CN117134670A - Double three-phase PMSM model-free prediction current control method based on EKO - Google Patents

Double three-phase PMSM model-free prediction current control method based on EKO Download PDF

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CN117134670A
CN117134670A CN202311169080.9A CN202311169080A CN117134670A CN 117134670 A CN117134670 A CN 117134670A CN 202311169080 A CN202311169080 A CN 202311169080A CN 117134670 A CN117134670 A CN 117134670A
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voltage vector
virtual voltage
axis
vector
model
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张志锋
孙全增
于佳正
张清艺
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Shenyang University of Technology
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Shenyang University of Technology
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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
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P21/0021—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using different modes of control depending on a parameter, e.g. the speed
    • 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
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • 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
    • 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
    • H02P25/16—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the circuit arrangement or by the kind of wiring
    • H02P25/22—Multiple windings; Windings for more than three phases
    • 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
    • H02P27/08—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 with pulse width modulation
    • H02P27/12—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 with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque 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
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Abstract

The invention provides an EKO-based double three-phase PMSM model-free predictive current control method, and relates to the technical field of multiphase motor control. Firstly, the super local model containing parameter disturbance items is established, and the robustness of the system under the condition of parameter mismatch is improved. Secondly, a Kalman observer is introduced to observe a nonlinear part of the system, the precision of a super local model is improved, a modulated virtual voltage vector is introduced, and by utilizing the dead beat principle, two adjacent virtual voltage vectors and a zero vector are utilized in one sampling period, so that the modulation range is enlarged, and the control error is reduced; then, in the generation mode of the switching sequence, a triangular wave is provided as a carrier wave to generate an asymmetric PWM wave, and the reference value modulation wave is updated at a position of Ts/2, so that the implementation difficulty on software is reduced, and the implementation on a low-cost microprocessor is easier.

Description

Double three-phase PMSM model-free prediction current control method based on EKO
Technical Field
The invention relates to the technical field of multiphase motor control, in particular to a double three-phase PMSM model-free predictive current control method based on EKO.
Background
The advent of high-performance semiconductor power devices and the advent of high-performance permanent magnet materials has laid a solid foundation for the application of PMSM in industrial fields since the 21 st century. Permanent magnet synchronous motors have advantages over induction motors in terms of power density and mechanical efficiency. Among them, the double three-phase PMSM is more advantageous in terms of torque ripple, system stability, power density, etc. than the three-phase motor. Therefore, the double three-phase PMSM is increasingly used in the fields of electric automobiles, aerospace, wind power generation and the like. Harmonic currents of the multiphase system can lead to larger copper losses, reducing the efficiency of the overall system. The students solve this problem from different technical levels. The PI-SVPWM algorithm based on FOC is a relatively mature three-phase drive development technology. With the development of multi-phase motors, PI-SVPWM algorithms have been extended from three-phase motor drives to multi-phase motor drive systems. Compared with FOC control, the direct torque control structure is simpler and has better robustness.
In the last 10 years, the MPC technology is rapidly developed by model predictive control, and the MPC has the advantages of simple concept, rapid transient response and easy realization of multi-objective optimization. MPC techniques can be divided into continuous set model predictive control that incorporates modulation techniques and finite set model predictive control that produces a finite number of voltage vectors. Model prediction techniques can be divided into model predicted torque control and model predicted current MPCC control, and the MPCC method is successfully applied to multiphase driving systems, but MPCC has inherent disadvantages: high harmonic currents, variable switching frequencies and heavy computational burden. The MPC method has very high lazy performance on motor parameters, parameters of a motor system can change along with external factors such as motor temperature, mechanical vibration and the like, and in addition, dead zone setting of an inverter, fluctuation of bus voltage and the like can influence establishment of an accurate model.
The model-free prediction method is developed rapidly in nearly five years, and has the characteristics of adaptability to various systems, independence of parameters and strong robustness. At present, a double three-phase PMSM model-free prediction control method is more studied, but the traditional model-free prediction method has some limitations. For example, the accuracy requirements for the sensor are high and the errors estimated for algebraic analysis are large. To address this problem, researchers have introduced observers to estimate nonlinear parts in a super local model, including: extended observer, sliding mode observer, etc., but the observer gain is a fixed value. On the contrary, the Kalman observer EKO takes the minimum variance as a criterion, can adaptively adjust a gain coefficient matrix, optimally estimates a nonlinear part in the super local model, and improves control performance; for the modulation part, the conventional model-free prediction method adopts a method of combining an effective vector and a zero vector in one sampling period, and is limited in voltage modulation range.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides the double three-phase PMSM model-free prediction current control method based on EKO, which improves the robustness of the system under the condition of parameter mismatch, improves the precision of a super local model, increases the modulation range, reduces the control error, reduces the implementation difficulty on software and is easier to realize on a microprocessor with low cost.
The model-free predictive current control method of the double three-phase PMSM based on EKO comprises the following steps:
step 1: establishing a mathematical model of the double three-phase motor;
establishing a mathematical model of the double three-phase permanent magnet synchronous motor under the d-q axis, as follows:
and establishing a mathematical model of the double three-phase permanent magnet synchronous motor in the x-y axis, wherein the mathematical model is as follows:
wherein u is d And u q Is the voltage on the d and q axes, i d And i q Is the current on the d and q axes, u x And u y Is the voltage on the x and y axes, i x And i y Is the current in the x and y axes, R s Is the stator resistance omega r Is the electrical angular velocity, L s Is inductance, L ls Represents leakage inductance, ψ f Representing the permanent magnet flux linkage, d/dt is a differential factor.
Step 2: synthesizing a virtual voltage vector;
amplitude in alpha-beta subspace is 0.64U dc Is defined as L 1 Group U dc For bus voltage, i.e. (V) 64 、V 44 、V 45 、V 55 、V 51 、V 11 、V 13 、V 33 、V 32 、V 22 、V 26 、V 66 ) Will have an amplitude of 0.47U dc Is defined as L 2 The group, i.e. (V) 46 、V 65 、V 54 、V 41 、V 15 、V 53 、V 31 、V 24 、V 15 、V 36 、V 54 、V 12 ) The method comprises the steps of carrying out a first treatment on the surface of the L in the same direction 1 Group sum L 2 The two voltage vectors of the set are in the same direction in the alpha-beta subspace and in opposite directions in the x-y subspace, from L in the same direction 1 Group sum L 2 Taking one basic voltage vector from each group to synthesize a virtual voltage vector, wherein L is 1 The selected voltage vector in the group is called V m The method comprises the steps of carrying out a first treatment on the surface of the The voltage vector in the L2 group is called V n The method comprises the steps of carrying out a first treatment on the surface of the The two basic voltage vectors act with a certain duty cycle such that the average value in the x-y plane is equal to zero, thus V m And V n The resulting virtual voltage vector is calculated as follows:
η 1 v of (V) n Duty cycle, eta 2 Is V (V) m Duty cycle of (2);
step 3: providing a modulation virtual voltage vector based on online synthesis;
each modulation virtual voltage vector is synthesized by two end virtual voltage vectors of the sector, namely two adjacent virtual voltage vectors and a zero vector; the modulated virtual voltage vector is named number MVV 1 -MVV 12 Modulating virtual voltage vector MVV j The synthesis expression of (2) is as follows:
MVV j ＝d j VV j +d j+1 VV (j+1) +d 0 V 0 (4)
wherein d j 、d j+1 And d 0 Duty cycles representing the first virtual voltage vector, the second virtual voltage vector, and the zero vector, respectively; wherein VV j 、VV (j+1) 、V 0 The method comprises the steps of respectively obtaining a first virtual voltage vector, a second virtual voltage vector and a zero vector, wherein the first virtual voltage vector represents a virtual voltage vector with smaller serial numbers at the edge of each sector, and the second virtual voltage vector represents a virtual voltage vector with larger serial numbers in the same sector as the first virtual voltage vector;
step 4: establishing a PMSM mathematical model and a super local model of motor parameter mismatch;
since the average value of the virtual voltage vector on the x-y plane is zero, the mathematical model of the motor on the x-y plane can be omitted, and only the mathematical model on the d-q axis is considered, and in the PMSM mathematical model, the voltage equation is specifically expressed as:
wherein DeltaR s 、ΔL s 、Δψ f Mismatch degree lambda of stator resistance, inductance and permanent magnet flux linkage respectively d 、λ q And (3) respectively rewriting the formula (6) to obtain a dynamic equation for current, wherein the dynamic equation is as follows:
by calculation of the above formula, the super-local model of the motor is expressed as:
wherein ζ=1/L s Linear interference term F d 、F q The concrete steps are as follows:
performing Euler treatment on the formula (9) by adopting a first-order Euler method to obtain a super-local model of the discrete system:
i s (k+1)＝i s (k)+T s (ξu(k)+G(k)) (10)
wherein T is s Is the sampling period; wherein,
wherein i is d (k) And i q (k) Currents of d axis and q axis at k time; u (u) d (k) And u q (k) Voltages applied at the time k to the d axis and the q axis respectively; f (F) d (k) And F q (k) The linear interference terms of the d-axis and the q-axis at the time k are respectively.
Step 5: designing a cost function and selecting an optimal voltage vector in the modulated virtual voltage vectors;
the cost function is specifically:
wherein i is d * (k) And i q * (k) The given values of d-axis and q-axis currents respectively; i.e d (k+1) and i q (k+1) is a current prediction estimation value at the time k+1 on the d axis and the q axis respectively;
screening out an optimal voltage vector in the 12 modulated virtual voltage vectors by using a cost function of a formula (12), wherein the optimal voltage vector refers to the modulated virtual voltage vector with the minimum cost function;
step 6: the duty cycle of each modulated virtual voltage vector is calculated.
In order to enable d-axis and q-axis currents to track to reference values without errors, the acting time of each modulated virtual voltage vector is calculated by using a dead beat current control principle, as shown in the following formula:
wherein T is s For sampling period, i d * And i q * Reference currents of d-axis and q-axis, respectively; d, d j 、d j+1 And d 0 The action time of the first virtual voltage vector, the second virtual voltage vector and the zero vector is respectively;and->The current slopes on d and q axes when the first virtual voltage vector, the second virtual voltage vector and the zero vector act are respectively calculated by a super local model of a discrete system in the formula (10), and the current slopes of the vectors are as follows:
wherein VV jz 、VV (j+1)z 、V 0z A first virtual voltage vector, a second virtual voltage vector, a zero vector, and z=d or z=q, respectively, of the d and q axes, respectively;
calculating the acting time of the vectors, and solving the acting time of each vector by using a simultaneous equation:
wherein,
t 0 ＝T s -t j -t j+1 (19)
when t j And t j+1 Greater than T s When the voltage is applied, the effectiveness of the applied voltage is ensured, for t j And t j+1 And (3) correcting:
step 7: designing an extended Kalman observer based on a super local model of a discrete system;
will be a linear interference term F d 、F q The extended Kalman observer state equation based on the discrete system super-local model design is defined as an extended state variable as follows:
wherein,
wherein I is 2×2 Is a 2-order identity matrix; o (O) 2×2 Is a 2-order unit zero matrix.
Discretizing the formula (22) by adopting a first-order Euler formula to obtain the following discrete equation:
wherein I is 4×4 Is a 4-order identity matrix;
the relevant jacobian matrix is calculated as:
wherein the superscript-is the predicted value, and the superscript-represents the estimated value;
the extended kalman observer is divided into a prediction stage and an updating stage, wherein the prediction stage comprises two parts, specifically:
(1) Predicting the state variable, predicting the state variable at the next time using the output and the state estimate at the previous time should be:
(2) Calculating an error covariance matrix p (k):
wherein Q represents a process performance noise covariance matrix;
the updating stage comprises three parts, specifically:
(1) Calculating a gain matrix K (K):
wherein R represents a measurement noise covariance matrix, H (k) = [ I ] 2×2 O 2×2 ]。
(2) Calculating an optimal estimated value
Where y (k) is the output value corresponding to the predicted quantity.
(3) Updating an error covariance matrix for calculating the next error covariance matrix:
step 8: performing switching sequences and digital implementation;
in the increasing/decreasing mode of the DSP, the registers CMPA and CMPB are in the T of the switching period s 2, updating, namely changing the reference value modulation wave to realize the generation of an asymmetric PWM signal, comparing the triangular carrier wave with four reference value modulation waves, wherein each of the six phases corresponds to one or two reference value modulation waves, and when the reference value modulation waves are equal to the triangular carrier wave value for the first time, the switching signal jumps from low level to high level; modulating waves and three when reference valuesWhen the angle carrier values are equal for the second time, the switching signal jumps from high level to low level, and an asymmetric PWM signal is realized.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in:
the invention provides an EKO-based double three-phase PMSM model-free predictive current control method. The robustness of the system under the condition of parameter mismatch is improved. The precision of the super local model is improved, the modulated virtual voltage vector is introduced, the dead beat principle is utilized, two adjacent virtual voltage vectors and one zero vector are utilized in one sampling period, the modulation range is enlarged, and the control error is reduced. Generating asymmetric PWM wave by using triangular wave as carrier wave, and modulating wave at T with reference value s And 2, updating the position of the software, thereby reducing the implementation difficulty on the software and being easier to implement on a low-cost microprocessor.
Drawings
FIG. 1 is a flowchart of a predictive current control method according to an embodiment of the present invention;
FIG. 2 is a graph of voltage vector distribution of an α - β subspace provided by an embodiment of the present invention;
FIG. 3 is a graph showing voltage vector distribution in an x-y subspace according to an embodiment of the present invention;
FIG. 4 is a graph of virtual voltage vector distribution in an α - β subspace provided by an embodiment of the present invention;
FIG. 5 is a diagram of a modulation virtual voltage vector and a synthesis mode according to an embodiment of the present invention;
fig. 6 is a switching sequence diagram provided in an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
The EKO-based double three-phase PMSM model-free prediction current control method, as shown in FIG. 1, comprises the following steps:
step 1: establishing a mathematical model of the double three-phase motor;
establishing a mathematical model of the double three-phase permanent magnet synchronous motor under the d-q axis, as follows:
and establishing a mathematical model of the double three-phase permanent magnet synchronous motor in the x-y axis, wherein the mathematical model is as follows:
wherein u is d And u q Is the voltage on the d and q axes, i d And i q Is the current on the d and q axes, u x And u y Is the voltage on the x and y axes, i x And i y Is the current in the x and y axes, R s Is the stator resistance omega r Is the electrical angular velocity, L s Is inductance, L ls Represents leakage inductance, ψ f Representing the permanent magnet flux linkage, d/dt is a differential factor.
Step 2: synthesizing a virtual voltage vector;
for DT-PMSM, the selection of the voltage vector has multiple degrees of freedom. The fundamental voltage vector on the alpha-beta subspace produces the rotational magnetomotive force of the motor, and the harmonic current is produced in the x-y subspace, the vector diagrams being shown in fig. 2 and 3. To suppress harmonic currents, virtual voltage vectors are introduced instead of basic voltage vectors, with an amplitude of 0.64U in the alpha-beta subspace dc Is defined as L 1 Group U dc For bus voltage, i.e. (V) 64 、V 44 、V 45 、V 55 、V 51 、V 11 、V 13 、V 33 、V 32 、V 22 、V 26 、V 66 ) Will have an amplitude of 0.47U dc Is defined as L 2 The group, i.e. (V) 46 、V 65 、V 54 、V 41 、V 15 、V 53 、V 31 、V 24 、V 15 、V 36 、V 54 、V 12 ) The method comprises the steps of carrying out a first treatment on the surface of the As can be seen from the view of figure 4,l in the same direction 1 Group sum L 2 The two voltage vectors of the set are in the same direction in the alpha-beta subspace and in opposite directions in the x-y subspace, so they have opposite characteristics on the harmonic components. L from the same direction 1 Group sum L 2 Taking one basic voltage vector from each group to synthesize a virtual voltage vector, wherein L is 1 The selected voltage vector in the group is called V m The method comprises the steps of carrying out a first treatment on the surface of the The voltage vector in the L2 group is called V n The method comprises the steps of carrying out a first treatment on the surface of the The two basic voltage vectors act according to a certain duty ratio, so that the average value is equal to zero on the x-y plane, and harmonic current can be effectively restrained. Thus V m And V n The resulting virtual voltage vector is calculated as follows:
η 1 v of (V) n Duty cycle, eta 2 Is V (V) m Duty cycle of (2); in the present embodiment, V is selected 65 、V 44 Then eta 1 ＝0.269，η 2 =0.731. Similarly, the rest 11 virtual vectors are derived from the theory, and the amplitude of the virtual voltage vector is 0.597U dc 。
Step 3: providing a modulation virtual voltage vector based on online synthesis; the full regular dodecagon modulation area can be covered, wherein each modulation virtual voltage vector is synthesized by two virtual voltage vectors at the two ends of the sector, namely two adjacent virtual voltage vectors and a zero vector; as shown in fig. 5, the modulated virtual voltage vector is named MVV 1 -MVV 12 Modulating virtual voltage vector MVV j The synthesis expression of (2) is as follows:
MVV j ＝d j VV j +d j+1 VV j+1 +d 0 V 0 (34)
wherein d j 、d j+1 And d 0 Duty cycles representing the first virtual voltage vector, the second virtual voltage vector, and the zero vector, respectively; wherein VV j 、VV j+1 、V 0 The method comprises the steps of respectively obtaining a first virtual voltage vector, a second virtual voltage vector and a zero vector, wherein the first virtual voltage vector represents a virtual voltage vector with smaller serial numbers at the edge of each sector, and the second virtual voltage vector represents a virtual voltage vector with larger serial numbers in the same sector as the first virtual voltage vector;
step 4: establishing a PMSM mathematical model and a super local model of motor parameter mismatch;
because the average value of the virtual voltage vector on the x-y plane is zero, the mathematical model of the motor on the x-y plane can be omitted, and only the mathematical model on the d-q axis is considered, when the motor parameters change and unknown interference items are considered, the voltage equation is specifically expressed as:
wherein DeltaR s 、ΔL s 、Δψ f Mismatch degree lambda of stator resistance, inductance and permanent magnet flux linkage respectively d 、λ q And (3) respectively rewriting the formula (6) to obtain a dynamic equation for current, wherein the dynamic equation is as follows:
by calculation of the above formula, the super-local model of the motor is expressed as:
wherein ζ=1/L s Linear interference term F d 、F q The concrete steps are as follows:
performing Euler treatment on the formula (9) by adopting a first-order Euler method to obtain a super-local model of the discrete system:
i s (k+1)＝i s (k)+T s (ξu(k)+G(k)) (40)
wherein T is s Is the sampling period; wherein,
wherein i is d (k) And i q (k) Currents of d axis and q axis at k time; u (u) d (k) And u q (k) Voltages applied at the time k to the d axis and the q axis respectively; f (F) d (k) And F q (k) The linear interference terms of the d-axis and the q-axis at the time k are respectively.
Step 5: designing a cost function and selecting an optimal voltage vector in the modulated virtual voltage vectors;
the function of the cost function is to compare the errors of the predicted value and the reference value to adjust the behavior of the system, and is specifically:
wherein i is d * (k) And i q * (k) The given values of d-axis and q-axis currents respectively; i.e d (k+1) and i q (k+1) is a current prediction estimation value at the time k+1 on the d axis and the q axis respectively;
the predictive current is corrected by using the feedback of an extended Kalman observer, the instability caused by parameter disturbance is reduced, the control precision is improved, and the optimal voltage vector in 12 modulated virtual voltage vectors is screened out by using the cost function of a formula (12), wherein the optimal voltage vector refers to the modulated virtual voltage vector with the minimum cost function; as can be seen from the formula (11),compared with the current prediction part in the traditional model prediction control, the predicted current value at the time of k+1 is only equal to voltage and F d 、F q And the motor parameter is not needed because of the relation with the scale factor, so that the control performance can be ensured when the motor parameter is mismatched.
Step 6: the duty cycle of each modulated virtual voltage vector is calculated.
In order to enable d-axis and q-axis currents to track to reference values without errors, the acting time of each modulated virtual voltage vector is calculated by using a dead beat current control principle, as shown in the following formula:
wherein T is s For sampling period, i d * And i q * Reference currents of d-axis and q-axis, respectively; d, d j 、d j+1 And d 0 The action time of the first virtual voltage vector, the second virtual voltage vector and the zero vector is respectively;and->The current slopes on d and q axes when the first virtual voltage vector, the second virtual voltage vector and the zero vector act are respectively calculated by a super local model of a discrete system in the formula (10), and the current slopes of the vectors are as follows:
wherein VV jz 、VV (j+1)z 、V 0z A first virtual voltage vector, a second virtual voltage vector, a zero vector, and z=d or z=q, respectively, of the d and q axes, respectively;
calculating the acting time of the vectors, and solving the acting time of each vector by using a simultaneous equation:
wherein,
t 0 ＝T s -t j -t j+1 (49)
when t j And t j+1 Greater than T s When the voltage is applied, the effectiveness of the applied voltage is ensured, for t j And t j+1 And (3) correcting:
step 7: designing an extended Kalman observer based on a super local model of a discrete system;
it is proposed here to design an extended kalman observer to improve the accuracy of the super local model of the discrete system. The extended Kalman observer can accurately estimate the state of the motor system in the measured data, and the linear interference term F d 、F q The extended Kalman observer state equation based on the discrete system super-local model design is defined as an extended state variable as follows:
wherein,
wherein I is 2×2 Is a 2-order identity matrix; o (O) 2×2 Is a 2-order unit zero matrix.
Discretizing the formula (22) by adopting a first-order Euler formula to obtain the following discrete equation:
wherein I is 4×4 Is a 4-order identity matrix;
the relevant jacobian matrix is calculated as:
wherein the superscript-is the predicted value, and the superscript-represents the estimated value;
the extended kalman observer is divided into a prediction stage and an updating stage, wherein the prediction stage comprises two parts, specifically:
(1) Predicting the state variable, predicting the state variable at the next time using the output and the state estimate at the previous time should be:
(2) Calculating an error covariance matrix p (k):
wherein Q represents a process performance noise covariance matrix;
the updating stage comprises three parts, specifically:
(1) Calculating a gain matrix K (K):
wherein R represents a measurement noise covariance matrix, H (k) = [ I ] 2×2 O 2×2 ]。
(2) Calculating an optimal estimated value
Where y (k) is the output value corresponding to the predicted quantity.
(3) Updating an error covariance matrix for calculating the next error covariance matrix:
step 8: carrying out a switching sequence and digital implementation, wherein the switching sequence diagram is shown in fig. 6;
in the increasing/decreasing mode of the DSP, the registers CMPA and CMPB are in the T of the switching period s 2, updating, namely changing the reference value modulation wave to realize the generation of an asymmetric PWM signal, comparing the triangular carrier wave with four reference value modulation waves, wherein each of the six phases corresponds to one or two reference value modulation waves, and when the reference value modulation waves are equal to the triangular carrier wave value for the first time, the switching signal jumps from low level to high level; when the reference value modulation wave is equal to the triangular carrier value for the second time, the switch signal jumps from high level to low level, and an asymmetric PWM signal is realized.
To modulate virtual voltage vector MVV 1 For example, six phases of P are listed hereWM wave principle.
First, the reference value modulated wave calculation is given:
wherein m is a 、m b 、m c And m d Modulating the values of the wave for four reference values; t (T) 1 、T 2 、T 3 And T 4 Is V (V) 44 、V 54 、V 65 And V 45 Is used for the action time of the (a).
The carrier wave is triangular wave, and the reference value of the modulated wave of A phase is identical before and after two half switching cycles, which is (T 1 +T 2 +T 3 +T 4 )/T s The method comprises the steps of carrying out a first treatment on the surface of the For phase B, the reference value of the modulated wave is (-T) in the first half period 1 -T 2 -T 3 -T 4 )/T s In the latter half period 2 x (T 3 -T 4 )/T s The method comprises the steps of carrying out a first treatment on the surface of the For phase C, the modulation wave reference value is also at T s The change occurs at/2, the first half period is 2 (T 2 -T 1 )/T s The second half period is (-T) 1 -T 2 -T 3 -T 4 )/T s The method comprises the steps of carrying out a first treatment on the surface of the The reference value of the modulated wave of the U phase is identical to that of the A phase and is (T 1 +T 2 +T 3 +T 4 )/T s The V-phase reference modulated wave is also unchanged in one period, and is (-T) 1 -T 2 -T 3 -T 4 )/T s The reference modulation wave value of the W phase is (-T) 1 -T 2 -T 3 -T 4 )/T s The second half period is (T 1 +T 2 +T 3 +T 4 )/T s ；
For T 1 、T 2 、T 3 、T 4 And T 0 Is calculated as follows:
in this embodiment, a modulated virtual voltage vector MVV is derived 1 As shown in the following table:
the foregoing description is only of the preferred embodiments of the present disclosure and description of the principles of the technology being employed. It will be appreciated by those skilled in the art that the scope of the invention in the embodiments of the present disclosure is not limited to the specific combination of the above technical features, but encompasses other technical features formed by any combination of the above technical features or their equivalents without departing from the spirit of the invention. Such as the above-described features, are mutually substituted with (but not limited to) the features having similar functions disclosed in the embodiments of the present disclosure.

Claims (9)

1. The model-free predictive current control method for the double three-phase PMSM based on the EKO is characterized by comprising the following steps of:
step 1: establishing a mathematical model of the double three-phase motor;
step 2: synthesizing a virtual voltage vector;
step 3: providing a modulation virtual voltage vector based on online synthesis;
step 4: establishing a PMSM mathematical model and a super local model of motor parameter mismatch;
step 5: designing a cost function and selecting an optimal voltage vector in the modulated virtual voltage vectors;
step 6: calculating the duty ratio of each modulated virtual voltage vector;
step 7: designing an extended Kalman observer based on a super local model of a discrete system;
step 8: and performing switching sequences and digital implementation.
2. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 1 is specifically:
establishing a mathematical model of the double three-phase permanent magnet synchronous motor under the d-q axis, as follows:
and establishing a mathematical model of the double three-phase permanent magnet synchronous motor in the x-y axis, wherein the mathematical model is as follows:
wherein u is d And u q Is the voltage on the d and q axes, i d And i q Is the current on the d and q axes, u x And u y Is the voltage on the x and y axes, i x And i y Is the current in the x and y axes, R s Is the stator resistance omega r Is the electrical angular velocity, L s Is inductance, L ls Represents leakage inductance, ψ f Representing the permanent magnet flux linkage, d/dt is a differential factor.
3. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 2 is specifically:
amplitude in alpha-beta subspace is 0.64U dc Is defined as L 1 Group U dc For bus voltage, i.e. (V) 64 、V 44 、V 45 、V 55 、V 51 、V 11 、V 13 、V 33 、V 32 、V 22 、V 26 、V 66 ) Will have an amplitude of 0.47U dc Is defined as L 2 The group, i.e. (V) 46 、V 65 、V 54 、V 41 、V 15 、V 53 、V 31 、V 24 、V 15 、V 36 、V 54 、V 12 ) The method comprises the steps of carrying out a first treatment on the surface of the L in the same direction 1 Group sum L 2 Two voltage vectors of the groupThe directions in the alpha-beta subspace are the same, and the directions in the x-y subspace are opposite, from L in the same direction 1 Group sum L 2 Taking one basic voltage vector from each group to synthesize a virtual voltage vector, wherein L is 1 The selected voltage vector in the group is called V m The method comprises the steps of carrying out a first treatment on the surface of the The voltage vector in the L2 group is called V n The method comprises the steps of carrying out a first treatment on the surface of the The two basic voltage vectors act with a certain duty cycle such that the average value in the x-y plane is equal to zero, thus V m And V n The resulting virtual voltage vector is calculated as follows:
η 1 v of (V) n Duty cycle, eta 2 Is V (V) m Is a duty cycle of (c).
4. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 3 is specifically:
each modulation virtual voltage vector is synthesized by two end virtual voltage vectors of the sector, namely two adjacent virtual voltage vectors and a zero vector; the modulated virtual voltage vector is named number MVV 1 -MVV 12 Modulating virtual voltage vector MVV j The synthesis expression of (2) is as follows:
MVV j ＝d j VV j +d j+1 VV (j+1) +d 0 V 0 (4)
wherein d j 、d j+1 And d 0 Duty cycles representing the first virtual voltage vector, the second virtual voltage vector, and the zero vector, respectively; wherein VV j 、VV (j+1) 、V 0 A first virtual voltage vector, a second virtual voltage vector, and a zero vector, respectively, the first virtual voltage vector representing each sectorThe virtual voltage vector with smaller edge number and the second virtual voltage vector represent the virtual voltage vector with larger number in the same sector as the first virtual voltage vector.
5. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 4 is specifically:
since the average value of the virtual voltage vector on the x-y plane is zero, the mathematical model of the motor on the x-y plane can be omitted, and only the mathematical model on the d-q axis is considered, and in the PMSM mathematical model, the voltage equation is specifically expressed as:
wherein DeltaR s 、ΔL s 、Δψ f Mismatch degree lambda of stator resistance, inductance and permanent magnet flux linkage respectively d 、λ q And (3) respectively rewriting the formula (6) to obtain a dynamic equation for current, wherein the dynamic equation is as follows:
by calculation of the above formula, the super-local model of the motor is expressed as:
wherein ζ=1/L s Linear interference term F d 、F q The concrete steps are as follows:
performing Euler treatment on the formula (9) by adopting a first-order Euler method to obtain a super-local model of the discrete system:
i s (k+1)＝i s (k)+T s (ξu(k)+G(k)) (10)
wherein T is s Is the sampling period; wherein,
wherein i is d (k) And i q (k) Currents of d axis and q axis at k time; u (u) d (k) And u q (k) Voltages applied at the time k to the d axis and the q axis respectively; f (F) d (k) And F q (k) The linear interference terms of the d-axis and the q-axis at the time k are respectively.
6. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 5 is specifically:
the cost function is specifically:
wherein i is d * (k) And i q * (k) The given values of d-axis and q-axis currents respectively; i.e d (k+1) and i q (k+1) is a current prediction estimation value at the time k+1 on the d axis and the q axis respectively;
and screening out the optimal voltage vector in the 12 modulated virtual voltage vectors by using the cost function of the formula (12), wherein the optimal voltage vector refers to the modulated virtual voltage vector with the minimum cost function.
7. The EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 6 is specifically:
in order to enable d-axis and q-axis currents to track to reference values without errors, the acting time of each modulated virtual voltage vector is calculated by using a dead beat current control principle, as shown in the following formula:
wherein T is s For sampling period, i d * And i q * Reference currents of d-axis and q-axis, respectively; d, d j 、d j+1 And d 0 The action time of the first virtual voltage vector, the second virtual voltage vector and the zero vector is respectively;and->The current slopes on d and q axes when the first virtual voltage vector, the second virtual voltage vector and the zero vector act are respectively calculated by a super local model of a discrete system in the formula (10), and the current slopes of the vectors are as follows:
wherein VV jz 、VV (j+1)z 、V 0z A first virtual voltage vector, a second virtual voltage vector, a zero vector, and z=d or z=q, respectively, of the d and q axes, respectively;
calculating the acting time of the vectors, and solving the acting time of each vector by using a simultaneous equation:
wherein,
t 0 ＝T s -t j -t j+1 (19)
when t j And t j+1 Greater than T s When the voltage is applied, the effectiveness of the applied voltage is ensured, for t j And t j+1 And (3) correcting:
8. the EKO-based double three-phase PMSM model-free predictive current control method according to claim 1, wherein the step 7 is specifically:
will be a linear interference term F d 、F q The extended Kalman observer state equation based on the discrete system super-local model design is defined as an extended state variable as follows:
wherein,
wherein I is 2×2 Is a 2-order identity matrix; o (O) 2×2 Is a 2-order unit zero matrix;
discretizing the formula (22) by adopting a first-order Euler formula to obtain the following discrete equation:
wherein I is 4×4 Is a 4-order identity matrix;
the relevant jacobian matrix is calculated as:
wherein the superscript-is the predicted value, and the superscript-represents the estimated value;
the extended kalman observer is divided into a prediction stage and an updating stage, wherein the prediction stage comprises two parts, specifically:
(1) Predicting the state variable, predicting the state variable at the next time using the output and the state estimate at the previous time should be:
(2) Calculating an error covariance matrix p (k):
wherein Q represents a process performance noise covariance matrix;
the updating stage comprises three parts, specifically:
(1) Calculating a gain matrix K (K):
wherein R represents a measurement noise covariance matrix, H (k) = [ I ] 2×2 O 2×2 ]；
(2) Calculating an optimal estimated value
Wherein y (k) is an output value corresponding to the predicted quantity;
(3) Updating an error covariance matrix for calculating the next error covariance matrix:
9. the EKO-based double three-phase PMSM model-free predictive current control method of claim 1, wherein said step 8 is specifically:
in the increasing/decreasing mode of the DSP, the registers CMPA and CMPB are in the T of the switching period s 2, updating, namely changing the reference value modulation wave to realize the generation of an asymmetric PWM signal, comparing the triangular carrier wave with four reference value modulation waves, wherein each of the six phases corresponds to one or two reference value modulation waves, and when the reference value modulation waves are equal to the triangular carrier wave value for the first time, the switching signal jumps from low level to high level; when the reference value modulation wave is equal to the triangular carrier value for the second time, the switch signal jumps from high level to low level, and an asymmetric PWM signal is realized.
CN202311169080.9A 2023-09-12 2023-09-12 Double three-phase PMSM model-free prediction current control method based on EKO Pending CN117134670A (en)

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