CN112994565B - Permanent magnet synchronous motor three-vector five-sector model prediction current control algorithm - 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
- 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
- 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
- H02P25/024—Synchronous motors controlled by supply frequency
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- 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 three-vector five-sector model prediction current control algorithm of a permanent magnet synchronous motor, which mainly comprises the following steps: establishing a mathematical model of the permanent magnet synchronous motor, and calculating the current change rates of a d axis and a q axis when different voltage vectors act; selecting five voltage vector groups, wherein each group comprises three non-zero voltage vectors, and solving the action time of each voltage vector in each group in a dead-beat manner for the five selected voltage vector groups; after pretreatment is carried out on the action time, a new voltage vector is synthesized; predicting the current of the d axis and the q axis at the next moment to obtain five groups of predicted d-q axis current values; and finally, correspondingly comparing the q-axis current value and the d-axis current value obtained by the five groups of predictions with the given current by using a cost function, and selecting an optimal group of voltage vectors. Compared with the traditional three-vector model prediction current control algorithm of the permanent magnet synchronous motor, the calculation amount is reduced by one sixth, and the suppression effect on the common-mode voltage is better.
Description
Technical Field
The invention belongs to the field of permanent magnet synchronous motor control, and particularly relates to a three-vector five-sector model prediction current control algorithm of a permanent magnet synchronous motor.
Background
In the driving of an alternating current motor, a permanent magnet synchronous motor is concerned by researchers and different industries in recent years due to the advantages of high power density, high efficiency, large torque-ampere ratio and the like. As a high-performance motor, the motor has the main characteristics of quick dynamic response, high tracking precision, easiness in realization, no influence of motor parameter change on operation, small torque ripple and the like. In order to fully utilize the advantages of the permanent magnet synchronous motor, many methods have been proposed to control the characteristics of the motor, among which the most commonly used methods are vector control, direct torque control, model predictive control, and the like.
As for model predictive control, it has been widely studied and used in recent years because of its advantages of simple control concept, fast dynamic response, multivariable control, and convenience in handling nonlinear constraints. Although the model predictive control has many advantages, the model predictive control has the defects of large current ripple, large common-mode voltage, large calculation amount and the like due to the fixed direction of the applied voltage vector, fixed amplitude, limited number of selectable vectors and the like. In order to improve the system performance, the existing methods are vector number increase, lag compensation, cost function optimization, multi-step prediction and the like. In the method of increasing the number of vectors, there are a single vector method, a double vector method, a three vector method, and the like according to the number of combinations of vectors. How to make the calculation process simpler and how to reduce the common mode voltage on the premise of being able to select the optimal voltage vector are the technical problems to be solved urgently at present.
Disclosure of Invention
In order to make the algorithm of the permanent magnet synchronous motor three-vector model prediction current control method simpler and restrain the common-mode voltage, the invention provides a permanent magnet synchronous motor three-vector five-sector model prediction current control algorithm. The method aims to solve the problems that the conventional permanent magnet synchronous motor three-vector model prediction current control method has more prediction times and larger common-mode voltage.
In order to achieve the purpose, the invention adopts the following technical scheme.
Firstly, obtaining a stator voltage equation set of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q axis, and obtaining u by using the equation set 0 -u 6 Rate of change of d-and q-axis currents acting on each other
And
the equation is:
wherein u d And u q Voltage components on the d-axis and q-axis, respectively; i.e. i d And i q The current components on the d axis and the q axis at the moment are respectively;
is the rotor flux linkage amplitude; l is d And L q The inductance components on the d-axis and the q-axis, respectively; r is s Is a stator resistor; omega e Is the electrical angular velocity; t is the time taken for the current to change.
When using zero-voltage vector effects
And
to indicate the action of other effective voltage vectors
And
and each sampling period is composed of three non-zero voltage vectors u i 、u j 、u h Function, the calculation equation is as follows:
wherein s is d0 And S q0 I at zero voltage vector action respectively d And i q The rate of change of (c); l is s Is a stator inductance; s is di And s qi Are each u i Time of action i d And i q The rate of change of (c); s dj And s qj Are each u j Time of action i d And i q The rate of change of (c); s dh And s qh Are each u h When acting i d And i q The rate of change of (c); u. u di And u qi Are each u i In d-axis and q-axisThe component of (a); u. of dj And u qj Are each u j Components on the d-axis and q-axis; u. of dh And u qh Are each u h The components on the d-axis and q-axis.
Then for this period at u i 、u j 、u h I at the next moment under the action of three voltage vectors d And i q Making prediction and using dead beat method to make next sampling time i q And i d Is respectively equal to the given q-axis current output by the speed loop PI and the given d-axis current output by the outside, the calculation equation is as follows:
wherein i d (k) And i q (k) Current components on a d axis and a q axis at the current moment are respectively; i.e. i d (k + 1) and i q (k + 1) are the current components on the d-axis and q-axis, respectively, of the predicted next time instant; t is t i 、t j 、t h Are each u i 、 u j 、u h The corresponding action time; i all right angle d * And i q * Are respectively i d And i q Given value of (a).
Knowing that the sum of the action times of the three effective vectors is one sampling period, the calculation equation is as follows:
T s ＝t i +t j +t h
wherein T is s Is the sampling period.
Combining the calculation equations mentioned in the above steps to solve t i 、t j 、t h The operation method is as follows:
where M is a quantity set for convenience of calculation.
Then to t i 、t j 、t h And (4) carrying out pretreatment.If some of the time is less than zero, it is made equal to zero. And further summing the three times, and if the result is more than one sampling period, performing overmodulation processing, wherein the overmodulation processing method comprises the following steps:
the sum of the three times after overmodulation is one sampling period.
Will u 2 、u 4 、u 6 And u 1 、u 3 、u 5 And u 1 、u 2 、u 3 And u 3 、u 4 、u 5 And u 5 、u 6 、u 1 The five groups of voltage vectors are solved through the steps to obtain five groups of t i 、t j 、t h Then, obtaining the components of the five groups of synthesized voltage vectors on the d axis and the q axis through each group of voltage vectors and the respective action time of each voltage vector, wherein the synthesis operation method comprises the following steps:
it is assumed that the sampling period is affected by the resultant voltage vector.
Finally, the obtained five groups u d And u q Are respectively brought into i d (k + 1) and i q The calculation formula of (k + 1) yields five groups i d (k + 1) and i q (k + 1). Then, a value function formula is utilized to select the nearest given value i from the five groups of results d * And i q * I of (a) d (k + 1) and i q (k + 1), selecting the group i d (k + 1) and i q (k + 1) as the voltage vector group to be applied in the next cycle, i d (k + 1) and i q The calculation formula of (k + 1) and the cost function g are as follows:
wherein u is d (k) And u q (k) Selecting components of the applied composite voltage vector on the d-axis and the q-axis for the current moment respectively; omega e (k) The current electrical angular velocity of the permanent magnet synchronous motor.
The invention provides a three-vector five-sector model prediction current control algorithm for a permanent magnet synchronous motor, which has the beneficial effects that: compared with the traditional permanent magnet synchronous motor three-vector model prediction current control which needs six times of prediction operation to select the optimal vector group and calculate the action time of each vector in the vector group, the method can select the optimal vector group and calculate the action time of each vector in the vector group by only five times of prediction operation; the optimal vector group selected by the invention does not contain a zero voltage vector, and compared with the traditional three-vector model prediction current control, the common-mode voltage of the optimal vector group is reduced.
Drawings
FIG. 1 is a block diagram of the system control of the present invention;
FIG. 2 is a voltage vector diagram according to the present invention;
FIG. 3 is a schematic diagram of the range of five voltage vectors combined in the present invention;
FIG. 4 is a waveform diagram of the simulation rotating speed of the permanent magnet synchronous motor of the present invention;
FIG. 5 is a diagram of a simulated torque waveform of the PMSM according to the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Fig. 1 is a system control block diagram of the present invention, describing the main steps of the technical solution of the present invention:
step one, obtaining a stator voltage equation set of a permanent magnet synchronous motor under a synchronous rotation coordinate system d-q axis, obtaining a calculation formula of current change rates of the d axis and the q axis by using the equation set, and measuring phase current i through a rotor angle theta a And i b To proceed withThe d-axis current and the q-axis current are obtained through coordinate transformation;
step two, calculating u 0 -u 6 Rate of change of current in d-and q-axes with seven voltage vectors acting alone, where u 0 -u 6 The size and direction of (A) are shown in FIG. 2;
step three, aligning at u 1 、u 3 、u 5 Predicting the currents of the d axis and the q axis at the next moment under the action of the three voltage vectors, and enabling the predicted values of the currents of the q axis and the d axis at the next moment to be respectively equal to the given q axis current and the given d axis current outside the speed loop PI by adopting a dead beat method;
step four, obtaining a group of three-dimensional linear equations and solving the three linear equations by using the equation written in the dead-beat method and knowing that the sum of the action time of the three vectors is equal to the sampling period to obtain the respective action time of the three vectors in one sampling period;
and step five, processing the action time of the vector, and if the action time is a negative value, taking the action time of the vector as zero. The three vector times are further summed, and if the result is greater than the sampling period, overmodulation processing is carried out on the result;
step six, synthesizing the expected voltage vectors of the three selected voltage vectors to obtain components of the synthesized voltage vectors on d-q axes of a synchronous rotating coordinate system;
step seven, using u 2 、u 4 、u 6 And u 1 、u 2 、u 3 And u 3 、u 4 、u 5 And u 5 、u 6 、u 1 Four groups of voltage vectors respectively replace u 1 、u 3 、u 5 Repeating the operation from the third step to the sixth step to finally obtain the components of the five groups of expected voltage vectors on the d-q axis of the synchronous rotating coordinate system;
step eight, substituting components of the five groups of expected voltage vectors on d-q axes of the synchronous rotating coordinate system into current prediction formulas of the d axis and the q axis respectively to obtain current prediction values of the five groups of d axis and q axis, obtaining the current prediction values of the d axis and the q axis closest to a given value by using a value function formula, selecting the current prediction values of the group of d axis and the q axis closest to the given valueThe voltage vector group corresponding to the predicted value is used as the voltage vector group to be applied in the next period, and the PWM switch control signal S is applied according to the action time of each of the three vectors calculated in the fourth step a 、S b 、S c The applied voltage vector is sent to the inverter.
Further description of the main steps is described in the following paragraphs.
Firstly, obtaining a stator voltage equation set of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q axis, and obtaining u by using the equation set 0 -u 6 Rate of change of d-and q-axis currents acting on each other
And
the equation is:
wherein u d And u q Voltage components on the d-axis and q-axis, respectively; i.e. i d And i q The current components on the d axis and the q axis at the moment are respectively;
is the rotor flux linkage amplitude; l is d And L q The inductance components on the d-axis and the q-axis, respectively; r is s Is a stator resistor; omega e Is the electrical angular velocity; t is the time taken for the current to change.
When using zero-voltage vector effects
And
to indicate the effect of other effective voltage vectors
And
and each sampling period is composed of three non-zero voltage vectors u i 、u j 、u h Function, the calculation equation is as follows:
wherein S d0 And S q0 I at zero voltage vector action respectively d And i q The rate of change of (c); l is s A stator inductor; s is di And s qi Are each u i When acting i d And i q The rate of change of (c); s dj And s qj Are each u j Time of action i d And i q The rate of change of (c); s is dh And s qh Are each u h When acting i d And i q The rate of change of (c); u. of di And u qi Are each u i Components on the d-axis and q-axis; u. of dj And u qj Are each u j Components on the d-axis and q-axis; u. of dh And u qh Are each u h The components on the d-axis and q-axis.
Then for this period at u i 、u j 、u h I at the next moment under the action of three voltage vectors d And i q Predicting, and adopting dead beat method to make the next time i q And i d Is equal to the given q-axis current output by the speed loop PI and the given d-axis current externally, respectively, the calculation equation is as follows:
wherein i d (k) And i q (k) Current components on a d axis and a q axis at the current moment are respectively; i all right angle d (k + 1) and i q (k + 1) are the predicted current components on the d-axis and q-axis, respectively, at the next time instant; t is t i 、t j 、t h Are each u i 、 u j 、u h The corresponding action time; i.e. i d * And i q * Are respectively i d And i q Given value of (a).
Knowing that the sum of the action times of the three effective vectors is one sampling period, the calculation equation is as follows:
T s ＝t i +t j +t h
wherein T is s Is the sampling period.
The calculation equations mentioned in the above steps are combined to solve t i 、t j 、t h The operation method is as follows:
where M is a quantity set for convenience of calculation.
Then to t i 、t j 、t h And (4) carrying out pretreatment. If a certain time is less than zero, the time is equal to zero. And further summing the three times, and if the result is greater than one sampling period, performing overmodulation processing, wherein the overmodulation processing method comprises the following steps:
the sum of the three times after overmodulation is one sampling period.
As shown in fig. 3, five groups of voltage vectors are selected, in the figure, solid line arrows indicate actually applied voltage vectors, dashed line arrows indicate non-applied voltage vectors, and inside the thick solid line closed region, there are regions where three applied voltage vectors are located, and the synthesized voltage vectors can be obtained by changing the acting time ratios of the three applied voltage vectors. It can be seen in the figure that the sum of five regions of the synthesized voltage vectors can fully cover the whole hexagon, namely, the selectable region of the synthesized voltage vectors and the conventional three-vector model predictive current control of the permanent magnet synchronous motorThe same is true. Will u 2 、 u 4 、u 6 And u 1 、u 3 、u 5 And u 1 、u 2 、u 3 And u 3 、u 4 、u 5 And u 5 、u 6 、u 1 The five groups of voltage vectors are solved through the steps to obtain five groups of t i 、t j 、t h Then, obtaining the components of the five groups of synthesized voltage vectors on the d axis and the q axis through each group of voltage vectors and the respective action time of each voltage vector, wherein the synthesis operation method comprises the following steps:
it is assumed that the sampling period is affected by the resultant voltage vector.
Finally, the obtained five groups u d And u q Are respectively brought into i d (k + 1) and i q The calculation formula of (k + 1) yields five groups i d (k + 1) and i q (k + 1). Then, a value function formula is utilized to select the nearest given value i from the five groups of results d * And i q * I of (a) d (k + 1) and i q (k + 1), selecting the group i d (k + 1) and i q (k + 1) as a voltage vector group to be applied in the next cycle, i d (k + 1) and i q The calculation formula of (k + 1) and the cost function g are as follows:
wherein u is d (k) And u q (k) Selecting components of the applied composite voltage vector on a d axis and a q axis for the current moment respectively; omega e (k) The current electrical angular velocity of the permanent magnet synchronous motor.
Fig. 4 and 5 are a rotation speed diagram and an electromagnetic torque diagram obtained by simulation, respectively, the simulation time is 0.2s, the rotation speed of the motor is set to 1000 revolutions per minute, and a load torque of 0.38Nm is suddenly added at 0.1 second. Important parameters of the motor applied in the simulation: the rotor flux linkage size is 0.35Wb; the voltage of the direct current bus is 150V; the stator resistance is 1.55 omega; the stator inductance is 6.71mH.
In summary, the principles of the present invention can be summarized as follows: in order to simplify the calculation of selecting an optimal vector group and acting time of each vector for the three-vector model prediction current control of the permanent magnet synchronous motor and to suppress common-mode voltage, the invention provides a three-vector five-sector model prediction current control algorithm of the permanent magnet synchronous motor. The alternative vector group does not contain a zero voltage vector, and the common-mode voltage is smaller than that of a traditional three-vector model current prediction method.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
Claims (9)
1. A three-vector five-sector model prediction current control algorithm of a permanent magnet synchronous motor is characterized by comprising the following steps:
acquiring a stator voltage equation set of a permanent magnet synchronous motor under a d-q axis of a synchronous rotation coordinate system, and obtaining a calculation formula of current change rates of the d axis and the q axis by using the equation set;
step two, calculating u 0 -u 6 The d-axis and q-axis current rates of change when seven voltage vectors act alone;
step three, aligning at u 1 、u 3 、u 5 Predicting the currents of the d axis and the q axis at the next moment under the action of the three voltage vectors, and enabling the predicted values of the currents of the q axis and the d axis at the next moment to be respectively equal to the given q axis current and the given d axis current outside the speed loop PI by adopting a dead beat method;
step four, obtaining a group of three-dimensional linear equations and solving the three linear equations by using the equation written by the dead-beat method and knowing that the sum of the action time of the three vectors is equal to the sampling period to obtain the respective action time of the three vectors in one sampling period;
step five, processing the vector action time, if the action time is a negative value, taking the vector action time as zero, further summing the three vector times, and if the result is greater than the sampling period, performing overmodulation processing on the vector action time;
step six, synthesizing the expected voltage vectors of the three selected voltage vectors to obtain components of the synthesized voltage vectors on d-q axes of a synchronous rotating coordinate system;
step seven, using u 2 、u 4 、u 6 And u 1 、u 2 、u 3 And u 3 、u 4 、u 5 And u 5 、u 6 、u 1 Four groups of voltage vectors respectively replace u 1 、u 3 、u 5 Repeating the operation from the third step to the sixth step to finally obtain the components of the five groups of expected voltage vectors on the d-q axis of the synchronous rotating coordinate system;
and step eight, substituting components of the five groups of expected voltage vectors on d-q axes of the synchronous rotating coordinate system into current prediction formulas of the d axis and the q axis respectively to obtain current prediction values of the five groups of d axis and q axis, obtaining the current prediction values of the d axis and the q axis closest to a given value by using a value function formula, selecting a voltage vector group corresponding to the current prediction values as a voltage vector group to be applied in the next period, and applying according to respective action time of the three vectors calculated in the step four.
2. The permanent magnet synchronous motor three-vector five-sector model prediction current control algorithm of claim 1, characterized in that a stator voltage equation set of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q axis is obtained, and first u is obtained by using the equation set 0 -u 6 Rate of change of d-axis and q-axis current when each acts
And
the equation is:
wherein u d And u q Voltage components on the d-axis and q-axis, respectively; i all right angle d And i q The current components on the d axis and the q axis at the moment are respectively;
is the rotor flux linkage amplitude; l is d And L q The inductance components on the d-axis and the q-axis respectively; r s Is a stator resistor; omega e Is the electrical angular velocity; t is the time taken for the current to change.
3. The algorithm for predicting the current of the PMSM three-vector five-sector model according to claim 2, wherein the algorithm is implemented by using zero-voltage vector
And
to indicate the action of other effective voltage vectors
And
and each sampling period is composed of three non-zero voltage vectors u i 、u j 、u h Function, the calculation equation is as follows:
wherein s is d0 And s q0 I at zero voltage vector action respectively d And i q The rate of change of (c); l is s Is a stator inductance; s di And s qi Are each u i Time of action i d And i q The rate of change of (c); s dj And s qj Are each u j Time of action i d And i q The rate of change of (c); s dh And s qh Are each u h When acting i d And i q The rate of change of (c); u. of di And u qi Are each u i Components on the d-axis and q-axis; u. of dj And u qj Are each u j Components on the d-axis and q-axis; u. of dh And u qh Are each u h The components on the d-axis and q-axis.
4. The PMSM three-vector five-sector model prediction current control algorithm of claim 3, wherein for the current period, u is i 、u j 、u h I at the next moment under the action of three voltage vectors d And i q Performing prediction, and enabling the next sampling time i to be the next sampling time by adopting a dead-beat method q And i d Is equal to the given q-axis current output by the speed loop PI and the given d-axis current externally, respectively, the calculation equation is as follows:
wherein i d (k) And i q (k) Current components on a d axis and a q axis at the current moment are respectively; i all right angle d (k + 1) and i q (k + 1) are the predicted current components on the d-axis and q-axis, respectively, at the next time instant; t is t i 、t j 、t h Are each u i 、u j 、u h The corresponding action time; i.e. i d * And i q * Are respectively i d And i q Given values of (a).
5. The algorithm for controlling the predicted current of the permanent magnet synchronous motor based on the three-vector five-sector model is characterized in that the sum of the acting time of three effective vectors is one sampling period, and the calculation equation is as follows:
T s ＝t i +t j +t h
wherein T is s Is the sampling period.
6. The PMSM three-vector five-sector model prediction current control algorithm as claimed in claim 5, wherein the calculation equations mentioned in the above steps are combined to solve t i 、t j 、t h The operation method is as follows:
where M is a quantity set for convenience of calculation.
7. The PMSM three-vector five-sector model predictive current control algorithm of claim 6, wherein t is to be measured i 、t j 、t h Preprocessing is carried out, if a certain time is less than zero, the certain time is equal to zero, then the three times are summed, and if the result is more than one sampling period, overmodulation processing is carried out, wherein the overmodulation processing method comprises the following steps:
the sum of the three times after overmodulation is one sampling period.
8. The permanent magnet synchronous motor three-vector five-sector model predictive current control algorithm of claim 7,characterized in that u is 2 、u 4 、u 6 And u 1 、u 3 、u 5 And u 1 、u 2 、u 3 And u 3 、u 4 、u 5 And u 5 、u 6 、u 1 The five groups of voltage vectors are solved through the steps to obtain five groups of t i 、t j 、t h Then, obtaining the components of the five groups of synthesized voltage vectors on the d axis and the q axis through each group of voltage vectors and the respective action time of each voltage vector, wherein the synthesis operation method comprises the following steps:
it is assumed that the sampling period is affected by the resultant voltage vector.
9. The PMSM three-vector five-sector model prediction current control algorithm as claimed in claim 8, wherein five groups u are obtained d And u q Are respectively brought into i d (k + 1) and i q The calculation formula of (k + 1) yields five groups i d (k + 1) and i q (k + 1), selecting the nearest given value i from the five groups of results by using a value function formula d * And i q * I of (a) d (k + 1) and i q (k + 1), selecting the group i d (k + 1) and i q (k + 1) as the voltage vector group to be applied in the next cycle, i d (k + 1) and i q The calculation formula of (k + 1) and the cost function g are as follows:
wherein u is d (k) And u q (k) Selecting components of the applied composite voltage vector on the d-axis and the q-axis for the current moment respectively; omega e (k) The current electrical angular velocity of the permanent magnet synchronous motor.
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