Position synchronization control method of multiple permanent magnet synchronous motors based on distributed observer

Abstract

The invention discloses a position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer. The position synchronization control method comprises the following steps: S1, establishing a mathematical model of a multi-permanent magnet synchronous motor system consisting of N permanent magnet synchronous motors; s2, dividing the motor into an informed motor group and an uninformed motor group according to whether the leader information can be directly acquired or not, and describing a position synchronization control problem of the multiple permanent magnet synchronous motors as a collaborative output adjustment problem of a multi-agent system; s3, establishing a directed communication topology to describe an information transfer relationship between agents in a multi-agent system formed by the external system and the multi-permanent magnet synchronous motor system; and S4, a cascade structure is adopted for controller design, a distributed observer is designed for the position-speed rings of the two motor sets, a PI controller is designed for the current rings, and a final controller is given. According to the method, the position synchronization control of the plurality of permanent magnet synchronous motors can be realized without speed information, and the method has anti-disturbance capability and good tracking performance.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology for multiple permanent magnet synchronous motors, specifically a position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer. Background Technology

[0002] In the field of industrial automation, multi-motor systems are widely used in CNC machine tools, printing equipment, textile machinery, and winding systems. The machining accuracy and production efficiency of these devices highly depend on the strict position synchronization between multiple actuators, making multi-motor position synchronization control widely applied. However, in actual control processes, communication links may experience problems such as data packet loss, transmission delays, and even communication interruptions. Furthermore, speed signals are often difficult to obtain accurately due to noise interference, especially in low-speed operating ranges. Therefore, traditional distributed control methods for multi-motor systems cannot solve the position coordination control problem of multi-motor systems under these circumstances. Summary of the Invention

[0003] The purpose of this invention is to provide a position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer, so as to solve the above-mentioned defects.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer proposed in this invention includes the following steps:

[0006] S1. Establish a mathematical model for a multi-permanent magnet synchronous motor system composed of N permanent magnet synchronous motors;

[0007] S2. Based on whether the leader's information can be directly obtained, the motors are divided into informed motor groups and uninformed motor groups, and the position synchronization control problem of multiple permanent magnet synchronous motors is described as a cooperative output regulation problem of a multi-agent system.

[0008] S3. Establish a directed communication topology to describe the information transmission relationship between agents in the multi-agent system composed of the external system and the multi-permanent magnet synchronous motor system.

[0009] Define a communication topology graph G = (V, E), where the vertex set V = {0, 1, ..., N} corresponds to N+1 agents; the edge set... This represents the information interaction relationship between N+1 intelligent agents; a ij Let a represent the adjacency relationship between agent j and agent i, where a is true when (j,i)∈E. ij >0 and a ii =0, where i,j = 1,…,N;

[0010] S4. For informed motor groups, Luneburger observers are used to observe the speed of each permanent magnet synchronous motor and the status of the external system; for uninformed motor groups, Luneburger observers are used to observe the speed of each permanent magnet synchronous motor; using the observer status of neighboring motors in the communication network, distributed observers are used to observe the status of the external system.

[0011] S5. The controller design adopts a cascaded structure. A distributed observer is designed for the position-speed loop of the two sets of motors, and a PI controller method is designed for the current loop. The final controller is given.

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

[0013]

[0014] In equation (1), i = 1, ..., N, N represents the number of permanent magnet synchronous motors; θ i ω ri i qi i di Let represent the rotor position, rotor angular velocity, q-axis stator current, and d-axis stator current of the i-th permanent magnet synchronous motor, respectively. Represent θ i ω 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; vi 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 F represents the rotor flux linkage of the i-th permanent magnet synchronous motor; vi T represents the viscous friction coefficient of the i-th permanent magnet synchronous motor; Li This represents the load torque of the i-th permanent magnet synchronous motor.

[0015] Preferably, in step S2, the N permanent magnet synchronous motors are divided into an informed motor group consisting of l motors and an uninformed motor group consisting of Nl motors, based on whether they can directly obtain leader information, where l < N; the position synchronization control problem of multiple permanent magnet synchronous motors under communication constraints is described as a cooperative output regulation problem of a multi-agent system.

[0016] Preferably, step S2 is as follows:

[0017] S21. Construct an external system using equation (2):

[0018]

[0019] In equation (2), v represents the state variable of the external system. Let θ denote the derivative of v, S denote the system matrix of the external system, and θ d Indicates the reference position, Q1 represents the constant matrix of the reference position, and T Li Q represents the load torque of the i-th permanent magnet synchronous motor. 2i Let represent the load torque constant matrix of the i-th permanent magnet synchronous motor;

[0020] S22. Define the state variable x of the i-th permanent magnet synchronous motor. i =[x i1 x i2 ] Τ , where x i1 =θ ri ,x i2 =ω ri The control input u of the i-th permanent magnet synchronous motor i =i qi Thus, the position-velocity loop equation of the i-th permanent magnet synchronous motor is established using equation (3):

[0021]

[0022] In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative of

[0023] S23. Using equation (4), establish the position tracking error equation for the i-th permanent magnet synchronous motor:

[0024] e i =C i x i +F i v, i=1,···,N (4),

[0025] In equation (4), C i =[1 0],F i =-Q1,e i This represents the position tracking error of the i-th permanent magnet synchronous motor;

[0026] S24. Using equation (5), establish the measurement output equation for the i-th permanent magnet synchronous motor:

[0027] y mi =C mi xi +F mi v, i=1,···,N (5),

[0028] In equation (5), C mi =[1 0],F mi =0, i=l+1,…,N., y mi This represents the measured output of the i-th permanent magnet synchronous motor;

[0029] S25. Rewrite equations (3), (4), and (5) in the following compact form:

[0030]

[0031] Thus, the position synchronization control problem of multiple permanent magnet synchronous motors in equation (3) can be described as a cooperative output regulation problem of a multi-agent system consisting of equations (2), (3), (4) and (5).

[0032] Preferably, step S4 is as follows:

[0033] S41. For the informed generator set, the Luneburg observer of the i-th permanent magnet synchronous motor is established using equation (6):

[0034]

[0035] In equation (6), ξ i =[ξ i1 ξ i2 ] Τ , where ξ i Let be the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor. Let η be the derivative of the observations of the i-th Luneburger observer on the position and velocity of the i-th permanent magnet synchronous motor. i These are observations of the external system state. L is the derivative of the observed values ​​of the external system state. 1i ,L 2i These are the two observer gain matrices of the Romberg observer, and they satisfy... The real parts of all eigenvalues ​​are less than zero;

[0036] S42. For the uninformed generator set, use Equations (7) and (8) to establish the Luneburger observer and distributed observer for the i-th permanent magnet synchronous motor of the uninformed generator set, respectively:

[0037]

[0038] In equations (7) and (8), ξ iη represents the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor; j η represents the observed state of the leader system of the j-th permanent magnet synchronous motor. i L represents the observed state of the leader system of the i-th permanent magnet synchronous motor; i It is the gain matrix of the Luneburg observer, and satisfies A i +L i C mi The real parts of all eigenvalues ​​are less than zero, i = l+1, ..., N, and μ is any positive number.

[0039] Preferably, step S5 is as follows:

[0040] S51. Using equation (9), construct the linear matrix equation corresponding to the closed-loop system of the i-th permanent magnet synchronous motor:

[0041]

[0042] In equation (9), X i =col(X) i1 X i2 ), and X i U i Let represent the steady-state matrix and steady-state input matrix of the i-th permanent magnet synchronous motor, and we have:

[0043]

[0044] In equation (10), X i v,U i v represents the steady-state state and steady-state input of the i-th permanent magnet synchronous motor, respectively;

[0045] S52. Using equations (11) and (12), establish a position synchronization controller for the position-speed loop of the aware and unaware motor sets:

[0046]

[0047] S53. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13):

[0048]

[0049] In equation (13), This represents the reference current of the q-axis of the i-th permanent magnet synchronous motor. Determined by the position-velocity loop; for the i-th permanent magnet synchronous motor, K Pi ,K IiLet represent the proportional gain and integral gain of the i-th motor along the d-axis and q-axis, respectively.

[0050] S54. Combining (11), (12), and (13), the final controller is obtained as follows:

[0051]

[0052] The beneficial effects of this invention are as follows:

[0053] (1) The position synchronization control method of multiple permanent magnet synchronous motors based on distributed observers of the present invention firstly, for motor groups that cannot directly obtain the leader system signal, a distributed observer is designed to estimate the leader system state by utilizing the observer state of neighboring motors, thereby solving the problem that some motors cannot directly obtain leader information due to communication constraints; secondly, a Luneburger observer is used to observe the motor speed, without needing to obtain motor speed information, and only using the position information of the motor for control, thereby achieving high-precision position synchronization and interference suppression of multiple permanent magnet synchronous motors under communication constraints.

[0054] (2) The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer in this invention adopts a cascaded control structure of position-velocity loop and current loop. Through the coordinated control of the outer position-velocity loop and the inner current loop, the dynamic response performance and steady-state control accuracy of the system are improved. Among them, the position-velocity loop controller is designed only based on the position-velocity equation model of the permanent magnet synchronous motor, thereby reducing the modeling complexity and facilitating engineering applications. Attached Figure Description

[0055] Figure 1 This is a block diagram illustrating the principle of position synchronization control of multiple permanent magnet synchronous motors according to the present invention.

[0056] Figure 2 This is a communication topology diagram of the multiple permanent magnet synchronous motors of the present invention;

[0057] Figure 3 This is a position tracking curve diagram of the multi-permanent magnet synchronous motor of the present invention;

[0058] Figure 4 The present invention relates to a multi-permanent magnet synchronous motor i d Current curve;

[0059] Figure 5 The present invention relates to a multi-permanent magnet synchronous motor i q Current curve. Detailed Implementation

[0060] 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.

[0061] Example 1:

[0062] Figure 1 This is a block diagram illustrating the principle of position synchronization control for multiple permanent magnet synchronous motors according to the present invention. Figure 1 As shown, the position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer proposed in this invention includes the following steps:

[0063] S1. Establish a mathematical model of a multi-permanent magnet synchronous motor system composed of N permanent magnet synchronous motors.

[0064] The mathematical model for the multi-permanent magnet synchronous motor system is as follows:

[0065]

[0066] In equation (1), i = 1, ..., N, where N represents the number of permanent magnet synchronous motors; θ i ,ω ri i qi i di Let represent the rotor position, rotor angular velocity, q-axis stator current, and d-axis stator current of the i-th permanent magnet synchronous motor, respectively. Represent θ i ,ω 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; vi 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 F represents the rotor flux linkage of the i-th permanent magnet synchronous motor; vi T represents the viscous friction coefficient of the i-th permanent magnet synchronous motor; Li This represents the load torque of the i-th permanent magnet synchronous motor.

[0067] S2. Based on whether the leader's information can be directly obtained, the motors are divided into informed motor groups and uninformed motor groups, and the position synchronization control problem of multiple permanent magnet synchronous motors is described as a cooperative output regulation problem of a multi-agent system.

[0068] Based on whether N permanent magnet synchronous motors can directly obtain leader information, they are divided into an informed motor group consisting of l motors and an uninformed motor group consisting of Nl motors, where l < N. The position synchronization control problem of multiple permanent magnet synchronous motors under communication constraints is described as a cooperative output regulation problem of a multi-agent system, as follows:

[0069] S21. Construct an external system using equation (2):

[0070]

[0071] In equation (2), v represents the state variable of the external system. Let θ denote the derivative of v, S denote the system matrix of the external system, and θ d Indicates the reference position, Q1 represents the constant matrix of the reference position, and T Li Q represents the load torque of the i-th permanent magnet synchronous motor. 2i Let represent the load torque constant matrix of the i-th permanent magnet synchronous motor.

[0072] At this point, the multi-permanent magnet synchronous motor system and the external system together constitute a multi-agent system containing N+1 agents, where the external system is the leader and the N permanent magnet synchronous motors are the followers. Due to communication constraints, some follower motors cannot directly obtain leader information. Therefore, the N motors are divided into two categories according to whether they can directly obtain leader information: those that can directly obtain leader information are called informed motors, totaling 1; those that cannot directly obtain leader information are called uninformed motors, totaling Nl, and satisfying 1 < N.

[0073] S22. Define the state variable x of the i-th permanent magnet synchronous motor. i =[x i1 x i2 ] Τ , where x i1 =θ ri ,x i2 =ω ri The control input u of the i-th permanent magnet synchronous motor i =i qi Thus, the position-velocity loop equation of the i-th permanent magnet synchronous motor is established using equation (3):

[0074]

[0075] In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative of

[0076] S23. Using equation (4), establish the position tracking error equation for the i-th permanent magnet synchronous motor:

[0077] e i =C i x i +F i v, i=1,···,N (4),

[0078] In equation (4), C i =[1 0],F i =-Q1,e i This represents the position tracking error of the i-th permanent magnet synchronous motor.

[0079] S24. Using equation (5), establish the measurement output equation for the i-th permanent magnet synchronous motor:

[0080] y mi =C mi x i +F mi v,i=1,···,N (5),

[0081] In equation (5), C mi =[1 0],F mi =0, i=l+1,…,N, y mi This represents the measured output of the i-th permanent magnet synchronous motor.

[0082] S25. Rewrite equations (3), (4), and (5) in the following compact form:

[0083]

[0084] Thus, the position synchronization control problem of multiple permanent magnet synchronous motors in equation (3) can be described as a cooperative output regulation problem of a multi-agent system composed of equations (2), (3), (4), and (5). The control objective is to make the closed-loop system of multiple permanent magnet synchronous motors stable and the tracking error asymptotically approach zero under communication constraints.

[0085] S3. Establish a directed communication topology to describe the information transmission relationship between agents in a multi-agent system composed of an external system and a multi-permanent magnet synchronous motor system.

[0086] Define a communication topology graph G = (V, E), where the vertex set V = {0, 1, ..., N} corresponds to N+1 agents; the edge set... This represents the information interaction relationship between N+1 intelligent agents; a ij Let a represent the adjacency relationship between agent j and agent i, where a is true when (j,i)∈E. ij >0 and a ii =0, where i,j = 1,…,N.

[0087] S4. For informed motor groups, Luenberger observers are used to monitor the speed of each permanent magnet synchronous motor and the external system status; for uninformed motor groups, Luenberger observers are used to monitor the speed of each permanent magnet synchronous motor; utilizing the observer status of neighboring motors in the communication network, a distributed observer system is used to monitor the external system status. Details are as follows:

[0088] S41. For the informed generator set, the Luneburg observer of the i-th permanent magnet synchronous motor is established using equation (6):

[0089]

[0090] In equation (6), ξ i =[ξ i1 ξ i2 ] Τ , where ξ i Let be the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor. Let η be the derivative of the observations of the i-th Luneburger observer on the position and velocity of the i-th permanent magnet synchronous motor. i These are observations of the external system state. L is the derivative of the observed values ​​of the external system state. 1i ,L 2i These are the two observer gain matrices of the Romberg observer, and they satisfy... The real parts of all eigenvalues ​​are less than zero;

[0091] S42. For the uninformed generator set, use Equations (7) and (8) to establish the Luneburger observer and distributed observer for the i-th permanent magnet synchronous motor of the uninformed generator set, respectively:

[0092]

[0093] In equations (7) and (8), ξ i η represents the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor; j η represents the observed state of the leader system of the j-th permanent magnet synchronous motor. i L represents the observed state of the leader system of the i-th permanent magnet synchronous motor; i It is the gain matrix of the Luneburg observer, and satisfies A i +L i Cmi The real parts of all eigenvalues ​​are less than zero, i = l+1, ..., N, and μ is any positive number.

[0094] S5. The controller design adopts a cascaded structure. A distributed observer is designed for the position-velocity loop of the two sets of motors, and a PI controller is designed for the current loop. The final controller is presented below.

[0095] S51. Using equation (9), construct the linear matrix equation corresponding to the closed-loop system of the i-th permanent magnet synchronous motor:

[0096]

[0097] In equation (9), X i =col(X) i1 X i2 ), and X i U i Let represent the steady-state matrix and steady-state input matrix of the i-th permanent magnet synchronous motor, and we have:

[0098]

[0099] In equation (10), X i v,U i v represents the steady-state state and steady-state input of the i-th permanent magnet synchronous motor, respectively.

[0100] S52. Using equations (11) and (12), establish a position synchronization controller for the position-speed loop of the aware and unaware motor sets:

[0101]

[0102] S53. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13):

[0103]

[0104] In equation (13), This represents the reference current of the q-axis of the i-th permanent magnet synchronous motor. Determined by the position-velocity loop; for the i-th permanent magnet synchronous motor, K Pi ,K Ii Let represent the proportional gain and integral gain of the i-th motor along the d-axis and q-axis, respectively.

[0105] Finally, combining (11), (12), and (13), the final controller is obtained as follows:

[0106]

[0107]

[0108] Figure 1 This is a block diagram illustrating the principle of position synchronization control for multiple permanent magnet synchronous motors according to the present invention. To verify the effectiveness of the proposed method, the control effect of the distributed internal model controller is simulated and verified.

[0109] The specific parameters of the selected permanent magnet synchronous motor are shown in Table 1:

[0110] Table 1. Parameters of Permanent Magnet Synchronous Motor

[0111] 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 <![CDATA[Inductance L v (mH)]]> 0.25 <![CDATA[Moment of inertia J (Kgm 2 )]]> 0.00003 <![CDATA[Coefficient of viscous friction B (Nms / rad 2 )]]> 0.0001

[0112] Figure 2 This is a communication topology diagram of the multiple permanent magnet synchronous motors of the present invention, such as... Figure 2 As shown, N=4, l=1, and the reference signal θ is selected. d =5πrad, load torque T L1 =0.4sin(t)N·m,T L2 =0.3sin(t)N·m,T L3 =0.2sin(t)N·m,T L4 =0.1sin(t)N·m, then the external system parameters are as follows:

[0113] Q1 = [1 0 0], Q 21 =[0 4 0],

[0114] Q 22 =[0 3 0],Q 23 =[0 2 0],Q 24 =[0 1 0],

[0115] The controller parameters are selected as follows:

[0116]

[0117] K 1i =[-800 -5],K 2i =[800 12.6753 0.0008],

[0118] μ = 1, a ij =1, if(j,i)∈ε

[0119] i d and i q The current loop PI parameter is: K pi =1,K Ii =0.2.

[0120] Using the above series of parameters, the method of this invention is applied to control multiple permanent magnet synchronous motors, and the simulation results shown in the attached figure are obtained. Figure 3 For position tracking curves of multiple permanent magnet synchronous motors, such as Figure 3 As shown in the figure, the curve reflects the good position synchronization performance of the designed controller under communication constraints. 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.

[0121] This invention relates to a position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer. First, for motor groups that cannot directly obtain leader system signals, a distributed observer is designed using the observer states of neighboring motors to estimate the leader system state, thereby solving the problem that some motors cannot directly obtain leader information due to communication constraints. Second, a Luneburger observer is used to observe the motor speed, eliminating the need to obtain motor speed information and enabling control using only the motor's position information, thus achieving high-precision position synchronization and interference suppression for multiple permanent magnet synchronous motors under communication constraints.

[0122] This invention presents a position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer. It employs a cascaded control structure of position-velocity loops and current loops. Through the coordinated control of the outer position-velocity loop and the inner current loop, the dynamic response performance and steady-state control accuracy of the system are improved. Notably, the position-velocity loop controller is designed solely based on the position-velocity equation model of the permanent magnet synchronous motor, thereby reducing modeling complexity and facilitating engineering applications.

[0123] 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 position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer, characterized in that, Includes the following steps: S1. Establish a mathematical model for a multi-permanent magnet synchronous motor system composed of N permanent magnet synchronous motors; S2. Based on whether the leader's information can be directly obtained, the motors are divided into informed motor groups and uninformed motor groups, and the position synchronization control problem of multiple permanent magnet synchronous motors is described as a cooperative output regulation problem of a multi-agent system. S3. Establish a directed communication topology to describe the information transmission relationship between agents in the multi-agent system composed of the external system and the multi-permanent magnet synchronous motor system. Define a communication topology graph G = (V, E), where the vertex set V = {0, 1, ..., N} corresponds to N+1 agents; the edge set... This represents the information interaction relationship between N+1 intelligent agents; a ij Let a represent the adjacency relationship between agent j and agent i, where a is true when (j,i)∈E. ij >0 and a ii =0, where i,j = 1,…,N; S4. For informed motor groups, Luneburger observers are used to observe the speed of each permanent magnet synchronous motor and the status of the external system; for uninformed motor groups, Luneburger observers are used to observe the speed of each permanent magnet synchronous motor; using the observer status of neighboring motors in the communication network, distributed observers are used to observe the status of the external system. S5. The controller design adopts a cascaded structure, in which the position-speed loop of the two sets of motors adopts the distributed observer method, and the current loop adopts the PI controller method. The final controller is given.

2. The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer according to claim 1, characterized in that, In step S1, the mathematical model of the multi-permanent magnet synchronous motor system is specifically as follows: In equation (1), i = 1, ..., N, N represents the number of permanent magnet synchronous motors; θ i ω ri i qi i di Let represent the rotor position, rotor angular velocity, q-axis stator current, and d-axis stator current of the i-th permanent magnet synchronous motor, respectively. Represent θ i ω 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; vi 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 F represents the rotor flux linkage of the i-th permanent magnet synchronous motor; vi T represents the viscous friction coefficient of the i-th permanent magnet synchronous motor; Li This represents the load torque of the i-th permanent magnet synchronous motor.

3. The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer according to claim 2, characterized in that, In step S2, the N permanent magnet synchronous motors are divided into informed motor groups consisting of l motors and uninformed motor groups consisting of Nl motors, based on whether they can directly obtain leader information, where l < N; the position synchronization control problem of multiple permanent magnet synchronous motors under communication constraints is described as a cooperative output regulation problem of a multi-agent system.

4. The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer according to claim 3, characterized in that, Step S2 is as follows: S21. Construct an external system using equation (2): In equation (2), v represents the state variable of the external system. Let θ denote the derivative of v, S denote the system matrix of the external system, and θ d Indicates the reference position, Q1 represents the constant matrix of the reference position, and T Li Q represents the load torque of the i-th permanent magnet synchronous motor. 2i 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 =[x i1 x i2 ] Τ , where x i1 =θ ri ,x i2 =ω ri The control input u of the i-th permanent magnet synchronous motor i =i qi Thus, the position-velocity loop equation of the i-th permanent magnet synchronous motor is established using equation (3): In equation (3), Let x represent the state variable of the i-th permanent magnet synchronous motor. i The derivative of S23. Using equation (4), establish the position tracking error equation for the i-th permanent magnet synchronous motor: e i =C i x i +F i v,i=1,···,N (4), In equation (4), C i =[1 0],F i =-Q1,e i This represents the position tracking error of the i-th permanent magnet synchronous motor; S24. Using equation (5), establish the measurement output equation for the i-th permanent magnet synchronous motor: y mi =C mi x i +F mi v,i=1,···,N (5), In equation (5), C mi =[1 0],F mi =0, i=l+1,…,N., y mi This represents the measured output of the i-th permanent magnet synchronous motor; S25. Rewrite equations (3), (4), and (5) in the following compact form: Thus, the position synchronization control problem of multiple permanent magnet synchronous motors in equation (3) can be described as a cooperative output regulation problem of a multi-agent system consisting of equations (2), (3), (4) and (5).

5. The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer according to claim 4, characterized in that, The S4 step is as follows: S41. For the informed generator set, the Luneburg observer of the i-th permanent magnet synchronous motor is established using equation (6): In equation (6), ξ i =[ξ i1 ξ i2 ] Τ , where ξ i Let be the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor. Let η be the derivative of the observations of the i-th Luneburger observer on the position and velocity of the i-th permanent magnet synchronous motor. i η represents the observed state of the external system. i L is the derivative of the observed values ​​of the external system state. 1i ,L 2i These are the two observer gain matrices of the Romberg observer, and they satisfy... The real parts of all eigenvalues ​​are less than zero; S42. For the uninformed generator set, use Equations (7) and (8) to establish the Luneburger observer and distributed observer for the i-th permanent magnet synchronous motor of the uninformed generator set, respectively: In equations (7) and (8), ξ i η represents the observations of the i-th Luneburg observer on the position and velocity of the i-th permanent magnet synchronous motor; j η represents the observed state of the leader system of the j-th permanent magnet synchronous motor. i L represents the observed state of the leader system of the i-th permanent magnet synchronous motor; i It is the gain matrix of the Luneburg observer, and satisfies A i +L i C mi The real parts of all eigenvalues ​​are less than zero, i = l+1, ..., N, and μ is any positive number.

6. The position synchronization control method for multiple permanent magnet synchronous motors based on a distributed observer according to claim 5, characterized in that, Step S5 is as follows: S51. Using equation (9), construct the linear matrix equation corresponding to the closed-loop system of the i-th permanent magnet synchronous motor: In equation (9), X i =col(X) i1 X i2 ), and X i U i Let represent the steady-state matrix and steady-state input matrix of the i-th permanent magnet synchronous motor, and we have: In equation (10), X i v,U i v represents the steady-state state and steady-state input of the i-th permanent magnet synchronous motor, respectively; S52. Using equations (11) and (12), establish a position synchronization controller for the position-speed loop of the aware and unaware motor sets: S53. Construct a PI controller for the current loop of the i-th permanent magnet synchronous motor using equation (13): In equation (13), This represents the reference current of the q-axis of the i-th permanent magnet synchronous motor. Determined by the position-velocity loop; for the i-th permanent magnet synchronous motor, K Pi ,K Ii Let represent the proportional gain and integral gain of the i-th motor along the d-axis and q-axis, respectively. S54. Combining (11), (12), and (13), the final controller is obtained as follows:

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