairly effective control scheme and is considered to be the most promising alternative to mainstream magnetic field-oriented control strategies^[1]。

When a finite set model predictive control strategy is employed to implement torque control of a permanent magnet synchronous machine, it is commonly referred to as a finite set predictive torque control strategy. When applying this type of controller, a cost function related to the torque error and flux linkage error is first constructed, and then the optimum voltage vector that minimizes the cost function is selected as the output^[2]. Obviously, this direct binding is controlledThe online optimization algorithm of the object can conveniently solve the related problems such as current limitation^[3]。

Despite its outstanding advantages, the limited set of predicted torque control strategies have some problems, the most important of which is that steady state torque fluctuations will inevitably be caused. The reason is that the limited set predictive torque control strategy typically employs a constant sampling period, the algorithm employs a single switching state throughout the sampling period, and the inverter can only change its switching state at the sampling instant. In addition, the control set of the method consists of only six basic non-zero vectors and two zero voltage vectors, both of which are fixed values in magnitude and phase angle. These limitations lead to a reduced freedom of control of torque and flux linkage, which ultimately leads to significant torque ripple^[4]. This phenomenon becomes more and more severe as the sampling period increases.

A typical strategy to solve this problem is to adjust the magnitude of the basic voltage vector by inserting a zero voltage vector. Based on the cost function minimization, the best voltage vector is selected from the six basis vectors and is acted on in the algorithm together with the zero voltage vector. This is achieved by introducing an additional duty cycle analysis^[5]. This strategy may cause the inverter to change its switching state at any time of the sampling period, not just at the sampling time. Thus, torque ripple may be relatively reduced compared to conventional limited set predicted torque control strategies.

In addition, in order to further inhibit the torque fluctuation, related researchers have proposed a limited set of predicted torque control strategies of multiple voltage vectors, which can flexibly adjust the phase angle and amplitude of an action vector and also obviously improve the torque fluctuation. To further adjust the phase angle and magnitude of the voltage vector, a continuum prediction control strategy may be employed^[6]. By embedding a modulation module, the reference voltage can be obtained more accurately, thereby accurately controlling the torque and flux linkage. However, such controllers typically require an offline solution to the optimization problem.

Unlike the control strategy described above, the finite control set can also be improved by adding more virtual vectorsTorque control performance, referred to as an Extended Control Set (ECS) control strategy. By adopting a cascade optimization process, the optimal vector is selected from the extended control set through sector identification, vector action evaluation and amplitude optimization^[7]. Due to the fact that the extended control set strategy is used, the degree of freedom of control is improved, and more importantly, the duty ratio signal can be directly determined in the prediction process without an additional modulation process. However, in order to achieve simultaneous adjustment of torque and flux linkage, in the case of different torque and flux linkage dimensions, a weight coefficient in the cost function needs to be carefully designed, and the selection of the weight coefficient needs a large amount of experimental data as support. In addition, due to the change of the rotor speed and the load torque, the fixed weight coefficient determined under the offline condition is difficult to be applicable under different working conditions. In particular, a step change in speed or a change in load torque may cause sector misjudgment, which in turn may cause large torque fluctuations.

Therefore, in order to improve the control performance of the controller, make the tracking effect of the flux linkage more accurate, further reduce torque fluctuation, and obtain a control system with faster dynamic response and more stable, it is necessary to improve the traditional model prediction torque control strategy.

Reference to the literature

[1]Xia C,Wang S,Wang Z,et al.Direct Torque Control for VSI–PMSMs Using Four-Dimensional Switching-Table[J].IEEE Transactions on Power Electronics,2016,31(8):5774-5785.

[2]J.Holtz and S.Stadtfeld,“A predictive controller for the stator current vector of AC-machines fed from a switched voltage source,”in Proc.Int.Power Electron.Conf.,vol.2,Tokyo,Japan,Mar.1983:1665–1675.

[3]Fuentes E J,Silva,César,Quevedo D E,et al.Predictive speed control of a synchronous permanent magnet motor[C].IEEE International Conference on Industrial Technology.IEEE,2009.

[4]Zhou Z,Xia C,Yan Y,et al.Torque Ripple Minimization of Predictive Torque Control for PMSM with Extended Control Set[J].IEEE Transactions on Industrial Electronics,2017,64(9):6930-6939.

[5]Davari S A,Khaburi D A,Kennel R.An Improved FCS–MPC Algorithm for an Induction Motor With an Imposed Optimized Weighting Factor[J].IEEE Transactions on Power Electronics,2012,27(3):0-1551.

[6]Morel F,Lin-Shi X,Retif J M,et al.A Comparative Study of Predictive Current Control Schemes for a Permanent-Magnet Synchronous Machine Drive[J].IEEE Transactions on Industrial Electronics,2009,56(7):2715-2728.

[7]Zhou Z,Xia C,Yan Y,et al.Torque Ripple Minimization of Predictive Torque Control for PMSM with Extended Control Set[J].IEEE Transactions on Industrial Electronics,2017，64(9):6930-6939.

Disclosure of Invention

The invention provides a permanent magnet synchronous motor prediction flux linkage control method based on an extended control set, which adopts a stator flux linkage vector as a control variable, considers the influence of different control sets in the whole sampling interval on flux linkage tracks in the construction process of a cost function, calculates average flux linkage fluctuation by an integral method, and directly obtains a duty ratio signal through the cascade synthesis process of an optimal stator voltage vector, which is described in detail as follows:

a permanent magnet synchronous motor prediction flux linkage control method based on an extended control set, the method comprising:

carrying out mathematical modeling on the permanent magnet synchronous motor;

aiming at a stator voltage vector in a mathematical model, acquiring a virtual voltage vector of which an end point is positioned on the boundary of a space voltage vector hexagonal plane, and forming an expansion control set together with a basic voltage vector;

acquiring a prediction flux linkage control model based on an extended control set, adopting a stator flux linkage vector as a control variable, and constructing a cost function according to the influence of different control sets on a stator flux linkage track in a sampling period, wherein the cost function quantifies the average value of a reference track and an actual track error of the stator flux linkage in the sampling period, which are calculated by an integral method;

determining an optimal sector through optimal solution of a cost function, searching an optimal extension voltage vector in the optimal sector, and performing amplitude optimization on the optimal extension voltage vector.

The prediction of the actual trajectory of the stator flux linkage is specifically as follows:

when t is more than or equal to 0 and less than or equal to tau₇When the temperature of the water is higher than the set temperature,

ψ_sα＝ψ_sα(k+1)+k_7αt

when tau is₇<t≤τ₇+τ_yWhen the temperature of the water is higher than the set temperature,

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yα(t-τ₇)

when tau is₇+τ_y<t≤τ₇+τ_y+τ_xWhen the temperature of the water is higher than the set temperature,

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xα(t-τ₇-τ_y)

when tau is₇+τ_y+τ_x<t≤T_SWhen the temperature of the water is higher than the set temperature,

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xατ_x+k_0α(t-τ₇-τ_y-τ_x)

wherein psi_sαA stator flux linkage component that is the alpha axis; k is a radical of_7α、k_yα、k_xα、k_0αRespectively at a voltage vector V₇，V_y，V_xAnd V₀Under the action of psi_sαA derivative of (a); tau is₇、τ_y、τ_xAre respectively a voltage vector V₇，V_yAnd V_xWorking time in one sampling period, x, y ∈ [1,2,3,4,5,6 ]]。

The method further comprises the following steps: a three-phase duty cycle is given that produces an extended voltage vector.

The technical scheme provided by the invention has the beneficial effects that:

1. the stator flux linkage vector is used as a control variable, so that sector misjudgment and a weight coefficient setting process can be avoided, and good torque and flux linkage control performance can be obtained under different working conditions;

2. different from the traditional control method, the method minimizes the instantaneous error at the end of the sampling period, considers the influence of different control sets in the whole sampling period on the stator flux linkage track in the construction process of the cost function, and calculates the average stator flux linkage fluctuation amount in each sampling period by using an integral method, so that the steady state fluctuation of the torque and the stator flux linkage can be further inhibited;

3. according to the invention, the three-phase duty ratio signal can be directly obtained through the cascade synthesis process of the optimal stator voltage vector, and the space vector pulse width modulation process is not needed;

4. the invention establishes the predictive controller based on the extended control set ECS, and compared with the traditional predictive controller, the control freedom degree is extended, so the control performance is obviously improved.

Drawings

FIG. 1 is a schematic diagram of an extended control set of a voltage source inverter (taking a sector I as an example);

(a) taking sector I as an example, an extended control set of a voltage source inverter; (b) extension vector V in sector I_ex,ISchematic synthesis of (a).

FIG. 2 shows an example of a sector V, denoted by V₁And V₂Synthesizing a schematic of the expanded vector;

FIG. 3 is a schematic diagram of a stator flux linkage vector trajectory that accounts for final tracking error;

FIG. 4 is a schematic diagram of a stator flux linkage vector trajectory that accounts for average tracking error;

FIG. 5 is a schematic diagram of an α -axis trajectory of a stator flux linkage vector in the time domain, taking into account an average tracking error;

FIG. 6 is a schematic diagram of the switching states and corresponding duty cycles;

fig. 7 is a structural diagram of a direct flux linkage vector control system according to the present invention.

Table 1 shows two non-zero vectors V corresponding to each sector_xAnd V_yA value of (d);

TABLE 2 Generation of the final stator Voltage vector V_sThe three-phase duty cycle of (d);

table 3 shows the specific implementation process of the algorithm of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.

Example 1

The embodiment of the invention adopts the stator flux linkage vector as the control variable, can avoid the sector misjudgment problem in the traditional extended control set model prediction torque control strategy, and also avoids the process of weight coefficient setting; in the construction process of the cost function, the influence of different control sets on flux linkage tracks in the whole sampling period is considered, and the average stator flux linkage fluctuation is calculated by an integral method, so that the steady state fluctuation of torque and stator flux linkages can be further inhibited; the duty ratio signal can be directly obtained through the cascade synthesis process of the optimal stator voltage vector, and the space vector pulse width modulation process is not needed. The embodiment of the invention is illustrated by the following parts:

101: carrying out mathematical modeling on a controlled object, namely a permanent magnet synchronous motor;

102: for a stator voltage vector in a mathematical model, subdividing a virtual voltage vector of which the end point is positioned on the boundary of a hexagonal plane of a space voltage vector, forming an Extended Control Set (ECS) together with 8 basic voltage vectors, and giving a three-phase duty ratio for generating the extended voltage vector;

103: designing a prediction flux linkage control method based on an extended control set ECS, adopting a stator flux linkage vector as a control variable, considering the influence of different control sets on a stator flux linkage track in the whole sampling period, designing a cost function, wherein the cost function quantifies the average value of the reference track and the actual track error of the stator flux linkage in one sampling period calculated by an integral method, and seeking the optimal solution of the cost function to realize the minimization of the average stator flux linkage fluctuation amount;

104: determining selection and application of an optimal stator voltage vector for predictive flux linkage control by an optimal solution search, comprising: determining an optimal sector, finding an optimal spreading voltage vector in the selected sector and performing amplitude optimization on the selected spreading voltage vector.

In summary, the embodiment of the present invention establishes the predictive flux linkage control method based on the extended control set ECS, and compared with the conventional finite control set predictive control method, the control degree of freedom is extended, and the influence of different control sets on the stator flux linkage trajectory in the whole sampling period is considered in constructing the cost function, and the integration method is used to minimize the average stator flux linkage fluctuation amount in each sampling period, thereby improving the steady-state performance of the stator flux linkage and the torque. In addition, only the stator flux linkage vector is adopted as a control variable, so that compared with the traditional torque prediction control which simultaneously uses flux linkage amplitude and torque as variables, the sector misjudgment and the weight coefficient setting process can be avoided, and good torque and flux linkage control performance can be obtained under different working conditions.

Example 2

The scheme in embodiment 1 is further described below with reference to specific calculation formulas, examples and drawings, and is described in detail in the following description:

modeling of permanent magnet synchronous motor

The method comprises the steps of establishing a mathematical model of the permanent magnet synchronous motor under a two-phase static coordinate system, performing variable representation by using vectors, and thickening vector variables, such as: the stator flux linkage vector may be expressed as psi_s＝ψ_sα+jψ_sβWherein ψ_sαFor the alpha-axis stator flux linkage vector component, psi_sβIs the beta axis stator flux linkage vector component. The stator voltage equation and flux linkage equation can be expressed as:

in the formula, R_sAnd L_sRepresenting stator resistance and inductance; v_sAnd i_sRepresenting stator voltage and current vectors; psi_sAnd psi_rRepresenting the stator flux linkage vector and the permanent magnet flux linkage vector, respectively.

The electromagnetic torque can be expressed as:

wherein p is the number of pole pairs.

ψ_rAnd psi_sAngle theta therebetween_esCan be expressed as:

in the formula, #_sAnd psi_rRepresenting stator flux linkage and permanent magnet flux linkage amplitude, respectively.

Wherein, the above equations (1) to (3) constitute a permanent magnet synchronous motor model.

Second, construction of extended control set ECS

Before introducing direct flux linkage prediction control, the concept of an extended control set is introduced. The two-level voltage source inverter can generate eight switch combinations, correspondingly can generate eight basic voltage vectors, and comprises the following components: two zero vectors and six non-zero vectors. The six non-zero vectors can be represented as:

in the formula, V_dcIs the dc bus voltage. These eight basis vectors constitute the conventional finite control set.

With these six uniformly distributed non-zero vectors as boundaries, the voltage vector space complex plane can be divided into six sectors. In each sector, a virtual voltage vector whose end points are located on the boundaries of the hexagonal region can be further subdivided. These virtual voltage vectors together with the eight base vectors constitute an extended control set. Taking sector I as an example, in the extended control set, each extended vector V_ex,IBoundary vector V passing through sector I₁And V₂To synthesize. Can be expressed as:

V_ex,I＝(1-λ_y)V₁+λ_yV₂ (5)

in the formula, λ_yIs a voltage vector V₂Takes up the whole sampling period T_SThe ratio of (a) to (b). Different spreading vectors can be generated when their values vary between 0 and 1. Generally, it needs to be at λ_yA fixed interval is set between two adjacent values of (a). As shown in figure 1 of the drawings, in which,

if using S_A、S_BAnd S_CRepresenting the three-phase switching state of the inverter, corresponding to each basic voltage vector V_iIs defined as S_i＝[S_A S_B S_C]. For example, S₀＝[0 0 0]，S₇＝[1 1 1]"1" indicates that the upper arm is on, and "0" indicates that the lower arm is on. Generating a voltage vector V_ex,IIs defined as d_ex,I＝[d_A d_B d_C]. According to the synthetic relationship in the formula (5), d_ex,ICan be expressed as:

d_ex,I＝(1-λ_y)S₁+λ_yS₂ (6)

interestingly, all six basic non-zero voltage vectors can pass through two voltage vectors V₁And V₂And combinations thereof, as shown in equation (7):

V_i＝λ₁V₁+λ₂V₂ (7)

in the formula, λ₁And λ₂Representing vectors V for resultant voltages_iCorresponding V₁And V₂The coefficient of (a). Further, each voltage vector in the voltage space may be represented by V₁And V₂And (4) synthesizing. The synthesis process is illustrated in fig. 2 by taking the spread voltage vector in sector V as an example, which simplifies the calculation of the proposed algorithm, as will be mentioned in the following.

Direct flux linkage vector prediction control method based on ECS

As previously mentioned, the tracking performance of the reference torque is determined by adjusting the torqueA sub-flux linkage vector. Angle theta between reference torque and reference stator-rotor flux linkage_es,refIt is related. According to the formula (3), θ_es,refThis can be derived from the following formula:

in the formula, T_e,refIs a reference torque; psi_s,refIs the magnitude of the reference stator flux linkage vector.

According to equation (1), the stator voltage equation can be rewritten as:

neglecting the effect of the stator resistance, equation (9) becomes:

as can be seen from the above equation, the stator voltage determines the variation of the stator flux linkage. The stator flux linkage trajectory depends on the applied voltage vector during one sampling period.

Due to the limited computation time of the microprocessor, in terms of kT_sThe duty ratio signal obtained by calculating the parameter of time sampling is (k +1) T_sThe time of day can be applied. This introduces a delay of one cycle in the control process, whereby a corresponding delay compensation should be taken into account. Thus, in the sampling period kT_sTo (k +1) T_sIn a period, the prediction process of the stator flux linkage track should look at (k +1) T_sTo (k +2) T_sA time period. It should be noted that during the sampling period kT_sTo (k +1) T_sDuring the time period, the stator flux linkage trajectory is known because the duty cycle signal applied in this cycle has been calculated in the last cycle.

In a conventional control strategy, the effect of the actual trajectory of the stator flux linkage on the reference trajectory is evaluated at each sampling instant, i.e. the control objective isThe difference between the stator flux linkage reference track and the actual track is reduced at the end of each sampling period. In other words, only the final tracking error is considered in the conventional control method, and the detailed variation trajectory of the stator flux linkage between two adjacent sampling instants is not considered, when the stator flux linkage trajectory is as shown in fig. 3. Assume that four voltage vectors V are contained within one sampling period₇，V_y，V_xAnd V₀Wherein x, y ∈ [1,2,3,4,5,6 ]]The action time of the four vectors is tau₇，τ_y，τ_xAnd τ₀. Track of reference stator flux linkage (by L (psi)_s,ref) Represented) is a standard circle. Actual stator flux linkage trajectory (by L (psi)_s) Representation) undulates up and down along the reference trajectory. Next, (k +1) T will be discussed in detail_sTo (k +2) T_sThe stator flux linkage of the time segment tracks the trajectory.

At (k +1) T_sAt time, the position of the stator flux linkage vector is referenced at point a. Then it moves along A-B-C-D-E at a speed equal to the rotor electrical angular frequency omega_ePoint E represents the end of the reference stator flux linkage vector trajectory during this sampling period. At (k +1) T_sAt the moment, the position of the actual stator flux linkage vector is at point P_fi. At voltage vector V₇Because the zero vector has no influence on the stator flux linkage vector, # is_sIs maintained at P_fiAnd (4) point. When voltage vector V_yWhen acting, psi_sMove to point Q_fiThen switching the voltage vector so that the vector V_xAnd (4) acting. At time of action τ_xAfter completion, psi_sTo a point S_fi. Due to zero vector V₀Action of phi_sAnd remains at the current position until the end of this sampling period.

In this conventional control algorithm, since psi is generated within one sampling period_sAre omitted even at the end points E and S_fiThe difference between them is not large, Q_fiMay also deviate far from the desired trajectory, resulting in large stator flux linkage fluctuations. To avoid this problem, the method is focused on the reference track L (ψ)_s,ref) With real railTrace L (psi)_s) Instead of only considering the final value error of the track, as shown in fig. 4, the actual stator flux linkage track follows P_av—Q_av—S_avThe trajectory of (2) is changed.

As can be clearly seen from fig. 4, the reference stator flux angle θ_s,refWith time t, at a rate of ω_e. At (k +1) T_sTime sum (k +2) T_sBetween moments with reference to stator flux linkage angle theta_s,refCan be expressed as:

θ_s,ref＝θ_s,ref(k+1)+ω_et (11)

＝θ_e(k)+θ_es,ref(k)+ω_eT_s+ω_et

in the formula, theta_s,refA reference angle is set for the stator flux linkage; theta_eIs the electrical angle of the rotor, and T is more than or equal to 0 and less than or equal to T_S。

The reference stator flux linkage vector may then be expressed as:

through coordinate transformation, the stator reference flux linkage vector in the two-phase stationary coordinate system can be expressed as:

ψ_sα,ref＝ψ_s,refcos(θ_s,ref) (13)

ψ_sβ,ref＝ψ_s,refsin(θ_s,ref)

in the formula, #_sα,refAnd psi_sβ,refThe alpha and beta components of the stator reference flux linkage vector, respectively.

To obtain (k +1) T_sThe actual position of the stator flux linkage at the time is obtained by discretizing equation (10):

ψ_s(k+1)＝ψ_s(k)+V_s(k)T_s (14)

according to formula (10) at (k +1) T_sTime to (k +2) T_sMoment stator flux linkage trajectory L (psi)_s) Can be predicted. For stator flux linkage tracks of alpha and beta axes respectivelyAnd (6) predicting. The derivative of the stator flux linkage in the α β coordinate system can be expressed as:

in the formula, #_sαAnd psi_sβStator flux linkage components of the α and β axes, respectively; v_sαAnd V_sβStator voltage components of the α and β axes, respectively; k is a radical of_αAnd k_βThe derivatives of the alpha and beta stator flux linkages, respectively.

The prediction process of the stator flux linkage is explained by taking an alpha-axis stator flux linkage as an example. In the time domain, #_sα,refAnd psi_sαThe trajectory of (2) is shown in fig. 5. At voltage vector V₇，V_y，V_xAnd V₀Under the action of psi_sαRespectively is k_7α，k_yα，k_xαAnd k_oα. Due to the effect of the zero vector, k_7αAnd k_oαEqual to zero. When t is 0, psi_sα,refAnd psi_sαRespectively is psi_sα,ref(k +1) and ψ_sα(k + 1). During this prediction period, it is possible to predict,

when t satisfies the condition 0 ≦ t ≦ τ₇When, psi_sαCan be expressed as:

ψ_sα＝ψ_sα(k+1)+k_7αt (16)

when t satisfies the condition τ₇<t≤τ₇+τ_yWhen, psi_sαCan be expressed as:

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yα(t-τ₇) (17)

when t satisfies the condition τ₇+τ_y<t≤τ₇+τ_y+τ_xWhen, psi_sαCan be expressed as:

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xα(t-τ₇-τ_y) (18)

when t satisfies the condition τ₇+τ_y+τ_x<t≤T_SWhen, psi_sαCan be expressed as:

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xατ_x (19)

+k_0α(t-τ₇-τ_y-τ_x)

in specific implementation, the prediction process of the stator flux linkage beta axis component is consistent with the alpha axis, and psi is obtained_sβThe specific expressions of (a) refer to expressions (16) to (19), which are not described in detail in the embodiments of the present invention.

Fourth, determination and application of optimal stator voltage vector

The tracking procedure for the stator reference flux linkage should suppress stator flux linkage fluctuations. The difference between the actual stator flux linkage and the reference stator flux linkage is defined as flux linkage ripple, using

To show that:

in embodiments of the invention, the main objective is to reduce the average stator flux linkage ripple. Averaging stator flux linkage fluctuations

Can be expressed as:

calculating the integral process of the actual stator flux linkage and the reference stator flux linkage separately, #_sα,ref、ψ_sβ,ref、ψ_sαAnd psi_sβThe integration result of (a) is represented by M (psi)_sα,ref)、M(ψ_sβ,ref)、M(ψ_sα) And M (psi)_sβ) Respectively, are shown. To quantify the average stator flux linkage fluctuation

Constructing a cost function:

J_av＝[M(ψ_sα)-M(ψ_sα,ref)]²+[M(ψ_sβ)-M(ψ_sβ,ref)]² (22)

according to formula (13), from (k +1) T_sTime to (k +2) T_sThe integral of the reference stator flux linkage at a time can be expressed as:

to minimize the cost function (equation (22)), an optimal composite stator voltage vector and the action time of each voltage vector that composites the vector within one sampling period should be determined. The process of obtaining the optimal composite stator voltage vector and corresponding duty cycle can be divided into three steps.

(1) Determining the sector in which the best resultant vector is located

It is readily understood that if a composite stator voltage vector V is used_SAfter the action, the best tracking performance can be obtained, then, the value is compared with V_SSimilar voltage vectors may yield a ratio with V_SThe deviated voltage vector has better tracking performance. In other words, the two boundary basis vectors of the sector in which the best composite vector is located act better than the other four non-zero basis vectors. Therefore, the best sector can be determined from the two best non-zero basis vectors.

The cost function is first used to determine the optimal base voltage vector. Taking the α -axis stator flux linkage component as an example, when only one fundamental voltage vector acts during the entire sampling period,. phi._sαThe trajectory of (d) can be expressed as:

ψ_sα＝ψ_sα(k+1)+k_iαt (24)

wherein T is more than or equal to 0 and less than or equal to T_S；k_iαIs a basic voltage vector V_iThe derivative of the alpha axis stator flux linkage component when active.

In the above case, from (k +1) T_sTime to (k +2)T_sThe actual stator flux linkage integral at a time is expressed as:

M(ψ_sα)＝ψ_sα(k+1)T_s+0.5k_iαT_s ² (25)

M(ψ_sβ)＝ψ_sβ(k+1)T_s+0.5k_iβT_s ²

in the formula, k_iβIs a basic voltage vector V_iThe derivative of the β -axis stator flux linkage component when active. From the above, any V_iAll can pass through V₁And V₂Are synthesized so that only k_1α、k_1β、k_2αAnd k_2βIt needs to be calculated in advance.

Sequentially substituting six basic voltage vectors into a cost function from i to 6, wherein the voltage vector with the minimum cost function is the optimal voltage vector V_opAnd the voltage vector that makes the cost function second-smallest is defined as V_sec. With V_opAnd V_secThe sector that is the boundary is the optimal sector.

(2) Determining an optimal spreading voltage vector in a selected sector

As described above, the expanded voltage vector consists of the boundary base voltage vector V_opAnd V_secAnd (4) synthesizing. Two candidate vectors V_opAnd V_secTwo non-zero vectors V as described in the third section_xAnd V_yAnd coact over a sampling period. V for each candidate vector according to the inverter switching law_xAnd V_yThe assignment of values can be determined according to table 1. When t satisfies the condition 0 ≦ t ≦ τ_yWhen, psi_sαCan be expressed as:

ψ_sα＝ψ_sα(k+1)+k_yαt (26)

in the formula, k_yαIs a basic voltage vector V_yThe derivative of the alpha axis stator flux linkage component when active.

When tau is_y≤t≤T_SWhen, psi_sαCan be expressed as

ψ_sα＝ψ_sα(k+1)+k_yατ_y+k_xα(t-τ_y) (27)

In the formula, k_xαIs a basic voltage vector V_xThe derivative of the alpha axis stator flux linkage component when active. From the formula (5):

τ_y＝λ_yT_s (28)

τ_x＝(1-λ_y)T_s

from (k +1) T according to formulae (26) to (28)_sTime to (k +2) T_sThe stator flux linkage integral at a time can be expressed as:

M(ψ_sα)＝ψ_sα(k+1)T_s+λ_y(1-0.5λ_y)k_yαT_s ²+0.5(1-λ_y)²k_xαT_s ² (29)

M(ψ_sβ)＝ψ_sβ(k+1)T_s+λ_y(1-0.5λ_y)k_yβT_s ²+0.5(1-λ_y)²k_xβT_s ²

in the formula, k_xβAnd k_yβRespectively representing basic voltage vectors V_xAnd V_yThe derivative of the β -axis stator flux linkage component is applied.

The cost function J is calculated according to the formula (29)_avThen, make the cost function J_avMinimum lambda_yAn optimal extension vector is determined. Obviously, the precision of the optimal vector is associated with λ_yIs proportional to the number of candidate vectors.

(3) Amplitude optimization of optimal extended voltage vector

The optimal extension vector has been selected in the previous step. However, in the prediction process, #_sWill be accompanied by V_xOr V_yUntil the action time is cut off. Due to V_xOr V_yExtra vector length of ψ_sThe ideal position may be exceeded. To further reduce torque and stator flux ripple, a zero vector V is introduced₇And V₀And V_xAnd V_yActing together to regulate the voltage vector V_xAnd V_yThe amplitude of (c). The proportion of the zero vector added in one sampling period is defined by₀And then the action time of the four voltage vectors can be respectively expressed as:

τ₇＝λ₀λ_yT_s (30)

τ_y＝(1-λ₀)λ_yT_s

τ_x＝(1-λ₀)(1-λ_y)T_s

τ₀＝λ₀(1-λ_y)T_s

in the formula, λ is more than or equal to 0₀≤1。

In this case, from (k +1) T_sTime to (k +2) T_sThe stator flux linkage integral at a time can be expressed as:

then, the (31) is brought into (22) to calculate the cost function J_av. Like lambda_ySelection process of λ₀The value of (c) can be selected from the arithmetic series {0, 1/8, 1/4, …, 1 }. So that the cost function J_avMinimum lambda₀For determining the action time of the zero vector. The action time τ is shown in the formula (30)₇，τ_y，τ_xAnd τ₀Can use the parameter lambda_yAnd λ₀So that A, B, C the duty cycles of the three phases can be obtained directly. Taking sector I as an example, V₇，V₂，V₁And V₀Will co-act within one sampling period as shown in fig. 6. The proportion of the working time of each voltage vector to the total sampling period is indicated, e.g. vector V₇The ratio of the action time to one sampling period is lambda₀λ_y. The resulting three-phase switching states are shown in the figure, where the switching states representing "on" are shaded. The final duty cycle of each phase is equal to the sum of the shaded area ratios, e.g. the duty cycle of phase A is equal to λ₀λ_y、(1-λ₀)λ_yAnd (1-lambda)₀)(1-λ_y) And (4) summing.

It should be noted that λ_yAnd λ₀The seek interval of (a) can be adjusted according to the accuracy requirements of the control performance. With N_VThe candidate vector number in the arithmetic progression is shown, and the precision and N of the finally obtained optimal voltage vector can be seen_VAnd (4) in proportion. However, N_VThis increase in the number of vectors can result in increased computational effort to find the optimal vector and longer algorithm run times. Thus, N_VThe choice of (c) requires a trade-off between performance requirements and computational burden. Based on determined lambda_yAnd λ₀And sector information, final three-phase duty cycle d_s＝[d_A d_B d_C]As shown in table 2. A block diagram of ECS-based predictive flux linkage control proposed by an embodiment of the present invention is shown in fig. 7. Assuming that in the first step sector III has been determined to be the optimal sector, the process of determining the final optimal composite vector is indicated in the dashed box. In order to more clearly present the algorithm proposed by the embodiment of the present invention, the whole implementation process of the algorithm is listed in table 3.

Table 1: two non-zero vectors V corresponding to each sector_xAnd V_yValue of (A)

Table 2: generating a final stator voltage vector V_sThree-phase duty cycle of

Table 3: the method is implemented by the following specific flow

In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.

Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for 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

1. A permanent magnet synchronous motor prediction flux linkage control method based on an extended control set is characterized by comprising the following steps:

carrying out mathematical modeling on the permanent magnet synchronous motor;

2. The permanent magnet synchronous motor prediction flux linkage control method based on the extended control set according to claim 1, wherein the prediction of the actual trajectory of the stator flux linkage is specifically:

ψ_sα＝ψ_sα(k+1)+k_7αt

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yα(t-τ₇)

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xα(t-τ₇-τ_y)

ψ_sα＝ψ_sα(k+1)+k_7ατ₇+k_yατ_y+k_xατ_x+k_0α(t-τ₇-τ_y-τ_x)

wherein psi_sαA stator flux linkage component that is the alpha axis; k is a radical of_7α、k_yα、k_xα、k_0αRespectively at a voltage vector V₇，V_y，V_xAnd V₀Under the action of psi_sαA derivative of (a); tau is₇、τ_y、τ_xAre respectively a voltage vector V₇，V_yAnd V_xWorking time in one sampling period, x, y ∈ [1,2,3,4,5,6 ]]，T_SIs the sampling period.

3. The extended control set-based permanent magnet synchronous motor predictive flux linkage control method according to claim 1, further comprising: a three-phase duty cycle is given that produces an extended voltage vector.