CN111162708A - Asynchronous motor model prediction control method - Google Patents

Asynchronous motor model prediction control method Download PDF

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CN111162708A
CN111162708A CN202010037002.3A CN202010037002A CN111162708A CN 111162708 A CN111162708 A CN 111162708A CN 202010037002 A CN202010037002 A CN 202010037002A CN 111162708 A CN111162708 A CN 111162708A
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vector
flux linkage
voltage vector
electromagnetic torque
cost function
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CN111162708B (en
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向超群
陈春阳
于天剑
成庶
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Central South University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/01—Asynchronous machines

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Abstract

The invention discloses an asynchronous motor model predictive control method, which comprises the steps of constructing a cost function containing a stator flux linkage item at the moment of k +1 and an electromagnetic torque item at the moment of k +1, selecting a first optimal voltage vector by adopting a DTC (digital time control) table, obtaining a voltage vector and a zero vector adjacent to the first optimal voltage vector, using the first optimal voltage vector as an alternative voltage vector, selecting an alternative voltage vector with the minimum cost function as a second optimal voltage vector, and calculating the vector control time of the second optimal voltage vector respectively to obtain two groups of predictive control results.

Description

Asynchronous motor model prediction control method
Technical Field
The invention relates to the technical field of model predictive control, in particular to a model predictive control method for an asynchronous motor.
Background
Model Predictive Control (MPC) is a kind of special control, its present control action is obtained by solving a finite time domain open loop optimal control problem at each sampling instant, model predictive control is an advanced control algorithm based on rolling time domain multi-parameter optimization, and is mainly used to solve the control problem in the process industry traditionally, especially in recent years with the rapid development of digital signal processors, the model predictive control strategy is rapidly developed and applied in the field of motor control;
in the conventional motor model prediction torque control, only one voltage vector is output in one control period, and when the switching frequency is low and the control period is long, the action time of a single optimal voltage vector can cause the control effect to exceed the expectation.
Disclosure of Invention
In view of this, the present invention provides a model predictive control method for an asynchronous motor, so as to improve the application range of the model predictive control.
Based on the above object, the present invention provides an asynchronous motor model prediction control method, which includes:
calculating to obtain a predicted value of a stator flux linkage at the moment k +1 and a predicted value of electromagnetic torque at the moment k +1 by using a mathematical model of the asynchronous induction motor under a two-phase static coordinate system;
constructing a cost function containing a stator flux linkage term at the moment k +1 and an electromagnetic torque term at the moment k + 1;
selecting a first optimal voltage vector by adopting a direct torque control table;
selecting a voltage vector and a zero vector adjacent to the first optimal voltage vector as alternative voltage vectors, and respectively substituting the alternative voltage vectors into a cost function for calculation;
selecting the candidate voltage vector with the minimum cost function as a second optimal voltage vector;
and respectively using the first optimal voltage vector and the second optimal voltage vector to calculate the corresponding vector action time to obtain a prediction control result.
Preferably, the calculating to obtain the predicted value of the stator flux linkage at the time k +1 and the predicted value of the electromagnetic torque at the time k +1 comprises:
the mathematical model of the asynchronous induction motor under the two-phase static coordinate system is established as
Figure BDA0002366385340000021
Wherein psisFor stator flux linkage vector, #rIs the rotor flux linkage vector, usIs stator voltage vector, RsIs stator resistance, isIs stator current vector, irIs the rotor current vector, LsIs a stator inductance, LrIs the rotor inductance, LmFor mutual inductance of stator, omegarIs the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
Figure BDA0002366385340000022
Discretizing a mathematical model of the asynchronous induction motor and a rotor flux linkage vector calculation formula to obtain a stator flux linkage predicted value at the moment of k +1
ψs(k+1)＝ψs(k)+Ts[us(k)-Rsis(k)]Predicted value of stator current at the time of k +1
Figure BDA0002366385340000023
Wherein T issRepresenting a control period, j being the sign of the complex number, omega being the electrical angular velocity of the rotor, vsIs a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
Figure BDA0002366385340000024
Obtaining a predicted value of the electromagnetic torque at the moment k +1 as
Figure BDA0002366385340000025
Preferably, constructing a cost function containing the stator flux linkage term at the time k +1 and the electromagnetic torque term at the time k +1 includes:
a cost function of
Figure BDA0002366385340000026
Wherein the content of the first and second substances,
Figure BDA0002366385340000031
is a given value of the electromagnetic torque,
Figure BDA0002366385340000032
given value of stator flux linkage, λ0Is the weighting factor of the stator flux linkage.
Preferably, after constructing the cost function including the stator flux linkage term and the electromagnetic torque term, the method further includes:
per-unit processing the cost function to obtain the cost function after per-unit processing
Figure BDA0002366385340000033
Wherein T isenFor the nominal value of the electromagnetic torque, | | ψsnAnd | is a rated value of the stator flux linkage.
Preferably, the per-unit processing the cost function to obtain the per-unit processed cost function further includes:
delay compensation is carried out on the cost function after per unit, and a cost function containing a stator flux linkage term at the moment of k +2 and an electromagnetic torque term at the moment of k +2 is constructed
Figure BDA0002366385340000034
Preferably, calculating the vector action time by respectively using the first optimal voltage vector and the second optimal voltage vector comprises:
the electromagnetic torque and the synthesized reference voltage are expressed as
Figure BDA0002366385340000035
Wherein S isj_TIs the slope of the change of the electromagnetic torque in one control cycle, uoptRepresenting a first optimum voltage vector, Sopt_TSlope of change, U, for optimum voltage vectorrefIs a reference voltageVector ujRepresenting a second optimal voltage vector;
calculating vector action time
Figure BDA0002366385340000036
Wherein, Te_j(k +1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, Te_opt(k +1) represents uoptAnd in the case of voltage vectors, the predicted value of the electromagnetic torque at the moment k + 1.
Preferably, when the calculated vector action time is greater than the control period, the vector action time is processed as follows
Figure BDA0002366385340000041
From the above, the asynchronous motor model predictive control method provided by the invention selects the first optimal voltage vector by constructing the cost function containing the stator flux linkage term at the moment k +1 and the electromagnetic torque term at the moment k +1 and adopting the DTC table, and obtaining a voltage vector and a zero vector adjacent to the voltage vector as alternative voltage vectors, selecting the alternative voltage vector with the minimum cost function as a second optimal voltage vector, respectively calculating the vector control time of the second optimal voltage vector, two groups of prediction control results can be obtained, compared with the traditional model prediction control method, the method improves the characteristics of low switching frequency and long control period, the action time of a single optimum voltage vector may cause problems in the control effect beyond what is expected, the obtained prediction control result can meet the control requirements under more practical conditions, and the application range and the accuracy of model prediction control are improved.
Drawings
Fig. 1 is a schematic flow chart of a model predictive control method for an asynchronous motor according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating an analysis of the effects of voltage vector torque and flux linkage according to an embodiment of the present invention;
FIG. 3 is a DTC voltage space vector diagram according to an embodiment of the present invention;
FIG. 4 is a vector diagram of flux linkage voltage space according to an embodiment of the present invention;
FIG. 5 is a block diagram of model predictive control according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
A method for model predictive control of an asynchronous machine, as shown in fig. 1, includes the following steps:
s101, obtaining a predicted value of the electromagnetic torque at the moment k +1 by using a mathematical model of the asynchronous induction motor under a two-phase (α) static coordinate system;
s102, constructing a cost function containing a stator flux linkage term at the moment k +1 and an electromagnetic torque term at the moment k + 1;
s103, selecting a first optimal voltage vector by adopting a Direct Torque Control (DTC) table;
s104, selecting a voltage vector and a zero vector adjacent to the first optimal voltage vector, and substituting the voltage vector and the zero vector as alternative voltage vectors into the cost function respectively for calculation;
s105, selecting a candidate voltage vector with the minimum cost function as a second optimal voltage vector;
s106, the first optimal voltage vector and the second optimal voltage vector are respectively used, corresponding vector action time is calculated, and a prediction control result is obtained.
The method comprises the steps of constructing a cost function comprising a stator flux linkage term at the moment k +1 and an electromagnetic torque term at the moment k +1, selecting a first optimal voltage vector by adopting a DTC table, obtaining a voltage vector and a zero vector which are adjacent to the first optimal voltage vector, using the first optimal voltage vector as an alternative voltage vector, selecting the alternative voltage vector with the minimum cost function as a second optimal voltage vector, and calculating vector control time of the second optimal voltage vector respectively.
As an embodiment, the step of calculating the predicted value of the stator flux linkage at the time k +1 and the predicted value of the electromagnetic torque at the time k +1 includes:
the mathematical model of the asynchronous induction motor under the two-phase static coordinate system is established as
Figure BDA0002366385340000051
Wherein psisFor stator flux linkage vector, #rIs the rotor flux linkage vector, usIs stator voltage vector, RsIs stator resistance, isIs stator current vector, irIs the rotor current vector, LsIs a stator inductance, LrIs the rotor inductance, LmFor mutual inductance of stator, omegarIs the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
Figure BDA0002366385340000052
Discretizing a mathematical model of the asynchronous induction motor and a rotor flux linkage vector calculation formula to obtain a stator flux linkage predicted value at the moment of k +1
ψs(k+1)＝ψs(k)+Ts[us(k)-Rsis(k)]
Predicted value of stator current at the time of k +1
Figure BDA0002366385340000061
Wherein T issRepresenting a control period, j being the sign of the complex number, omega being the electrical angular velocity of the rotor, vsIs a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
Figure BDA0002366385340000062
Obtaining a predicted value of the electromagnetic torque at the moment k +1 as
Figure BDA0002366385340000063
For example, when the mathematical model of the asynchronous induction motor and the rotor flux linkage vector calculation formula are discretized, a first-order euler method is used for discretizing the formula.
As an embodiment, constructing a cost function containing a stator flux linkage term at time k +1 and an electromagnetic torque term at time k +1 includes:
the cost function is
Figure BDA0002366385340000064
Wherein the content of the first and second substances,
Figure BDA0002366385340000065
is a given value of the electromagnetic torque,
Figure BDA0002366385340000066
given value of stator flux linkage, λ0Is the weighting factor of the stator flux linkage.
For a three-phase asynchronous motor control system, the main targets of model predictive control comprise a motor stator flux linkage and an electromagnetic torque tracking given value, so that a cost function containing a stator flux linkage item at the moment of k +1 and an electromagnetic torque item at the moment of k +1 is constructed according to the predictive control target.
As an embodiment, after constructing the cost function including the stator flux linkage term and the electromagnetic torque term, the method further includes:
per-unit processing the cost function to obtain the cost function after per-unit processing
Figure BDA0002366385340000067
Wherein T isenFor the nominal value of the electromagnetic torque, | | ψsnAnd | is a rated value of the stator flux linkage.
Because the dimensions of the given values of the electromagnetic torque and the stator flux linkage are different, the cost function is unified, and the control difficulty is reduced.
As an implementation manner, performing per-unit on the cost function to obtain a per-unit cost function, further including:
delay compensation is carried out on the cost function after per unit, and a cost function containing a stator flux linkage term at the moment of k +2 and an electromagnetic torque term at the moment of k +2 is constructed
Figure BDA0002366385340000071
In a discrete digital system, the optimal voltage vector calculated at the time k starts to function at the time k +1 because the calculation time cannot be ignored. Therefore, the system has a one-beat delay, and if the system is not compensated, the system performance is deteriorated, and large control errors of the stator current and the electromagnetic torque occur. To compensate for the adverse effects of one beat delay, the electromagnetic torque and stator flux linkage at time k +2 need to be predicted.
As an embodiment, calculating the vector action time by using the first optimal voltage vector and the second optimal voltage vector respectively comprises:
the electromagnetic torque and the synthesized reference voltage are expressed as
Figure BDA0002366385340000072
Wherein S isj_TIs the slope of the change of the electromagnetic torque in one control cycle, uoptRepresenting a first optimum voltage vector, Sopt_TSlope of change, U, for optimum voltage vectorrefTo be a vector of reference voltages, the reference voltage vector,ujrepresenting a second optimal voltage vector;
calculating vector action time
Figure BDA0002366385340000073
Wherein, Te_j(k +1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, Te_opt(k +1) represents uoptAnd in the case of voltage vectors, the predicted value of the electromagnetic torque at the moment k + 1.
In the conventional model-predicted torque control, one control period TsOnly one voltage vector is output, and when the switching frequency is low and the control period is long, the action time of a single optimal voltage vector can cause the control effect to exceed the expectation. As shown in fig. 2, one control period TsSlope of change of internal torque Sj_TCan be represented as Te_j(k+1)-Te(k)＝Sj_T·Ts
In fig. 2, different voltage vectors correspond to different slopes, and the minimum torque ripple can be obtained in the deadbeat control of the torque, but the flux linkage ripple is large, and different torque and flux linkage control effects can be obtained when the action time of the voltage vector is adjusted.
One optimal voltage vector u can be quickly selected by adopting a traditional DTC tableoptAs shown in table 1.
Figure BDA0002366385340000081
TABLE 1
Where, Φ -1 represents increasing flux linkage, Φ -0 represents decreasing flux linkage, τ -1 represents increasing torque, τ -0 represents decreasing torque, and the DTC voltage space vector diagram is shown in fig. 3.
According to the principle that only one-phase switch is allowed to switch at the same time, the adjacent vector or zero vector u of the optimal voltage vector is selectedj. With deadbeat control, the torque output in the next sampling period is equal to the setpoint, and therefore the torque and the resultant reference voltageCan be expressed as
Figure BDA0002366385340000082
The vector action time can be calculated
Figure BDA0002366385340000083
As shown in FIG. 4, assuming the flux linkage is at (0, π/3)), an optimal vector is selected as u according to the conventional Model Predictive Control (MPC) method2According to the voltage vector selection principle, another voltage vector participating in the synthesis is u1、u3Or u0。
In one embodiment, when the calculated vector action time is greater than the control period, the vector action time is processed as follows
Figure BDA0002366385340000084
It can be seen from fig. 4 that different voltage vectors have different effects on the torque, and when the action time of the voltage vector is obtained, the dead-beat method is adopted, but under some special conditions (such as sudden disturbance of load), a given voltage cannot be followed in a control period, and the action time of the voltage vector is longer than the control period, so that it is required to ensure that the action time of the two voltage vectors is between 0 and TsWithin the range, and when exceeded, calculated according to the following formula:
Figure BDA0002366385340000085
the control block diagram of the method is shown in fig. 5.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (7)

1. A method for model predictive control of an asynchronous machine, the method comprising:
calculating to obtain a predicted value of a stator flux linkage at the moment k +1 and a predicted value of electromagnetic torque at the moment k +1 by using a mathematical model of the asynchronous induction motor under a two-phase static coordinate system;
constructing a cost function containing a stator flux linkage term at the moment k +1 and an electromagnetic torque term at the moment k + 1;
selecting a first optimal voltage vector by adopting a direct torque control table;
selecting a voltage vector and a zero vector adjacent to the first optimal voltage vector as alternative voltage vectors, and substituting the alternative voltage vectors into the cost function for calculation;
selecting the candidate voltage vector with the minimum cost function as a second optimal voltage vector;
and respectively using the first optimal voltage vector and the second optimal voltage vector to calculate the corresponding vector action time to obtain a prediction control result.
2. The method for model predictive control of an asynchronous machine according to claim 1, characterized in that said calculating a predicted value of stator flux linkage at time k +1 and a predicted value of electromagnetic torque at time k +1 comprises:
the mathematical model of the asynchronous induction motor under the two-phase static coordinate system is established as
Figure FDA0002366385330000011
Wherein psisFor stator flux linkage vector, #rIs the rotor flux linkage vector, usIs stator voltage vector, RsIs stator resistance, isIs stator current vector, irIs the rotor current vector, LsIs a stator inductance, LrIs the rotor inductance, LmFor mutual inductance of stator, omegarIs the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
Figure FDA0002366385330000012
Discretizing a mathematical model of the asynchronous induction motor and a rotor flux linkage vector calculation formula to obtain a stator flux linkage predicted value at the moment of k +1
ψs(k+1)＝ψs(k)+Ts[us(k)-Rsis(k)]Predicted value of stator current at the time of k +1
Figure FDA0002366385330000013
Wherein T issRepresenting a control period, j being the sign of a complex number, ω being the electrical angular velocity of the rotor, vsIs a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
Figure FDA0002366385330000021
Obtaining a predicted value of the electromagnetic torque at the moment k +1 as
Figure FDA0002366385330000022
3. The method for model predictive control of an asynchronous machine according to claim 1, wherein the constructing a cost function containing a stator flux linkage term at time k +1 and an electromagnetic torque term at time k +1 comprises:
the cost function is
Figure FDA0002366385330000023
Wherein the content of the first and second substances,
Figure FDA0002366385330000024
is a given value of the electromagnetic torque,
Figure FDA0002366385330000025
given value of stator flux linkage, λ0Is the weighting factor of the stator flux linkage.
4. The method for model predictive control of an asynchronous machine according to claim 3, wherein, after constructing the cost function comprising the stator flux linkage term and the electromagnetic torque term, the method further comprises:
per-unit processing the cost function to obtain the cost function after per-unit processing
Figure FDA0002366385330000026
Wherein T isenFor the nominal value of the electromagnetic torque, | | ψsnAnd | is a rated value of the stator flux linkage.
5. The method according to claim 4, wherein the per-unit processing of the cost function to obtain a per-unit cost function further comprises:
delay compensation is carried out on the cost function after per unit, and a cost function containing a stator flux linkage term at the moment of k +2 and an electromagnetic torque term at the moment of k +2 is constructed
Figure FDA0002366385330000027
6. The method for model predictive control of an asynchronous machine according to claim 1, characterized in that said calculating the vector action time for the first and second optimal voltage vectors, respectively, comprises:
the electromagnetic torque and the synthesized reference voltage are expressed as
Figure FDA0002366385330000028
Wherein S isj_TIs the slope of the change of the electromagnetic torque in one control cycle, uoptRepresenting a first optimum voltage vector, Sopt_TSlope of change, U, for optimum voltage vectorrefIs a vector of reference voltages, ujRepresenting a second optimal voltage vector;
calculating vector action time
Figure FDA0002366385330000031
Wherein, Te_j(k +1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, Te_opt(k +1) represents uoptAnd in the case of voltage vectors, the predicted value of the electromagnetic torque at the moment k + 1.
7. The method of claim 6 wherein the vector action time is processed as follows when the calculated vector action time is greater than the control period
Figure FDA0002366385330000032
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