CN113965109B - Multi-motor layered total amount optimal synergistic anti-saturation control method - Google Patents
Multi-motor layered total amount optimal synergistic anti-saturation control method Download PDFInfo
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/04—Arrangements for controlling or regulating the speed or torque of more than one motor
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
- H02P21/28—Stator flux based control
- H02P21/30—Direct torque control [DTC] or field acceleration method [FAM]
Abstract
The invention provides an anti-saturation control method for optimal cooperation of layered total quantity of multiple motors. The control input saturation term is directly introduced into a dynamic integral part of the supercoiled algorithm, a novel saturated supercoiled sliding mode control algorithm is designed, and the control input constraint is effectively proved by using an obstacle Lyapunov function through mathematical conversion, so that the problems of input saturation constraint and sliding mode buffeting are solved. The invention can effectively solve the problem of input and output double saturation constraint in the total amount coordination of multiple motors by combining the integral frames, and provides a certain theoretical basis and engineering application for the distributed coordination optimization control of an actual multiple-motor network system.
Description
Technical Field
The invention relates to the field of multi-motor traction systems, in particular to an anti-saturation control method for optimal cooperation of layered total quantity of multiple motors.
Background
Multi-motor traction is a common driving mode of an electric locomotive, although in the research of a multi-motor cooperative control technology, a control algorithm based on a consistency theory is adopted; a multi-motor coordination control algorithm based on beeping, clustering and formation; and a multi-motor cooperative control strategy based on total consistency are widely developed. However, when the locomotive running environment changes, in order to ensure the normal running of the locomotive, the coordination control of multiple motors is very easy to cause saturation phenomenon of part of motors, and especially in the coordination control technology based on the total amount consistency, namely, the coordination of redundant power of the multiple motors is used for ensuring that the total sum of traction force provided by each motor is unchanged, so that the phenomenon of saturation caused by disordered coordination among the motors is easier to occur under the condition.
The research on the saturation constraint problem is very extensive and can be divided into two major categories, namely an additional anti-saturation compensator and a saturation constraint algorithm. CN202011086853.3 discloses a method for controlling total amount of multiple motors to cooperate with limited time to resist saturation, which solves the saturation problem in complex multiple motor system by adding an anti-saturation compensator, i.e. an auxiliary anti-saturation system is designed aiming at the saturation constraint problem of multiple motors, but has a certain limitation because it only plays a role in weakening the influence of saturation when the saturation constraint problem occurs. Therefore, when considering the input and output double saturation constraint, how to solve from the algorithm design level and ensure the overall traction performance of the multi-motor network system is more challenging and practical engineering.
Disclosure of Invention
Aiming at the problem that input and output are subjected to double saturation constraint due to disordered coordination under the condition of consistent total quantity of a complex multi-motor traction system, the invention provides an anti-saturation control method with optimal cooperation of layered total quantity of multiple motors.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
an anti-saturation control method for optimal cooperation of layered total quantity of multiple motors comprises the following steps:
s1, establishing an equation of stator flux linkage and electromagnetic torque according to an x-y coordinate system of synchronous rotation of two phases of stator flux linkage of a permanent magnet synchronous motor, and deducing a state equation of stator flux linkage and electromagnetic torque control of a plurality of motors:
the state equation of the stator flux linkage control is as follows:
the state equation for electromagnetic torque control is:
wherein j=1, 2..n, the number of multi-motor is n, ψ sj 、ψ fj Stator and rotor flux linkage vectors, T of the jth motor respectively ej Is electromagnetic torque omega rj For rotor flux linkage rotational electrical angular velocity, delta j For the load angle, L j Is inductance, u xj 、u yj Respectively an x-axis component and a y-axis component of motor stator voltage under an x-y coordinate system, R sj Is stator resistance, n pj Is the pole pair number;
s2, designing optimal multi-axis total coordinated allocation given target torque of each motor in a total layer according to a target with the lowest total coordinated energy consumption of multiple motors, wherein the optimal multi-axis total coordinated allocation is given as follows:
p 1 T e1 ＝p 2 T e2 ＝...＝p n T en ，
wherein p is 1 ,p 2 ...p n To assign weight coefficients, T ej (j=1, 2..n.) is the electromagnetic torque of the j-th motor;
s3, designing a saturated supercoiled sliding mode tracking control algorithm at a control layer according to the state equation of multi-motor direct torque and flux linkage control in S1 and optimal distribution given torque in S2:
wherein s is ψj Sum s Tj Is a slip form surface, k ψ1j 、k ψ2j 、k T1j 、k T2j Is a positive parameter to be designed;
s4, proving the input saturation constraint of the controller in S3;
s5, finishing the stability demonstration of the controller in S3, and obtaining the upper limit of the finite time.
Further, in step S1, the stator flux linkage equation is:
the electromagnetic torque equation is:
further, the step of optimally multi-axis total amount cooperative allocation given in step S2 includes:
s21, constructing a total energy function of n motor traction networks, wherein the total energy function is as follows:
s22, converting into the following optimization problems:
wherein T is * For a given traction characteristic T ejmax The saturation constraint value is output by the jth motor;
s23, introducing KKT optimization conditions to solve and obtain: p is p 1 T e1 ＝p 2 T e2 ＝...＝p n T en 。
Further, the KKT optimization condition solving step includes:
s231, firstly, expressing constraint conditions of the optimization problem in the S22 as follows:g 1j (T ej )＝0-T ej ≤0，g 2j (T ej )＝T ej -T ejmax less than or equal to 0, then introducing a relaxation variablea 1j And b 1j Then:
s232, defining a Lagrangian function equation as follows:
where ε is the Lagrangian factor, μ 1j Sum mu 2j Is the factor KKT.
S233 derivation of T by partial derivative e1 ,T e2 ,...,T en ,ε,a 1j ,b 1j ,μ 1j ,μ 2j The method comprises the following steps of:
s234, analyzing the KKT condition shows that the partial derivative in the above formula is 0 when the energy function is minimum, and the result is that:
s235, deducing a solving result as follows: p is p 1 T e1 ＝p 2 T e2 ＝...＝p n T en 。
Further, the steps of the saturated supercoiled sliding mode tracking control algorithm comprise:
s31, defining stator flux linkage deviation and electromagnetic torque deviation as follows according to a state equation of electromagnetic torque and stator flux linkage control:
wherein, the liquid crystal display device comprises a liquid crystal display device,ideal given stator flux for the jth motor,/->The target torque obtained by optimal allocation for the jth motor;
s32, orderAnd->The following error dynamics equations are obtained respectively:
s33, when u xjmin ≤u xj ≤u xjmax ，u yjmin ≤u yj ≤u yjmax Then the stator flux linkage control input saturation is:
the electromagnetic torque control input saturation is:
s34, selecting nonsingular terminal sliding mode surfaces as follows:
wherein 1/2 < q ψ ,q T ＜1And alpha is ψ1j ,α T1j And (3) obtaining the novel saturated supercoiled sliding mode controller with stator flux linkage and electromagnetic torque more than 0.
Further, in step S3, the conditional techniques and signs are used to equalizeIs converted into->And introducing an input saturation term into a dynamic integration part of the supercoiled sliding mode algorithm, so as to solve the problem of control input saturation.
Further, the input saturation constraint in step S4 is proved according to the lyapunov function theorem of obstacle.
Further, the stability demonstration of step S5 is derived from the limited time lyapunov stability theorem.
Further, the finite time upper bound in step S5 is:
wherein the positive definite matrixBy->Q is a symmetric positive definite matrix, V 2 To construct a positive fixed Lyapunov function, x 0 As an initial value, λ represents a characteristic value of the matrix.
Further, the step of calculating the finite time upper bound in step S5 includes:
constructing a positive Lyapunov function as follows:
and (3) deriving to obtain:
therefore, the upper bound of finite time can be found:
the beneficial effects of the invention are as follows:
the invention simultaneously considers the multi-motor network system with input and output double saturation constraint, builds an anti-saturation control frame with optimal cooperation of layered total amount, designs a novel saturated supercoiled sliding mode control strategy, realizes the lowest coordination of energy consumption of the total amount of the multi-motor under the double saturation constraint, and ensures the invariable total traction torque. Based on the traditional total consistent framework, a layered total optimally coordinated anti-saturation control framework is constructed, and the problem of double input and output saturation constraint is effectively solved. According to the invention, the optimal total cooperative distribution given torque is solved through the KKT condition, the output saturation problem is solved, and the minimum total energy consumption is ensured. And a novel saturated supercoiled sliding mode control algorithm is designed, so that the problem of saturation of control input is solved. And the input constraint of the controller is proved by using an asymmetric barrier lyapunov function.
Drawings
FIG. 1 is a diagram of a hierarchical total amount optimally coordinated anti-saturation control framework;
FIG. 2 is a coordinate system of a permanent magnet synchronous motor;
FIG. 3 is a graph of total tractive torque tracking;
fig. 4 is a graph of output torque tracking of the motor 1;
FIG. 5 is a graph of output torque tracking for motor 2;
fig. 6 is a graph of output torque tracking for motor 3
FIG. 7 is a graph of output torque tracking of the motor 4;
FIG. 8 is a graph of flux linkage control inputs for each motor stator;
FIG. 9 is a graph of electromagnetic torque control inputs for each motor;
FIG. 10 is a connection diagram of an RT-Lab semi-physical experiment platform;
FIG. 11 is a waveform diagram of a total tractive torque trace;
FIG. 12 is a graph of a waveform of optimal distributed torque for each motor;
FIG. 13 is a waveform diagram of actual output torque of each motor;
FIG. 14 is a waveform diagram of a flux linkage control input for each motor stator;
FIG. 15 is a waveform diagram of the electromagnetic torque control inputs for each motor;
Detailed Description
The present invention is further illustrated and described below with reference to examples, which are not intended to be limiting in any way. Unless otherwise indicated, the methods and apparatus used in the examples are conventional in the art.
Example 1
As in fig. 2, a coordinate system of the permanent magnet synchronous motor is established, wherein u s 、u x And u y Respectively a stator voltage vector and components thereof under an x-y coordinate system; i.e s 、i x And i y Respectively a stator current vector and components thereof under an x-y coordinate system; psi phi type s 、ψ f Respectively a stator flux linkage vector and a rotor flux linkage vector; omega s 、ω r The rotation electric angular velocity of the stator and rotor magnetic linkage is respectively; θ r The angle between the alpha axis and the d axis is set; θ s The angle between the alpha axis and the x axis; delta is the angle between the x axis and the d axis, namely the included angle between the stator and the rotor flux linkage, and is also called as the load angle.
Taking the jth permanent magnet synchronous motor as an example, under the synchronous rotation coordinate system of the x-y two-phase stator, the stator magnetic chain psi is arranged sj ＝ψ xj ，ψ yj =0, the relative equilibrium equation for this motor is as follows:
wherein omega sj 、ω rj Respectively is fixed toSub-flux linkage rotational electrical angular velocity and rotor flux linkage rotational electrical angular velocity, delta j As load angle, ψ xj 、ψ yj Stator flux linkage in x-axis and y-axis coordinate systems respectively, i xj 、i yj Respectively an x-axis component and a y-axis component of motor stator current under an x-y coordinate system, L dj 、L qj The direct axis inductance and the quadrature axis inductance are respectively, u xj 、u yj Respectively an x-axis component and a y-axis component of the motor stator voltage under an x-y coordinate system; r is R sj Is the stator resistance.
The electromagnetic torque equation is simplified by using the component relation among the coordinate systems in fig. 2 as follows:
example 2
The method for controlling the optimal cooperative anti-saturation of the layered total quantity of the multiple motors comprises the following steps:
s1, establishing an equation of stator flux linkage and electromagnetic torque according to an x-y coordinate system of synchronous rotation of two-phase stator flux linkage of the permanent magnet synchronous motor in embodiment 1, wherein L is the hidden pole type permanent magnet synchronous motor dj ＝L qj ＝L j Based on the above, deducing the state equation of electromagnetic torque and stator flux linkage control of multiple motors:
the state equation of the stator flux linkage control is as follows:
the state equation for electromagnetic torque control is:
wherein j=1, 2..n, the number of multi-motor is n, ψ sj 、ψ fj Stator and rotor flux linkage vectors, T of the jth motor respectively ej Is electromagnetic torque omega rj For rotor flux linkage rotational electrical angular velocity, delta j For the load angle, L j Is inductance, u xj 、u yj Respectively an x-axis component and a y-axis component of motor stator voltage under an x-y coordinate system, R sj Is stator resistance, n pj Is the pole pair number;
s2, designing optimal multi-axis total amount cooperative distribution given target torque of each motor in a total amount layer according to the target that the total energy consumption of multi-motor coordination is the lowest:
s21, constructing a total energy function of n motor traction networks, wherein the total energy function is as follows:
s22, converting into the following optimization problems:
wherein T is * For a given traction characteristic T ejmax The saturation constraint value is output by the jth motor;
s23, introducing KKT optimization condition solution to obtain the optimal multi-axis total collaborative distribution given as:
p 1 T e1 ＝p 2 T e2 ＝...＝p n T en ，
wherein p is 1 ,p 2 ...p n Weight coefficient is distributed for each motor, T ej (j=1, 2..n.) is the electromagnetic torque of the j-th motor;
s3, designing a saturated supercoiled sliding mode tracking control algorithm at a control layer according to the state equation of multi-motor direct torque and flux linkage control in S1 and optimal distribution given torque in S2:
s31, defining stator flux linkage deviation and electromagnetic torque deviation as follows according to a state equation of electromagnetic torque and stator flux linkage control:
wherein, the liquid crystal display device comprises a liquid crystal display device,ideal given stator flux for the jth motor,/->The target torque obtained by optimal allocation for the jth motor;
s32, orderAnd->The following error dynamics equations can be obtained respectively:
s33, when u xjmin ≤u xj ≤u xjmax ，u yjmin ≤u yj ≤u yjmax Then the stator flux linkage control input saturation is:
the electromagnetic torque control input saturation is:
s34, selecting nonsingular terminal sliding mode surfaces as follows:
wherein 1/2 < q ψ ,q T < 1, and alpha ψ1j ,α T1j More than 0, obtaining a novel saturated supercoiled sliding mode controller of stator flux linkage and electromagnetic torque;
s4, proving the input saturation constraint of the controller in S3;
s5, finishing the stability demonstration of the controller in S3, and obtaining the upper limit of the finite time.
Example 3
The embodiment provides the KKT optimization condition solving step comprising:
s231, firstly, expressing constraint conditions of the optimization problem in the S22 as follows:g 1j (T ej )＝0-T ej ≤0，g 2j (T ej )＝T ej -T ejmax less than or equal to 0, then introducing a relaxation variable a 1j And b 1j Then:
s232, defining a Lagrangian function equation as follows:
where ε is the Lagrangian factor, μ 1j Sum mu 2j Is the factor KKT.
S233 derivation of T by partial derivative e1 ,T e2 ,...,T en ,ε,a 1j ,b 1j ,μ 1j ,μ 2j The method comprises the following steps of:
s234, analyzing the KKT condition shows that the partial derivative in the above formula is 0 when the energy function is minimum, and the result is that:
s235, deriving a solving result as follows: p is p 1 T e1 ＝p 2 T e2 ＝...＝p n T en 。
Example 4
The present embodiment provides proving u using the barrier lyapunov function yj (t)∈(u yjmin ,u yjmax ) An input saturation constraint in the controller.
Taking outThen->
And (3) deriving to obtain:
in the method, in the process of the invention,
definition of positive definite matrixBy->Q is a symmetric positive definite matrix:
the asymmetric barrier Lyapunov function is selected as follows:
the method comprises the following steps:
when u is yj > 0, then α=1, thenThen:
when u is yj Less than or equal to 0, wherein alpha=0, thenThen:
for V 1 And (3) deriving to obtain:
from the following componentsObtain |s Tj | 1/2 ≤||ξ j I; and then (I) is->The method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
therefore, when the control parameters satisfyThen the initial condition u can be reached yj (0)∈(u yjmin ,u yjmax ) U is yj Can be constrained in interval u yj (t)∈(u yjmin ,u yjmax ) In, the input constraint is satisfied.
Example 5
The present example provides a demonstration of completion stability according to the lyapunov stability theorem:
constructing a positive Lyapunov function as follows:
and (3) deriving to obtain:
therefore, the upper bound of finite time can be found:
thus, s Tj Can converge to 0 within a finite time T. Due toThen get sigma T2j Converging to 0 for a limited time. And is also by->Then get->And the total amount of the motor output torque tracking is cooperatively optimized to distribute the target torque obtained by a given algorithm. By the same token, the stator flux linkage can also effectively track the upper given value.
Example 6
The embodiment provides numerical simulation and semi-physical experiment to verify the effectiveness and feasibility of the framework:
the invention adopts a multi-motor traction network system consisting of 4 permanent magnet synchronous motors as a simulation object, and the parameters of each permanent magnet synchronous motor are the same, and the parameters are set as follows: r is R s ＝1.2Ω，L＝8.5×10 -3 H，ψ f ＝0.175Wb，n p ＝4，J＝0.8×10 -3 kg·m 2 . The given traction characteristic consists of a piecewise function, as follows: simulating a motor starting stage in 0-1 s; in the constant-speed running stage of the 1-4 s simulation motor; and simulating a motor deceleration and stopping stage in 4-5 s.
The simulation process is set as follows: firstly, starting and running each motor according to average distribution; when 2s, feeding back the weights of the motors to be 0.2, 0.3 and 0.3 according to the rail surface state and traction characteristics, and simultaneously considering that the output torque constraint of the motor 1 is +5 at the moment, and carrying out total optimal cooperative allocation and control; then at 3s, assuming that at this time motor 1 loses 40% of its traction due to idle or coasting, and taking into account at this time motor 2 output torque constraint +7, the total optimal coordinated allocation and control is performed. Meanwhile, the saturation limit of the controller was ±2, and the following results were obtained in fig. 3 to 9.
Fig. 3 includes a graph of the trace effect of the sum of the output torques and a given traction characteristic, and also includes a graph of the real-time output torque of each motor. The control framework constructed can be seen from fig. 3, and when the problem of double saturation constraint of input and output exists, the overall traction tracking performance can be still ensured efficiently.
Figures 4-7 show the effect of each motor output torque tracking to optimally distribute a given torque. The detailed analysis results in: when 2s, the upper limit value of the output torque +5 of the motor 1 is considered to carry out optimal total collaborative distribution setting, and at the moment, each motor can effectively complete optimal distribution and control at about 0.04 s; when the speed is 3s, under the constraint of loss of the motor 1 and output torque +7 of the motor 2, each motor can still effectively complete optimal distribution and control within about 0.05s, and the high efficiency of a designed control algorithm is shown.
Fig. 8 and 9 are graphs of stator flux linkage and electromagnetic torque control input of each motor, respectively, and it can be obviously seen that the control input curves without considering input constraint exceeds the input constraint by ±2 more or less, and under the novel saturated supercoiled sliding mode control action of the invention, each motor can effectively realize high-efficiency control performance under the input saturation constraint.
Example 7
In order to verify the effectiveness of the invention and ensure that the system simulation is as close to the actual engineering environment as possible, an RT-Lab semi-physical experiment is performed, and the experiment platform is shown in FIG. 10. In the experimental process, experimental parameters and conditions are the same as those of simulation, a system model in a Matlab/Simulink environment is imported into an RT-Lab semi-physical experimental platform, the system model runs in an OP56000 simulation motor, and program codes of a control algorithm are downloaded into a DSP controller to obtain oscillograms, as shown in figures 11 to 15:
as can be seen from the total traction torque tracking waveform chart of FIG. 11, the total traction torque sum of all motors in the whole process is basically consistent with a given traction characteristic curve, and the overall traction performance of the locomotive is effectively ensured.
FIG. 12 is a waveform diagram of an optimal distribution of torque given for each motor, illustrating the efficient energy consumption distribution under guaranteed output saturation constraints;
fig. 13 is a waveform diagram of actual output torque of each motor under the novel saturated supercoiled sliding mode control strategy, and from the diagram, it can be seen that the optimum distribution of given torque of each motor in fig. 12 is basically tracked, and the superiority of the present invention is verified.
Fig. 14 and 15 are graphs of motor stator flux linkage and electromagnetic torque control inputs, respectively, from which each control input can be effectively controlled within set saturation limits.
In summary, the experimental result of the RT-Lab semi-physical experiment shows that the distributed total amount optimally coordinated anti-saturation control framework has high efficiency in solving the problem of double input and output saturation constraint.
The above-described embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present invention.
Claims (10)
1. The anti-saturation control method for optimal cooperation of layered total quantity of multiple motors is characterized by comprising the following steps of:
s1, establishing an equation of stator flux linkage and electromagnetic torque according to an x-y coordinate system of synchronous rotation of two phases of stator flux linkage of a permanent magnet synchronous motor, and deducing a state equation of stator flux linkage and electromagnetic torque control of a plurality of motors:
the state equation of the stator flux linkage control is as follows:
the state equation for electromagnetic torque control is:
wherein j=1, 2..n, the number of multi-motor is n, ψ sj 、ψ fj Stator and rotor flux linkage vectors, T of the jth motor respectively ej Electromagnetic torque of the jth motor omega rj For rotor flux linkage rotational electrical angular velocity, delta j For the load angle, L j Is inductance, u xj 、u yj Respectively an x-axis component and a y-axis component of motor stator voltage under an x-y coordinate system, R sj Is stator resistance, n pj Is the pole pair number;
s2, designing optimal multi-axis total coordinated allocation given target torque of each motor in a total layer according to the target that the total coordinated energy consumption of multiple motors is the lowest, wherein the optimal multi-axis total coordinated allocation is given as follows:
p 1 T e1 ＝p 2 T e2 ＝...＝p n T en ，
wherein p is 1 ,p 2 ...p n To assign weight coefficients, T ej (j=1, 2..n.) is the electromagnetic torque of the j-th motor;
s3, designing a saturated supercoiled sliding mode tracking control algorithm at a control layer according to the state equation of multi-motor direct torque and flux linkage control in S1 and optimal distribution given torque in S2:
wherein s is ψj Sum s Tj Is a slip form surface, k ψ1j 、k ψ2j 、k T1j 、k T2j As a positive parameter to be designed,
s4, proving the input saturation constraint of the controller in S3;
s5, finishing the stability demonstration of the controller in S3, and obtaining the upper limit of the finite time.
2. The method for controlling optimal coordinated anti-saturation of a hierarchical total of multiple motors according to claim 1, wherein in step S1, the stator flux equation is:
i xj 、i yj the x-axis component and y-axis component of the motor stator current in the x-y coordinate system are respectively Cheng Qiudao, then i is eliminated xj Simplifying to obtain a state equation of stator flux linkage control;
the electromagnetic torque equation is:
L dj 、L qj the direct axis inductance and the quadrature axis inductance are respectively;
under the condition of constant stator flux linkage amplitude, deriving to obtain a state equation of electromagnetic torque control.
3. The method for controlling the optimal coordinated total amount of anti-saturation of a multi-motor hierarchy according to claim 1, wherein the step of assigning a given optimal multi-axis total amount of coordination in step S2 comprises:
s21, constructing a total energy function of n motor traction networks, wherein the total energy function is as follows:
s22, converting into the following optimization problems:
wherein T is * For a given traction characteristic T ejmax The saturation constraint value is output by the jth motor;
s23, introducing KKT optimization conditions to solve and obtain: p is p 1 T e1 ＝p 2 T e2 ＝...＝p n T en 。
4. A multi-motor hierarchical total optimal cooperative anti-saturation control method according to claim 3, wherein said KKT optimization condition solving step in step S23 comprises:
s231, firstly, expressing constraint conditions of the optimization problem in the S22 as follows:g 1j (T ej )＝0-T ej ≤0，g 2j (T ej )＝T ej -T ejmax less than or equal to 0, then introducing a relaxation variable a 1j And b 1j Then:
s232, defining a Lagrangian function equation as follows:
where ε is the Lagrangian factor, μ 1j Sum mu 2j Is a factor KKT;
s233 derivation of T by partial derivative e1 ,T e2 ,...,T en ,ε,a 1j ,b 1j ,μ 1j ,μ 2j The method comprises the following steps of:
s234, analyzing the KKT condition shows that the partial derivative in the above formula is 0 when the energy function is minimum, and the result is that:
s235, deducing a solving result as follows: p is p 1 T e1 ＝p 2 T e2 ＝...＝p n T en 。
5. The method for controlling the optimal coordinated total multi-motor layered anti-saturation according to claim 1, wherein the step of the saturated supercoiled sliding mode tracking control algorithm comprises the following steps:
s31, defining stator flux linkage deviation and electromagnetic torque deviation as follows:
in the middle ofIdeal given stator flux for the jth motor,/->The target torque obtained by optimal distribution and solving for the jth motor is obtained;
s32, orderAnd->The following error dynamics equations are obtained respectively:
s33, when u xjmin ≤u xj ≤u xjmax ，u yjmin ≤u yj ≤u yjmax Then the stator flux linkage control input saturation is:
the electromagnetic torque control input saturation is:
s34, selecting nonsingular terminal sliding mode surfaces as follows:
wherein 1/2 < q ψ ,q T < 1, and alpha ψ1j ,α T1j And (3) obtaining the novel saturated supercoiled sliding mode controller with stator flux linkage and electromagnetic torque more than 0.
6. The method for controlling the optimal coordinated total of multiple motor layers according to claim 1, wherein in step S3, the method comprises the following steps ofIs converted into->The input saturation term is introduced into the dynamic integration part of the supercoiled sliding mode algorithm, so that the problem of controlling input saturation is solved.
7. The method for controlling optimal coordinated anti-saturation of a hierarchical total amount of multiple motors according to claim 1, wherein the input saturation constraint in step S4 is proved according to the lyapunov function theorem of obstacle.
8. The method according to claim 1, wherein the stability proof in step S5 is obtained by the lyapunov stability theorem of finite time.
9. The method for controlling optimal coordinated anti-saturation of a hierarchical total amount of multiple motors according to claim 1, wherein the finite time upper bound in step S5 is:
wherein the positive definite matrixBeta > 0; by->Q is a symmetric positive definite matrix, V 2 To construct a positive fixed Lyapunov function, x 0 For initial values, lambda represents the eigenvalues of the matrix,
10. the method for controlling optimal coordinated anti-saturation of a hierarchical total of multiple motors according to claim 9, wherein the step of calculating the finite time upper bound in step S5 comprises:
constructing a positive Lyapunov function as follows:
and (3) deriving to obtain:
therefore, the finite time upper bound is found:
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