CN113093542A - Motor torque optimization finite set prediction control parallel computing method - Google Patents

Motor torque optimization finite set prediction control parallel computing method Download PDF

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CN113093542A
CN113093542A CN202110351424.2A CN202110351424A CN113093542A CN 113093542 A CN113093542 A CN 113093542A CN 202110351424 A CN202110351424 A CN 202110351424A CN 113093542 A CN113093542 A CN 113093542A
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CN113093542B (en
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许芳
陈虹
孟强
李斌
张琳
胡浩奇
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Jilin University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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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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    • H02P21/20—Estimation of torque
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Abstract

The invention relates to a motor torque optimization finite set predictive control parallel computing method, which comprises the following steps: s1: according to the target of motor torque optimization control, giving a description form of an optimization problem and obtaining a target function; s2: performing Euler discretization according to a continuous time model of the motor driving system to construct a prediction model of the system; s3: and performing parallel computing solution optimization on the prediction model and the objective function by adopting a trigger type parallel computing method to realize the optimal prediction control of the motor torque. Compared with the prior art, the method has the advantages that the algorithm is accelerated through a production line and a parallel computing method, and the real-time control of the motor torque optimization is realized.

Description

Motor torque optimization finite set prediction control parallel computing method
Technical Field
The invention relates to the field of motor control, in particular to a motor torque optimization finite set predictive control parallel computing method.
Background
The motor driving system is one of three core technologies of an electric automobile, and as a bottom layer execution unit, the motor driving system directly influences the yaw stability of the whole automobile and the execution of an energy management strategy, and the effective control of an inverter as a motor core component is the key of the motor driving control. Considering actual system constraints such as discrete switch states of the inverter, maximum stator current and the like, and a plurality of control requirements such as motor torque tracking, energy conservation and the like, the motor torque optimization control is a discontinuous multi-objective constraint optimization problem. The finite control set predictive control can directly optimize inverter discrete switch variables by considering system constraints, so as to realize multi-objective optimization of motor torque control, and inverter switch devices generally adopt high-frequency (dozens to hundreds of kHz) IGBTs or MOSFETs, and the switching frequency has high real-time requirements, but the finite set predictive control on-line traversal solving has large computational burden, so how to improve the computational performance of the finite set predictive control is a main bottleneck restricting the finite set predictive control application in motor control.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a motor torque optimization finite set predictive control parallel computing method.
The purpose of the invention can be realized by the following technical scheme:
a motor torque optimization finite set predictive control parallel computing method comprises the following steps:
s1: according to the target of motor torque optimization control, giving a description form of an optimization problem and obtaining a target function;
s2: performing Euler discretization according to a continuous time model of the motor driving system to construct a prediction model of the system;
s3: and performing parallel computing solution optimization on the prediction model and the objective function by adopting a trigger type parallel computing method to realize the optimal prediction control of the motor torque.
Preferably, the objective of the motor torque optimization control in step S1 is to control the motor stator d-q axis current to track the expected current value quickly, so as to realize the torque tracking and meet the dynamic requirement, and reduce the copper loss E inside the motorm。
Preferably, the objective function is:
Figure BDA0003002265360000021
s.t. x(k+i|k)＝f(x(k+i-1|k),u(k+i-1))，
u(k+i-1)∈{u0,u1,…,u7},i＝1,2,…p
wherein x (k + I | k) ═ I is definedd(k+i|k),Iq(k+i|k)]TIn order to predict the control sequence for the state,
Figure BDA0003002265360000022
for reference to the input sequence, Ts is a discrete step size, RmIs the resistance of the electrical winding or windings,
Figure BDA0003002265360000023
x(k)is a state quantity, u(k)To control the quantity, Id(k+i|k)Is the d-axis current of the ith step at time k,
Figure BDA0003002265360000024
is a d-axis current desired value, I, at the k + I timeq(k+i|k)Is the q-axis current of the ith step in the kth time,
Figure BDA0003002265360000025
is a desired value of the q-axis current at the k + I time(k+p)Is the current at time k + p, I(k+p)The current expectation value at the k + P moment is shown, P is the prediction step length, Q is a positive definite weighting matrix, P is a positive definite terminal punishment matrix, and R is a positive definite control quantity punishment matrix.
Preferably, the calculation of the objective function is divided into two layers of nodes, the first layer of nodes includes two nodes K1And two nodes K2The second layer node comprises a node Ji+1(1)、Ji+1(2)、Ji+1(3)、Ji+1(4) The calculation formula of each node is as follows:
Figure BDA0003002265360000026
Figure BDA0003002265360000027
Figure BDA0003002265360000028
Figure BDA0003002265360000029
Figure BDA00030022653600000210
Figure BDA00030022653600000211
wherein, Id(k + i +1| k) is the d-axis current of step i +1 at time k,
Figure BDA0003002265360000031
d-axis current expectation value of the (I + 1) th step in the k timeq(k + i +1| k) is the desired value of the q-axis current at step i +1 at time k,
Figure BDA0003002265360000032
is the q-axis current expected value m of the (i + 1) th step in the k-th time1Is the motor rotor mass.
Preferably, in step S2, the future dynamic prediction is performed according to the system dynamic model, euler discretization is performed according to the continuous time model of the motor driving system, and Ts is a discrete step size, so as to obtain the following discrete model:
Figure BDA0003002265360000033
wherein x is(k+i|k)Is the state quantity, x, of the ith step at the kth time(k+i-1|k)Is the state quantity of the step i-1 at the kth time, u(k+i-1|k)The control quantity of the step (i-1) at the k time,
Figure BDA0003002265360000034
are system matrix parameters.
Preferably, the system matrix parameters are respectively:
Figure BDA0003002265360000035
Figure BDA0003002265360000036
Figure BDA0003002265360000037
wherein L isd,LqEquivalent inductances of d-and q-axes, p, respectivelymIs the magnetic pole pair of the motor, phimFor the magnetic flux generated in the permanent magnet re-stator phase, d is the motor speed omegarAnd integrated to obtain thetae，VdcIs a DC supply voltage, RmBeing the resistance of the electronic winding, TsIn discrete steps.
Preferably, the prediction model includes a plurality of intermediate layer nodes when calculating: d(1,i)、D(2,i)、E(1,i)、E(2,i)The calculation formula is as follows:
D(1,i)＝a11Id(k+i)+a12(ωr)Iq(k+i)
D(2,i)＝a21(ωr)Id(k+i)+a12Iq(k+i)
E(1,i)＝b11(θe)Sa+b12(θe)Sb+b13(θe)Sc
E(2,i)＝b11(θe)Sa+b22(θe)Sb+b23(θe)Sc
wherein S isa,Sb,ScThe system input at the time k + i, a11,a12(ωr),a21(ωr),a22Is a matrix
Figure BDA0003002265360000038
Corresponding element, b11(θe),b12(θe),b13(θe),b21(θe),b22(θe),b23(θe) Is a matrix
Figure BDA0003002265360000039
Corresponding element, h21Is a matrix
Figure BDA0003002265360000041
Corresponding element, ωrAnd thetaeIs a time-varying parameter of the system,
the prediction model obtains a future state formula of the system current as follows:
Id(k+i+1)＝D(1,i)+D(2,i)
Iq(k+i+1)＝E(1,i)+E(2,i)+ωrh21。
preferably, the calculation formula of the objective function and the prediction model in step S3 is as follows:
J0＝0
Figure BDA0003002265360000042
Figure BDA0003002265360000043
wherein J is an objective function, x(k+i|k)Is the state quantity of the ith step at the kth time, rk+i|kAnd Q is a positive definite weighting matrix, P is a positive definite terminal punishment matrix, and R is a positive definite control quantity punishment matrix.
Preferably, in the triggered parallel computing method in step S3, the flag indicating that both the solution of the prediction model and the solution of the objective function in the current computation step are completed is used as the flag indicating the start of the next computation step, so as to implement the parallel computation of the prediction model and the objective function.
Preferably, in step S3, an FPGA chip is used to perform parallel computation solution.
Compared with the prior art, the method accelerates the solving process of the motor torque optimization finite set predictive control based on the trigger type parallel computation, namely, the computation of each level is completely finished, and then the node solving of the next level is started. Then, according to the characteristic that mutually independent nodes exist between the prediction model and the target function, on the basis of simplifying an optimization algorithm, a parallel computing structure of the prediction model and the target function in each prediction time domain is provided, so that the computing efficiency and the computing accuracy are effectively improved, the real-time control of the motor torque optimization is realized, and the real-time control effect is further improved.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a block diagram of the parallel computing of the motor drive system control of the present invention;
FIG. 3 is a diagram of a motor drive system predictive model calculation according to the present invention;
FIG. 4 is a future p-step dynamic prediction calculation chart of the motor drive system of the present invention;
FIG. 5 is a diagram of objective function J of the motor driving system of the present inventionk+i+1Calculating a graph;
FIG. 6 is a parallel calculation chart of motor torque optimization finite set predictive control realized based on FPGA;
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. Note that the following description of the embodiments is merely a substantial example, and the present invention is not intended to be limited to the application or the use thereof, and is not limited to the following embodiments.
Examples
A parallel computing method for motor torque optimization finite set predictive control, as shown in FIG. 1, comprises the following steps:
s1: and according to the target of the motor torque optimization control, giving a description form of an optimization problem and obtaining an objective function.
According to the expected torque Te of the motor, the expected current value under an expected d-q reference frame can be calculated
Figure BDA0003002265360000051
And
Figure BDA0003002265360000052
therefore, the motor torque control target is to control the d-q axis current of the motor stator to track the expected current value quickly, realize that the torque tracks quickly to meet the dynamic requirement, reduce the copper loss Em inside the motor and meet the economic requirement. And (3) giving a specific description form of the optimization problem according to the control target:
Figure BDA0003002265360000053
s.t. x(k+i|k)＝f(x(k+i-1|k),u(k+i-1))，
u(k+i-1)∈{u0,u1,…,u7},i＝1,2,…p
wherein x (k + I | k) ═ I is definedd(k+i|k),Iq(k+i|k)]TIn order to predict the control sequence for the state,
Figure BDA0003002265360000054
for reference to the input sequence, Ts is a discrete step size, RmIs the resistance of the electrical winding or windings,
Figure BDA0003002265360000055
x(k)is a state quantity, u(k)To control the quantity, Id(k+i|k)Is the d-axis current of the ith step at time k,
Figure BDA0003002265360000056
is a d-axis current desired value, I, at the k + I timeq(k+i|k)Is the q-axis current of the ith step in the kth time,
Figure BDA0003002265360000057
is a desired value of the q-axis current at the k + I time(k+p)Is the current at time k + p, I(k+p)The current expectation value at the k + P moment is shown, P is the prediction step length, Q is a positive definite weighting matrix, P is a positive definite terminal punishment matrix, and R is a positive definite control quantity punishment matrix.
S2: and carrying out Euler discretization according to a continuous time model of the motor driving system to construct a prediction model of the system.
According to the optimization problem, the finite set prediction control needs to perform future dynamic prediction according to a system dynamic model, perform Euler discretization according to a continuous time model of a motor driving system, and obtain the following discrete model with Ts as a discrete step length:
Figure BDA0003002265360000061
wherein x is(k+i|k)Is the state quantity, x, of the ith step at the kth time(k+i-1|k)Is the state quantity of the step i-1 at the kth time, u(k+i-1|k)The control quantity of the step (i-1) at the k time,
Figure BDA0003002265360000062
are system matrix parameters.
The system matrix parameters are respectively:
Figure BDA0003002265360000063
Figure BDA0003002265360000064
Figure BDA0003002265360000065
wherein L isd,LqEquivalent inductances of d-and q-axes, p, respectivelymIs the magnetic pole pair of the motor, phimFor the magnetic flux generated in the permanent magnet re-stator phase, d is the motor speed omegarAnd integrated to obtain thetae，VdcIs a DC supply voltage, RmBeing the resistance of the electronic winding, TsIn discrete steps.
In this embodiment, the calculation process is represented by a data structure diagram by using a calculation graph, and parallel calculation steps in the algorithm can be conveniently analyzed by representing through a plurality of nodes and edges. In order to fully excavate parallel computing steps in the algorithm, each prediction time model is subjected to node division according to the idea of a computation graph, and a computed value of each node is stored in a storage unit of a microprocessor. Taking the prediction of the k + i +1 moment at the k + i moment as an example, a motor system dynamic equation calculation chart is shown in fig. 3. The input u (k + i) ═ S at the time k + ia,Sb,Sc) The value is {0,1 }. a is11,a12(ωr),a21(ωr),a22Is a matrix in formula (3)
Figure BDA0003002265360000066
Corresponding element, b11(θe),b12(θe),b13(θe),b21(θe),b22(θe),b23(θe) Is a matrix in formula (3)
Figure BDA0003002265360000071
Corresponding element, h21Is a matrix in formula (3)
Figure BDA0003002265360000072
Corresponding element, ωrAnd thetaeIs a time-varying parameter of the system. The calculation formula of the 4 nodes defined therein is as follows:
D(1,i)＝a11Id(k+i)+a12(ωr)Iq(k+i)
D(2,i)＝a21(ωr)Id(k+i)+a12Iq(k+i)
E(1,i)＝b11(θe)Sa+b12(θe)Sb+b13(θe)Sc
E(2,i)＝b11(θe)Sa+b22(θe)Sb+b23(θe)Sc
wherein S isa,Sb,ScThe system input at the time k + i, a11,a12(ωr),a21(ωr),a22Is a matrix
Figure BDA0003002265360000073
Corresponding element, b11(θe),b12(θe),b13(θe),b21(θe),b22(θe),b23(θe) Is a matrix
Figure BDA0003002265360000074
Corresponding element, h21Is a matrix
Figure BDA0003002265360000075
Corresponding element, ωrAnd thetaeIs a time-varying parameter of the system,
the prediction model obtains a future state formula of the system current as follows:
Id(k+i+1)＝D(1,i)+D(2,i)
Iq(k+i+1)＝E(1,i)+E(2,i)+ωrh21。
s3: and performing parallel computing solution optimization on the prediction model and the objective function by adopting a trigger type parallel computing method to realize the optimal prediction control of the motor torque. The triggered parallel computing method in step S3 is to use the sign that the solution of the prediction model and the objective function in the current computing step is completed as the sign that the next step computing starts, so as to implement the parallel computing of the prediction model and the objective function.
And (3) predicting the state of the system in the future p steps according to a system dynamic model f shown in FIG. 2 by knowing the state value at the moment k and the initial value of the control quantity, wherein the predicting process is shown in FIG. 4. Because of the coupling relationship between the state predictions, the prediction of each step is performed sequentially.
Aiming at solving the optimization problem of the finite set prediction control, a dynamic programming algorithm is adopted for traversal optimization solution, and in order to reduce the calculated amount in the multi-step prediction process, a simplified optimization algorithm is adopted to reduce the calculated amount. Although the computational burden is reduced by the refinement and optimization, when each node in the search tree is optimized, the future dynamics of the system needs to be calculated first, and then an objective function needs to be calculated, which is a time-consuming key calculation step of the algorithm. According to the system future state calculation and the calculation chart of the objective function, x is calculated for each time domain system state in the process of forward recursionk+i+1|kAnd JiThe objective function and the calculation formula of the prediction model in step S3 can be calculated in parallel as follows:
J0＝0
Figure BDA0003002265360000081
Figure BDA0003002265360000082
wherein J is an objective function, x(k+i|k)Is the state quantity of the ith step at the kth time, rk+i|kIs the reference quantity of the ith step at the kth moment, Q is a positive definite weighting matrix, and P is a positive definite finalAnd an end penalty matrix, wherein R is a positive definite control quantity penalty matrix.
In the calculation of the objective function, as shown in fig. 5, in order to fully utilize parallel calculation, the objective function in the P-step prediction time domain can be rewritten as:
Figure BDA0003002265360000083
the calculation of the objective function is divided into two layers of nodes, wherein the first layer of nodes comprises two nodes K1And two nodes K2The second layer node comprises a node Ji+1(1)、Ji+1(2)、Ji+1(3)、Ji+1(4) The calculation formula of each node is as follows:
Figure BDA0003002265360000084
Figure BDA0003002265360000085
Figure BDA0003002265360000086
Figure BDA0003002265360000087
Figure BDA0003002265360000088
Figure BDA0003002265360000089
wherein, Id(k + i +1| k) is the d-axis current of step i +1 at time k,
Figure BDA00030022653600000810
d-axis current expectation value of the (I + 1) th step in the k timeq(k + i +1| k) is the desired value of the q-axis current at step i +1 at time k,
Figure BDA00030022653600000811
is the q-axis current expected value m of the (i + 1) th step in the k-th time1Is the motor rotor mass.
As shown in fig. 6, because the FPGA has the advantages of low power consumption, programmability, parallel computing hardware structure, and the like, the parallel computing method for the motor torque optimization finite set predictive control proposed above is implemented by performing hardware parallel acceleration on an FPGA chip, as shown in fig. 5.
The calculation steps with coupling relation in the algorithm are accelerated by adopting a production line, and the mutually independent calculation steps in the algorithm are accelerated by adopting hardware parallel triggering calculation. The relation between resources and performance is fully considered for the data storage mode, and the register storage is adopted to accelerate the data access speed under the condition that the resources allow.
For the prediction process of each step, data are independent, and because the two are different in computational complexity, parallel computation cannot be completed simultaneously, so that a triggered parallel computation mode is combined, namely a mark that forward derivation in the step P (namely parallel computation content one) and solving of an objective function (namely parallel computation content two) are completed is used as a mark for starting prediction computation in the step P +1, so as to ensure the sequence of data computation numbers.
The above embodiments are merely examples and do not limit the scope of the present invention. These embodiments may be implemented in other various manners, and various omissions, substitutions, and changes may be made without departing from the technical spirit of the present invention.

Claims (10)

1. A motor torque optimization finite set predictive control parallel computing method is characterized by comprising the following steps:
s1: according to the target of motor torque optimization control, giving a description form of an optimization problem and obtaining a target function;
s2: performing Euler discretization according to a continuous time model of the motor driving system to construct a prediction model of the system;
s3: and performing parallel computing solution optimization on the prediction model and the objective function by adopting a trigger type parallel computing method to realize the optimal prediction control of the motor torque.
2. The method of claim 1, wherein the objective of the motor torque optimization control in the step S1 is to control the d-q axis current of the motor stator to quickly track the upper expected current value, so as to realize the quick tracking of the torque and meet the dynamic requirement, and reduce the copper loss E inside the motorm。
3. The method of claim 2, wherein the objective function is:
Figure FDA0003002265350000011
s.t. x(k+i|k)＝f(x(k+i-1|k),u(k+i-1))，
u(k+i-1)∈{u0,u1,…,u7},i＝1,2,…p
wherein x (k + I | k) ═ I is definedd(k+i|k),Iq(k+i|k)]TIn order to predict the control sequence for the state,
Figure FDA0003002265350000012
for reference to the input sequence, Ts is a discrete step size, RmIs the resistance of the electrical winding or windings,
Figure FDA0003002265350000013
x(k)is a state quantity, u(k)To control the quantity, Id(k+i|k)Is the d-axis current of the ith step at time k,
Figure FDA0003002265350000014
is a d-axis current desired value, I, at the k + I timeq(k+i|k)Is the q-axis current of the ith step in the kth time,
Figure FDA0003002265350000015
is a desired value of the q-axis current at the k + I time(k+p)Is the current at time k + p, I(k+p)The current expectation value at the k + P moment is shown, P is the prediction step length, Q is a positive definite weighting matrix, P is a positive definite terminal punishment matrix, and R is a positive definite control quantity punishment matrix.
4. The method of claim 3, wherein the objective function is calculated in two layers, the first layer comprises two nodes K1And two nodes K2The second layer node comprises a node Ji+1(1)、Ji+1(2)、Ji+1(3)、Ji+1(4) The calculation formula of each node is as follows:
Figure FDA0003002265350000021
Figure FDA0003002265350000022
Figure FDA0003002265350000023
Figure FDA0003002265350000024
Figure FDA0003002265350000025
Figure FDA0003002265350000026
wherein, Id(k + i +1| k) is the d-axis current of step i +1 at time k,
Figure FDA0003002265350000027
d-axis current expectation value of the (I + 1) th step in the k timeq(k + i +1| k) is the desired value of the q-axis current at step i +1 at time k,
Figure FDA0003002265350000028
is the q-axis current expected value m of the (i + 1) th step in the k-th time1Is the motor rotor mass.
5. The parallel computing method for the predictive control of the limited set of the motor torque optimization according to claim 1, wherein in step S2, the future dynamic prediction is performed according to a system dynamic model, the euler discretization is performed according to a continuous time model of a motor driving system, Ts is a discrete step length, and the following discrete models are obtained:
Figure FDA0003002265350000029
wherein x is(k+i|k)Is the state quantity, x, of the ith step at the kth time(k+i-1|k)Is the state quantity of the step i-1 at the kth time, u(k+i-1|k)The control quantity of the step (i-1) at the k time,
Figure FDA00030022653500000210
are system matrix parameters.
6. The method of claim 5, wherein the system matrix parameters are respectively as follows:
Figure FDA00030022653500000211
Figure FDA0003002265350000031
Figure FDA0003002265350000032
wherein L isd,LqEquivalent inductances of d-and q-axes, p, respectivelymIs the magnetic pole pair of the motor, phimFor the magnetic flux generated in the permanent magnet re-stator phase, d is the motor speed omegarAnd integrated to obtain thetae，VdcIs a DC supply voltage, RmBeing the resistance of the electronic winding, TsIn discrete steps.
7. The method of claim 6, wherein the predictive model is calculated to include a plurality of intermediate nodes: d(1,i)、D(2,i)、E(1,i)、E(2,i)The calculation formula is as follows:
D(1,i)＝a11Id(k+i)+a12(ωr)Iq(k+i)
D(2,i)＝a21(ωr)Id(k+i)+a12Iq(k+i)
E(1,i)＝b11(θe)Sa+b12(θe)Sb+b13(θe)Sc
E(2,i)＝b11(θe)Sa+b22(θe)Sb+b23(θe)Sc
wherein S isa,Sb,ScThe system input at the time k + i, a11,a12(ωr),a21(ωr),a22Is a matrix
Figure FDA0003002265350000033
Corresponding element, b11(θe),b12(θe),b13(θe),b21(θe),b22(θe),b23(θe) Is a matrix
Figure FDA0003002265350000034
Corresponding element, h21Is a matrix
Figure FDA0003002265350000035
Corresponding element, ωrAnd thetaeIs a time-varying parameter of the system,
the prediction model obtains a future state formula of the system current as follows:
Id(k+i+1)＝D(1,i)+D(2,i)
Iq(k+i+1)＝E(1,i)+E(2,i)+ωrh21。
8. the method of claim 1, wherein the objective function and the predictive model in step S3 are calculated by the following formula:
J0＝0
Figure FDA0003002265350000041
Figure FDA0003002265350000042
wherein J is an objective function, x(k+i|k)Is the state quantity of the ith step at the kth time, rk+i|kAnd Q is a positive definite weighting matrix, P is a positive definite terminal punishment matrix, and R is a positive definite control quantity punishment matrix.
9. The method of claim 1, wherein the triggered parallel computing method in step S3 is implemented by using a flag indicating that the solution of the prediction model and the objective function in the current computing step is completed as a flag indicating the start of the next-step computing, so as to implement the parallel computing of the prediction model and the objective function.
10. The method for parallel computation of predictive control over a limited set of motor torque optimization according to claim 1, wherein in step S3, the FPGA chip is used to perform parallel computation solution.
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