Urban rail multi-permanent magnet synchronous motor speed control method based on distributed internal model

Abstract

The invention discloses an urban rail multi-permanent magnet synchronous motor speed control method based on a distributed internal model, and the method comprises the following steps: S1, selecting a permanent magnet synchronous motor as a traction motor of an urban rail train, and building a mathematical model of a multi-permanent magnet synchronous motor system; s2, describing a multi-permanent magnet synchronous motor speed synchronization and interference suppression problem under the condition that parameters are unknown as a collaborative robust output adjustment problem of a multi-agent system; s3, constructing directed communication topology to describe information transmission between the motors; and S4, a speed-current loop cascade structure is adopted, a speed loop adopts a distributed internal model control method, a current loop adopts a PI control method, a PI controller is constructed, and a final controller is given. The speed synchronization controller based on the distributed internal model is designed for the conditions of communication constraint and parameter uncertainty in actual control, speed synchronization and interference suppression of the multi-permanent magnet synchronous motor system for the urban rail are achieved, and all motor parameters are allowed to be unknown.

Description

Technical Field

[0001] This invention relates to the field of multi-permanent magnet synchronous motor cooperative control technology, specifically to a speed control method for multi-permanent magnet synchronous motors used in urban rail transit based on distributed internal models. Background Technology

[0002] As a crucial component of urban rail transit, the traction system is the power source for urban rail trains, and its performance directly impacts the safety, efficiency, and reliability of these trains. In recent years, permanent magnet synchronous motors have become the development direction for next-generation traction motors for urban rail trains due to their advantages of high torque, high power density, and low maintenance costs.

[0003] In urban rail trains based on permanent magnet synchronous motors, each carriage contains multiple permanent magnet synchronous motors, and the motor rotors are not mechanically connected. Due to the different operating conditions of each wheel and traction motor, the different loads of each carriage, and the unstable friction between the wheels and the track, the speeds of the motors are not synchronized, which can easily lead to safety problems. Achieving good speed synchronization performance is often quite difficult.

[0004] In the past decade or so, the cooperative output regulation problem has attracted increasing attention due to its wide application in attitude synchronization of multi-spacecraft systems, consistency of Eulerian-Lagrange systems, and power distribution in grid-connected microgrids. The cooperative output regulation problem can be solved using distributed observer methods and distributed internal model methods, with the latter capable of handling parameter uncertainties. However, in practical control systems, communication often suffers from delays and packet loss, or even complete communication failures. Furthermore, perturbations in motor parameters can also affect control performance, making it difficult for distributed observer methods to achieve satisfactory control performance. Summary of the Invention

[0005] The purpose of this invention is to provide a speed control method for multiple permanent magnet synchronous motors used in urban rail transit based on distributed internal models, so as to solve the above-mentioned defects.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models proposed in this invention includes the following steps:

[0008] S1. Establish a mathematical model for a multi-permanent magnet synchronous motor system for urban rail transit, consisting of N permanent magnet synchronous motors.

[0009] S2. Construct an external system as the leader, which together with the urban rail multi-permanent magnet synchronous motor system forms a multi-agent system with N+1 agents, where the N permanent magnet synchronous motors in the urban rail multi-permanent magnet synchronous motor system act as followers; then, describe the speed synchronization and interference suppression problem of the multi-permanent magnet synchronous motor under unknown parameters as a cooperative robust output regulation problem of a multi-agent system.

[0010] S3. Construct a directed communication topology to describe the information transmission between each agent in a multi-agent system consisting of an external system and multiple permanent magnet synchronous motors;

[0011] S4. A cascaded structure of speed-current loops is adopted, in which the speed loop adopts a distributed internal model control method and the current loop adopts a PI control method. A PI controller is constructed and the final controller is given.

[0012] Preferably, in step S1, the mathematical model of the urban rail multi-permanent magnet synchronous motor system is as follows:

[0013]

[0014] In equation (1), i = 1, ..., N, N represents the number of permanent magnet synchronous motors; ω ri i qi i di Let ω represent the rotor angular velocity of the i-th permanent magnet synchronous motor, respectively. ri q-axis stator current i qi and d-axis stator current i di ; They represent ω respectively ri i qi i di The derivative of u; qi ,u di J represents the stator voltages of the i-th permanent magnet synchronous motor along the q-axis and d-axis, respectively; i L represents the moment of inertia of the i-th permanent magnet synchronous motor; i R represents the armature inductance of the i-th permanent magnet synchronous motor; si Φ represents the stator resistance of the i-th permanent magnet synchronous motor; p represents the number of pole pairs of the i-th permanent magnet synchronous motor; Φ vi T represents the rotor flux linkage of the i-th permanent magnet synchronous motor; Li F represents the load torque of the i-th permanent magnet synchronous motor; vi Let represent the viscous friction coefficient of the i-th permanent magnet synchronous motor.

[0015] Preferably, step S2 includes the following steps:

[0016] S21. Construct an external system using equation (2):

[0017]

[0018] In equation (2), v represents the state variable of the external system. Let ω denote the derivative of v, S denote the system matrix of the external system, and ω d Let F represent the reference velocity, and T represent the constant matrix of the reference velocity. Li Q represents the load torque of the i-th permanent magnet synchronous motor. i Let represent the load torque constant matrix of the i-th permanent magnet synchronous motor;

[0019] S22. Define the state variable x of the i-th permanent magnet synchronous motor. i =ω ri The state matrix of the i-th permanent magnet synchronous motor The input matrix of the i-th permanent magnet synchronous motor The state disturbance matrix of the i-th permanent magnet synchronous motor i qi As control input u i And will be used as i q The reference signal of the current loop is used to establish the speed loop equation of the i-th permanent magnet synchronous motor using equation (3):

[0020]

[0021] In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative;

[0022] S23. Using equation (4), establish the speed tracking error equation for the i-th permanent magnet synchronous motor:

[0023] e i =x i -Fv (4),

[0024] In equation (4), e i This represents the speed tracking error of the i-th permanent magnet synchronous motor;

[0025] S24. Considering the perturbation of motor parameters caused by uncertainties, let col(L) i ,R si ,Φ vi J i ,F vi ) = col(L,R s ,Φ v ,J,F v )+ε i , where L,R s ,Φ v ,J,F vL represents the nominal values ​​of each parameter of the i-th permanent magnet synchronous motor. i ,R si ,Φ vi J i ,F vi This represents the actual values ​​of each parameter of the i-th permanent magnet synchronous motor. This represents the deviation between the actual and nominal values ​​of the parameters of the i-th permanent magnet synchronous motor;

[0026] S25. Rewrite equations (2), (3), and (4) in the following compact form:

[0027]

[0028] At this point, the speed synchronization and interference suppression problem of multiple permanent magnet synchronous motors under unknown motor parameters has been described as a cooperative robust output regulation problem of system (5). Its control objective is to make the closed-loop system stable and the tracking error of system (5) asymptotically approach zero under the condition of parameter uncertainty.

[0029] Preferably, step S3 is as follows:

[0030] Define the communication topology. in, Node 0 represents the external system, and the remaining N nodes represent N permanent magnet synchronous motors. Let...

[0031] definition The subgraph G = (V, E), where V = {1, ..., N}, and E is the subgraph that has been removed from the subgraph. The edges connected to node 0 are obtained by N. i ={j,(j,i)∈E}, Let G be the weighted adjacency matrix, and when (j,i)∈E, a ij >0 and a ii =0, i,j=1,…,N; and Is with The corresponding Laplace matrix of G, where, When i ≠ j, l ij =-a ij ;

[0032] Let Δ = diag(a) 10 ,…,a N0 ), where for i = 1, ..., N, when At that time, a i0 >0, otherwise a i0 =0, and H = L + Δ.

[0033] Preferably, step S4 specifically includes the following steps:

[0034] S41. Define the virtual error e of the i-th permanent magnet synchronous motor. vi :

[0035]

[0036] In equation (6), y i =x i , where i = 1, ..., N, and when i = 0, y0 = Fv;

[0037] S42. Design the inner mold using formula (7):

[0038]

[0039] In equation (7), G1 represents a constant matrix whose characteristic polynomial is the smallest characteristic polynomial of the external system matrix S, and G2 is a constant column vector such that (G1, G2) is controllable.

[0040] S43. Let x = [x1, ..., x2] N ] T ,e v =[e v1 ,…,e vN ] T ,u=[u1,…,u N ] T , Among them, 1 N This represents an N-dimensional column vector where all elements are 1; Representing the identity matrix, we obtain the following augmented system:

[0041]

[0042] At this point, the cooperative robust output regulation problem of system (5) has been transformed into the robust stabilization problem of system (8);

[0043] S44, Order in P is a positive definite symmetric matrix that satisfies the following Riccati equation:

[0044] Y T P+PY-PWW T P+I=0 (9),

[0045] In equation (9), I is the identity matrix;

[0046] S45. According to the solution P of the Riccati equation, we get:

[0047] [K x Kz ] = K = -μ -1 W T P (10),

[0048] In equation (10), μ satisfies 0 < μ < Re(λ) i ), i = 1, ..., N; where λ i These are the eigenvalues ​​of matrix H;

[0049] S46. The following control law is obtained to solve the robust stabilization problem of system (8):

[0050]

[0051] S47. The distributed internal model controller of the velocity loop is obtained as follows:

[0052]

[0053] S48. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13):

[0054]

[0055] In equation (13), K p1i ,K I1i K represents the proportional coefficient and integral coefficient of the d-axis of the i-th motor, respectively. p2i ,K I2i Let represent the proportional coefficient and integral coefficient of the q-axis of the i-th motor, respectively;

[0056] The final controller for the i-th permanent magnet synchronous motor, composed of equations (12) and (13), is as follows:

[0057]

[0058] The beneficial effects of this invention are as follows:

[0059] (1) The present invention is a speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal model. The method uses internal model to handle the uncertainty of system model parameters. This method solves the problem that some motors cannot directly obtain information from the leader for feedback control due to communication constraints in actual control systems. Thus, it realizes speed synchronization and interference suppression of multiple permanent magnet synchronous motors under communication constraints, giving them good tracking performance, while allowing unknown motor parameters.

[0060] (2) The present invention is a speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal model. It adopts a speed-current cascade structure and integrates a dual control mechanism of speed loop and current loop, which can effectively improve the dynamic performance and steady-state performance of the system. Moreover, the speed loop controller only needs to be designed based on the speed equation model of the permanent magnet synchronous motor, which simplifies the model and makes it easier to apply in practice. Attached Figure Description

[0061] Figure 1 This is a block diagram illustrating the principle of speed synchronization control for multiple permanent magnet synchronous motors according to the present invention.

[0062] Figure 2 This is a communication topology diagram of the multiple permanent magnet synchronous motors of the present invention;

[0063] Figure 3 This is a speed tracking curve diagram of the multi-permanent magnet synchronous motor of the present invention;

[0064] Figure 4 The present invention relates to a multi-permanent magnet synchronous motor i d Current curve;

[0065] Figure 5 The present invention relates to a multi-permanent magnet synchronous motor i q Current curve. Detailed Implementation

[0066] The present invention will be further described below with reference to the embodiments. It should be noted that these are merely examples and descriptions of the inventive concept. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in the claims, they should all be considered to fall within the protection scope of the present invention.

[0067] Example 1:

[0068] The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models proposed in this invention includes the following steps:

[0069] S1. Establish a mathematical model for a multi-permanent magnet synchronous motor system for urban rail transit, consisting of N permanent magnet synchronous motors.

[0070] A mathematical model of a multi-permanent magnet synchronous motor system for urban rail transit is established using equation (1):

[0071]

[0072] In equation (1), i = 1, ..., N, N represents the number of permanent magnet synchronous motors; ω ri i qi i di Let ω represent the rotor angular velocity of the i-th permanent magnet synchronous motor, respectively.ri q-axis stator current i qi and d-axis stator current i di ; They represent ω respectively ri i qi i di The derivative of u; qi ,u di J represents the stator voltages of the i-th permanent magnet synchronous motor along the q-axis and d-axis, respectively; i L represents the moment of inertia of the i-th permanent magnet synchronous motor; i R represents the armature inductance of the i-th permanent magnet synchronous motor; si Φ represents the stator resistance of the i-th permanent magnet synchronous motor; p represents the number of pole pairs of the i-th permanent magnet synchronous motor; Φ vi T represents the rotor flux linkage of the i-th permanent magnet synchronous motor; Li F represents the load torque of the i-th permanent magnet synchronous motor; vi Let represent the viscous friction coefficient of the i-th permanent magnet synchronous motor.

[0073] S2. Construct an external system as the leader, forming a multi-agent system with N+1 agents together with the urban rail multi-permanent magnet synchronous motor system. The N permanent magnet synchronous motors in the urban rail multi-permanent magnet synchronous motor system act as followers. Then, the speed synchronization and interference suppression problem of the multi-permanent magnet synchronous motors under unknown parameters is described as a cooperative robust output regulation problem of a multi-agent system. The specific steps are as follows:

[0074] S21. Construct an external system using equation (2):

[0075]

[0076] In equation (2), v represents the state variable of the external system, v' represents the derivative of v, S represents the system matrix of the external system, and ω' represents the system matrix of the external system. d Let F represent the reference velocity, and T represent the constant matrix of the reference velocity. Li Q represents the load torque of the i-th permanent magnet synchronous motor. i Let represent the load torque constant matrix of the i-th permanent magnet synchronous motor.

[0077] S22. Define the state variable x of the i-th permanent magnet synchronous motor. i =ω ri The state matrix of the i-th permanent magnet synchronous motor The input matrix of the i-th permanent magnet synchronous motor The state disturbance matrix of the i-th permanent magnet synchronous motor i qi As control input u i And will be used as iq The reference signal of the current loop is used to establish the speed loop equation of the i-th permanent magnet synchronous motor using equation (3):

[0078]

[0079] In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative of .

[0080] S23. Using equation (4), establish the speed tracking error equation for the i-th permanent magnet synchronous motor:

[0081] e i =x i -Fv (4),

[0082] In equation (4), e i This represents the speed tracking error of the i-th permanent magnet synchronous motor.

[0083] S24. Considering the perturbation of motor parameters caused by uncertainties, let col(L) i ,R si ,Φ vi J i ,F vi ) = col(L,R s ,Φ v ,J,F v )+ε i , where L,R s ,Φ v ,J,F v L represents the nominal values ​​of each parameter of the i-th permanent magnet synchronous motor. i ,R si ,Φ vi J i ,F vi This represents the actual values ​​of each parameter of the i-th permanent magnet synchronous motor. This represents the deviation between the actual and nominal values ​​of the parameters of the i-th permanent magnet synchronous motor.

[0084] S25. Rewrite equations (2), (3), and (4) in the following compact form:

[0085]

[0086] At this point, the speed synchronization and interference suppression problem of multiple permanent magnet synchronous motors under unknown motor parameters has been described as a cooperative robust output regulation problem of system (5). Its control objective is to make the closed-loop system stable and the tracking error of system (5) asymptotically approach zero under the condition of parameter uncertainty.

[0087] S3. Construct a directed communication topology to describe the information transfer between each agent in the multi-agent system composed of the external system and multiple permanent magnet synchronous motors, as follows:

[0088] Define the communication topology. in, Node 0 represents the external system, and the remaining N nodes represent N permanent magnet synchronous motors. Let...

[0089] definition The subgraph G = (V, E), where V = {1, ..., N}, and E is the subgraph that has been removed from the subgraph. The edges connected to node 0 are obtained by N. i ={j,(j,i)∈E}, Let G be the weighted adjacency matrix, and when (j,i)∈E, a ij >0 and a ii =0, i,j=1,…,N; and Is with The corresponding Laplace matrix of G, where, When i ≠ j, l ij =-a ij ;

[0090] Let Δ = diag(a) 10 ,…,a N0 ), where for i = 1, ..., N, when At that time, a i0 >0, otherwise a i0 =0, and H = L + Δ.

[0091] S4. A cascaded speed-current loop structure is adopted, where the speed loop uses a distributed internal model control method and the current loop uses a PI control method. A PI controller is constructed and the final controller is given. The specific steps are as follows:

[0092] S41. Define the virtual error e of the i-th permanent magnet synchronous motor. vi :

[0093]

[0094] In equation (6), y i =x i , where i = 1, ..., N, and when i = 0, y0 = Fv.

[0095] S42. Design the inner mold using formula (7):

[0096]

[0097] In equation (7), G1 represents a constant matrix whose characteristic polynomial is the minimum characteristic polynomial of the external system matrix S, and G2 is a constant column vector such that (G1, G2) is controllable.

[0098] S43. Let x = [x1, ..., x2] N ] T ,e v =[e v1 ,…,e vN ] T ,u=[u1,…,u N ] T , Among them, 1 N This represents an N-dimensional column vector where all elements are 1; Representing the identity matrix, we obtain the following augmented system:

[0099]

[0100] At this point, the cooperative robust output regulation problem of system (5) has been transformed into the robust stabilization problem of system (8).

[0101] S44, Order in P is a positive definite symmetric matrix that satisfies the following Riccati equation:

[0102] Y T P+PY-PWW T P+I=0 (9),

[0103] In equation (9), I is the identity matrix.

[0104] S45. According to the solution P of the Riccati equation, we get:

[0105] [K x K z ] = K = -μ -1 W T P (10),

[0106] In equation (10), μ satisfies 0 < μ < Re(λ) i ), i = 1, ..., N; where λ i Let H be the eigenvalues ​​of matrix H.

[0107] S46. The following control law is obtained to solve the robust stabilization problem of system (8):

[0108]

[0109] S47. The distributed internal model controller of the velocity loop is obtained as follows:

[0110]

[0111] S48. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13):

[0112]

[0113] In equation (13), K p1i ,K I1i K represents the proportional coefficient and integral coefficient of the d-axis of the i-th motor, respectively. p2i ,K I2i Let represent the proportional coefficient and integral coefficient of the q-axis of the i-th motor, respectively;

[0114] The final controller for the i-th permanent magnet synchronous motor, composed of equations (12) and (13), is as follows:

[0115]

[0116] Figure 1 This is a block diagram illustrating the principle of speed synchronization control for multiple permanent magnet synchronous motors according to the present invention. Figure 1 As shown, the first to the l-th permanent magnet synchronous motors can directly obtain the leader's information, while the (l+1)-th to the Nth permanent magnet synchronous motors cannot. To verify the effectiveness of the proposed method, this invention performs simulation verification on the control effect of the distributed internal model controller. The specific parameters of the selected permanent magnet synchronous motors are shown in Table 1:

[0117] Table 1. Parameters of Permanent Magnet Synchronous Motor

[0118] Motor parameters numerical values Extreme number p 4 <![CDATA[Stator resistance R s (Ω)]]> 0.125 <![CDATA[Magnetic flux Φ v (Vs / rad)]]> 0.013255 Inductance L (mH) 0.25 <![CDATA[Moment of inertia J (Kgm 2 )]]> 0.00003 <![CDATA[Coefficient of viscous friction B (Nms / rad 2 )]]> 0.0001

[0119] Figure 2 This is the communication topology diagram for the multiple permanent magnet synchronous motors of the present invention. N is selected as 4, and the reference signal is ω. d =200 sintr / min.

[0120] Select the load torque as:

[0121] T L1 =0.1sin(2t)N·m,

[0122] T L2 =0.2sin(2t)N·m,

[0123] T L3 = 0.4sin(2t) N·m,

[0124] T L4 = 0.6sin(2t) N·m.

[0125] The external system parameters are as follows:

[0126] P = [1 0 0 0],

[0127] Q1=[0 0 1 0], Q2=[0 0 2 0],

[0128] Q3=[0 0 4 0], Q4=[0 0 6 0].

[0129] The controller parameters are selected as follows:

[0130]

[0131] K x =-1,K z =[-0.12-3.52-1.23-1.86],μ=1.

[0132] The actual values ​​of the motor parameters are selected as follows:

[0133] L1=0.5L, L2=1.5L, L3=0.8L, L4=2L,

[0134] R s1 =0.5R s ,R s2 =1.5R s ,R s3 =0.8R s ,R s4 =2R s ,

[0135] Φ v1 =0.5Φ v ,Φ v2 =1.5Φ v ,Φ v3 =0.8Φ v ,Φ v4 =2Φ v ,

[0136] J1=0.5J, J2=1.5J, J3=0.8J, J4=2J,

[0137] F v1 =0.5F v ,F v2 =1.5F v ,F v2 =0.8F v ,F v4 =2F v .

[0138] id and i q The current controller parameters for the current loop are as follows:

[0139] K p1i =0.4,K I1i =563,K p2i =0.4,K I2i =563, i=1,2,3,4.

[0140] The initial value is chosen to be: x i (0) = 0 rpm, i di (0)=i qi (0) = 1A, i = 1, 2, 3, 4.

[0141] Using the above parameters, the control method of this invention is used to control multiple permanent magnet synchronous motors, and the simulation results shown in the attached figure are obtained. Figure 3 For example, the speed synchronization curves of multiple permanent magnet synchronous motors, such as Figure 3 As shown, the speed synchronization effect of the permanent magnet synchronous motor is good under the designed controller, and the unknown motor parameters are also allowed. Figure 4 and Figure 5 These are multi-permanent magnet synchronous motors i d and i q Current curve, such as Figure 4 , Figure 5 As shown, all of them are within the rated current of the permanent magnet synchronous motor, verifying the practical feasibility of the present invention.

[0142] This invention relates to a speed control method for multiple permanent magnet synchronous motors used in urban rail transit based on distributed internal models. By using internal models to handle the uncertainty of system model parameters, this method solves the problem in actual control systems where some motors cannot directly obtain information from the leader for feedback control due to communication constraints. This achieves speed synchronization and interference suppression of multiple permanent magnet synchronous motors under communication constraints, giving them good tracking performance, while allowing for unknown motor parameters.

[0143] This invention relates to a speed control method for multiple permanent magnet synchronous motors used in urban rail transit based on a distributed internal model. It adopts a cascaded speed-current structure and integrates a dual control mechanism of speed loop and current loop, which can effectively improve the dynamic and steady-state performance of the system. Furthermore, the speed loop controller only needs to be designed based on the speed equation model of the permanent magnet synchronous motor, which simplifies the model and makes it easier to apply in practice.

[0144] The above is an exemplary description of the invention. Obviously, the specific implementation of the invention is not limited to the above-described manner. Any non-substantial improvement made using the inventive concept and technical solution of the invention, or the direct application of the inventive concept and technical solution to other situations without modification, is within the protection scope of the invention.

Claims

1. A speed control method for multiple permanent magnet synchronous motors used in urban rail transit based on distributed internal models, characterized in that, Includes the following steps: S1. Establish a mathematical model for a multi-permanent magnet synchronous motor system for urban rail transit, consisting of N permanent magnet synchronous motors. S2. Construct an external system as the leader, which together with the urban rail multi-permanent magnet synchronous motor system forms a multi-agent system with N+1 agents, where the N permanent magnet synchronous motors in the urban rail multi-permanent magnet synchronous motor system act as followers; then, describe the speed synchronization and interference suppression problem of the multi-permanent magnet synchronous motor under unknown parameters as a cooperative robust output regulation problem of a multi-agent system. S3. Construct a directed communication topology to describe the information transmission between each agent in a multi-agent system consisting of an external system and multiple permanent magnet synchronous motors; S4. A cascaded structure of speed-current loops is adopted, in which the speed loop adopts a distributed internal model control method and the current loop adopts a PI control method. A PI controller is constructed and the final controller is given.

2. The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models according to claim 1, characterized in that, In step S1, the mathematical model of the urban rail multi-permanent magnet synchronous motor system is as follows: In equation (1), i = 1, ..., N, N represents the number of permanent magnet synchronous motors; ω ri i qi i di Let ω represent the rotor angular velocity of the i-th permanent magnet synchronous motor, respectively. ri q-axis stator current i qi and d-axis stator current i di ; They represent ω respectively ri i qi i di The derivative of u; qi ,u di J represents the stator voltages of the i-th permanent magnet synchronous motor along the q-axis and d-axis, respectively; i L represents the moment of inertia of the i-th permanent magnet synchronous motor; i R represents the armature inductance of the i-th permanent magnet synchronous motor; si Φ represents the stator resistance of the i-th permanent magnet synchronous motor; p represents the number of pole pairs of the i-th permanent magnet synchronous motor; Φ vi T represents the rotor flux linkage of the i-th permanent magnet synchronous motor; Li F represents the load torque of the i-th permanent magnet synchronous motor; vi Let represent the viscous friction coefficient of the i-th permanent magnet synchronous motor.

3. The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models according to claim 2, characterized in that, The specific steps of step S2 are as follows: S21. Construct an external system using equation (2): In equation (2), v represents the state variable of the external system. Let ω denote the derivative of v, S denote the system matrix of the external system, and ω d Let F represent the reference velocity, and T represent the constant matrix of the reference velocity. Li Q represents the load torque of the i-th permanent magnet synchronous motor. i Let represent the load torque constant matrix of the i-th permanent magnet synchronous motor; S22. Define the state variable x of the i-th permanent magnet synchronous motor. i =ω ri The state matrix of the i-th permanent magnet synchronous motor The input matrix of the i-th permanent magnet synchronous motor The state disturbance matrix of the i-th permanent magnet synchronous motor i qi As control input u i And will be used as i q The reference signal of the current loop is used to establish the speed loop equation of the i-th permanent magnet synchronous motor using equation (3): In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative; S23. Using equation (4), establish the speed tracking error equation for the i-th permanent magnet synchronous motor: e i =x i -Fv (4), In equation (4), e i This represents the speed tracking error of the i-th permanent magnet synchronous motor; S24. Considering the perturbation of motor parameters caused by uncertainties, let col(L) i ,R si ,Φ vi J i ,F vi ) = col(L,R s ,Φ v ,J,F v )+ε i , where L,R s ,Φ v ,J,F v L represents the nominal values ​​of each parameter of the i-th permanent magnet synchronous motor. i ,R si ,Φ vi J i ,F vi This represents the actual values ​​of each parameter of the i-th permanent magnet synchronous motor. This represents the deviation between the actual and nominal values ​​of the parameters of the i-th permanent magnet synchronous motor; S25. Rewrite equations (2), (3), and (4) in the following compact form: At this point, the speed synchronization and interference suppression problem of multiple permanent magnet synchronous motors under unknown motor parameters has been described as a cooperative robust output regulation problem of system (5). Its control objective is to make the closed-loop system stable and the tracking error of system (5) asymptotically approach zero under the condition of parameter uncertainty.

4. The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models according to claim 3, characterized in that, The specific steps in S3 are as follows: Define the communication topology. in, Node 0 represents the external system, and the remaining N nodes represent N permanent magnet synchronous motors. Let... definition The subgraph G = (V, E), where V = {1, ..., N}, and E is the subgraph that has been removed from the subgraph. The edges connected to node 0 are obtained by N. i ={j,(j,i)∈E}, Let G be the weighted adjacency matrix, and when (j,i)∈E, a ij >0 and a ii =0, i,j=1,…,N; and Is with The corresponding Laplace matrix of G, where, When i ≠ j, l ij =-a ij ; Let Δ = diag(a) 10 ,…,a N0 ), where for i = 1, ..., N, when At that time, a i0 >0, otherwise a i0 =0, and H = L + Δ.

5. The speed control method for multiple permanent magnet synchronous motors for urban rail transit based on distributed internal models according to claim 4, characterized in that, The specific steps of step S4 are as follows: S41. Define the virtual error e of the i-th permanent magnet synchronous motor. vi : In equation (6), y i =x i , where i = 1, ..., N, and when i = 0, y0 = Fv; S42. Design the inner mold using formula (7): In equation (7), G1 represents a constant matrix whose characteristic polynomial is the smallest characteristic polynomial of the external system matrix S, and G2 is a constant column vector such that (G1, G2) is controllable. S43. Let x = [x1, ..., x2] N ] T ,e v =[e v1 ,…,e vN ] T ,u=[u1,…,u N ] T , Among them, 1 N This represents an N-dimensional column vector where all elements are 1; Representing the identity matrix, we obtain the following augmented system: At this point, the cooperative robust output regulation problem of system (5) has been transformed into the robust stabilization problem of system (8); S44, Order in P is a positive definite symmetric matrix that satisfies the following Riccati equation: Y T P+PY-PWW T P+I=0 (9), In equation (9), I is the identity matrix; S45. According to the solution P of the Riccati equation, we get: [K x K z ]=K=-μ -1 W T P (10), In equation (10), μ satisfies 0 < μ < Re(λ) i ), i = 1, ..., N; where λ i These are the eigenvalues ​​of matrix H; S46. The following control law is obtained to solve the robust stabilization problem of system (8): S47. The distributed internal model controller of the velocity loop is obtained as follows: S48. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13): In equation (13), K p1i ,K I1i K represents the proportional coefficient and integral coefficient of the d-axis of the i-th motor, respectively. p2i ,K I2i Let represent the proportional coefficient and integral coefficient of the q-axis of the i-th motor, respectively; The final controller for the i-th permanent magnet synchronous motor, composed of equations (12) and (13), is as follows:

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