Multi-objective optimization design strategy and cooperative control method for multiple motors

Abstract

The invention discloses a multi-target optimization design strategy of multiple motors and a cooperative control method, and relates to the technical field of multi-motor optimization design and control. The multi-target optimization design strategy for multiple motors comprises the following steps: constructing a dual-motor two-speed power system analysis model, and establishing a multi-target optimization function containing motor design parameters and a transmission ratio; constructing and training an artificial neural network model; optimizing the function by adopting a second-generation non-dominated genetic algorithm; iteratively updating and solving the parameters; the multi-motor cooperative control method comprises the following steps: modeling motors, a controlled object and a communication network; designing a distributed control law, and determining control parameters based on average dynamics; analyzing stability and performance according to different communication network conditions, and designing a coupling matrix; according to the invention, the energy efficiency and dynamic performance collaborative optimization capability and optimization efficiency of the multi-motor system are improved, multi-motor high-performance collaborative control is realized, and the system stability and load balance are ensured.

Description

Technical Field

[0001] The present invention relates to the field of multi-motor optimization design and control technology, and in particular to a multi-objective optimization design strategy and a coordinated control method for multi-motor. Background Art

[0002] As the global demand for low-carbon transportation becomes increasingly urgent, electric vehicles, as the core carrier of zero-emission transportation, have become key technical goals in the industry in terms of optimizing the energy efficiency and dynamic performance of their power systems. Multi-motor power systems are considered an important direction for breaking through the performance bottleneck of single-motor systems because they can take into account both low-speed high-torque output and high-speed and efficient operation. However, the design of this system needs to balance the electromagnetic characteristics of the motor, transmission parameters and the dynamic requirements of the entire vehicle, involving multi-physics field coupling and multi-objective optimization, which places extremely high demands on engineering design methods. However, current research on the optimization of multi-motor systems usually pre-sets the motor characteristics and only optimizes the transmission parameters, ignoring the direct impact of specific motor design parameters on the energy efficiency and dynamic performance of the multi-motor system. As a result, the motor operating point easily deviates from the high-efficiency zone, making it difficult to achieve optimal system-level performance. At the same time, the multi-objective optimization of complex power systems in research also faces extremely high computational costs.

[0003] In addition, with the continuous development of science and technology, the performance requirements for multi-motor coordinated control systems are also increasing. In the field of electric vehicles, in-wheel motors or multi-motor drive systems can improve the vehicle's handling, power performance and space utilization. However, under the configuration of in-wheel motors, traditional control methods face many challenges in the coordinated control of multiple permanent magnet synchronous motors. On the one hand, each motor requires precise speed and position control. The traditional method of relying on sensors to obtain information not only increases costs and system complexity, but also has reliability issues and is susceptible to noise interference. On the other hand, the coordinated operation control of multiple motors when running simultaneously is more difficult, and uneven load distribution can easily cause single or multiple motors to overload or underload, making it difficult to simultaneously take into account overall energy efficiency and vehicle performance.

[0004] It can be seen from this that how to design a multi-objective optimization design strategy that can simultaneously consider the optimization of motor specific parameters and transmission parameters with high optimization efficiency to optimize multi-motor design, and design a collaborative control method that can ensure the coordinated work of multiple motors and reasonably distribute loads to improve overall energy efficiency and vehicle performance, is a difficult problem that needs to be solved urgently in this field. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects existing in the above-mentioned background technology. The present invention proposes a multi-objective optimization design strategy and collaborative control method for multiple motors. The multi-objective optimization design strategy incorporates the specific design parameters of the motor and the transmission system parameters into a unified optimization framework to improve the energy efficiency and dynamic performance collaborative optimization capabilities of the multi-motor system; the collaborative control method adopts a distributed control law and designs control parameters based on average dynamics to improve the overall performance and reliability of the multi-motor system.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A multi-objective optimization design strategy for multiple motors includes the following steps:

[0008] Step S1-1, establish a multi-objective optimization function including motor design parameters and transmission ratio; the motor design parameters include the motor stack length L1 and the number of coil turns N1 of the first motor, the motor stack length L2 and the number of coil turns N2 of the second motor, the transmission ratio is the transmission ratio r1 of the first motor and the transmission ratio r2 of the second motor, the optimization objectives of the multi-objective optimization are energy efficiency index and power performance index, and select the electric energy consumption per 100 kilometers EC 100 As the energy efficiency indicator, the unit is kWh, and the acceleration time from 0 to 100 km / h is selected as T acc As a power performance indicator, the unit is seconds;

[0009] Step S1-2, construct and train an artificial neural network model: take the motor stack length L1 and motor stack length L2, coil turns N1 and coil turns N2, transmission ratio r1 and transmission ratio r2 as inputs of the artificial neural network model, and take the energy consumption per 100 kilometers EC 100 and acceleration time T from 0 to 100 km / h acc As the output of the artificial neural network model, an initial sample set is generated based on the optimal Latin hypercube design, and the artificial neural network model of the multi-objective optimization function in step S1-1 is constructed and trained;

[0010] Step S1-3, optimization based on genetic algorithm: using a second-generation non-dominated genetic algorithm to optimize the input of the artificial neural network model in step S1-2 to solve a Pareto front solution set; each solution in the solution set corresponds to a set of motor design parameters and transmission ratios;

[0011] Step S1-4, iterative parameter update and solution: Use the artificial neural network optimized in step S1-3 to solve the objective function. When the normalized root mean square error of the objective function is greater than the preset threshold, based on the initial sample set, new samples are added by maximizing the minimum distance design, and the artificial neural network model is updated and re-optimized and solved until the normalized root mean square error of the objective function is less than the preset threshold, thereby obtaining the motor design parameters and transmission ratio that take into account both energy efficiency indicators and power performance indicators.

[0012] Furthermore, in step S1-1, the multi-objective optimization function is:

[0013]

[0014] Where x = [L, N, r], L = [L1, L2], N = [N1, N2], r = [r1, r2];

[0015] Optimize the objective weight function:

[0016]

[0017] Among them, λ1 is the weight corresponding to the energy efficiency index, and λ2 is the weight corresponding to the power performance index.

[0018] Furthermore, in step S1-1, the constraint condition of the motor stack length is:

[0019] 50≤L1≤100

[0020] 50≤L2≤100

[0021] L1+L2=150

[0022] The constraints on the number of coil turns are:

[0023] 15≤N1≤40

[0024] 15≤N2≤40

[0025] The constraints on the transmission ratio are:

[0026] r1>r2

[0027]

[0028] Among them, r1 is the transmission ratio of the first motor, r2 is the transmission ratio of the second motor, is the maximum transmission ratio of the first motor, is the maximum transmission ratio of the second motor, ω 1max is the maximum speed of the first motor, ω 2max is the maximum speed of the second motor, R t is the effective radius of the tire, is the maximum average vehicle speed, μ r is the rolling friction coefficient, M is the total weight of the vehicle, g is the acceleration of gravity, c d is the drag coefficient, ρ is the air density, A is the front area, T 2max is the maximum torque of the second motor.

[0029] Furthermore, in step S1-2, during the training of the artificial neural network model, the accuracy and reliability of the model are improved by gradually increasing the number of samples and hidden layer nodes and cross-validating.

[0030] A method for coordinated control of multiple motors comprises the following steps:

[0031] Step S2-1: First, model the multi-motor coordinated control system: model the motors, controlled objects, and communication networks in the system separately. This includes constructing an accurate mathematical model for each motor in the multi-motor coordinated control system, building a dynamic model for the controlled objects affected by the multi-motor coordinated control, and modeling the communication network between the multiple motors using graph theory.

[0032] Step S2-2: After the system model is established, the control law is designed based on the modeling results: first, a distributed control law is constructed and its control principle is analyzed, and then the control parameters are determined based on the average dynamics concept;

[0033] Step S2-3: After the control law design is completed, perform system stability and performance analysis: perform undirected coupling analysis and directed coupling analysis for the communication network as an undirected graph and directed graph, respectively;

[0034] Step S2-4: Design a coupling matrix based on the stability analysis results to ultimately achieve system stability control: Design a coupling matrix based on stability theory to achieve the required performance of the controlled object.

[0035] Furthermore, the step S2-1 is specifically as follows:

[0036] Step S2-1-1, motor modeling:

[0037] For each motor in the multi-motor coordinated drive system, an accurate mathematical model is constructed. In a stationary reference frame, the dynamic characteristics of the permanent magnet synchronous motor can be described by the following set of differential equations:

[0038]

[0039]

[0040] e α =-ψ fl ω ersinθ er

[0041] e β =ψ fl ω er cosθ er

[0042] Among them, i α,s and i β,s Represent the stator current of α-axis and β-axis respectively; v α,s and v β,s are the stator voltages of the α-axis and β-axis respectively; ω er is the rotor angular velocity, θ er is the rotor position; e α and e β are the back electromotive force of α-axis and β-axis respectively; L st is the stator inductance, R st is the stator resistance, ψ fl represents magnetic linkage;

[0043] The above motor model is represented in state space to obtain the general form:

[0044]

[0045] y i =C a x i

[0046] in, is the state vector of the i-th motor, which contains the key state variables of current and speed. is the updated state vector of the i-th motor; is the input vector, is the control voltage; is the output vector, which is the speed or torque of the motor; A a is the system matrix 1, B a For input matrices 1 and C a is the output matrix 1; and n α 、m a and m p Dimensional real vector space; Step S2-1-2, modeling of the controlled object:

[0047] For the motors affected by the multi-motor cooperative control, a dynamic model is established; the relationship between the motor state and output error and input can be expressed by the following state space equation:

[0048]

[0049] e=C p xp +Q p w

[0050] in, is the state vector of the controlled object, is the updated state vector of the controlled object; It is the input vector of the controlled object, consisting of the output torque or speed of the motor; is the output error vector, which is used to measure the difference between the actual output and the expected output of the controlled object; is an exogenous input, i.e., an external disturbance or load change, and n p 、p p and r p dimensional real vector space; A p is the system rectangle 2, which is determined by the dynamic change characteristics of the motor's internal state, B p is the input matrix 2, which is determined by the relationship between the motor output and the state change of the controlled object, C p is the output matrix 2, which is determined by the relationship between the output error and the state variable of the controlled object, P p is the disturbance input matrix, which is determined by the influence of external disturbance on the state of the controlled object and Q p is the disturbance output matrix, which is determined by the influence of external disturbance on the output error. These matrices reflect the dynamic characteristics and input-output relationship of the controlled object;

[0051] Step S2-1-3, communication network modeling:

[0052] Graph theory is used to model the communication network between multiple motors. A directed graph G = (ν, ε, W) is defined, where the node set ν represents the controllers corresponding to each motor, the edge set ε represents the communication links between the controllers, and the weight matrix W reflects the weight of each communication link, reflecting the reliability and importance of the communication. The topology of the communication network is described by the Laplace matrix L of the directed graph. The element l of the Laplace matrix L is ij The definition is as follows:

[0053]

[0054] where w ij is the weight of edge (j,i), and the Laplace matrix L contains the connection information between nodes in the communication network.

[0055] Furthermore, the step S2-2 is specifically as follows:

[0056] Step S2-2-1, construction of control law:

[0057] Design a distributed control law to achieve coordinated control among multiple motors; the control law is as follows:

[0058]

[0059] u i =Hξ i

[0060] in, is the state vector of controller i, is the updated state vector of controller i; G is the output error feedback matrix, F and H are constant matrices of corresponding dimensions, which respectively reflect the interaction relationship between the internal state variables of the controller and the relationship between the internal state of the controller and the actual control input; is the output error vector, n c dimensional real vector space; J is the coupling gain matrix, which is used to adjust the degree of coordination between motors; w ij is the weight of edge (j,i), is the neighbor set of controller i, which represents the set of other controllers that have communication connections with controller i;

[0061] The control law introduces the state information of neighboring controllers, so that each motor can adjust its own control input in real time according to the operating status of other motors, thus achieving coordinated control;

[0062] Step S2-2-2, determination of control parameters:

[0063] Design F, G, H matrices based on the idea of ​​average dynamics and define the average state and the average controller state Where N is the number of motors. By analyzing the average dynamic characteristics of the system, the linear matrix inequality constraint relationship between the system matrices is established, and the linear matrix inequality optimization method is used to solve the F, G, and H matrices that meet the system stability and performance requirements.

[0064] Furthermore, the step S2-3 is specifically as follows:

[0065] Step S2-3-1: Analyze the undirected coupling situation based on the designed control law:

[0066] In the case of an undirected communication network, certain assumptions must first be met: the dynamic characteristics of the exogenous input are stable, a control law can be found to make the system state asymptotically stable, and the system state can be accurately estimated through the output;

[0067] If exists and Satisfies the following equation:

[0068] ΠS=AΠ+BΓ+P

[0069] 0=CΠ+Q

[0070] in, is the system rectangle, is the input matrix, is the output matrix, is the interference input matrix, is the interference output matrix; is the coupling matrix, through the Kronecker product The Laplace matrix L of the communication topology is combined with the control gain matrix J to achieve coordinated regulation between motors; and A a 、A p 、B a 、B p 、C a 、C p 、P p and Q p They are system matrix 1, system matrix 2, input matrix 1, input matrix 2, output matrix 1, output matrix 2, interference input matrix and interference output matrix respectively; then the system can achieve output regulation performance, that is, the output of the controlled object can track the expected reference signal;

[0071] When the communication graph is undirected and connected, the matrix A a The real parts of all eigenvalues ​​are negative, i.e., Hurwitz matrices, which ensure the stability of the motor subsystem and satisfy

[0072]

[0073] where λ j is the eigenvalue of the Laplace matrix L, σ(·) is the spectrum of the matrix, F is the constant matrix of the corresponding dimension, J is the coupling gain matrix, is the set of all complex numbers whose real part is less than 0; the above formula is the matrix F-λ j If all eigenvalues ​​of J, (j=2,…,N) are in the left half-complex plane, the system can achieve input sharing performance of the controlled object, which means that each motor can reasonably distribute the control input and jointly complete the control task of the controlled object;

[0074] Step S2-3-2: Perform directed coupling analysis based on the designed control law:

[0075] When the communication network is a directed graph, a spanning tree is required to ensure that information can be effectively transmitted in the network. Similarly, if A a is a Hurwitz matrix; if there exists Π and Γ that satisfy the equation, the system can achieve output regulation performance; when it satisfies When , the system can realize the input sharing performance of the controlled object;

[0076] After the analysis is completed, it lays the foundation for the subsequent coupling matrix design and system stability performance requirements.

[0077] Furthermore, the steps S2-4 are specifically as follows:

[0078] According to Lyapunov stability theory, a suitable coupling matrix J is selected, and the coupling matrix J is selected to satisfy the following inequality:

[0079] (F-λ i J) * P J +P J (F-λ i J)<0

[0080] Among them, (F-λ i J) * Yes (F-λ i J) is the conjugate transpose, Is a positive definite matrix; it ensures that the system can converge to a stable state in the presence of coupling, thereby achieving coordinated control between the motors;

[0081] The specific design method of the coupling matrix is ​​to select the coupling matrix J by solving the linear matrix inequality. Specifically, the linear matrix inequality is solved:

[0082]

[0083] in, is a positive definite matrix, F T is the transposed matrix of F, α2 is the minimum real part value among the non-zero eigenvalues ​​of the Laplace matrix L, Represents the nc-order unit matrix; take The coupling matrix J obtained in this way can ensure that the system meets the input sharing performance requirements of the controlled object.

[0084] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0085] (1) The multi-objective optimization design strategy for multiple motors proposed in the present invention incorporates the specific design parameters of the motor (motor stack length, number of coil turns) and the motor transmission ratio into a unified optimization framework, which solves the limitations of the existing technology of only optimizing transmission parameters or presetting motor characteristics, and significantly improves the collaborative optimization capability of energy efficiency and dynamic performance.

[0086] (2) The multi-objective optimization design strategy for multiple motors proposed in the present invention addresses the problem of excessive computational burden in multi-objective optimization. An artificial neural network is constructed, and samples are dynamically generated through optimal Latin hypercube design and maximized minimum distance design. Cross-validation and a gradual increase in the number of samples and hidden layer nodes are used to optimize the model accuracy, which can effectively improve the optimization efficiency and provide a feasible solution for multi-objective real-time optimization of complex power systems.

[0087] (3) The present invention proposes a collaborative control method for multiple motors. Through the system modeling steps, the motors, controlled objects and communication networks are accurately modeled respectively to construct a complete system framework with wide applicability. This systematic modeling method provides a solid theoretical basis for subsequent control law design, stability analysis and coupling matrix design, enabling the method to be applied to different types of multi-motor systems with strong versatility.

[0088] (4) The present invention proposes a method for collaborative control of multiple motors. In terms of control law design, a distributed control law is adopted and the state information of neighbor controllers is introduced, so that each motor can adjust the control input in real time according to the operating status of other motors to achieve collaborative control. By designing control parameters based on average dynamics and solving linear matrix inequalities, the stability of the system under different communication network topologies is ensured, thereby improving the overall performance and reliability of the system.

[0089] (5) The present invention proposes a multi-motor collaborative control method that satisfies the requirements of system stability and input sharing performance of the controlled object by rationally designing the coupling matrix, thereby avoiding load imbalance among motors and reducing unnecessary energy loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 A flowchart of the steps of the multi-objective optimization design strategy for multiple motors of the present invention;

[0091] Figure 2 This is a flow chart of the multi-motor coordinated control method of the present invention;

[0092] Figure 3 This is a modeling flow chart of the multi-motor coordinated control system of the present invention;

[0093] Figure 4 This is a block diagram of the multi-motor coordinated control system of the present invention;

[0094] Figure 5 It is the control law design flow chart of the present invention;

[0095] Figure 6 It is a flow chart of stability and performance analysis of the present invention. DETAILED DESCRIPTION

[0096] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0097] A multi-objective optimization design strategy for multiple motors includes the following steps:

[0098] Step S1-1, establish a multi-objective optimization function including motor design parameters and transmission ratio; the motor design parameters include the motor stack length L1 and the number of coil turns N1 of the first motor, the motor stack length L2 and the number of coil turns N2 of the second motor, the transmission ratio is the transmission ratio r1 of the first motor and the transmission ratio r2 of the second motor, the optimization objectives of the multi-objective optimization are energy efficiency index and power performance index, and select the electric energy consumption per 100 kilometers EC 100 As the energy efficiency indicator, the unit is kWh, and the acceleration time from 0 to 100 km / h is selected as T acc As a power performance indicator, the unit is seconds;

[0099] Step S1-2, construct and train an artificial neural network model: take the motor stack length L1 and motor stack length L2, coil turns N1 and coil turns N2, transmission ratio r1 and transmission ratio r2 as inputs of the artificial neural network model, and take the energy consumption per 100 kilometers EC 100 and acceleration time T from 0 to 100 km / h acc As the output of the artificial neural network model, an initial sample set is generated based on the optimal Latin hypercube design, and the artificial neural network model of the multi-objective optimization function in step S1-1 is constructed and trained;

[0100] Step S1-3, optimization based on genetic algorithm: using a second-generation non-dominated genetic algorithm to optimize the input of the artificial neural network model in step S1-2 to solve a Pareto front solution set; each solution in the solution set corresponds to a set of motor design parameters and transmission ratios;

[0101] Step S1-4, iterative parameter update and solution: Use the artificial neural network optimized in step S1-3 to solve the objective function. When the normalized root mean square error of the objective function is greater than the preset threshold, based on the initial sample set, new samples are added by maximizing the minimum distance design, and the artificial neural network model is updated and re-optimized and solved until the normalized root mean square error of the objective function is less than the preset threshold, thereby obtaining the motor design parameters and transmission ratio that take into account both energy efficiency indicators and power performance indicators.

[0102] Furthermore, in step S1-1, the multi-objective optimization function is:

[0103]

[0104] Where x = [L, N, r], L = [L1, L2], N = [N1, N2], r = [r1, r2];

[0105] Optimize the objective weight function:

[0106]

[0107] Among them, λ1 is the weight corresponding to the energy efficiency index, and λ2 is the weight corresponding to the power performance index.

[0108] Furthermore, in step S1-1, different designs of motor parameters such as motor stack length, number of coil turns, stator and rotor shapes will affect the motor characteristics. The maximum torque and efficiency characteristics of the motor directly affect the energy consumption and performance of the motor system. In actual motor design, the motor stack length and number of coil turns are easier to adjust than the stator and rotor shapes. Therefore, the motor stack length and number of coil turns are considered as motor design parameters to establish a multi-objective optimization function.

[0109] Furthermore, in step S1-1, the motor stack length and the number of coil turns need to be set with upper and lower limits according to actual needs. If the motor stack length is too high, it will lead to increased cost and quality. If the motor stack length is too low, the torque density and service life will be reduced. Increasing the number of coil turns can reduce the line current while maintaining the armature magnetomotive force, but at the same time it will reduce the motor efficiency of weak magnetic control in the high-speed domain.

[0110] Furthermore, in step S1-1, the constraint condition of the motor stack length is:

[0111] 50≤L1≤100

[0112] 50≤L2≤100

[0113] L1+L2=150

[0114] The constraints on the number of coil turns are:

[0115] 15≤N1≤40

[0116] 15≤N2≤40

[0117] The constraints on the transmission ratio are:

[0118] r1>r2

[0119]

[0120]

[0121]

[0122] Among them, r1 is the transmission ratio of the first motor, r2 is the transmission ratio of the second motor, is the maximum transmission ratio of the first motor, is the maximum transmission ratio of the second motor, ω 1max is the maximum speed of the first motor, ω 2max is the maximum speed of the second motor, R t is the effective radius of the tire, is the maximum average vehicle speed, μ r is the rolling friction coefficient, M is the total weight of the vehicle, g is the acceleration of gravity, c d is the drag coefficient, ρ is the air density, A is the front area, T 2max is the maximum torque of the second motor.

[0123] Furthermore, in step S1-2, during the training of the artificial neural network model, the accuracy and reliability of the model are improved by gradually increasing the number of samples and hidden layer nodes and cross-validating.

[0124] A multi-motor coordinated control method, such as Figure 2 As shown, the following steps are included:

[0125] Step S2-1: First, model the multi-motor coordinated control system: model the motors, controlled objects, and communication networks in the system separately. This includes constructing an accurate mathematical model for each motor in the multi-motor coordinated control system, building a dynamic model for the controlled objects affected by the multi-motor coordinated control, and modeling the communication network between the multiple motors using graph theory.

[0126] Step S2-2: After the system model is established, the control law is designed based on the modeling results: first, a distributed control law is constructed and its control principle is analyzed, and then the control parameters are determined based on the average dynamics concept;

[0127] Step S2-3: After the control law design is completed, perform system stability and performance analysis: perform undirected coupling analysis and directed coupling analysis for the communication network as an undirected graph and directed graph, respectively;

[0128] Step S2-4: Design a coupling matrix based on the stability analysis results to ultimately achieve system stability control: Design a coupling matrix based on stability theory to achieve the required performance of the controlled object.

[0129] Further, such as Figure 3 As shown, the step S2-1 is specifically as follows:

[0130] Step S2-1-1, motor modeling:

[0131] For each motor in the multi-motor coordinated drive system, an accurate mathematical model is constructed. In a stationary reference frame, the dynamic characteristics of the permanent magnet synchronous motor can be described by the following set of differential equations:

[0132]

[0133]

[0134] e α =-ψ fl ω er sinθ er

[0135] e β =ψ fl ω er cosθ er

[0136] Among them, i α,s and i β,s Represent the stator current of α-axis and β-axis respectively; v α,s and v β,s are the stator voltages of the α-axis and β-axis respectively; ω er is the rotor angular velocity, θ er is the rotor position; e α and e β are the back electromotive force of α-axis and β-axis respectively; L st is the stator inductance, R st is the stator resistance, ψ fl represents magnetic linkage;

[0137] The above motor model is represented in state space to obtain the general form:

[0138]

[0139] y i =C a x i

[0140] in, is the state vector of the i-th motor, which contains the key state variables of current and speed. is the updated state vector of the i-th motor; is the input vector, is the control voltage; is the output vector, which is the speed or torque of the motor; A a is the system matrix 1, B a For input matrices 1 and C a is the output matrix 1; and n α 、ma and m p dimensional real vector space;

[0141] A a 、B a and C a The derivation process is as follows:

[0142] According to the dynamic characteristic differential equation of the permanent magnet synchronous motor in the stationary reference frame, the state vector x i =[i α,s ,i β,s ,ω er ] T , contains the key current and speed state variables; input vector u i =[v α,s ,v β,s ] T , that is, the control voltage; output vector, assuming the output is the speed of the motor, that is, y i =ω er ;

[0143] For the state vector x i Derivative:

[0144] General Substitution have to:

[0145]

[0146] for According to the general form of the motor motion equation Here J is the moment of inertia, T e is the electromagnetic torque, T l is the load torque, B is the viscosity coefficient, assuming a ij 、b ij It is a coefficient determined according to the physical parameters of the motor;

[0147] but:

[0148]

[0149] We can get:

[0150]

[0151] By y i =C a x i ,y i =ω er , x i =[i α,s ,i β,s ,ωer ] T , we can get: C a =[0 0 1].

[0152] Step S2-1-2, modeling of the controlled object:

[0153] For the motors affected by the multi-motor cooperative control, a dynamic model is established; the relationship between the motor state and output error and input can be expressed by the following state space equation:

[0154]

[0155] e=C p x p +Q p w

[0156] in, is the state vector of the controlled object, is the updated state vector of the controlled object; It is the input vector of the controlled object, consisting of the output torque or speed of the motor; is the output error vector, which is used to measure the difference between the actual output and the expected output of the controlled object; is an exogenous input, i.e., an external disturbance or load change, and n p 、p p and r p dimensional real vector space; A p is the system rectangle 2, which is determined by the dynamic change characteristics of the motor's internal state, B p is the input matrix 2, which is determined by the relationship between the motor output and the state change of the controlled object, C p is the output matrix 2, which is determined by the relationship between the output error and the state variable of the controlled object, P p is the disturbance input matrix, which is determined by the influence of external disturbance on the state of the controlled object and Q p is the disturbance output matrix, which is determined by the influence of external disturbance on the output error. These matrices reflect the dynamic characteristics and input-output relationship of the controlled object;

[0157] Step S2-1-3, communication network modeling:

[0158] Graph theory is used to model the communication network between multiple motors. A directed graph G = (ν, ε, W) is defined, where the node set ν represents the controllers corresponding to each motor, the edge set ε represents the communication links between the controllers, and the weight matrix W reflects the weight of each communication link, reflecting the reliability and importance of the communication. The topology of the communication network is described by the Laplace matrix L of the directed graph. The element l of the Laplace matrix L isij The definition is as follows:

[0159]

[0160] where w ij is the weight of edge (j,i), and the Laplace matrix L contains the connection information between nodes in the communication network. The block diagram of the multi-motor cooperative control system is as follows: Figure 4 shown.

[0161] Further, such as Figure 5 As shown, the step S2-2 is specifically as follows:

[0162] Step S2-2-1, construction of control law:

[0163] Design a distributed control law to achieve coordinated control among multiple motors; the control law is as follows:

[0164]

[0165] u i =Hξ i

[0166] in, is the state vector of controller i, is the updated state vector of controller i; G is the output error feedback matrix, F and H are constant matrices of corresponding dimensions, which respectively reflect the interaction relationship between the internal state variables of the controller and the relationship between the internal state of the controller and the actual control input; is the output error vector, n c dimensional real vector space; J is the coupling gain matrix, which is used to adjust the degree of coordination between motors; w ij is the weight of edge (j,i), is the neighbor set of controller i, which represents the set of other controllers that have communication connections with controller i;

[0167] The control law introduces the state information of neighboring controllers, so that each motor can adjust its own control input in real time according to the operating status of other motors, thus achieving coordinated control;

[0168] Step S2-2-2, determination of control parameters:

[0169] Design F, G, H matrices based on the idea of ​​average dynamics and define the average state and the average controller state Where N is the number of motors. By analyzing the average dynamic characteristics of the system, the linear matrix inequality constraint relationship between the system matrices is established, and the linear matrix inequality optimization method is used to solve the F, G, and H matrices that meet the system stability and performance requirements.

[0170] Further, such as Figure 6 As shown, the steps S2-3 are specifically as follows:

[0171] Step S2-3-1: Analyze the undirected coupling situation based on the designed control law:

[0172] In the case of an undirected communication network, certain assumptions must first be met: the dynamic characteristics of the exogenous input are stable, a control law can be found to make the system state asymptotically stable, and the system state can be accurately estimated through the output;

[0173] If exists and Satisfies the following equation:

[0174] ΠS=AΠ+BΓ+P

[0175] 0=CΠ+Q

[0176] in, is the system rectangle, is the input matrix, is the output matrix, is the interference input matrix, is the interference output matrix; is the coupling matrix, through the Kronecker product The Laplace matrix L of the communication topology is combined with the control gain matrix J to achieve coordinated regulation between motors; and A a 、A p 、B a 、B p 、C a 、C p 、P p and Q p They are system matrix 1, system matrix 2, input matrix 1, input matrix 2, output matrix 1, output matrix 2, interference input matrix and interference output matrix respectively; then the system can achieve output regulation performance, that is, the output of the controlled object can track the expected reference signal;

[0177] When the communication graph is undirected and connected, the matrix A a The real parts of all eigenvalues ​​are negative, i.e., Hurwitz matrices, which ensure the stability of the motor subsystem and satisfy

[0178]

[0179] where λj is the eigenvalue of the Laplace matrix L, σ(·) is the spectrum of the matrix, F is the constant matrix of the corresponding dimension, J is the coupling gain matrix, is the set of all complex numbers whose real part is less than 0; the above formula is the matrix F-λ j If all eigenvalues ​​of J, (j=2,…,N) are in the left half-complex plane, the system can achieve input sharing performance of the controlled object, which means that each motor can reasonably distribute the control input and jointly complete the control task of the controlled object;

[0180] Step S2-3-2: Perform directed coupling analysis based on the designed control law:

[0181] When the communication network is a directed graph, a spanning tree is required to ensure that information can be effectively transmitted in the network. Similarly, if A a is a Hurwitz matrix; if there exists Π and Γ that satisfy the equation, the system can achieve output regulation performance; when it satisfies When , the system can realize the input sharing performance of the controlled object;

[0182] After the analysis is completed, it lays the foundation for the subsequent coupling matrix design and system stability performance requirements.

[0183] Furthermore, the steps S2-4 are specifically as follows:

[0184] According to Lyapunov stability theory, a suitable coupling matrix J is selected, and the coupling matrix J is selected to satisfy the following inequality:

[0185] (F-λ i J) * P J +P J (F-λ i J)<0

[0186] Among them, (F-λ i J) * Yes (F-λ i J) is the conjugate transpose, Is a positive definite matrix; it ensures that the system can converge to a stable state in the presence of coupling, thereby achieving coordinated control between the motors;

[0187] The specific design method of the coupling matrix is ​​to select the coupling matrix J by solving the linear matrix inequality. Specifically, the linear matrix inequality is solved:

[0188]

[0189] in, is a positive definite matrix, F Tis the transposed matrix of F, α2 is the minimum real part value among the non-zero eigenvalues ​​of the Laplace matrix L, Represents the nc-order unit matrix; take The coupling matrix J obtained in this way can ensure that the system meets the input sharing performance requirements of the controlled object.

[0190] Furthermore, in the application scenario of electric vehicles:

[0191] In order to improve the control performance of the motor, the particle swarm optimization algorithm is used to optimize the PI controller parameters of the motor. The specific steps are as follows:

[0192] Initialize the particle swarm: Randomly initialize the position and velocity of the particles, each particle represents a set of PI controller parameters; the particle position vector x i =[K p ,K i ], where K p , is the proportionality coefficient, K i is the integral coefficient; the velocity vector v i Indicates the speed of the particle in the parameter space;

[0193] Fitness value calculation: Define the fitness function and select the sum of squares of the motor speed error as the fitness function f(x i ), calculate the fitness value of each particle. The smaller the fitness value, the better the PI controller parameters represented by the particle can make the motor control performance;

[0194] Individual optimal and global optimal update: For each particle, compare its current fitness value with the historical best fitness value. If the current fitness value is better, update the individual optimal position P best,i At the same time, find the particle with the smallest fitness value among all particles, and its position is the global optimal position G best ;

[0195] Particle speed and position update: Update the particle speed and position using the following formula:

[0196]

[0197]

[0198] in, and are the velocities of the particle at time t+1 and time t respectively; and are the positions of the particle at time t+1 and time t respectively; is the optimal position of particle i at time t; is the global optimal position; C1 and C2 are positive acceleration constants, ranging from 0 to 2; and is a random number in the interval [0,1];

[0199] Iteration termination condition: Repeat the above steps until the upper limit of the number of iterations is met or the fitness value reaches the preset threshold. At this time, the global optimal position G is obtained. best These are the optimized PI controller parameters.

[0200] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization design strategy for multiple motors, characterized in that: The following steps are involved: Step S1-1, establish a multi-objective optimization function including motor design parameters and transmission ratio; the motor design parameters include the motor stack length L1 and the number of coil turns N1 of the first motor, the motor stack length L2 and the number of coil turns N2 of the second motor, the transmission ratio is the transmission ratio r1 of the first motor and the transmission ratio r2 of the second motor, the optimization objectives of the multi-objective optimization are energy efficiency index and power performance index, and select the electric energy consumption per 100 kilometers EC 100 As the energy efficiency indicator, the unit is kilowatt-hour, and the acceleration time from 0 to 100 km / h is selected as T acc As a power performance indicator, the unit is seconds; Step S1-2, construct and train an artificial neural network model: take the motor stack length L1 and motor stack length L2, coil turns N1 and coil turns N2, transmission ratio r1 and transmission ratio r2 as inputs of the artificial neural network model, and take the energy consumption per 100 kilometers EC 100 and acceleration time T from 0 to 100 km / h acc As the output of the artificial neural network model, an initial sample set is generated based on the optimal Latin hypercube design, and the artificial neural network model of the multi-objective optimization function in step S1-1 is constructed and trained; Step S1-3, optimization based on genetic algorithm: using a second-generation non-dominated genetic algorithm to optimize the input of the artificial neural network model in step S1-2 to solve a Pareto front solution set; each solution in the solution set corresponds to a set of motor design parameters and transmission ratios; Step S1-4, iterative parameter update and solution: Use the artificial neural network optimized in step S1-3 to solve the objective function. When the normalized root mean square error of the objective function is greater than the preset threshold, based on the initial sample set, new samples are added by maximizing the minimum distance design, and the artificial neural network model is updated and re-optimized and solved until the normalized root mean square error of the objective function is less than the preset threshold, thereby obtaining the motor design parameters and transmission ratio that take into account both energy efficiency indicators and power performance indicators.

2. A multi-objective optimization design strategy for multiple motors according to claim 1, characterized in that: In step S1-1, the multi-objective optimization function is: Where x = [L, N, r], L = [L1, L2], N = [N1, N2], r = [r1, r2]; Optimize the objective weight function: Among them, λ1 is the weight corresponding to the energy efficiency index, and λ2 is the weight corresponding to the power performance index.

3. The multi-objective optimization design strategy for multiple motors according to claim 1, characterized in that: In step S1-1, the constraint condition of the motor stack length is: 50≤L1≤100 50≤L2≤100 L1+L2=150 The constraints on the number of coil turns are: 15≤N1≤40 15≤N2≤40 The constraints on the transmission ratio are: r1＞r2 Among them, r1 is the transmission ratio of the first motor, r2 is the transmission ratio of the second motor, is the maximum transmission ratio of the first motor, is the maximum transmission ratio of the second motor, ω 1max is the maximum speed of the first motor, ω 2max is the maximum speed of the second motor, R t is the effective radius of the tire, is the maximum average speed, μ r is the rolling friction coefficient, M is the total weight of the vehicle, g is the acceleration of gravity, c d is the drag coefficient, ρ is the air density, A is the front area, T 2max is the maximum torque of the second motor.

4. The multi-objective optimization design strategy for multiple motors according to claim 1, characterized in that: In step S1-2, during the training of the artificial neural network model, the accuracy and reliability of the model are improved by gradually increasing the number of samples and hidden layer nodes and cross-validating.

5. A method for coordinated control of multiple motors, characterized in that: The multi-motor coordinated control method is applied to the multi-motor optimized based on the multi-objective optimization design strategy described in any one of claims 1 to 4, comprising the following steps: Step S2-1: First, model the multi-motor coordinated control system: model the motors, controlled objects, and communication networks in the system separately. This includes constructing an accurate mathematical model for each motor in the multi-motor coordinated control system, building a dynamic model for the controlled objects affected by the multi-motor coordinated control, and modeling the communication network between the multiple motors using graph theory. Step S2-2: After the system model is established, the control law is designed based on the modeling results: first, a distributed control law is constructed and its control principle is analyzed, and then the control parameters are determined based on the average dynamics concept; Step S2-3: After the control law design is completed, perform system stability and performance analysis: perform undirected coupling analysis and directed coupling analysis for the communication network as an undirected graph and directed graph, respectively; Step S2-4: Design a coupling matrix based on the stability analysis results to ultimately achieve system stability control: Design a coupling matrix based on stability theory to achieve the required performance of the controlled object.

6. The method for coordinated control of multiple motors according to claim 5, characterized in that: The step S2-1 is specifically as follows: Step S2-1-1, motor modeling: For each motor in the multi-motor coordinated drive system, an accurate mathematical model is constructed. In a stationary reference frame, the dynamic characteristics of the permanent magnet synchronous motor can be described by the following set of differential equations: e α =-ψ fl oh er sinth er e β =ψ fl oh er cosθ er Among them, i α,s and i β,s Represent the stator current of α-axis and β-axis respectively; v α,s and v β,s are the stator voltages of the α-axis and β-axis respectively; ω er is the rotor angular velocity, θ er is the rotor position; e α and e β are the back electromotive force of α-axis and β-axis respectively; L st is the stator inductance, R st is the stator resistance, ψ fl represents magnetic linkage; The above motor model is represented in state space to obtain the general form: y i =C a x i in, is the state vector of the i-th motor, which contains the key state variables of current and speed. is the updated state vector of the i-th motor; is the input vector, is the control voltage; is the output vector, which is the speed or torque of the motor; A a is the system matrix 1, B a For input matrices 1 and C a is the output matrix 1; and n α 、m a and m p Dimensional real vector space; Step S2-1-2, modeling of the controlled object: For the motors affected by the multi-motor cooperative control, a dynamic model is established; the relationship between the motor state and output error and input can be expressed by the following state space equation: e=C p x p +Q p w in, is the state vector of the controlled object, is the updated state vector of the controlled object; It is the input vector of the controlled object, consisting of the output torque or speed of the motor; is the output error vector, which is used to measure the difference between the actual output and the expected output of the controlled object; is an exogenous input, i.e., an external disturbance or load change, and n p 、p p and r p dimensional real vector space; A p is the system rectangle 2, which is determined by the dynamic change characteristics of the motor's internal state, B p is the input matrix 2, which is determined by the relationship between the motor output and the state change of the controlled object, C p is the output matrix 2, which is determined by the relationship between the output error and the state variable of the controlled object, P p is the disturbance input matrix, which is determined by the influence of external disturbance on the state of the controlled object and Q p is the disturbance output matrix, which is determined by the influence of external disturbance on the output error. These matrices reflect the dynamic characteristics and input-output relationship of the controlled object; Step S2-1-3, communication network modeling: Graph theory is used to model the communication network between multiple motors. A directed graph G = (ν, ε, W) is defined, where the node set ν represents the controllers corresponding to each motor, the edge set ε represents the communication links between the controllers, and the weight matrix W reflects the weight of each communication link, reflecting the reliability and importance of the communication. The topology of the communication network is described by the Laplace matrix L of the directed graph. The element l of the Laplace matrix L is ij The definition is as follows: where w ij is the weight of edge (j,i), and the Laplace matrix L contains the connection information between nodes in the communication network.

7. The method for coordinated control of multiple motors according to claim 5, characterized in that: The step S2-2 is specifically as follows: Step S2-2-1, construction of control law: Design a distributed control law to achieve coordinated control among multiple motors; the control law is as follows: in i =Hξ i in, is the state vector of controller i, is the updated state vector of controller i; G is the output error feedback matrix, F and H are constant matrices of corresponding dimensions, which respectively reflect the interaction relationship between the internal state variables of the controller and the relationship between the internal state of the controller and the actual control input; is the output error vector, n c dimensional real vector space; J is the coupling gain matrix, which is used to adjust the degree of coordination between motors; w ij is the weight of edge (j,i), is the neighbor set of controller i, which represents the set of other controllers that have communication connections with controller i; The control law introduces the state information of neighboring controllers, so that each motor can adjust its own control input in real time according to the operating status of other motors, thus achieving coordinated control; Step S2-2-2, determination of control parameters: Design F, G, H matrices based on the idea of ​​average dynamics and define the average state and the average controller state Where N is the number of motors. By analyzing the average dynamic characteristics of the system, the linear matrix inequality constraint relationship between the system matrices is established, and the linear matrix inequality optimization method is used to solve the F, G, and H matrices that meet the system stability and performance requirements.

8. The method for coordinated control of multiple motors according to claim 5, characterized in that: The steps S2-3 are as follows: Step S2-3-1: Analyze the undirected coupling situation based on the designed control law: In the case of an undirected communication network, certain assumptions must first be met: the dynamic characteristics of the exogenous input are stable, a control law can be found to make the system state asymptotically stable, and the system state can be accurately estimated through the output; If exists and Satisfies the following equation: ΠS=AΠ+BΓ+P 0=CΠ+Q in, is the system rectangle, is the input matrix, is the output matrix, is the interference input matrix, is the interference output matrix; is the coupling matrix, through the Kronecker product The Laplace matrix L of the communication topology is combined with the control gain matrix J to achieve coordinated regulation between motors; and A a 、A p 、B a 、B p 、C a 、C p 、P p and Q p They are system matrix 1, system matrix 2, input matrix 1, input matrix 2, output matrix 1, output matrix 2, interference input matrix and interference output matrix respectively; then the system can achieve output regulation performance, that is, the output of the controlled object can track the expected reference signal; When the communication graph is undirected and connected, the matrix A a The real parts of all eigenvalues ​​are negative, i.e., Hurwitz matrices, which ensure the stability of the motor subsystem and satisfy where λ j is the eigenvalue of the Laplace matrix L, σ(·) is the spectrum of the matrix, F is the constant matrix of the corresponding dimension, J is the coupling gain matrix, is the set of all complex numbers whose real part is less than 0; the above formula is the matrix F-λ j If all eigenvalues ​​of J, (j=2,…,N) are in the left half-complex plane, the system can achieve input sharing performance of the controlled object, which means that each motor can reasonably distribute the control input and jointly complete the control task of the controlled object; Step S2-3-2: Perform directed coupling analysis based on the designed control law: When the communication network is a directed graph, a spanning tree is required to ensure that information can be effectively transmitted in the network. Similarly, if A a is a Hurwitz matrix; if there exists Π and Γ that satisfy the equation, the system can achieve output regulation performance; when it satisfies When , the system can realize the input sharing performance of the controlled object; After the analysis is completed, it lays the foundation for the subsequent coupling matrix design and system stability performance requirements.

9. The method for coordinated control of multiple motors according to claim 5, characterized in that: The steps S2-4 are as follows: According to Lyapunov stability theory, a suitable coupling matrix J is selected, and the coupling matrix J is selected to satisfy the following inequality: (F-λ i J) * P J +P J (F-λ i J)<0 Among them, (F-λ i J) * Yes (F-λ i J) is the conjugate transpose, Is a positive definite matrix; it ensures that the system can converge to a stable state in the presence of coupling, thereby achieving coordinated control between the motors; The specific design method of the coupling matrix is ​​to select the coupling matrix J by solving the linear matrix inequality. Specifically, the linear matrix inequality is solved: in, is a positive definite matrix, F T is the transposed matrix of F, α2 is the minimum real part value among the non-zero eigenvalues ​​of the Laplace matrix L, Represents the nc-order unit matrix; take The coupling matrix J obtained in this way can ensure that the system meets the input sharing performance requirements of the controlled object.

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