CN117544038A - Permanent magnet synchronous motor model predictive control method based on rapid weight optimization - Google Patents
Permanent magnet synchronous motor model predictive control method based on rapid weight optimization Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/20—Estimation of torque
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
- H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
- H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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Abstract
The invention discloses a permanent magnet synchronous motor model prediction control method based on rapid weight optimization, which relates to the technical field of motor control, and the specific implementation process comprises the steps of constructing a mathematical model by a stator voltage equation, predicting multiple control targets, predicting and controlling the multiple target optimization model, reducing the dimension of multiple target cost functions, rapidly sequencing errors and evaluating indexes, and outputting an optimal voltage vector to a two-level three-phase inverter after the index evaluation; compared with the prior art, the method and the device have the advantages that the weight coefficient is not required to be designed and optimized, the sequencing index is obtained by sequencing each error item respectively, and the sequencing ranking of each error item is evaluated, so that the system-level optimization of multiple control targets, namely the multi-target global optimization of the target model predictive control method, can be realized.
Description
Technical Field
The invention relates to the technical field of motor control, in particular to a permanent magnet synchronous motor model predictive control method based on rapid weight optimization.
Background
The permanent magnet synchronous motor has the advantages of simple structure, low noise, high power density and the like, and has been widely applied to the fields of aerospace, railway transportation, numerical control machine tools, electric automobiles, robot control and the like; the permanent magnet synchronous motor control method also becomes a research hot spot of domestic and foreign scholars, and in the field of alternating current speed regulation, besides vector control and direct torque control, model predictive control is favored by more scholars.
When the traditional model predictive control is used for processing a multi-objective function, a plurality of weight coefficients are required to be introduced for adjusting each control target, for example, the objective function comprises control variables with different dimensions of torque and flux linkage, and the weight coefficients are required to be introduced to weigh the specific weights of the two variables in the cost function to achieve the expected control requirement in consideration of different orders of magnitude of the two variables, so that the control effect of the model predictive control is greatly influenced by the weight coefficients of each control target.
Based on the above, the present application has been made on the basis of the intensive studies, and the present application has been developed.
Disclosure of Invention
The invention aims to provide a fast weight optimization permanent magnet synchronous motor model prediction control method which can effectively eliminate all weight coefficients and realize global optimization of target model prediction control.
To achieve the above object, the solution of the present invention is:
the permanent magnet synchronous motor model prediction control method based on rapid weight optimization comprises an inverter, wherein the inverter comprises a three-phase bridge arm, each phase of bridge arm is respectively provided with two switching tubes, and the two switching tubes in each phase of bridge arm are respectively and correspondingly positioned on an upper bridge arm and a lower bridge arm, and the method comprises the following steps:
s1, establishing a mathematical model of a permanent magnet synchronous motor as follows;
（1），
（2），
（3），
（4），
wherein, electromagnetic torque expression is:（5）；
in the method, in the process of the invention,u sd 、u sq respectively represent the stator voltages in the dq axis coordinate system,i sd 、i sq respectively represent the stator currents in the dq axis coordinate system,L sd 、L sq respectively represent the dq-axis component of the stator inductance,ψ sd 、ψ sq respectively represent the dq-axis component of the stator flux linkage,R s for the resistance of the stator,pin the form of an polar pair number,ψ m is a magnetic linkage of a permanent magnet,ω r for the angular velocity of the rotor,T e for electromagnetic torque, d/dt is a differential operator;
s2, predicting multiple control targets, wherein the specific method comprises the following steps of:
the predicted value of the control target is obtained through forward Euler discretization by the following formula:(6) Wherein x (k) represents the value of the control target x in the kth sampling period, x (k+1) represents the value of the control target x in the (k+1) th sampling period, k represents the kth sampling period, k+1 represents the (k+1) th sampling period, T s Time for a single sampling period;
according to the mathematical model of the permanent magnet synchronous motor, the differential of the stator current at the moment k under the dq axis coordinate system is obtained as follows:
（7），
（8）；
wherein the formula (6) is substituted into the formula (7) and the formula (8), respectively, to obtain the firstkThe equation for the stator current prediction for +1 sample periods is:
（9），
（10）；
the formula for obtaining the stator flux linkage predicted value of the (k+1) th sampling period is as follows:
（11），
（12），
obtain the firstkThe equation for the electromagnetic torque prediction for +1 sample periods is:
（13）；
wherein i is sd (k + 1)、i sq (k+1) represents the predicted value of the stator current in the kth+1th sampling period, ψ, in the dq-axis coordinate system, respectively sd (k + 1)、ψ sq (k+1) represents the predicted value, T, of the dq-axis component of the stator flux linkage at the (k+1) th sampling period, respectively e Omega is the predicted value of the electromagnetic torque in the (k+1) th sampling period r (k) Rotor angular velocity for the kth sampling period;
s3, predicting a multi-control target optimization model, wherein the specific method comprises the following steps of: the multi-objective model predictive control cost function is established as follows:
，
in the method, in the process of the invention,T e * as a reference value for the electromagnetic torque,ψ sd * 、ψ sq * respectively representdqStator flux linkage reference values in the axis coordinate system,λ ψ andλ nw are all weight coefficients;
wherein,，hrepresenting one of the phases a, b or c of the three-phase bridge arm in the inverter, if the phase has a switching state of the switching tube, the phase is +.>=1, whereas 0; n is n sw (k) Switching times when the sampling period is k; />、/>And->Respectively and correspondingly expressed as the switch states of upper bridge arm switch tubes of a phase, b phase and c phase in the two-level three-phase inverter,/->=0、/>=0 and +.>=0 indicates the conduction of the upper bridge arm switching tubes correspondingly indicated as a phase, b phase and c phase in the inverter, respectively, +.>=1、/>=1 and->=1 indicates that upper bridge arm switching tubes of a phase, b phase and c phase in the inverter are turned off, respectively;
s4, reducing the dimension of the multi-objective cost function, wherein the specific method comprises the following steps of: decomposing the cost function g into a plurality of error terms, wherein the expressions of the error terms are respectively as follows:
（15），
（16）,
（17）；
wherein,representing a torque error optimization term,/->Representing flux linkage error optimization term,/->Representing a switching frequency error optimization term;
s5, quick error sorting, wherein the specific method comprises the following steps:
step S5.1: according to the switching state of the three-phase switching tube of the two-level three-phase inverter, a three-bit binary number S= [ is obtained,/>,/>]Adopting a control input i and a control input j as input variables respectively, wherein i and j are respectively represented as serial numbers S of the three-bit binary numbers in decimal, i=0-7, and j=i+1-7;
step S5.2, establishing the voltage vectorThe relation of (2) is as follows: />=/>(/>+a/>+a 2 />) The method comprises the steps of carrying out a first treatment on the surface of the In the method, in the process of the invention,represents the dc bus voltage, a is a coefficient, and a=e j·2π/3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein the voltage vector->The subscript S in (a) represents the sequence number of the three-bit binary of the voltage vector in decimal, i.e., subscript s=i or j; inputting the saidControl input i and said control input j, i=0 to 7, j=i+1 to 7, yielding said voltage vector +.>Different values can be obtainedg n N is defined according to the selected error optimization term, and n=1-2; and, according to the conduction state of the upper bridge arm switch tube of the three phases in the single sampling period in the step S4, the +.>And byg 3 (j) Voltage vector reordering with monotonically increasing values as a criterion;
comparing the control input i and the control input j in pairs, ifg n (i) ＞g n (j) The serial numbers of the control input i and the control input j are exchanged and stored, ifg n (i)≤g n (j) The serial numbers of the control input i and the control input j are kept unchanged, and the comparison is completed to obtaing n (j) Voltage vector reordering with monotonically increasing error value as a criterion;
step S5.3: according to step S5.2, respectivelyg 1 (j)、g 2 (j) Andg 3 (j) Voltage vector reordering with monotonically increasing error value as a criterion;
step S5.4: according to the describedg n (j) The error values of (2) are arranged in order from small to large, and the ranking sequentially corresponds to A n [0]、A n [1]、……、A n [7]；
S6, index evaluation, wherein the specific method comprises the following steps: the ranking of each of said control inputs j is added as follows,(18) Wherein->Representing the torque error optimization term +.>Ranking of said control input j in step S5,/for>Representing said flux linkage error optimization term +.>Ranking of said control input j in step S5,/for>Representing the switching frequency error optimization term +.>Ranking of said control input j in step S5; and then selecting the control input j corresponding to the ranking addition minimum as global optimal quantity input.
According to the control input j obtained in the step S6, combining with the step S5.2 to obtain a voltage vectorTo output +.>(k+1) to the controller.
The inverter is a two-level three-phase inverter.
After the structure is adopted, the invention has the following beneficial effects: according to the method, the cost function is designed into a plurality of control targets, the dimension of the plurality of target cost functions is reduced, the cost function is decomposed into a plurality of error optimization items, namely a torque error optimization item, a flux linkage error optimization item and a switching frequency optimization item, so that all weight coefficients are eliminated, the method does not need to design and optimize the weight coefficients, the sorting indexes are obtained by sorting the error items respectively, the sorting ranking of the error items is evaluated, and the system-level optimization of a plurality of control targets, namely the multi-target global optimization of a target model predictive control method can be realized.
Drawings
FIG. 1 is a schematic block diagram of a model predictive control method of the present invention.
FIG. 2 is a schematic diagram of the cost reduction of the multi-objective model predictive function in the present invention.
FIG. 3 is a schematic diagram of optimized ordering of neutron problems in the present invention.
Detailed Description
In order to further explain the technical scheme of the invention, the invention is explained in detail by specific examples.
The invention provides a permanent magnet synchronous motor model predictive control method based on rapid weight optimization, wherein a control system of the permanent magnet synchronous motor is shown in figure 1, the control system comprises an inverter, in the embodiment, the inverter adopts a conventional two-level three-phase inverter, the inverter comprises a three-phase bridge arm, the three-phase bridge arm is respectively corresponding to an a phase, a b phase and a c phase, each phase is respectively provided with two switching tubes, and the two switching tubes in each phase bridge arm are respectively corresponding to an upper bridge arm and a lower bridge arm; and, in the present embodiment, the permanent magnet synchronous motor is a conventional miniature permanent magnet synchronous motor,
the specific implementation flow of the embodiment comprises a mathematical model formed by a stator voltage equation, multi-control target prediction, multi-target optimization model prediction control, multi-target cost function dimension reduction, error rapid sequencing and index evaluation, and the embodiment outputs variables to the inverter after index evaluation.
As shown in fig. 1 to 3, the model predictive control method of the present embodiment includes the steps of:
s1, establishing a mathematical model formed by a stator voltage equation, namely establishing a mathematical model of the permanent magnet synchronous motor on a two-phase rotation dq coordinate system as follows:
（1），
（2），
（3），
（4）；
in the method, in the process of the invention,u sd 、u sq respectively represent the stator voltages in the dq axis coordinate system,i sd 、i sq respectively represent the stator currents in the dq axis coordinate system,L sd 、L sq respectively represent the dq-axis component of the stator inductance,ψ sd 、ψ sq respectively represent the dq-axis component of the stator flux linkage,R s for the resistance of the stator,pin the form of an polar pair number,ψ m is a magnetic linkage of a permanent magnet,ω r for the angular velocity of the rotor,T e for electromagnetic torque, d/dt is the differential operator.
In this embodiment, the electromagnetic torque expression is:(5) In which, in the process,ω r is the angular velocity of the rotor of the permanent magnet synchronous motor,T e is electromagnetic torque; wherein the rotor angular velocity may be obtained in a conventional manner, such as with an encoder.
S2, predicting multiple control targets, wherein the specific method comprises the following steps of: the predicted value of the control target is obtained by a conventional forward Euler discrete method, and the formula is as follows:(6) Where x (k) represents the value of the control target x in the kth sampling period, x (k+1) represents the value of the control target x in the kth+1th sampling period, and k represents the kth sampling period.
According to the mathematical model of the permanent magnet synchronous motor (formula (1) -formula (4)), the differential of the stator current on the dq axis at the time k is obtained as follows:
（7），
（8）；
substituting the formula (6) into the formulas (7) and (8), respectively, wherein the control target x is dq-axis stator current, to obtain the firstkThe stator current prediction value for +1 sampling period is:
（9），
（10）；
similarly, the stator flux linkage prediction value for the (k+1) th sampling period can be obtained as follows:
（11），
（12）；
similarly, the first can be obtainedkThe electromagnetic torque predicted value for +1 sampling period is:
（13）；
wherein i is sd (k + 1)、i sq (k+1) are respectively expressed as predictive values of stator currents in the dq coordinate system in the (k+1) th sampling period, ψ sd (k + 1)、ψ sq (k+1) represents the predicted value, T, of the dq-axis component of the stator flux linkage at the (k+1) th sampling period, respectively e Omega is the predicted value of the electromagnetic torque in the (k+1) th sampling period r (k) Rotor angular velocity for the kth sampling period.
The control target x is the stator flux when calculating the stator flux predicted value, and is the electromagnetic torque when calculating the electromagnetic torque predicted value.
S3, predicting a multi-control target optimization model, wherein the specific method comprises the following steps of: the multi-objective model predictive control cost function is established as follows:
in the method, in the process of the invention,T e * as a reference value for the electromagnetic torque,ψ sd * 、ψ sq * respectively representdqStator flux linkage reference values in the axis coordinate system.
Further, the method comprises the steps of,in the formula (14),ha, b, c, if the phase has switching state of the switching tube>=1, whereas 0; n is n sw (k) Switching times when the sampling period is k;
wherein,=0、/>=0 and +.>=0 indicates the conduction of the upper bridge arm switch tubes of a phase, b phase and c phase respectively, and +.>=1、=1 and->The upper bridge arm switching tubes of the a phase, the b phase and the c phase are respectively turned off in a corresponding manner; k denotes the kth sampling period, and k-1 denotes the kth-1 sampling period.
Wherein the cost function comprises three control targets, namely a torque error, a flux linkage error and a switching frequency, and the three control targets have two weight coefficientsλ ψ 、λ nw Therefore, the multi-objective comprehensive optimization of torque, flux linkage error and switching frequency is realized, and the flux linkage error is correspondingly a current error in the embodiment.
The above-mentionedIs also defined artificially according to a condition, for example, 1000rpm, 4Nm, at which the electromagnetic torque reference value +.>Set to 4Nm; stator flux linkage reference valueψ s Is a motor rated parameter, such as the magnitude of the motor rated stator flux linkageψ s * ||= 0.71Wb，ψ sd * 、ψ sq * Is its component, (||ψ sd * ||） 2 +（||ψ sq * ||） 2 =||ψ s * || 2 。
S4, reducing the dimension of the multi-objective cost function, wherein the specific method comprises the following steps of: decomposing the cost function g into a plurality of error terms, wherein the expressions of the error terms are respectively as follows:
（15），
= (||ψ s * ||-||/>||) 2 （16）,
（17）；
in the method, in the process of the invention,representing a torque error optimization term,/->Representing flux linkage error optimization term,/->Representing the switching frequency optimization term.
Further, in this embodiment, the weight coefficient in the multi-objective model predictive control is eliminated by converting the complex multi-objective model predictive control problem into a plurality of sub-problems aiming at optimizing a single control objective, that is, as described above, as shown in fig. 3, the multi-objective cost function is reduced in dimension.
S5, quick error sorting, wherein the specific method comprises the following steps:
step S5.1, obtaining a three-bit binary number S= [ according to the switching state of the three-phase upper bridge arm switching tube of the two-level three-phase inverter,/>,/>]The control input i and the control input j are used as input variables respectively; wherein i and j are respectively represented as serial numbers S of the three-bit binary number in decimal system, i=0 to 7, and j=i+1 to 7.
Further, in the further course of this,the switch state of an a-phase upper bridge arm switch tube in the two-level three-phase inverter is expressed as +.>The switch state of a b-phase upper bridge arm switch tube in the two-level three-phase inverter is expressed as +.>The switching state of a switching tube of a c-phase upper bridge arm in the two-level three-phase inverter is shown; wherein (1)>=0、/>=0 and +.>=0 indicates the upper bridge arm switch tube of a phase, b phase and c phase is conducted, respectively, +.>=1、/>=1 and->=1 indicates that the upper arm switching tubes of the a-phase, b-phase, and c-phase are turned off, respectively.
For easy understanding, for example, when j=0, that is, when s= [0, 0], the three-phase upper bridge arm switching tubes are all turned off; for another example, when j=1, that is, s= [0, 1], the switching tubes of the a-phase and b-phase upper arms are both turned off, and the switching tube of the c-phase upper arm is turned on.
It should be noted that, in the bridge arm circuit in the inverter, when the upper bridge arm switching tube of each phase is turned on, the corresponding lower bridge arm switching tube must be turned off; when the upper bridge arm switching tube of each phase is turned off, the corresponding lower bridge arm switching tube is necessarily turned on, so that the normal operation of each switching tube is ensured.
Step S5.2, first, establishing the voltage vectorThe relation of (2) is as follows: />=/>(/>+a/>+a 2 />) The method comprises the steps of carrying out a first treatment on the surface of the In (1) the->Represents the dc bus voltage, a is a coefficient, and a=e j·2π/3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein the voltage vector->The subscript S in (a) represents the sequence number of the three-bit binary of the voltage vector in decimal, i.e., subscript s=i or j; and the switching frequency optimization term is obtained according to the switching times of the three-phase upper bridge arm switching tube in the single sampling period in the step S4, namely ∈10 is obtained according to the on-off state of the three-phase upper bridge arm switching tube and the combination of (17)>And byg 3 (j) The error value of (2) monotonically rises to a standard voltage vector reordering.
For the sake of easy understanding, for example, when the a-phase upper arm is on (the lower arm is off at this time) at time k, and the b-phase and c-phase upper arms are off (the lower arm is on at this time),(k)=1、/>(k)=0、/>=0, i.e. input at this timeControl j=4, s= [1,0]The method comprises the steps of carrying out a first treatment on the surface of the When the upper bridge arm of the a phase is turned off (the lower bridge arm is turned on at the moment) and the upper bridge arms of the b and c phases are turned on (the lower bridge arm is turned off at the moment) at the moment of k-1, the upper bridge arm of the a phase is turned off, and the lower bridge arm of the b and c phases are in the +.>(k)=0、/>(k)=1、/>=1, i.e. the input control j=3, s= [0,1]At this time->= 3。
Wherein the voltage vectors are of different valuesSubstituting into equation (15), and combining the above mathematical model, electromagnetic torque predictive value equation (13) and stator current predictive value equation (7-8) to obtaing 1 The method comprises the steps of carrying out a first treatment on the surface of the Similarly, the voltage vector is +.>Substituting into formula (16), and combining with stator flux predicted value formula (formulas 11-12) to obtaing 2 。
Then, i and j are respectively substituted into the voltage vectorsIn the relation of (a), i=0 to 7, j=i+1 to 7, and comparing the error terms obtained by the input i and j with each other, if at each comparisong n (i) ＞g n (j) The serial numbers of the control input i and the control input j are exchanged and stored, ifg n (i)≤g n (j) The sequence numbers of the control input i and the control input j are kept unchanged, and the comparison is completed so as to obtaing n (j) The error value of (c) monotonically rises to a standard voltage vector reordering,
note that, n is defined according to the error optimization term selected, n=1 to 2, and when n=1g 1 Representing a torque error optimization term, n=2g 2 Representing a flux linkage error optimization term; in this embodiment, the error values of n=1 and n=2 need to be compared two by two.
Step S5.3, according to step S5.2, respectively obtaing 1 (j)、g 2 (j) Andg 3 (j) The error values of (a) monotonically increase to a standard voltage vector reordering.
It is worth mentioning that the voltage vector before ranking in the voltage vector reordering corresponds toThe smaller the error value.
Step S5.4:g 1 (j)、g 2 (j) Andg 3 (j) Respectively arranged according to the order of the respective error values from small to large, and the ranking order is A in turn n [0]、A n [1]、……、A n [7]。
In particular, the method comprises the steps of,g 1 (j) The error values of (a) are arranged from small to large and respectively correspond to A 1 [0]、A 1 [1]、……、A 1 [7]；g 2 (j) The error values of (a) are arranged from small to large and respectively correspond to A 2 [0]、A 2 [1]、……、A 2 [7]；g 3 (j) The error values of (a) are arranged from small to large and respectively correspond to A 3 [0]、A 3 [1]、……、A 3 [7]The method comprises the steps of carrying out a first treatment on the surface of the For example, when j=0 represents the input switch state s= [0,1]When j=0, as compared with other input switch statesg 1 If the error value of (1) is the smallest, j=0 is located in array a 1 [0]In, i.e. in array A 1 Is the first bit of (2); for another example, there are two voltage vectorsg 1 Obtained at a ratio j=1g 1 Smaller, meaning that there are two input controls j before j=1, where j=1 is the third position, theng 1 (j=1) is located at a 1 [3]In (a) and (b); for another example, if there are five input controls jg 1 Obtained at a ratio j=1g 1 Smaller, then there are five input controls j before j=1, where j=1 is arranged in the sixth bit,g 1 (j=1) is located at a 1 [6]Is a kind of medium.
S6, index evaluation, wherein the specific method comprises the following steps: the ranking of the control inputs j is added as follows,(18) Then select +.>The control input j corresponding to the smallest rank is used as the global optimal quantity input, namely, the control input j corresponding to the smallest rank addition is used as the global optimal quantity input.
In the formula (18), the amino acid sequence of the compound,representing a torque error optimization term +.>Ranking of control input j in step S5,/->Representation of flux linkage error optimization term->Ranking of control input j in step S5,/->Representing a switching frequency error optimization termThe ranking of the control input j in step S5.
It should be noted that, according to the control input j obtained in step S6, a voltage vector is obtained in step S5.2Control input j and voltage vector +.>Is a corresponding relationship, thereby outputting +.>And (k+1), wherein the on-off state required by each phase switching tube in the two-level three-phase inverter can be obtained according to the control input j so as to control the on-off of each phase switching tube in the inverter.
It should be noted that, the method is based on a common control system for permanent magnet motor control, and comprises a conventional two-level inverter topology and a coordinate transformation method, wherein the coordinate transformation method comprises Clarke transformation and Park transformation; in addition, as shown in fig. 1, the speed regulator PI, the flux linkage estimation, and the control target prediction are mainly included, and the respective input amounts thereof can be obtained by conventional means in the art, so that description thereof will not be repeated.
The foregoing description is only of the preferred embodiments of the present invention, and all equivalent changes and modifications that come within the scope of the following claims are intended to be embraced therein.
Claims (3)
1. The utility model provides a permanent magnet synchronous motor model predictive control method based on quick weight optimization, the control system of this permanent magnet synchronous motor includes the dc-to-ac converter, the dc-to-ac converter includes three-phase bridge arm, each phase the bridge arm has two switching tubes respectively, two in each phase the bridge arm switching tubes correspond to and lie in upper bridge arm and lower bridge arm respectively, its characterized in that: the method comprises the following steps:
s1, establishing a mathematical model of a permanent magnet synchronous motor as follows;
（1），
（2），
（3），
（4），
wherein, electromagnetic torque expression is:（5）；
in the method, in the process of the invention,u sd 、u sq respectively represent the stator voltages in the dq axis coordinate system,i sd 、i sq respectively represent the stator currents in the dq axis coordinate system,L sd 、L sq respectively represent the dq-axis component of the stator inductance,ψ sd 、ψ sq respectively represent the dq-axis component of the stator flux linkage,R s for the resistance of the stator,pin the form of an polar pair number,ψ m is a magnetic linkage of a permanent magnet,ω r for the angular velocity of the rotor,T e for electromagnetic torque, d/dt is a differential operator;
s2, predicting multiple control targets, wherein the specific method comprises the following steps of:
the predicted value of the control target is obtained through forward Euler discretization by the following formula:(6) Wherein x (k) represents the value of the control target x in the kth sampling period, x (k+1) represents the value of the control target x in the (k+1) th sampling period, k represents the kth sampling period, k+1 represents the (k+1) th sampling period, T s Time for a single sampling period;
according to the mathematical model of the permanent magnet synchronous motor, the differential of the stator current at the moment k under the dq axis coordinate system is obtained as follows:
（7），
（8）；
wherein the formula (6) is substituted into the formula (7) and the formula (8), respectively, to obtain the firstk The equation for the stator current prediction for +1 sample periods is:
（9），
（10）；
the formula for obtaining the stator flux linkage predicted value of the (k+1) th sampling period is as follows:
（11），
（12），
obtain the firstk The equation for the electromagnetic torque prediction for +1 sample periods is:
（13）；
wherein i is sd (k + 1)、i sq (k+1) represents the predicted value of the stator current in the kth+1th sampling period, ψ, in the dq-axis coordinate system, respectively sd (k + 1)、ψ sq (k+1) represents the predicted value, T, of the dq-axis component of the stator flux linkage at the (k+1) th sampling period, respectively e Omega is the predicted value of the electromagnetic torque in the (k+1) th sampling period r (k) Rotor angular velocity for the kth sampling period;
s3, predicting a multi-control target optimization model, wherein the specific method comprises the following steps of: the multi-objective model predictive control cost function is established as follows:
，
in the method, in the process of the invention,T e * as a reference value for the electromagnetic torque,ψ sd * 、ψ sq * respectively representdqStator flux linkage reference values in the axis coordinate system,λ ψ andλ nw are all weight coefficients;
wherein,，hrepresenting one of the phases a, b or c of the three-phase bridge arm in the inverter, if the phase has a switching state of the switching tube, the phase is +.>=1, whereas 0; n is n sw (k) Switching times when the sampling period is k; />、/>And->Respectively and correspondingly expressed as the switch states of upper bridge arm switch tubes of a phase, b phase and c phase in the two-level three-phase inverter,/->=0、/>=0 and +.>Respectively expressed as a phase a, b phase and c phase in the inverterThe upper bridge arm switch tube of the c phase is conducted, and +.>=1、/>=1 and->=1 indicates that upper bridge arm switching tubes of a phase, b phase and c phase in the inverter are turned off, respectively;
s4, reducing the dimension of the multi-objective cost function, wherein the specific method comprises the following steps of: decomposing the cost function g into a plurality of error terms, wherein the expressions of the error terms are respectively as follows:
（15），
（16）,
（17）；
wherein,representing a torque error optimization term,/->Representing flux linkage error optimization term,/->Representing a switching frequency error optimization term;
s5, quick error sorting, wherein the specific method comprises the following steps:
step S5.1: according to the switching state of the three-phase switching tube of the two-level three-phase inverter, a three-bit binary number S= [ is obtained, />, />]Adopting a control input i and a control input j as input variables respectively, wherein i and j are respectively represented as serial numbers S of the three-bit binary numbers in decimal, i=0-7, and j=i+1-7;
step S5.2, establishing the voltage vectorThe relation of (2) is as follows: />= />(/>+a/>+a 2 />) The method comprises the steps of carrying out a first treatment on the surface of the In (1) the->Represents the dc bus voltage, a is a coefficient, and a=e j·2π/3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein the voltage vector->The subscript S in (a) represents the sequence number of the three-bit binary of the voltage vector in decimal, i.e., subscript s=i or j; inputting the control input i and the control input j, i=0 to 7, j=i+1 to 7 to obtain the voltage vector +.>Different values can be obtainedg n N is defined according to the selected error optimization term, and n=1-2; and, according to the conduction state of the upper bridge arm switch tube of the three phases in the single sampling period in the step S4, the +.>And byg 3 (j) Voltage vector reordering with monotonically increasing values as a criterion;
comparing the control input i and the control input j in pairs, ifg n (i) ＞g n (j) The serial numbers of the control input i and the control input j are exchanged and stored, ifg n (i)≤g n (j) The serial numbers of the control input i and the control input j are kept unchanged, and the comparison is completed to obtaing n (j) Voltage vector reordering with monotonically increasing error value as a criterion;
step S5.3: according to step S5.2, respectivelyg 1 (j)、g 2 (j) Andg 3 (j) Voltage vector reordering with monotonically increasing error value as a criterion;
step S5.4: according to the describedg n (j) The error values of (2) are arranged in order from small to large, and the ranking sequentially corresponds to A n [0]、A n [1]、……、A n [7]；
S6, index evaluation, wherein the specific method comprises the following steps: the ranking of each of said control inputs j is added as follows,(18) Wherein->Representing the torque error optimization term +.>Ranking of said control input j in step S5,/for>Representing said flux linkage error optimization term +.>Ranking of said control input j in step S5,/for>Representing the switching frequency error optimization term +.>Ranking of said control input j in step S5; and then selecting the control input j corresponding to the ranking addition minimum as global optimal quantity input.
2. The permanent magnet synchronous motor model predictive control method based on rapid weight optimization according to claim 1, wherein the method comprises the following steps: according to the control input j obtained in the step S6, combining with the step S5.2 to obtain a voltage vectorTo output +.>(k+1) to the controller.
3. The permanent magnet synchronous motor model predictive control method based on rapid weight optimization according to claim 1 or 2, characterized by comprising the following steps: the inverter is a two-level three-phase inverter.
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| CN108923698A (en) * | 2018-07-04 | 2018-11-30 | 天津大学 | A kind of motor control method of predicted voltage vector sequence |
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| CN108923698A (en) * | 2018-07-04 | 2018-11-30 | 天津大学 | A kind of motor control method of predicted voltage vector sequence |
| CN112019113A (en) * | 2020-09-01 | 2020-12-01 | 合肥工业大学 | Wind turbine generator optimization control method based on multi-objective model prediction |
| US11616462B1 (en) * | 2021-12-21 | 2023-03-28 | Industrial Technology Research Institute | Motor parameter estimation device and method |
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