CN110647105B - Limited control set model prediction contour control method suitable for double-shaft or three-shaft feed driving system - Google Patents

Limited control set model prediction contour control method suitable for double-shaft or three-shaft feed driving system Download PDF

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CN110647105B
CN110647105B CN201910894918.8A CN201910894918A CN110647105B CN 110647105 B CN110647105 B CN 110647105B CN 201910894918 A CN201910894918 A CN 201910894918A CN 110647105 B CN110647105 B CN 110647105B
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张秀云
王志强
徐征
周海松
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Tianjin Pengcheng Duoxing Technology Co.,Ltd.
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Tianjin University of Technology and Education China Vocational Training Instructor Training Center
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    • G05—CONTROLLING; REGULATING
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    • G05B19/00—Programme-control systems
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a finite control set model prediction contour control method suitable for a double-shaft or three-shaft feed driving system, which provides a double-shaft or three-shaft feed driving system unified control framework applying finite control set model prediction control on the basis of unified modeling, interacts output information among shafts and unifies loop controllers of the shafts. Meanwhile, under the control framework, a compact stepless prediction controller is designed, and a unified value function is established by taking contour errors, motor running performance and current amplitude limit as evaluation indexes to realize multivariable collaborative optimization control. Different from the traditional contour control strategy, the finite control set model predictive control strategy can carry out predictive control on contour errors before the contour errors occur, can improve the dynamic response speed and the contour precision at the turning point of the track, and has the advantages of visual modeling, simple structure and the like.

Description

Limited control set model prediction contour control method suitable for double-shaft or three-shaft feed driving system
Technical Field
The invention relates to the technical field of profile control of a double-shaft feed driving system, in particular to a finite control set model prediction profile control method suitable for a double-shaft or multi-shaft feed driving system.
Background
The contour machining precision is an important performance index of a multi-axis motion control technology and is used for evaluating the contour precision of multi-axis contour tracking. How to control the multi-axis feeding driving system to cooperate to realize the precise contour tracking of the end actuating mechanism is one of the key topics studied in the field of motion control. In recent years, model predictive control provides a new idea for improvement of a multi-axis feed driving system due to the advantages of intuitive modeling, quick dynamic response, easy processing of multi-target control problems and the like.
The traditional control strategy mainly comprises single-axis decoupling contour control and cross coupling contour control, wherein the single-axis decoupling contour control is essentially to improve the multi-axis contour accuracy by improving the single-axis tracking accuracy, and a typical method adopts zero-phase error tracking control and friction compensation control, wherein the zero-phase error tracking control is a typical feed-forward control method based on zero-pole cancellation, but the zero-pole cancellation needs an accurate object model, so the zero-phase error tracking control is very sensitive to modeling errors and non-modeling disturbance; friction compensation control is a feed forward control method that relies on an accurate friction model, however, in practice it is difficult to achieve accurate modeling of friction. Although profile accuracy can be improved to a certain extent by reducing tracking errors of a single axis, the control strategy does not consider coordination control among multiple axes, and the performance of the profile of the system is degraded in the high-speed processing field.
Whether each axis can ensure the self processing precision and simultaneously give consideration to the coordination action among multiple axes to reduce the contour error is the original intention of cross-coupling contour control. The cross-coupling contour control is to regard the contour error as a direct control target, distribute the contour error to each axis according to a certain proportional relation and then perform compensation control, and can be regarded as a closed-loop control method of the contour error without changing each single-axis position control loop. Numerous researchers develop research on the basis of the structure, such as adopting a cross-coupling fuzzy logic controller to improve the profile performance, and designing the cross-coupling controller by combining advanced control theories such as robust control, adaptive control, sliding mode variable structure control, iterative learning control and the like to improve the robustness and the profile performance of the system; for example, the gain structure of the traditional cross-coupling control is improved in the variable gain cross-coupling control, so that the nonlinear profile control performance is better. While many researchers have made a number of improvements in this regard, it is limited to the case of cross-coupling gain determination, which is unpredictable when estimated using more accurate contour error estimation methods.
In addition, the traditional control strategy usually adopts a feedforward compensation method, aims to control the generated contour error, cannot realize advanced control before the contour error occurs, has limited degree of reducing the contour error, and has important significance for researching the precise contour tracking control of the multi-axis feed driving system because factors such as complex contour tracks with more turns, motion inertia and the like can influence the dynamic response speed of track tracking.
Disclosure of Invention
The invention aims to provide a finite control set model prediction contour control method suitable for a double-shaft or three-shaft feed driving system aiming at the technical defects of hysteresis existing in contour error reduction by existing feedforward compensation and low tracking dynamic response speed at a track turning point, breaks through the traditional cascade control structure, provides a unified control framework of the double-shaft or three-shaft feed driving system applying the finite control set model prediction control on the basis of unified modeling, interacts output information among shafts, and unifies loop controllers of the shafts. Meanwhile, under the control framework, a compact stepless prediction controller is designed, and a unified value function is established by taking contour errors, motor running performance and current amplitude limit as evaluation indexes to realize multivariable collaborative optimization control. Different from the traditional contour control strategy, the finite control set model predictive control strategy can carry out predictive control on contour errors before the contour errors occur, can improve the dynamic response speed and the contour precision at the turning point of the track, and has the advantages of visual modeling, simple structure and the like.
The technical scheme adopted for realizing the purpose of the invention is as follows:
a finite control set model predictive profile control method suitable for a double-shaft feed driving system comprises the following steps:
step 1, measuring currents and rotor position signals of two motors driving the motors to move in the directions of an x axis and a y axis, and observing x (k) through an extended Kalman filter observer; (x (k) represents d-axis current, q-axis current, mechanical angular speed of rotor, and mechanical angle of rotor for each motor at the present time
Step 2, delay compensation, namely acting the optimal voltage vector selected at the previous moment on the moment to realize the action of the optimal voltage vector at the middle moment of the control period and reduce the time delay;
step 3, establishing a double-shaft feed driving system unified model based on discrete Taylor series, and determining the position of a reference voltage vector and a sector according to an expected position by combining the double-shaft feed driving system unified model;
step 4, integrating the performance of the tracking error and the contour error, and determining each alternative voltage vector;
step 5, constructing a unified cost function of the double-shaft feed driving system by taking the contour error, the motor running performance and the current amplitude limit as evaluation indexes, predicting the current, the rotating speed, the position and the contour error at the next moment through a unified model of the double-shaft feed driving system, and calculating the cost function values corresponding to all alternative voltage vectors;
and 6, selecting a voltage vector (switching state) which enables the value function value to be minimum as an optimal voltage vector to act on each inverter of the two motors moving in the x-axis direction and the y-axis direction respectively.
In the above technical solution, the unified model of the dual-axis feeding driving system is:
Figure BDA0002209907700000021
in the formula (1), x ═ idx iqx ωx θx idy iqy ωy θy ε]T；u＝[udx uqx udy uqy]T；
Figure BDA0002209907700000031
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)；
Figure BDA0002209907700000032
Figure BDA0002209907700000033
idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; omegaiIs the rotor mechanical angular velocity; thetaiIs the rotor mechanical angle; epsilon is the contour error; u. ofdiIs the d-axis component, u, of the stator voltageqiIs a statorA voltage q-axis component; l isiIs a contour error coefficient, niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; omegai *A desired rotor mechanical angular velocity; l issiIs a stator inductance; rsiIs a stator resistor; v. ofiIs the number of pole pairs; psifiIs a permanent magnet flux linkage; j. the design is a squareeqi＝Ji+Miniri/2π；Beqi＝Bi+Ciniri/2π；JeqiEquivalent moment of inertia; b iseqiIs the equivalent viscous friction coefficient; miIs the moving part mass; ciIs the coefficient of viscous friction of the moving parts; j. the design is a squareiIs the rotational inertia of the motor; b isiThe viscous friction coefficient of the motor; r isiThe radius of a synchronizing wheel of the moving part; ktiIs the motor torque coefficient, and Kti＝1.5viψfi(ii) a x and y correspond to x and y axes respectively; t denotes transposition.
Discretizing the unified model of the double-shaft feeding driving system based on a discrete Taylor series expansion method to obtain the unified model of the discrete Taylor series double-shaft feeding driving system:
Figure BDA0002209907700000034
in the formula, N is the expansion order of Taylor series; t issIs the sampling period.
In the above technical solution, in the step 3, the future position predicted value is made equal to the future position expected value, the position of the reference voltage vector is determined, and the sector where the reference voltage vector is located is determined according to the vector partition.
In the above technical solution, in the step 3, a future position predicted value is made first
Figure BDA0002209907700000035
For future position desired values, the q-axis current reference value required when the slider is moved to the desired position is obtained from equation (2)
Figure BDA0002209907700000036
Reissue to order
Figure BDA0002209907700000037
Obtaining the d and q axis components of the reference voltage vector
Figure BDA0002209907700000038
And
Figure BDA0002209907700000039
is composed of
Figure BDA00022099077000000310
To sum the reference voltage vector with V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111)8 basic voltage vectors are compared, where V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111) The switching state of the upper bridge arm of the two-level voltage source inverter is complementary to the switching state of the lower bridge arm. A switch state of "1" indicates that the switch is on, and a switch state of "0" indicates that the switch is off. Converting the d-q axis reference voltage vector to the alpha-beta axis, thereby obtaining a reference voltage vector position angle thetarefiIs composed of
Figure BDA00022099077000000311
Firstly, an effective vector and a zero vector which are nearest to a reference voltage vector are selected as two alternative vectors, and two effective vectors adjacent to the selected effective vector are added on the basis of the two alternative voltage vectors to serve as alternative voltage vectors.
In the above technical solution, in step 5, the cost function is predicted from i ═ 0 and j ═ 0, and if i is not greater than 3 and j is not greater than 3, step 6 is performed, otherwise, step 5 is performed again. i and j represent the number of times of x-axis and y-axis circulation respectively, and correspond to the number of the candidate voltage vectors.
In the above technical solution, in the step 5, the cost function is defined as:
Figure BDA0002209907700000041
in the formula (5), ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value of the y-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFor the y-axis filtered q-axis current prediction, λε、λe、λid、λiqThe weight coefficients are respectively profile error, speed tracking error, d-axis current tracking error and q-axis current high-frequency component term. By using omegaeq *Instead of omega*＝[ωx *ωy *]TAs the desired speed value, this is because only ω is set*In the case of the expected speed value, when the expected position is a ramp signal, the response is slow and the ideal tracking performance cannot be obtained, so that the expected speed value needs to be corrected. According to the principle of single-axis position feedforward/feedback composite control, at omegai *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved. The corrected expected speed value is
Figure BDA0002209907700000042
In the formula (I), the compound is shown in the specification,
Figure BDA0002209907700000043
the desired position is tracked for the i-axis.
To suppress the high frequency component of the q-axis current, the q-axis current is usually filtered by an Infinite Impulse Response (IIR) high-pass filter, i in equation (5)qfIs through filtered q-axis current, IIR digital filter is a recursive type of linear time invariant causal system, the difference equation of which can be written as
Figure BDA0002209907700000044
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRAnd the coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulation times.
To account for the current maximum amplitude limit, the nonlinear function in equation (5) is defined as
Figure BDA0002209907700000045
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure BDA0002209907700000046
and
Figure BDA0002209907700000047
the d and q axis components of the maximum stator current, respectively.
Another aspect of the invention:
a finite control set model prediction contour control method suitable for a three-axis feed driving system comprises the following steps:
step 1, measuring currents and rotor position signals of three motors driving an x axis, a y axis and a z axis to move, and observing x (k) through an extended Kalman filter observer; (x (k) represents d-axis current, q-axis current, mechanical angular speed of rotor, and mechanical angle of rotor for each motor at the present time
Step 2, delay compensation, namely acting the optimal voltage vector selected at the previous moment on the moment to realize the action of the optimal vector at the middle moment of the control period and reduce the time delay;
step 3, establishing a three-axis feed driving system unified model based on a discrete Taylor series, and determining the position of a reference voltage vector and a sector according to an expected position by combining the three-axis feed driving system unified model;
step 4, integrating the performance of the tracking error and the contour error, and determining each alternative voltage vector;
step 5, constructing a unified cost function of the three-axis feed driving system by taking the contour error, the motor running performance and the current amplitude limit as evaluation indexes, predicting the current, the rotating speed, the position and the contour error at the next moment through a unified model of the three-axis feed driving system, and calculating the cost function values corresponding to all alternative voltage vectors;
and 6, selecting a voltage vector (switching state) which enables the value function value to be minimum as an optimal voltage vector to act on each inverter of the motor moving in the directions of the x axis, the y axis and the z axis.
In the above technical solution, the unified model of the three-axis feeding driving system is:
Figure BDA0002209907700000051
in formula (9), x ═ idx iqx ωx θx idy iqy ωy θy idz iqz ωz θz ε]T；u＝[udx uqx udyuqy udz uqz]T；
Figure BDA0002209907700000052
Figure BDA0002209907700000053
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)+Lznz/2π·(ωz *-ωz)；
Figure BDA0002209907700000054
Figure BDA0002209907700000055
i∈{x，y，z}。idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; omegaiIs the rotor mechanical angular velocity; thetaiIs the rotor mechanical angle; epsilon is the contour error; u. ofdiIs the d-axis component, u, of the stator voltageqiIs the stator voltage q-axis component; l isiIs a contour error coefficient, niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; omegai *A desired rotor mechanical angular velocity; l issiIs a stator inductance; rsiIs a stator resistor; v. ofiIs the number of pole pairs; psifiIs a permanent magnet flux linkage; j. the design is a squareeqi＝Ji+Miniri/2π；Beqi＝Bi+Ciniri/2π；JeqiEquivalent moment of inertia; b iseqiIs the equivalent viscous friction coefficient; miIs the moving part mass; ciIs the coefficient of viscous friction of the moving parts; j. the design is a squareiIs the rotational inertia of the motor; b isiThe viscous friction coefficient of the motor; r isiThe radius of a synchronizing wheel of the moving part; ktiIs the motor torque coefficient, and Kti＝1.5viψfi(ii) a x, y and z respectively correspond to x, y and z axes; t denotes transposition.
Discretizing the unified model of the three-axis feeding driving system based on a discrete Taylor series expansion method to obtain the unified model of the three-axis feeding driving system of the discrete Taylor series:
Figure BDA0002209907700000061
in the formula, N is the expansion order of Taylor series; t issIs the sampling period.
In the above technical solution, in the step 3, the future position predicted value is made equal to the future position expected value, the position of the reference voltage vector is determined, and the sector where the reference voltage vector is located is determined according to the vector partition.
In the above technical solution, in the step 3, a future position predicted value is made first
Figure BDA0002209907700000062
For future position desired values, the q-axis current reference value required when the slider is moved to the desired position is obtained from equation (2)
Figure BDA0002209907700000063
Reissue to order
Figure BDA0002209907700000064
Obtaining the d and q axis components of the reference voltage vector
Figure BDA0002209907700000065
And
Figure BDA0002209907700000066
is composed of
Figure BDA0002209907700000067
To sum the reference voltage vector with V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111)8 basic voltage vectors are compared, where V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111) The switching state of the upper bridge arm of the two-level voltage source inverter is complementary to the switching state of the lower bridge arm. The switch state is "A 1' indicates that the switch is on and a "0" state indicates that the switch is off. Converting the d-q axis reference voltage vector to the alpha-beta axis, thereby obtaining a reference voltage vector position angle thetarefiIs composed of
Figure BDA0002209907700000068
Firstly, an effective vector and a zero vector which are nearest to a reference voltage vector are selected as two alternative vectors, and two effective vectors adjacent to the selected effective vector are added on the basis of the two alternative voltage vectors to serve as alternative voltage vectors.
In the above technical solution, in step 5, the cost function is predicted from i ═ 0, j ═ 0, and r ═ 0, and if i is less than or equal to 3, j is less than or equal to 3, and r is less than or equal to 3, step 6 is performed, otherwise, step 5 is performed again. Wherein i, j, r respectively represent the times of x, y, z axis circulation, corresponding to the number of the alternative voltage vectors.
In the above technical solution, in the step 5, the cost function is defined as:
Figure BDA0002209907700000069
in formula (13), ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1) ωeqz *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1) iqfz(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value, ω, of the y-axiseqz *For corrected speed desired value of z-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFor the y-axis filtered q-axis current prediction value, iqfzFor the predicted value of the z-axis filtered q-axis current, lambdaε、λe、λid、λiqRespectively, the weight coefficient of the contour error, the weight coefficient of the velocity tracking error, and the d-axis current tracking errorThe weight coefficient of the difference, the weight coefficient of the q-axis current high frequency component term. By using omegaeq *Instead of omega*＝[ωx * ωy * ωz *]TAs the desired speed value, this is because only ω is set*In the case of the expected speed value, when the expected position is a ramp signal, the response is slow and the ideal tracking performance cannot be obtained, so that the expected speed value needs to be corrected. According to the principle of single-axis position feedforward/feedback composite control, at omegai *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved. The corrected expected speed value is
Figure BDA0002209907700000071
In the formula (I), the compound is shown in the specification,
Figure BDA0002209907700000072
the desired position is tracked for the i-axis.
To suppress the high frequency component of the q-axis current, the q-axis current is usually filtered by an Infinite Impulse Response (IIR) high-pass filter, i in equation (13)qfIs through filtered q-axis current, IIR digital filter is a recursive type of linear time invariant causal system, the difference equation of which can be written as
Figure BDA0002209907700000073
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRAnd the coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulation times.
To account for the current maximum amplitude limit, the nonlinear function in equation (13) is defined as
Figure BDA0002209907700000074
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure BDA0002209907700000075
and
Figure BDA0002209907700000076
the d and q axis components of the maximum stator current, respectively.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides a finite control set model prediction contour control method suitable for a double-shaft or three-shaft feed driving system, which can carry out prediction control on contour errors before the contour errors occur.
2. The method is based on the idea of unified modeling, a compact model prediction contour controller is designed, and the system contour error can be reduced on the premise of ensuring the single-axis tracking error.
3. The invention can improve the transient profile tracking performance of the system on the premise of ensuring that the steady-state profile tracking performance is maintained unchanged, and particularly, when a large turn occurs, the profile error can be reduced, and the dynamic response speed can be accelerated.
4. The invention is not only suitable for straight-line tracks, but also suitable for complex contour tracks with continuously changing tangent angular velocity.
Drawings
FIG. 1 is a block diagram of a finite control set model predictive contour control system.
FIG. 2 is a flow chart of a finite control set model predictive contour control algorithm.
Fig. 3 is a block diagram of a two-level voltage source inverter.
Detailed Description
The present invention will be described in further detail with reference to specific examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
The invention provides a finite control set model prediction contour control strategy suitable for a double-shaft or three-shaft feed driving system based on the idea of unified modeling. Firstly, combining a mechanical equation of a motion mechanism of a double-shaft or three-shaft feeding drive system with a motion equation, an electrical equation and a change rate equation of a contour error of a drive motor, and establishing a unified model based on a discrete Taylor series; then, in order to reduce the online calculated amount, a proper number of alternative voltage vectors are determined by taking the tracking error as a main index; then, a uniform cost function of the double-shaft or three-shaft feed driving system is constructed by taking the contour error, the motor running performance and the current amplitude limit as evaluation indexes to realize multivariate cooperative optimization control; and then, the optimal voltage vector is selected from the alternative vectors through the principle of minimizing a cost function and is respectively acted on each inverter, so that the dynamic response speed and the profile accuracy of the double-shaft or three-shaft feed driving system are finally improved, the modeling is more intuitive, and the pulse width modulation is not needed.
For the finite control set model predictive profile control strategy of the double-shaft feed driving system, the structural block diagram of the finite control set model predictive profile control system is shown in FIG. 1. Aiming at a series of problems in the traditional cascade contour control method, the invention breaks through the traditional cascade control structure, provides a unified control framework of the double-shaft feed driving system applying the limited control set model predictive control on the basis of unified modeling, interacts output information among shafts and unifies the loop controllers of the shafts. Meanwhile, under the control framework, a compact stepless joint prediction controller is designed. Different from the traditional contour control strategy, the finite control set model predictive control strategy can carry out predictive control on contour errors before the contour errors occur, and has the advantages of visual modeling, simple structure, high dynamic response speed and the like.
In the figure, θ ═ θxθy]T，P*＝[px *py *]T，θ*＝[θx *θy *]TAnd thetax *And thetay *Desired angular positions of the rotor, p, for the x-and y-axis motors, respectively, for moving the slide to the desired positionx *And py *Respectively, are desired position points P*And v (k) is a candidate voltage vector set.
A flow chart of the finite control set model predictive contour control algorithm is shown in fig. 2. Mainly comprises the following 6 steps:
1) the stator current and rotor position signals are measured and x (k) is observed by an extended kalman filter observer.
2) And (4) delay compensation.
3) The position of the reference voltage vector and the sector in which it is located are determined from the desired position.
4) And integrating the performance of the tracking error and the contour error to determine an alternative voltage vector.
5) And predicting the current, the rotating speed, the position and the profile error at the next moment, and calculating the value function values corresponding to all the alternative voltage vectors.
6) The switching state that minimizes the cost function value is selected to be applied to each inverter.
Example 2
For the finite control set model prediction contour control method of the double-shaft feed driving system, the unified model and the finite control set model prediction contour controller of the double-shaft feed driving system are as follows:
firstly, constructing a unified model of a double-shaft feed driving system based on discrete Taylor series:
based on the idea of unified modeling, two permanent magnet synchronous motors driving the x-axis and the y-axis to move are regarded as a whole, and a unified model of a double-shaft feeding driving system is established. Firstly, modeling is carried out on a motion part and a motion equation of two driving motors in an experimental platform of a double-shaft feeding driving system, and the modeling can be expressed as follows:
Figure BDA0002209907700000091
Figure BDA0002209907700000092
in the formula, piA desired position for the trajectory; miIs the equivalent mass of the motion mechanism; ciIs the viscous friction coefficient of the motion mechanism; f. ofiThe driving force is used for driving the sliding block to move; j. the design is a squareiIs the rotational inertia of the motor; t iseiIs an electromagnetic torque; tau isiIs the load torque; b isiThe viscous friction factor of the motor; thetaiIs the rotor mechanical angle; omegaiIs the rotor mechanical angular velocity; i belongs to { x, y }, and x and y correspond to x and y axes respectively.
According to the relation between the driving force and the driving torque for driving the slide block to move and the displacement of the slide block and the position of the motor, an equivalent dynamic model of the double-shaft feed driving system is obtained:
Figure BDA0002209907700000093
in the formula, JeqiIs equivalent moment of inertia, and Jeqi＝Ji+Miniri/2π；BeqiIs an equivalent coefficient of friction, and Beqi＝Bi+Ciniri/2π；niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; r isiThe radius of the synchronizing wheel of the moving part.
Combining an electrical equation and a torque equation of the permanent magnet synchronous motor under a d-q coordinate system, respectively:
Figure BDA0002209907700000094
Tei＝Ktiiqi (5)
in the formula idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; u. ofdiIs the d-axis component, u, of the stator voltageqiIs the stator voltage q-axis component; l issiIs a stator inductance; rsiIs a stator resistor; omegaeiIs electricityElectrical angular velocity of the rotor, and omegaei＝viωi；ψfiIs a permanent magnet flux linkage; ktiIs the torque coefficient of the permanent magnet synchronous motor, and Kti＝1.5viψfi；viIs the number of pole pairs.
According to the change rate formula of the contour error epsilon of the double-shaft feed driving system, the change rate formula is expressed as follows:
Figure BDA0002209907700000101
in the formula, LiIs the profile error coefficient, ωi *The desired rotor mechanical angular velocity.
A unified model of a double-shaft feed driving system is established by the formulas (1) to (6) as
Figure BDA0002209907700000102
Wherein x is ═ idx iqx ωx θx idy iqy ωy θy ε]T；u＝[udx uqx udy uqy]T；
Figure BDA0002209907700000103
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)；
Figure BDA0002209907700000104
Figure BDA0002209907700000105
T denotes transposition.
Because the unified model simultaneously comprises dynamic indexes of position, rotating speed and current tracking, in order to obtain a more accurate discretization model, the unified model of the double-shaft feed driving system is discretized by adopting a discrete Taylor series expansion method, some methods are
Figure BDA0002209907700000106
In the formula, N is the expansion order of Taylor series; t issIs the sampling period.
Secondly, designing a finite control set model prediction contour controller:
(1) determination of the candidate voltage vector:
in order to reduce the online calculation amount, the number of the alternative voltage vector combinations should be reduced appropriately. In order to comprehensively consider the tracking error and the contour error, the alternative voltage vector determination method comprises the following steps: 1) first, the future position predicted value is equal to the expected value, the position of the reference voltage vector is determined, and the sector where the reference voltage vector is located is determined according to the vector partition. 2) And then, considering the influence of the contour error at the same time, and determining an alternative voltage vector.
First order
Figure BDA0002209907700000107
The q-axis current reference value required when the slider is moved to the desired position is obtained from equation (8)
Figure BDA0002209907700000108
Reissue to order
Figure BDA0002209907700000109
Obtaining the d and q axis components of the reference voltage vector
Figure BDA00022099077000001010
And
Figure BDA00022099077000001011
is composed of
Figure BDA0002209907700000111
To sum the reference voltage vector with V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111) Comparing 8 basic voltage vectors, converting the d-q axis reference voltage vector into an alpha-beta axis so as to obtain a reference voltage vector position angle thetarefiIs composed of
Figure BDA0002209907700000112
Wherein, V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111) The switching state of the upper bridge arm of the two-level voltage source inverter is complementary to the switching state of the lower bridge arm. A switch state of "1" indicates that the switch is on, and a switch state of "0" indicates that the switch is off. The partition structure of 8 basic voltage vectors is shown in FIG. 3, which contains 6 valid vectors (V)1-V6) And 2 zero vectors (V)0，V7) The zero vector is selected on the basis of the lowest switching frequency, namely, the zero vector with less switching change compared with the voltage vector at the last moment is selected. Meanwhile, "I", "II", "III", "IV", "V", "VI" denotes a sector number, and each sector includes one valid vector and one zero vector.
The active vector and the zero vector closest to the reference voltage vector are first selected as the two candidate vectors. Taking FIG. 3 as an example, select V1And V0Or selecting V1And V7. In order to simultaneously consider the influence of the profile error, the possibility of the combination of the x-axis voltage vector and the y-axis voltage vector should be increased as much as possible, but the minimum tracking error target cannot be violated at the same time. Therefore, on the basis of the two candidate voltage vectors selected previously, two effective vectors adjacent to the selected effective vector are added together as the candidate voltage vectors, and V is selected as an example in fig. 32And V6. Then, voltage vectors are applied to the inverter, and then current, speed and position signals of the motor are added into a cost function so as to calculate and optimize the cost functionTable 1 shows the reference voltage vector partition and the candidate voltage vector corresponding to each sector.
TABLE 1 reference Voltage vector partition and alternative Voltage vectors for each sector
Figure BDA0002209907700000113
(2) Optimizing a value function: the position tracking error and the contour error need to be considered simultaneously in the cost function, and the alternative voltage vector selected in the last step is determined according to the position expected value, so that when the cost function is defined, the position tracking error item can be omitted, the influence of the contour error is mainly considered, and the cost function is defined as
Figure BDA0002209907700000121
In the formula, ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value of the y-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFor the y-axis filtered q-axis current prediction, λε、λe、λid、λiqThe weight coefficients are respectively profile error, speed tracking error, d-axis current tracking error and q-axis current high-frequency component term. By using omegaeq *Instead of omega*＝[ωx * ωy *]TAs the desired speed value, this is because only ω is set*In the case of the expected speed value, when the expected position is a ramp signal, the response is slow and the ideal tracking performance cannot be obtained, so that the expected speed value needs to be corrected. According to the principle of single-axis position feedforward/feedback composite control, at omegai *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved. The corrected expected speed value is
Figure BDA0002209907700000122
In order to suppress the high frequency component of the q-axis current, the q-axis current is usually filtered by an Infinite Impulse Response (IIR) high-pass filter, and the IIR digital filter is a recursive linear time invariant causal system, and the difference equation can be written as
Figure BDA0002209907700000123
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRAnd the coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulation times.
To account for the current maximum amplitude limit, a nonlinear function is defined as
Figure BDA0002209907700000124
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure BDA0002209907700000125
and
Figure BDA0002209907700000126
the d and q axis components of the maximum stator current, respectively.
Example 3
The finite control set model prediction contour control method of the triaxial feed driving system is the same as that of the embodiment 2, and the unified model and the cost function of the triaxial feed driving system are as follows:
the unified model of the triaxial feed driving system is as follows:
Figure BDA0002209907700000127
in formula (15), x ═ idx iqx ωx θx idy iqy ωy θy idz iqz ωz θz ε]T；u＝[udx uqx udyuqy udz uqz]T；
Figure BDA0002209907700000128
Figure BDA0002209907700000131
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)+Lznz/2π·(ωz *-ωz)；
Figure BDA0002209907700000132
Figure BDA0002209907700000133
Figure BDA0002209907700000134
idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; omegaiIs the rotor mechanical angular velocity; thetaiIs the rotor mechanical angle; epsilon is the contour error; u. ofdiIs the d-axis component, u, of the stator voltageqiIs the stator voltage q-axis component; l isiIs a contour error coefficient, niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; omegai *A desired rotor mechanical angular velocity; l issiIs a stator inductance; rsiIs a stator resistor; v. ofiIs the number of pole pairs; psifiIs a permanent magnet flux linkage; j. the design is a squareeqi＝Ji+Miniri/2π；Beqi＝Bi+Ciniri/2π；JeqiEquivalent moment of inertia; b iseqiIs the equivalent viscous friction coefficient; miIs the moving part mass; ciIs the coefficient of viscous friction of the moving parts; j. the design is a squareiIs the rotational inertia of the motor; b isiThe viscous friction coefficient of the motor; r isiThe radius of a synchronizing wheel of the moving part; ktiIs the motor torque coefficient, and Kti＝1.5viψfi(ii) a x, y and z respectively correspond to x, y and z axes; t denotes transposition.
Discretizing the unified model of the three-axis feeding driving system based on a discrete Taylor series expansion method to obtain the unified model of the three-axis feeding driving system of the discrete Taylor series:
Figure BDA0002209907700000135
in the formula, N is the expansion order of Taylor series; t issIs the sampling period.
Defining the cost function as:
Figure BDA0002209907700000136
in the formula (17), ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1) ωeqz *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1) iqfz(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value, ω, of the y-axiseqz *For corrected speed desired value of z-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFor the y-axis filtered q-axis current prediction value, iqfzFor the predicted value of the z-axis filtered q-axis current, lambdaε、λe、λid、λiqAre respectively provided withThe weighting coefficients of the contour error, the weighting coefficient of the speed tracking error, the weighting coefficient of the d-axis current tracking error and the weighting coefficient of the q-axis current high-frequency component term are used. By using omegaeq *Instead of omega*＝[ωx * ωy * ωz *]TAs the desired speed value, this is because only ω is set*In the case of the expected speed value, when the expected position is a ramp signal, the response is slow and the ideal tracking performance cannot be obtained, so that the expected speed value needs to be corrected. According to the principle of single-axis position feedforward/feedback composite control, at omegai *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved. The corrected expected speed value is
Figure BDA0002209907700000137
In the formula (I), the compound is shown in the specification,
Figure BDA0002209907700000138
the desired position is tracked for the i-axis.
To suppress the high frequency component of the q-axis current, the q-axis current is usually filtered by an Infinite Impulse Response (IIR) high-pass filter, i in equation (17)qfIs through filtered q-axis current, IIR digital filter is a recursive type of linear time invariant causal system, the difference equation of which can be written as
Figure BDA0002209907700000141
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRAnd the coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulation times.
To account for the current maximum amplitude limit, the nonlinear function in equation (17) is defined as
Figure BDA0002209907700000142
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure BDA0002209907700000143
and
Figure BDA0002209907700000144
the d and q axis components of the maximum stator current, respectively.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (6)

1. A finite control set model predictive profile control method suitable for a double-shaft feed driving system comprises the following steps:
step 1, measuring current and rotor position signals of two motors driving the x-axis and y-axis directions to move, and observing x (k) by an extended Kalman filter observer, wherein x (k) represents d-axis current, q-axis current, rotor mechanical angular speed and rotor mechanical angle of each motor at the current moment;
step 2, delay compensation, namely acting the optimal voltage vector selected at the previous moment on the moment to realize the action of the optimal voltage vector at the middle moment of the control period and reduce the time delay;
step 3, establishing a discrete Taylor series-based double-shaft feed driving system unified model, and determining the position of a reference voltage vector and the sector of the reference voltage vector according to an expected position by combining the discrete Taylor series-based double-shaft feed driving system unified model;
step 4, integrating the performance of the tracking error and the contour error, and determining each alternative voltage vector;
step 5, constructing a unified cost function of the double-shaft feed driving system by taking the contour error, the motor running performance and the current amplitude limit as evaluation indexes, predicting the current, the rotating speed, the position and the contour error at the next moment through a unified model of the double-shaft feed driving system based on the discrete Taylor series, and calculating the cost function values corresponding to all alternative voltage vectors;
step 6, selecting the voltage vector which enables the value function value to be minimum as an optimal voltage vector to act on each inverter of the two motors moving in the directions of the x axis and the y axis respectively;
the unified model of the double-shaft feeding driving system is as follows:
Figure FDA0003509053660000011
in the formula (1), x ═ idx iqx ωx θx idy iqy ωy θy ε]T；u＝[udx uqx udy uqy]T；
Figure FDA0003509053660000012
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)；
Figure FDA0003509053660000013
Figure FDA0003509053660000014
idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; omegaiIs the rotor mechanical angular velocity; thetaiIs the rotor mechanical angle; epsilon is the contour error; u. ofdiIs the d-axis component, u, of the stator voltageqiIs the stator voltage q-axis component; l isiIs a contour error coefficient, niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; omegai *A desired rotor mechanical angular velocity; l issiIs a stator inductance; rsiIs a stator resistor; v. ofiIs the number of pole pairs; psifiIs a permanent magnet flux linkage; j. the design is a squareeqi＝Ji+Miniri/2π；Beqi＝Bi+Ciniri/2π；JeqiEquivalent moment of inertia; b iseqiIs the equivalent viscous friction coefficient; miIs the moving part mass; ciIs the coefficient of viscous friction of the moving parts; j. the design is a squareiIs the rotational inertia of the motor; b isiThe viscous friction coefficient of the motor; r isiThe radius of a synchronizing wheel of the moving part; ktiIs the motor torque coefficient, and Kti＝1.5viψfi(ii) a x and y correspond to x and y axes respectively; t represents transposition;
discretizing the unified model of the double-shaft feeding driving system by a discrete Taylor series expansion method to obtain the unified model of the double-shaft feeding driving system based on discrete Taylor series:
Figure FDA0003509053660000021
in the formula, N is the expansion order of Taylor series; t issIs a sampling period;
in step 5, the cost function is defined as:
Figure FDA0003509053660000022
in the formula (3), ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value of the y-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFiltered for the y-axisPredicted value of q-axis current, λε、λe、λid、λiqThe weight coefficients of profile error, speed tracking error, d-axis current tracking error and q-axis current high-frequency component term are adoptedeq *Instead of omega*＝[ωx * ωy *]TAs the desired speed value, this is because only ω is set*When the desired position is a ramp signal as the desired value of the velocity, the response is slow and the ideal tracking performance cannot be obtained, so the desired value of the velocity needs to be corrected, and the principle of the single-axis position feedforward/feedback composite control is used at ωi *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved, and the corrected speed expected value is
Figure FDA0003509053660000023
In the formula (I), the compound is shown in the specification,
Figure FDA0003509053660000024
the expected position of the i-axis track;
to suppress the high frequency component of the q-axis current, the q-axis current is filtered by an Infinite Impulse Response (IIR) high-pass filter, i in equation (3)qfIs through filtered q-axis current, IIR digital filter is a recursive type of linear time invariant causal system, the difference equation of which can be written as
Figure FDA0003509053660000025
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRThe coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulated times;
to account for the current maximum amplitude limit, the nonlinear function in equation (3) is defined as
Figure FDA0003509053660000026
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure FDA0003509053660000027
and
Figure FDA0003509053660000028
the d and q axis components of the maximum stator current, respectively.
2. The finite control set model predictive profile control method of claim 1, wherein in step 5, a cost function is predicted from i ═ 0 and j ═ 0, and if i ≦ 3 and j ≦ 3, step 6 is entered, otherwise step 5 is entered again; i and j represent the number of times of x-axis and y-axis circulation respectively, and correspond to the number of the candidate voltage vectors.
3. A method for controlling a limited control set model prediction contour suitable for a three-axis feed driving system is characterized by comprising the following steps:
step 1, measuring currents and rotor position signals of three motors driving an x axis, a y axis and a z axis to move, and observing x (k) by an extended Kalman filter observer, wherein x (k) represents d-axis current, q-axis current, rotor mechanical angular velocity and rotor mechanical angle of each motor at the current moment;
step 2, delay compensation, namely acting the optimal voltage vector selected at the previous moment on the moment to realize the action of the optimal vector at the middle moment of the control period and reduce the time delay;
step 3, establishing a three-axis feed driving system unified model based on a discrete Taylor series, and determining the position of a reference voltage vector and a sector according to an expected position by combining the three-axis feed driving system unified model based on the discrete Taylor series;
step 4, integrating the performance of the tracking error and the contour error, and determining each alternative voltage vector;
step 5, constructing a unified cost function of the three-axis feed driving system by taking the contour error, the motor running performance and the current amplitude limit as evaluation indexes, predicting the current, the rotating speed, the position and the contour error at the next moment through a unified model of the three-axis feed driving system based on the discrete Taylor series, and calculating the cost function values corresponding to all alternative voltage vectors;
step 6, selecting the voltage vector which enables the value function value to be minimum as an optimal voltage vector to act on each inverter of the motor moving in the directions of the x axis, the y axis and the z axis respectively;
the unified model of the triaxial feeding driving system is as follows:
Figure FDA0003509053660000031
in the formula (7), x ═ idx iqx ωx θx idy iqy ωy θy idz iqz ωz θz ε]T；u＝[udx uqx udy uqyudz uqz]T；
Figure FDA0003509053660000032
Figure FDA0003509053660000033
η＝Lxnx/2π·(ωx *-ωx)+Lyny/2π·(ωy *-ωy)+Lznz/2π·(ωz *-ωz)；
Figure FDA0003509053660000034
Figure FDA0003509053660000035
Figure FDA0003509053660000036
idiIs the d-axis current of the motor; i.e. iqiIs the motor q-axis current; omegaiIs the rotor mechanical angular velocity; thetaiIs the rotor mechanical angle; epsilon is the contour error; u. ofdiIs the d-axis component, u, of the stator voltageqiIs the stator voltage q-axis component; l isiIs a contour error coefficient, niThe displacement of the corresponding sliding block movement is realized when the motor rotates for one circle; omegai *A desired rotor mechanical angular velocity; l issiIs a stator inductance; rsiIs a stator resistor; v. ofiIs the number of pole pairs; psifiIs a permanent magnet flux linkage; j. the design is a squareeqi＝Ji+Miniri/2π；Beqi＝Bi+Ciniri/2π；JeqiEquivalent moment of inertia; b iseqiIs the equivalent viscous friction coefficient; miIs the moving part mass; ciIs the coefficient of viscous friction of the moving parts; j. the design is a squareiIs the rotational inertia of the motor; b isiThe viscous friction coefficient of the motor; r isiThe radius of a synchronizing wheel of the moving part; ktiIs the motor torque coefficient, and Kti＝1.5viψfi(ii) a x, y and z respectively correspond to x, y and z axes; t represents transposition;
discretizing the unified model of the three-axis feed driving system by a discrete Taylor series expansion method to obtain the unified model of the three-axis feed driving system based on the discrete Taylor series:
Figure FDA0003509053660000041
in the formula, N is the expansion order of Taylor series; t issIs a sampling period;
in step 5, the cost function is defined as:
Figure FDA0003509053660000042
in the formula (9), ωeq *(k+1)＝[ωeqx *(k+1) ωeqy *(k+1) ωeqz *(k+1)]TAnd iqf(k+1)＝[iqfx(k+1) iqfy(k+1) iqfz(k+1)]T，ωeqx *For the corrected speed desired value, omega, of the x-axiseqy *For the corrected speed desired value, ω, of the y-axiseqz *For corrected speed desired value of z-axis, iqfxFor the predicted value of the x-axis filtered q-axis current, iqfyFor the y-axis filtered q-axis current prediction value, iqfzFor the predicted value of the z-axis filtered q-axis current, lambdaε、λe、λid、λiqRespectively is the weight coefficient of the profile error, the weight coefficient of the speed tracking error, the weight coefficient of the d-axis current tracking error and the weight coefficient of the q-axis current high-frequency component term, and adopts omegaeq *Instead of omega*＝[ωx * ωy * ωz *]TAs the desired speed value, this is because only ω is set*When the desired position is a ramp signal as the desired value of the velocity, the response is slow and the ideal tracking performance cannot be obtained, so the desired value of the velocity needs to be corrected, and the principle of the single-axis position feedforward/feedback composite control is used at ωi *On the basis of the position ratio controller lambdaθThe position tracking performance can be improved, and the corrected speed expected value is
Figure FDA0003509053660000043
In the formula (I), the compound is shown in the specification,
Figure FDA0003509053660000044
is a i-axis railA trace expected position;
to suppress the high frequency component of the q-axis current, the q-axis current is filtered by an Infinite Impulse Response (IIR) high-pass filter, i in equation (9)qfIs through filtered q-axis current, IIR digital filter is a recursive type of linear time invariant causal system, the difference equation of which can be written as
Figure FDA0003509053660000045
In the formula, yIIRIs the output of an IIR digital filter, xIIRAs input to IIR digital filters, MIIRAnd NIIROrder of IIR digital filter, aIIRAnd bIIRThe coefficient is corresponding to the IIR digital filter, k is the current moment, and delta is the accumulated times;
to account for the current maximum amplitude limit, the nonlinear function in equation (9) is defined as
Figure FDA0003509053660000046
Wherein C is greater than 1000 lambdaεIs determined by the constant of (a) and (b),
Figure FDA0003509053660000047
and
Figure FDA0003509053660000048
the d and q axis components of the maximum stator current, respectively.
4. The finite control set model predictive profile control method of claim 3, wherein in step 5, a cost function is predicted from i-0, j-0, r-0, and if i ≦ 3, j ≦ 3, r ≦ 3, step 6 is entered, otherwise step 5 is entered again; wherein i, j, r respectively represent the times of x, y, z axis circulation, corresponding to the number of the alternative voltage vectors.
5. The finite control set model predictive profile control method of claim 1 or 3, wherein in step 3, the future position predicted value is first made equal to the future position expected value, the position of the reference voltage vector is determined, and the sector in which the reference voltage vector is located is determined according to the vector partition.
6. The finite control set model predictive profile control method of claim 1 or 3, wherein in step 3, the future position prediction value is first made
Figure FDA0003509053660000051
Figure FDA0003509053660000052
For future position desired values, a q-axis current reference value required when the slider is moved to a desired position is obtained from equation (2) or (8)
Figure FDA0003509053660000053
Reissue to order
Figure FDA0003509053660000054
Figure FDA0003509053660000055
Obtaining the d and q axis components of the reference voltage vector
Figure FDA0003509053660000056
And
Figure FDA0003509053660000057
is composed of
Figure FDA0003509053660000058
To sum the reference voltage vector with V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111)8 basic voltage vectors are compared, where V0(000)、V1(100)、V2(110)、V3(010)、V4(011)、V5(001)、V6(101)、V7(111) The reference voltage vector position angle theta is obtained by converting the d-q axis reference voltage vector into an alpha-beta axis when the switch state of the upper bridge arm of the two-level voltage source inverter is complementary with the switch state of the lower bridge arm, the switch state is '1' to indicate that the switch is switched on, the switch state is '0' to indicate that the switch is switched off, and the reference voltage vector position angle theta is obtainedrefiIs composed of
Figure FDA0003509053660000059
Firstly, an effective vector and a zero vector which are closest to a reference voltage vector are selected as two alternative vectors, and two effective vectors adjacent to the selected effective vector are added on the basis of the two alternative vectors to be used as alternative voltage vectors.
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