CN111162708B - Asynchronous motor model prediction control method - Google Patents
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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
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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
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- H02P2207/01—Asynchronous machines
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Abstract
The invention discloses an asynchronous motor model prediction control method, which comprises the steps of constructing a cost function containing a stator flux linkage item at the k +1 moment and an electromagnetic torque item at the k +1 moment, 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 prediction control results.
Description
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 an application range of model predictive control.
Based on the above purpose, the invention provides a model prediction control method for an asynchronous motor, which comprises the following steps:
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
Wherein psi s Is stator flux linkage vector, psi r Is the rotor flux linkage vector, u s Is stator voltage vector, R s Is stator resistance, i s Is stator current vector, i r Is the rotor current vector, L s Is a stator inductance, L r Is the rotor inductance, L m For mutual inductance of stator, omega r Is the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
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
ψ s (k+1)＝ψ s (k)+T s [u s (k)-R s i s (k)]Predicted value of stator current at the time of k +1
Wherein T is s Representing a control period, j being the sign of the complex number, omega being the electrical angular velocity of the rotor, v s Is a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
Obtaining a predicted value of the electromagnetic torque at the moment k +1 as
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
Wherein,
for a given value of the electromagnetic torque, is greater or less than>
Given value of stator flux linkage, λ 0 Is 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
Wherein T is en For the nominal value of the electromagnetic torque, | | ψ sn And | 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
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
Wherein S is j_T Is the slope of the change of the electromagnetic torque in one control cycle, u opt Represents a first optimal voltage vector, S opt_T Slope of change, U, for optimum voltage vector ref As vector of reference voltage, u j Representing a second optimal voltage vector;
calculating vector action time
Wherein, T e_j (k + 1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, T e_opt (k + 1) represents u opt And 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
From the above, it can be seen that the asynchronous motor model predictive control method provided by the invention constructs the cost function including the stator flux linkage term at the time of k +1 and the electromagnetic torque term at the time of k +1, adopts the DTC table to select the first optimal voltage vector, obtains the voltage vector and the zero vector adjacent to the first optimal voltage vector, and selects the candidate voltage vector with the smallest cost function as the second optimal voltage vector, and calculates the vector control time of the second optimal voltage vector respectively, so as to obtain two groups of predictive control results.
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 further described in detail with reference to the following 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 (alpha, beta) 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 the 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 containing a stator flux linkage item at the k +1 moment and an electromagnetic torque item at the k +1 moment, 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 the 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
Wherein psi s Is stator flux linkage vector, psi r Is the rotor flux linkage vector, u s Is stator voltage vector, R s Is stator resistance, i s Is stator current vector, i r Is the rotor current vector, L s Is a stator inductance, L r Is the rotor inductance, L m For mutual inductance of stator, omega r Is the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
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
ψ s (k+1)＝ψ s (k)+T s [u s (k)-R s i s (k)]
And the predicted value of the stator current at the moment k +1
Wherein T is s Representing a control period, j being the sign of a complex number, omega being the electrical angular velocity of the rotor, v s Is a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
Obtaining the pre-torque of the electromagnetic torque at the moment k +1Measured value is
For example, when discretizing a mathematical model of an asynchronous induction motor and a rotor flux linkage vector calculation formula, a first-order euler method is used to discretize 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
Wherein,
for a given value of the electromagnetic torque, is greater or less than>
Given value of stator flux linkage, λ 0 Is 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
Wherein T is en For the nominal value of the electromagnetic torque, | | ψ sn And | is a rated value of the stator flux linkage.
Because the dimensions of the electromagnetic torque and the given value of 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
In a discrete digital system, the optimal voltage vector calculated at the time k starts to act only 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 the 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
Wherein S is j_T Is the slope of the change of the electromagnetic torque in one control cycle, u opt Representing a first optimum voltage vector, S opt_T Slope of change, U, for optimum voltage vector ref As vector of reference voltage, u j Representing a second optimal voltage vector;
calculating vector action time
Wherein, T e_j (k + 1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, T e_opt (k + 1) represents u opt And 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 T s Only 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 T s Slope of change of internal torque S j _ T Can be represented as T e_j (k+1)-T e (k)＝S j_T ·T s
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 table opt As shown in table 1.
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 selected j . With deadbeat control, the output of torque at the next sampling period is equal to the setpoint, so that the torque and the resultant reference voltage can be expressed as
The vector action time can be calculated
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) method 2 According to the voltage vector selection principle, another voltage vector participating in the synthesis is u 1 、u 3 Or u 0 。
In one embodiment, when the calculated vector action time is greater than the control period, the vector action time is processed according to the following formula
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, a dead beat method is adopted, but under some special conditions (such as load sudden disturbance), 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 times of the two voltage vectors are both between 0 and T s Within the range, and when exceeded, calculated according to the following formula:
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, equivalents, improvements, and the like that may be made without departing from the spirit or scope of the present invention are intended to be included within the scope of the present invention.
Claims (6)
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, and substituting the voltage vector and the zero vector as 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;
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;
the calculating the vector action time of the first optimal voltage vector and the second optimal voltage vector respectively comprises the following steps:
the electromagnetic torque and the synthesized reference voltage are expressed as
Wherein S is j_T Is the slope of the change of the electromagnetic torque in one control cycle, u opt Representing a first optimum voltage vector, S opt_T Slope of change, U, for optimum voltage vector ref As a vector of reference voltages，u j Representing a second optimal voltage vector;
calculating vector action time
Wherein, T e (k + 1) represents a predicted value of the electromagnetic torque at the time k +1, T e_j (k + 1) is a predicted value of the electromagnetic torque at the time of k +1 when the voltage vector is used, T e_opt (k + 1) represents u opt The predicted value of the electromagnetic torque at the time k +1 in the case of the voltage vector,
given value of electromagnetic torque, T e (k) Predicted value, t, representing electromagnetic torque at time k opt Representing the vector action time, T s Indicating one control cycle.
2. The method for model predictive control of an asynchronous machine according to claim 1, wherein 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
Wherein psi s Is stator flux linkage vector, psi r Is the rotor flux linkage vector, u s Is stator voltage vector, R s Is stator resistance, R r Is the rotor resistance, i s Is stator current vector, i r Is the rotor current vector, L s Is stator inductance, L r Is the rotor inductance, L m For mutual inductance of stator, omega r Is the rotor electrical angular velocity, p is the pole pair number;
calculating to obtain a rotor flux linkage vector calculation formula
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
ψ s (k+1)＝ψ s (k)+T s [u s (k)-R s i s (k)]Predicted value of stator current at the time of k +1
Where j is the sign of the complex number, ω is the rotor electrical angular velocity, v s Is a voltage vector;
the calculation formula of the electromagnetic torque obtained by estimation is
The predicted value of the electromagnetic torque at the moment of k +1 is obtained
Wherein->
Representing the complex conjugate of the stator flux linkage vector.
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
Wherein,
given value of stator flux linkage, λ 0 Is a weight coefficient of the stator flux linkage, T e (k + 1) represents a predicted value, ψ, of the electromagnetic torque at the time of k +1 s And (k + 1) represents a stator flux linkage vector at the moment of k +1, and | x | | | is a mathematical operator and represents the absolute value of a vector modulus.
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 per-unit processed cost function
Wherein T is en For the nominal value of the electromagnetic torque, | | ψ sn And | 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 per-unit cost function, 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
6. The method of claim 1 wherein when the calculated vector application time is greater than the control period, the vector application time is processed as follows
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