Local average deviation coupling and synchronization control method for multi-motor drive system based on acceleration inversion technology

Abstract

The application relates to a local average deviation coupling and synchronization control method of a multi-motor driving system based on an acceleration inversion technology, and belongs to the field of multi-motor driving systems, and comprises the following steps: S1, establishing a multi-motor driving system dynamics model with dead zones, friction and interference characteristics; S2, performing interference compensation on the multi-motor driving system dynamics model; S3, using a speed function to accelerate the convergence process of a tracking error; S4, using a cosine barrier function to constrain the output of the system; S5, using a second-order tracking differentiator to solve a 'complex term explosion' problem; S6, adopting an interference compensator to compensate centralized interference in the system; S7, integrating steps S3-S6 into inversion control, and designing an acceleration inversion tracking controller; and S8, designing a local average deviation coupling and synchronization control scheme based on the acceleration inversion tracking controller.

Description

Technical Field

[0001] This invention belongs to the field of multi-motor drive systems and relates to a local average deviation coupling synchronization control method for multi-motor drive systems based on accelerated inversion technology. Background Technology

[0002] Multi-motor drive systems, as large and complex machine systems, are widely used in high-inertia, high-power systems due to their high reliability, large output power, good control performance, and energy efficiency. Compared with single-motor drive systems, multi-motor drive systems can overcome their disadvantages such as low output power, poor system performance, and high production cost of high-power motors. However, due to the complex nonlinear dynamics and inherent dead-zone characteristics of multi-motor drive systems, it is difficult to achieve high-performance load tracking control. Furthermore, load tracking control interacts with synchronization control, making the synchronization problem of multi-motor drive systems challenging. Therefore, in engineering applications, simultaneously ensuring the load tracking performance and synchronization performance of multi-motor drive systems is both meaningful and challenging.

[0003] Establishing an accurate gear transmission model is a prerequisite for improving load tracking performance. For rigid torque transmission systems, Nordin and Gutman first proposed a reliable dead-zone model, but they did not apply it to controller design. In gear transmission units of multi-motor drive systems, a dead-zone model can also be used to describe the transmission torque. Furthermore, to obtain smooth control input, Wang et al. used a continuously differentiable function to approximate a piecewise continuous dead-zone model. However, the complex expression of the dead-zone model is not conducive to increasing the design freedom of nonlinear systems, especially for multi-motor drive systems.

[0004] Tracking control of multi-motor drive systems has always been a hot topic in academia. Several effective control schemes have been proposed, such as sliding mode control and inversion control, due to their simple control framework and excellent control performance. However, sliding mode control inevitably leads to chattering. Therefore, some methods have been used to adjust the switching gain of sliding mode control to reduce chattering. Additionally, Li et al. used a saturation function to replace the sign function of sliding mode control to address chattering. Although these methods improve robustness, how to completely suppress chattering in sliding mode control remains an unresolved issue. Inversion, as an effective nonlinear control method, requires repeated calculation of the derivative of the virtual control law. This leads to a "complexity term explosion." To address this problem, some useful tools have been proposed to track the derivative of the virtual control law, such as first-order filters, second-order tracking differentiators, and hybrid differentiators. Compared to second-order tracking differentiators, first-order filters have weaker approximation capabilities. Meanwhile, hybrid differentiators have double the design parameters, leading to a complex parameter tuning process. Furthermore, in multi-motor drive systems, nonlinearity becomes more complex with the increase in the number of motors, thus the aforementioned work can no longer meet the requirements of high-performance control. At the same time, they did not address the issues of accelerating convergence and constraining tracking errors.

[0005] For multi-motor drive systems, coupling structures and corresponding synchronization control schemes have been widely reported to address synchronization issues. Ring coupling structures, due to their simplicity, are often used in conjunction with other control methods to achieve the desired synchronization. Master-slave coupling structures, due to their simple framework, are also widely used in motion synchronization. Adjacent cross-coupling control, due to its complex controller design process, is usually combined with local coupling structures. However, as the number of motors in a multi-motor drive system increases, the network diameter and average path length of the aforementioned traditional local coupling structures inevitably increase, leading to poor synchronization performance. Some researchers have adopted global coupling structures to address this problem. These structures are typically used in conjunction with specific synchronization control methods, such as correlated coupling control and average deviation coupling synchronization control. However, global coupling structures result in excessive communication overhead. Therefore, designing a communication network with low communication overhead, small network diameter, and short average path length, and proposing corresponding synchronization methods for the synchronization problem of multi-motor drive systems, is both meaningful and challenging.

[0006] Intricate multi-motor drive systems are highly susceptible to internal and external disturbances, leading to poor system performance. To address this, numerous neural network algorithms have been proposed to approximate the unknown functions of nonlinear systems, such as radial basis function neural networks, Chebyshev neural networks, echo state networks, and interval type-2 fuzzy neural networks. However, their excessive computational burden makes them difficult to apply in practical engineering. On the other hand, observers with lower computational burdens have been used to handle concentrated disturbances and unknown states. For example, disturbance observers are used to handle concentrated disturbances composed of external disturbances, unknown dynamic terms, and modeling errors. Extended state observers are used to approximate unknown system states and concentrated disturbances. However, the parameter tuning process of these traditional tools is complex, resulting in poor approximation capabilities. Therefore, further improvements in approximation capabilities are needed to effectively handle the intricate unknown dynamic terms of multi-motor drive systems, thereby improving system performance.

[0007] Synchronization control is crucial for multi-motor drive systems with n independent motors. However, describing their complex communication coupling structure and designing corresponding synchronization control schemes is very difficult. To address this issue, the multi-motor drive system can be viewed as a multi-agent system, transforming the complex coupling synchronization problem into a simple distributed synchronization problem. In this way, the results of distributed control can also be applied to multi-motor drive systems to simplify controller design and improve system performance. However, in multi-agent systems, the communication network structure that facilitates information exchange and coordinated action has received little further investigation. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology includes the following steps:

[0011] S1: Establish a dynamic model of a multi-motor drive system with dead zone, friction and disturbance characteristics;

[0012] S2: Perform disturbance compensation on the dynamic model of the multi-motor drive system;

[0013] S3: Utilize the velocity function to accelerate the convergence process of tracking errors;

[0014] S4: Constrain the system output using a cosine barrier function;

[0015] S5: Use a second-order tracking differentiator to solve the "complexity term explosion" problem;

[0016] S6: Use an interference compensator to compensate for concentrated interference in the system;

[0017] S7: Integrate steps S3-S6 into the inversion control and design an accelerated inversion tracking controller;

[0018] S8: Design of a local average deviation coupling synchronization control scheme for tracking technology based on accelerated inversion tracking controller.

[0019] Furthermore, the dynamic model of the multi-motor drive system with dead zone, friction, and interference characteristics described in step S1 includes:

[0020] n permanent magnet synchronous motors are connected to n pinions through reducers. The n pinions mesh with a large gear, which is connected to a load device, thereby enabling the n permanent magnet synchronous motors to drive a load device together.

[0021] The controller sends control signals to the actuator based on the reference trajectory and feedback signals. The feedback signals are obtained through an optical encoder, Parker transform, and Clarke transform. The control signals are converted through an inverse Parker transform and then space vector pulse width modulation (SVPWM) technology is used to control the insulated gate bipolar transistor (IGBT) inverter. Finally, the controller is connected to the permanent magnet synchronous motor to drive the motor.

[0022] The dynamic model of a single, independent permanent magnet synchronous motor is represented as follows:

[0023]

[0024] Where i d and i q These are the stator currents along the d-axis and q-axis; u d and u q These are the stator voltages along the d-axis and q-axis; L d and L q These are the stator inductances along the d-axis and q-axis; R,p n ω, ψ, and J are the stator resistance, number of pole pairs, angular velocity, magnetic flux, and moment of inertia, respectively; T f d and τ are the friction torque, the unknown dynamic term, and the transmission torque, respectively;

[0025] To improve the efficiency of the permanent magnet synchronous motor, the d-axis reference current is set to zero, and the coupling effect between angular velocity and current is approximately eliminated. The model is then rewritten as follows:

[0026]

[0027] The friction torque of a multi-motor drive system is approximated using a continuously differentiable friction model, written as:

[0028] Tf =F p +f v ω,

[0029] Where F p = p1(tanh(p3ω)-tanh(p4ω))+p2 tanh(p5ω), where f v It is the coefficient of friction, p i i = 1, ..., 5 are positive constants; in the controller design process, the frictional torque T f via f v ω is compensated for, and the unknown dynamic term F p It should be categorized into centralized interference for processing;

[0030] Introducing y = ω, x = i q ,γ=1.5p n ψ / J,ε=f v / J,δ=(F p +d) / J, α=R / L q ,β=p n ψ / L q and u=u q / L q ,get:

[0031]

[0032] The dynamic model of the load end is given as follows:

[0033]

[0034] Where subscript 0 represents the load end, subscript i represents the i-th motor, i = 1, ..., n, z0 is the angular velocity of the load end, and w is the load end disturbance including unknown dynamic terms and working load;

[0035] Each motor provides the same transmission torque to the multi-motor drive system, and then the drive burden at the load end is evenly distributed among the n permanent magnet synchronous motors, as follows:

[0036]

[0037] Where z i =z0 / n and w i =w / n;

[0038] The transmission torque model is expressed as:

[0039]

[0040] in

[0041] Where k, c, χ, θ and r are the torque coefficient, damping coefficient, half clearance, angular displacement and transmission ratio, respectively;

[0042] The dynamic model of the entire multi-motor drive system is represented as follows:

[0043]

[0044] The ideal trajectory z of the load end angular velocity d Its derivative is continuous and bounded;

[0045] An undirected graph G is used to describe the information exchange network between n motors and to simplify the design process of the synchronous controller.

[0046] For a leaderless multi-agent system, information exchange follows an undirected graph G = {V, E, A}, where V = {υ} i The set of vertices is {i=1,…,n}. It is an edge set, and A = [a ij ]∈R n×n Let G be the adjacency matrix of an undirected graph; if there is an edge between agents i and j, i.e. (υ i ,υ j If )∈E, then a ij =a ji =1, otherwise a ij =a ji =0, a ii =0 for i=1,…,n; node υ i The neighbor set is N i ={j,(υ i ,υ j )∈E};Node υ i The degree of exit is The degree distribution matrix of an undirected graph G is The Laplace matrix of an undirected graph G is L = DA.

[0047] Furthermore, the interference compensation in step S2 includes:

[0048] Interference compensation at the load end: An improved second-order tracking differentiator is used to approximate the interference at the load end as follows:

[0049]

[0050]

[0051] Where τ i i = 1, ..., n and z0 are the input signals of this second-order tracking differentiator, and λ1 and λ2 are positive constants. It is an estimate of w. Λ1 and τ are the state variables of this second-order tracking differentiator. i i = 1, ..., n is measurable;

[0052] Interference compensation at the motor end: Improve the second-order tracking differentiator as follows:

[0053]

[0054]

[0055] Where λ3 and λ4 are positive constants. It is δ i The estimated values ​​for i = 1, ..., n and Λ 2,i These are the state variables of this second-order tracking differentiator.

[0056] Furthermore, the velocity function described in step S3 is expressed as:

[0057]

[0058] Where T c It is a positive constant, and φ(t) is a smooth function that does not decrease to infinity;

[0059] φ(t) satisfies φ(0)=1 and It is a design parameter and satisfies P(t) is positive and increasing, P(0) = 1 and will increase to... φ(t) affects P(t) in the condition 0 ≤ t < T c The rate of increase during the period, T c This indicates that P(t) increases from 1 to... The time.

[0060] Furthermore, the cosine barrier function described in step S4 is expressed as:

[0061]

[0062] if So

[0063] Furthermore, the accelerated inversion tracking controller described in step S7 is constructed as follows:

[0064] Acceleration error is defined as

[0065]

[0066] Where z id =z d / n, and It is the virtual control law for the i-th motor, i = 1, ..., n;

[0067] Step 1: S 11 The derivative is derived as follows:

[0068]

[0069] in

[0070] Define the first barrier Lyapunov function as:

[0071] V 11 =S 11 2 / cos(πS 11 / 2B 11 ),

[0072] Among them B 11 It is a positive constant and satisfies B 11 >|S 11 |;

[0073] V 11 The derivative is calculated to be:

[0074]

[0075] in

[0076] Virtual control law Designed as follows:

[0077]

[0078] in c 11 It is a positive constant;

[0079] Therefore, we get:

[0080]

[0081] in

[0082] Step 2: S 12 The derivative is calculated to be:

[0083]

[0084] Introducing a second-order tracking differentiator to approximate the virtual control law The derivative; the second-order tracking differentiator is written as:

[0085]

[0086] in This is the input signal, μ1 and μ2 are positive constants, and σ i1 and σ i2 ,i=1,…,n, are the outputs of the second-order tracking differentiator; the approximation error is defined as and h i1 and h i2 By selecting appropriate parameters, the value can be reduced to an arbitrarily small level;

[0087] The second obstacle is the choice of the Lyapunov function:

[0088] V 12 =V 11 +S 12 2 / cos(πS 12 / 2B 12 ),

[0089] Among them B 12 It is a positive constant and satisfies B 12 >|S 12 |;

[0090] V 12 The derivative is:

[0091]

[0092] in

[0093] Virtual control law Designed as follows:

[0094]

[0095] Where c 12 It is a positive constant;

[0096] Therefore, we get:

[0097]

[0098] in

[0099] Step 3: S 13 The derivative is:

[0100]

[0101] A second-order tracking differentiator is used to approximate the virtual control law. The derivative is written as:

[0102]

[0103] in This is the input signal, μ3 and μ4 are positive constants, and σ i3 and σ i4 ,i=1,…,n, are the outputs of this second-order tracking differentiator; the approximation error is defined as and h i3 and h i4 By selecting appropriate parameters, the value can be reduced to an arbitrarily small level;

[0104] The third barrier, the Lyapunov function, is defined as:

[0105] V 13 =V 12 +S 13 2 / cos(πS 13 / 2B 13 ),

[0106] Among them B 13 It is a positive constant and satisfies B 13 >|S 13 |;

[0107] V 13 The derivative is calculated as follows:

[0108]

[0109] in

[0110] The tracking control law u of the first motor 1t Designed as follows:

[0111]

[0112] Where c 13 It is a positive constant;

[0113] Therefore, we get:

[0114]

[0115] The design process for the acceleration inversion tracking controller for each motor is the same;

[0116] Step 3n-2: S n1 The derivative is calculated as follows:

[0117]

[0118] The Lyapunov function for the 3n-2th obstacle is chosen as:

[0119] V n1 =V (n-1)3 +S n12 / cos(πS n1 / 2B n1 ),

[0120] Among them B n1 It is a positive constant and satisfies B n1 >|S n1 |;

[0121] V n1 The derivative is calculated to be:

[0122]

[0123] in

[0124] Virtual control law Selected as:

[0125]

[0126] in c n1 It is a positive constant;

[0127] Therefore, we get:

[0128]

[0129] in

[0130] Step 3n-1: S n2 The derivative is given as:

[0131]

[0132] The Lyapunov function for the 3n-1th obstacle is defined as:

[0133] V n2 =V n1 +S n2 2 / cos(πS n2 / 2B n2 ),

[0134] Among them B n2 It is a positive constant and satisfies B n2 >|S n2 |;

[0135] Calculate V n2 The derivative is:

[0136]

[0137] in

[0138] Virtual control law Select as:

[0139]

[0140] Where c n2 It is a positive constant;

[0141] Therefore, we get:

[0142]

[0143] in

[0144] Step 3n: S n3 The derivative is calculated as follows:

[0145]

[0146] The Lyapunov function for the 3nth obstacle is defined as:

[0147] V n3 =V n2 +S n3 2 / cos(πS n3 / 2B n3 ),

[0148] Among them B n3 It is a positive constant and satisfies B n3 >|S n3 |;

[0149] Calculate V n3 The derivative is obtained as follows:

[0150]

[0151] in

[0152] The tracking control law u of the nth motor nt Designed as follows:

[0153]

[0154] Where c n3 It is a positive constant;

[0155] Therefore, we get:

[0156]

[0157] Furthermore, the local average deviation coupling synchronization control scheme described in step S8 specifically includes:

[0158] In a multi-motor drive system, each motor is treated as an independent intelligent agent. A rule-based communication network is established for information exchange to achieve synchronization between the agents. In the communication network, each agent has an equal out-degree, and each agent has d... e There are two types of agents: one is the connecting node, which connects to the adjacent connecting node and the hidden node; the other is the hidden node, which connects only to the adjacent connecting node. A new agent is selected as a hidden node until an entire row of hidden nodes is transformed into an entire row of connecting nodes. If there is an empty space in a row of hidden nodes, then the adjacent connecting nodes are connected to each other.

[0159] The torque input of each motor is expressed as follows:

[0160] T i (t)=γ i J i x i ,i=1,…,n.

[0161] T i The derivative of (t) is derived as follows:

[0162]

[0163] Where u i =u it +Δu it +u is ,i=1,…,n, is the total control input of the i-th motor, Δu it ,i=1,…,n, represents tracking synchronization compensation, u is ,i=1,…,n, is the torque synchronization control law;

[0164] The following auxiliary variables are introduced:

[0165]

[0166] During the operation of a multi-motor drive system, different Q values... it The values ​​of i = 1, ..., n will result in different torque inputs; the synchronization scheme is divided into two parts: Q it Synchronization of i = 1, ..., n and synchronization of torque input for each motor;

[0167] In this local average deviation coupled synchronous control scheme, the reference trajectory is the average state of each motor and its corresponding neighbor, Q. it The reference trajectory Q of i = 1, ..., n id i = 1, ..., n, given as:

[0168]

[0169] Define T is =T i (t)+ΔT i ,i=1,…,n, are the synchronous torques used solely for information exchange, where ΔT i ,i=1,…,n, are virtual torques; T is The reference trajectory T of i = 1, ..., n id i = 1, ..., n, given as:

[0170]

[0171] The tracking error of local average deviation coupled synchronization control is defined as

[0172]

[0173] Step 1: Consider Q it The synchronization error between the ,i=1,…,n and their corresponding neighbors is chosen using the Lyapunov function:

[0174]

[0175] Q t =[Q 1t ,…,Q nt ] T ;

[0176] V s1 The derivative is calculated to be:

[0177]

[0178] Q 1u =[Q 1,1u ,…,Q n,1u ] T and Q 2u =]Q 1,2u ,…,Q n,2u ] T ;

[0179] Tracking and Synchronization Compensation Δu it The design is as follows: i = 1, ..., n

[0180]

[0181] in It is a positive constant;

[0182] Therefore, we get:

[0183]

[0184] Step 2: Introduce virtual torque ΔT i ,i=1,…,n, to the information exchange; if the i-th motor requires a reduction in torque input, then ΔT i It will continue to increase until the torque input T i (t) is reduced to the desired state, and the excess torque load is distributed to other motors through the synchronous controller; if the i-th motor is operating normally, then ΔT i =0; ΔT i ,i=1,…,n, is represented as:

[0185]

[0186] Where T i ,i=1,…,n are the input signals, η1 and η2 are positive constants, Δ i ,i=1,…,n, are state variables; T ir =T im tanhz d ,i=1,…,n, are the desired torque inputs; T im ,i=1,…,n, are selected as 0.5T m 0.3T m Or 0, T m It is the rated torque;

[0187] Considering the torque synchronization error of a multi-motor drive system, the Lyapunov function is defined as:

[0188]

[0189] Where T s =[T 1s ,…,T ns ] T ;

[0190] V s2 The derivative is calculated as follows:

[0191]

[0192] Q s =[Q 1s ,…,Q ns ] T and ΔT=[ΔT1,…,ΔT n ] T ;

[0193] Torque synchronization control law u is The design is as follows: i = 1, ..., n

[0194]

[0195] in It is a positive constant;

[0196] Therefore, we get:

[0197]

[0198] In a multi-motor drive system, the concentrated interference at the motor end is d i i = 1, ..., n, which are related to the state of the load end;

[0199] The total torque input setpoint for the multi-motor drive system is:

[0200]

[0201] T in The derivative of (t) is calculated as follows:

[0202]

[0203] because Then we can deduce that:

[0204]

[0205] Among them 1 T =[1,…,1] T ;

[0206] Integrating both sides of the above equation, we get...

[0207] because Then we can deduce that:

[0208]

[0209] because and have to:

[0210]

[0211] This indicates the total torque input T of the multi-motor drive system in (t) is determined solely by the tracking control law u it The order of i = 1, ..., n is determined.

[0212] The beneficial effects of this invention are as follows:

[0213] Unlike neural network approximators, the interference compensator of this invention has a lower computational burden for the same performance. Compared to observers, the interference compensator of this invention has better approximation performance within a specified time. Compared to locally coupled structures, in multi-motor drive systems with a large increase in the number of motors, the communication network designed in this invention has higher synchronization efficiency due to its smaller average path length and network diameter. Compared to globally coupled structures, the local coupling properties of the communication network designed in this invention can reduce the average degree to alleviate the communication burden. The control scheme proposed in this invention simultaneously ensures the load tracking performance and torque synchronization performance of the multi-motor drive system. Furthermore, distributed control can be used to simplify the design process of the synchronization controller.

[0214] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0215] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0216] Figure 1 This is a control principle diagram for a multi-motor drive system.

[0217] Figure 2 A block diagram of the control scheme;

[0218] Figure 3 Diagram of the communication network structure for a multi-motor drive system;

[0219] Figure 4 The left and right figures represent z0 with respect to z. d1 and z d2 The load speed tracking graphs are shown, with (a)-(d) being scaled-down views.

[0220] Figure 5 Synchronous torque T of a multi-motor drive system s The simulation results are shown in the figure. (a)-(e) are all scaled-down views.

[0221] Figure 6 The actual torque input diagrams for four of the motors are shown, with (a)-(d) in the diagrams being scaled-down.

[0222] Figure 7 The diagram shows the control voltage signals for four of the motors. (a)-(d) in the diagram are all scaled-down views. Detailed Implementation

[0223] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0224] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0225] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0226] Due to their high reliability and excellent system performance, multi-motor drive systems play a vital role in industrial production. Their control principles are as follows: Figure 1 As shown, the load device is connected to a large gear, and each permanent magnet synchronous motor is connected to a small gear via a reducer. The permanent magnet synchronous motors provide torque input to the multi-motor drive system through gear transmission. The load device is then driven by n identical permanent magnet synchronous motors, which track the reference trajectory with high precision. In the closed-loop control system of the multi-motor drive system, the controller sends a control signal u based on the reference trajectory and feedback signal. q and u d These feedback signals are obtained from the actuator via an optical encoder, Parker transform, and Clarke transform. Control signal u q and u d It needs to be converted to u via the inverse Parker transform. α and u β , then u α and u βInsulated Gate Bipolar Transistor (IGBT) inverters can be controlled using Space Vector Pulse Width Modulation (SVPWM) technology.

[0227] In a multi-motor drive system, the dynamic model of a single independent permanent magnet synchronous motor is represented as follows:

[0228]

[0229] Where i d and i q These are the stator currents along the d-axis and q-axis; u d and u q These are the stator voltages along the d-axis and q-axis; L d and L q These are the stator inductances along the d-axis and q-axis; R,p n ω, ψ, and J represent the stator resistance, number of pole pairs, angular velocity, magnetic flux, and moment of inertia, respectively. f d and τ are the friction torque, the unknown dynamic term, and the transmission torque, respectively.

[0230] In engineering, the d-axis reference current is set to zero to improve the efficiency of the permanent magnet synchronous motor and to approximately eliminate the coupling effect between angular velocity and current. Then, model (1) is rewritten as...

[0231]

[0232] Frictional nonlinearity, which significantly affects the performance of multi-motor drive systems, is unavoidable. Therefore, it is necessary to take measures to compensate for this nonlinearity. A continuously differentiable frictional model is used to approximate the frictional torque of a multi-motor drive system, written as...

[0233] T f =F p +f v ω, (3)

[0234] Where F p =p1(tanh(p3ω)-tanh(p4ω))+p2 tanh(p5ω),

[0235] Where f v It is the coefficient of friction, p i i = 1, ..., 5 are positive constants. In the controller design process, the frictional torque T... f Through f v ω is compensated for, the unknown dynamic term F p It is categorized into centralized interference for processing.

[0236] Introducing y = ω, x = i q ,γ=1.5p n ψ / J,ε=fv / J,δ=(F p +d) / J, α=R / L q ,β=p n ψ / L q and u=u q / L q Simplify (2) to get

[0237]

[0238] like Figure 1 As shown, according to Newton's second law, the dynamic model of the load end is given as follows:

[0239]

[0240] Where subscript 0 represents the load end, subscript i represents the i-th motor, i = 1, ..., n, z0 is the angular velocity of the load end, and w is the load end disturbance including unknown dynamic terms and working load.

[0241] Under ideal conditions, each motor provides the same transmission torque to the multi-motor drive system, and the drive burden at the load end is then evenly distributed among the n permanent magnet synchronous motors, as follows:

[0242]

[0243] Where z i =z0 / n and w i =w / n.

[0244] Due to the inherent characteristics of gear drives, dead zone is an unavoidable nonlinearity that significantly affects the control performance of multi-motor drive systems. To describe the dynamic characteristics of gear drives, the transmission torque model is expressed as:

[0245]

[0246] in

[0247] Where k, c, χ, θ and r are the torque coefficient, damping coefficient, half clearance, angular displacement and transmission ratio, respectively.

[0248] Integrating (4), (6), and (7), the dynamic model of the entire multi-motor drive system is expressed as follows:

[0249]

[0250] Assumption 1: The ideal trajectory z of the angular velocity at the load end d Its derivative is continuous and bounded.

[0251] A multi-motor drive system with n identical permanent magnet synchronous motors needs to handle synchronization and complex communication coupling issues. Therefore, an undirected graph G is used to describe the information exchange network between the n motors and to simplify the design process of the synchronization controller.

[0252] For a leaderless multi-agent system, information exchange follows an undirected graph G = {V, E, A}, where V = {υ} i The set of vertices is {i=1,…,n}. It is an edge set, and A = [a ij ]∈R n×n Let G be the adjacency matrix of an undirected graph. If there is an edge between agents i and j, i.e. (υ i ,υ j If )∈E, then a ij =a ji =1, otherwise a ij =a ji =0, note a ii =0 for i=1,…,n. Node υ i The neighbor set is N i ={j,(υ i ,υ j )∈E}. Node υ i The degree of exit is The degree distribution matrix of an undirected graph G is And the Laplace matrix of an undirected graph G is L = DA.

[0253] Interference Compensation: Load-side Interference Compensation: In multi-motor drive systems, uncertainties are difficult to handle at the load end, such as external interference p. 06 sin t, workload d L Unknown dynamic term F in friction nonlinearity 0p , where p 06 These are positive constants. These uncertainties significantly impact the control performance of multi-motor drive systems. Therefore, an improved second-order tracking differentiator is used to approximate the load-side disturbances.

[0254]

[0255] and

[0256] Where τ i i = 1, ..., n and z0 are the input signals of this second-order tracking differentiator, and λ1 and λ2 are positive constants. It is an estimate of w. Let Λ1 and Λ1 be the state variables of this second-order tracking differentiator. Note that τ... i i = 1, ..., n is measurable.

[0257] if It approximates z0 very well, then It will approximate w very well.

[0258] Proof: Substituting into formula (9) arrive From

[0259]

[0260] To simplify the subsequent proof process, we introduce... and Where ι1 and ι2 are arbitrarily small positive constants. Then the approximation error is derived as follows:

[0261]

[0262] Substituting (10) into (11) yields

[0263]

[0264] Where ξ1 is a positive constant. The proof ends here.

[0265] Interference compensation at the motor end: In multi-motor drive systems, interference compensation at the motor end differs from that at the load end. The uncertainty at the motor end only includes external interference p. i6 sin t, i=1,…,n, and the unknown dynamic term F ip ,i=1,…,n,where p i6 Let i = 1, ..., n be positive constants. These uncertainties are smaller than those at the load end, but they still affect the control accuracy of multi-motor drive systems. To compensate for the interference at the motor end, the second-order tracking differentiator is improved to...

[0266]

[0267] and

[0268] Where λ3 and λ4 are positive constants. It is δ i The estimated values ​​for i = 1, ..., n and Λ 2,i These are the state variables of this second-order tracking differentiator.

[0269] Similarly, if It approximates y very well i If i = 1, ..., n, then It will approximate δ very well. i ,i=1,…,n.

[0270] The proof process here is similar to that in (10)-(12), and the approximation error can be derived. ξ2 is a positive constant.

[0271] Note 1: In the design of this second-order tracking differentiator, only two parameters, λ1 and λ2 or λ3 and λ4, need to be adjusted appropriately. Then, by choosing suitable parameters, the approximation errors ξ1 and ξ2 can be made arbitrarily small. However, during parameter adjustment, small λ1, λ2, or λ3 and λ4 will lead to a longer convergence process, excessively large λ1 or λ3 will cause overshoot, and excessively large λ2 or λ4 will cause harmful oscillations. Therefore, it is necessary to find a balance between fast response and high accuracy.

[0272] The performance of a multi-motor drive system is primarily determined by its manufacturing process and core control algorithm. Compared to the significant costs associated with improving the manufacturing process, refining the control algorithm is an effective means of enhancing the performance of multi-motor drive systems. Figure 1 The control principle of a multi-motor drive system was demonstrated. Figure 2 The demonstration showcases the core control technology. Ideally, the accelerated inversion tracking controller sends control signals to the actuators based on interference compensation and tracking error. However, the torque inputs of each motor are not equal, which can lead to overload or even failure. Therefore, a local average deviation coupled synchronous controller is used to synchronize the torque input of each motor.

[0273] The control scheme consists of two parts: an accelerated inversion tracking control part and a local average deviation coupled synchronization control part. The design process of the accelerated inversion tracking controller is as follows:

[0274] To accelerate the convergence of tracking errors, a velocity function is introduced, which is expressed as follows:

[0275]

[0276] Where T c It is a positive constant, and φ(t) is a smooth function that does not decrease to infinity.

[0277] φ(t) satisfies φ(0)=1 and It is a design parameter and satisfies P(t) is positive and increasing, P(0) = 1 and will increase to... φ(t) affects P(t) in the condition 0 ≤ t < T. c The rate of increase during the period, T c This indicates that P(t) increases from 1 to... The time.

[0278] In the actual operation of a multi-motor drive system, its state variables are constrained by physical factors and specific performance requirements. Therefore, a cosine barrier function is used to ensure the stability of the multi-motor drive system and to prevent the output constraints from being violated. This cosine barrier function is expressed as follows:

[0279]

[0280] From (15), if... So

[0281] Acceleration error is defined as

[0282]

[0283] Where z id =z d / n, and It is the virtual control law for the i-th motor, i = 1, ..., n.

[0284] Step 1: S 11 The derivative is derived as follows

[0285]

[0286] in

[0287] Define the first barrier Lyapunov function as:

[0288] V 11 =S 11 2 / cos(πS 11 / 2B 11 ), (18)

[0289] Among them B 11 It is a positive constant and satisfies B 11 >|S 11 |

[0290] V 11 The derivative is calculated to obtain

[0291]

[0292] in

[0293] According to formula (17), the virtual control law Designed for

[0294]

[0295] in c11 It is a normal number.

[0296] Substituting (20) into (19) yields

[0297]

[0298] in

[0299] Step 2: S 12 The derivative is calculated to obtain

[0300]

[0301] In traditional inversion techniques, the derivative of the virtual control law needs to be calculated repeatedly, leading to a "complexity explosion." To address this issue, a second-order tracking differentiator is introduced to approximate the virtual control law. The derivative of . This second-order tracking differentiator is written as

[0302]

[0303] in This is the input signal, μ1 and μ2 are positive constants, and σ i1 and σ i2 ,i=1,…,n is the output of this second-order tracking differentiator. The approximation error is defined as... and h i1 and h i2 By selecting appropriate parameters, the value can be reduced to an arbitrarily small level.

[0304] The second obstacle is the choice of the Lyapunov function.

[0305] V 12 =V 11 +S 12 2 / cos(πS 12 / 2B 12 ), (twenty four)

[0306] Among them B 12 It is a positive constant and satisfies B 12 >|S 12 |

[0307] V 12 The derivative is derived as follows

[0308]

[0309] in

[0310] According to formula (22), the virtual control law Designed for

[0311]

[0312] Where c 12 It is a normal number.

[0313] Substituting (26) into (25) yields

[0314]

[0315] in

[0316] Step 3: S 13 The derivative is derived as follows

[0317]

[0318] Similar to the second step, in order to solve the "complexity term explosion", a second-order tracking differentiator is used to approximate the virtual control law. The derivative of . It is written as

[0319]

[0320] in This is the input signal, μ3 and μ4 are positive constants, and σ i3 and σ i4 ,i=1,…,n is the output of this second-order tracking differentiator. The approximation error is defined as... and h i3 and h i4 By selecting appropriate parameters, the value can be reduced to an arbitrarily small level.

[0321] The third barrier, the Lyapunov function, is defined as follows:

[0322] V 13 =V 12 +S 13 2 / cos(πS 13 / 2B 13 ), (30)

[0323] Among them B 13 It is a positive constant and satisfies B 13 >|S 13 |

[0324] V 13 The derivative is calculated as

[0325]

[0326] in

[0327] According to formula (28), the tracking control law u of the first motor 1t Designed for

[0328]

[0329] Where c 13 It is a normal number.

[0330] Substituting (32) into (31) yields

[0331]

[0332] The design process for the acceleration inversion tracking controller for each motor is the same; therefore, only the design process for the first and nth motors will be shown.

[0333] Step 3n-2: S n1 The derivative is calculated as

[0334]

[0335] The Lyapunov function for the 3n-2th obstacle is chosen as...

[0336] V n1 =V (n-1)3 +S n1 2 / cos(πS n1 / 2B n1 ),(35)

[0337] Among them B n1 It is a positive constant and satisfies B n1 >|S n1 |

[0338] V n1 The derivative is calculated to obtain

[0339]

[0340] in

[0341] According to formula (34), the virtual control law Selected as

[0342]

[0343] in c n1 It is a normal number.

[0344] Substituting (37) into (36) yields

[0345]

[0346] in

[0347] Step 3n-1: S n2 The derivative is given as

[0348]

[0349] The Lyapunov function of the 3n-1th obstacle is defined as

[0350] V n2 =V n1 +S n2 2 / cos(πS n2 / 2B n2 ), (40)

[0351] Among them B n2 It is a positive constant and satisfies B n2 >|S n2 |

[0352] Calculate V n2 The derivative is

[0353]

[0354] in

[0355] According to formula (39), the virtual control law Select as

[0356]

[0357] Where c n2 It is a normal number.

[0358] Substituting (42) into (41) yields

[0359]

[0360] in

[0361] Step 3n: S n3 The derivative is calculated as

[0362]

[0363] The Lyapunov function for the 3nth obstacle is defined as follows:

[0364] V n3 =V n2 +S n3 2 / cos(πSn3 / 2B n3 ), (45)

[0365] Among them B n3 It is a positive constant and satisfies B n3 >|S n3 |

[0366] Calculate V n3 The derivative is obtained

[0367]

[0368] in

[0369] According to formula (44), the tracking control law u of the nth motor nt Designed for

[0370]

[0371] Where c n3 It is a normal number.

[0372] Substituting (47) into (46) yields

[0373]

[0374] Note 2: When adjusting parameters, the smaller c i1 c i2 and c i3 Setting the parameters i = 1, ..., n results in long response times and low control accuracy. Excessively large parameters can also lead to harmful oscillations and overshoot. Furthermore, the acceleration error S... i2 and S i3 The convergence process of i = 1, ..., n will inevitably be affected by the local average deviation coupled synchronization control, so c i2 and c i3 The values ​​of i = 1, ..., n should not be too large. Therefore, the acceleration error S should be considered first. i1 We first consider the rapid convergence and high-precision control of i = 1, ..., n, and then we consider the acceleration error S. i2 and S i3 Tracking performance of i = 1, ..., n.

[0375] Stability Analysis: Theorem 1: Based on Assumption 1, for a multi-motor drive system (8), design acceleration inversion tracking control inputs (32) and (47). If the initial state satisfies z0(0)∈(-B 11 +z d (0),z d (0)+B 11If the angular velocity at the load end is high-precision, the reference trajectory will be tracked, all signals of the closed-loop system will be bounded, and the output constraints will not be violated.

[0376] Proof: The Lyapunov function is chosen as

[0377]

[0378] V t The derivative is derived as follows

[0379]

[0380] Where C0 = min{c ij ,i=1,…,n,j=1,2,3}, B0=B1+B2+B3, It is a positive constant and satisfies

[0381] As t→∞, we have

[0382]

[0383] This indicates that all signals in this closed-loop system are bounded. Furthermore, with |S 11 |→B 11 S 11 2 / cos(πS 11 / 2B 11 →∞. When |S 11 |≠B 11 At that time, S 11 and S 11 2 / cos(πS 11 / 2B 11 It is uniformly and ultimately bounded. At the same time... in It is a positive constant and satisfies This shows that the output z0 is constrained. The proof ends here.

[0384] Considering the various external disturbances, unknown dynamic terms, and different operating conditions at the motor ends of a multi-motor drive system, and the different torque inputs and operating performance of each motor, overload and potential failures are possible. Therefore, the study of synchronization control schemes is necessary to ensure torque synchronization in the multi-motor drive system.

[0385] This invention proposes a local average deviation coupling synchronization control scheme, which aims to achieve synchronization while simultaneously controlling the acceleration error S. i1 Effective control is achieved by assigning values ​​i = 1, ..., n to the motors. Furthermore, based on the operating performance of some motors, their torque input is reduced to prevent overload damage.

[0386] Communication Network: In a multi-motor drive system, each motor is connected to the load, and there is no coupling effect between these motors. Therefore, a communication network must be established for information exchange in the multi-motor drive system. Assume there are n independent agents that are not coupled to each other. To achieve synchronization between these agents, a rule-based communication network for information exchange is established, such as... Figure 3 As shown, this communication network has a relatively small average degree, a small network diameter, and a small average path length.

[0387] In this communication network, each agent has the same out-degree, and each agent has d. e Each agent has a neighbor and communicates only with its adjacent neighbors. These agents can be divided into two categories: connecting nodes, which connect to both adjacent connecting nodes and hidden nodes, and hidden nodes, which connect only to their adjacent connecting nodes. Building this communication network is like assembling building blocks; new agents are selected as hidden nodes until an entire row of hidden nodes becomes a row of connecting nodes. If there are empty spaces in a row of hidden nodes, adjacent connecting nodes will connect to each other.

[0388] Note 3: This communication network reduces communication overhead due to its relatively low average degree and improves synchronization efficiency due to its small network diameter and average path length. The designed communication network has a regular structure, clear logic, and is easy to construct. Furthermore, its local coupling properties avoid the need for global state information.

[0389] In a multi-motor drive system, in order to ensure that the acceleration error S determined by the total torque input is within a certain range... i1 To assess the control performance of motors with i = 1, ..., n, a local average deviation coupled synchronization control scheme is proposed to synchronize the torque input of each motor.

[0390] The torque input of each motor is expressed as:

[0391] T i (t)=γ i J i x i ,i=1,…,n. (52)

[0392] T i The derivative of (t) is derived as follows:

[0393]

[0394] Where u i =u it +Δu it +u is,i=1,…,n, is the total control input of the i-th motor, Δu it ,i=1,…,n, represents tracking synchronization compensation, u is ,i=1,…,n, is the torque synchronization control law.

[0395] To simplify the subsequent controller design process, the following auxiliary variables are introduced.

[0396]

[0397] During the operation of a multi-motor drive system, different Q values... it The values ​​of i = 1, ..., n will result in different torque inputs. Therefore, this synchronization scheme is divided into two parts: Q it Synchronization of i = 1, ..., n and synchronization of torque input for each motor.

[0398] In this locally averaged deviation coupled synchronous control scheme, the reference trajectory is the average state of each motor and its corresponding neighbor. Therefore, Q it The reference trajectory Q of i = 1, ..., n id ,i=1,…,n, given as

[0399]

[0400] To synchronize the torque input of each motor and reduce the torque of some motors, T is defined. is =T i (t)+ΔT i ,i=1,…,n, are the synchronous torques used solely for information exchange, where ΔT i ,i=1,…,n, are virtual torques. Similar to (55), T is The reference trajectory T of i = 1, ..., n id ,i=1,…,n, given as

[0401]

[0402] The tracking error of local average deviation coupled synchronization control is defined as

[0403]

[0404] Step 1: Consider Q it The synchronization error between the ,i=1,…,n and their corresponding neighbors is chosen as the Lyapunov function.

[0405]

[0406] Q t =[Q 1t ,…,Qnt ] T .

[0407] V s1 The derivative is calculated to obtain

[0408]

[0409] Q 1u =[Q 1,1u ,…,Q n,1u ] T and Q 2u =[Q 1,2u ,…,Q n,2u ] T .

[0410] Tracking and Synchronization Compensation Δu it i = 1, ..., n, designed as

[0411]

[0412] in It is a normal number.

[0413] Substituting (60) into (59) yields

[0414]

[0415] Step 2: During the operation of a multi-motor drive system, some motors need to reduce their torque input based on their operating performance, so a virtual torque ΔT is introduced. i The information is exchanged from i to n. If the i-th motor requires a reduction in torque input, then ΔT... i It will continue to increase until the torque input T i (t) is reduced to the desired state, and the excess torque load is distributed to other motors through the synchronous controller. If the i-th motor is operating normally, then ΔT i =0. ΔT i ,i=1,…,n, is represented as

[0416]

[0417] Where T i ,i=1,…,n are the input signals, η1 and η2 are positive constants, Δ i Let i = 1, ..., n be the state variables. ir =T im tanhz d ,i=1,…,n, is the desired torque input. T im ,i=1,…,n, can be chosen as 0.5T m0.3T m Or 0, T m That is the rated torque.

[0418] Considering the torque synchronization error of a multi-motor drive system, the Lyapunov function is defined as follows:

[0419]

[0420] Where T s =[T 1s ,…,T ns ] T .

[0421] V s2 The derivative is calculated as

[0422]

[0423] Q s =[Q 1s ,…,Q ns ] T and ΔT=[ΔT1,…,ΔT n ] T .

[0424] Torque synchronization control law u is i = 1, ..., n, designed as

[0425]

[0426] in It is a normal number.

[0427] Substituting (65) into (64) yields

[0428]

[0429] Assumption 2: In a multi-motor drive system, the concentrated interference d at the motor end... i ,i=1,…,n, are related to the state of the load end.

[0430] The design of the local average deviation coupled synchronization controller is now complete. The following section discusses the impact of synchronization control on load tracking performance.

[0431] The total torque input setpoint of the multi-motor drive system is

[0432]

[0433] T in The derivative of (t) is calculated as follows:

[0434]

[0435] From (61), we obtain Therefore, the derivation yields

[0436]

[0437] Among them 1 T =[1,…,1] T .

[0438] Integrating both sides of (69) yields... Furthermore, from (66), we obtain The derivation is

[0439]

[0440] because and (68) Rewritten as

[0441]

[0442] This indicates the total torque input T of the multi-motor drive system in (t) is determined solely by the tracking control law u it The values ​​of i = 1, ..., n are determined. If assumption 2 holds, the impact of synchronous control on load tracking performance in a multi-motor drive system is very small.

[0443] Note 4: In the design of the local average deviation coupled synchronous controller, the reference trajectory is the average state of each motor and its corresponding neighbor, and the Lyapunov function is also related to the synchronization error between each motor and its corresponding neighbor. During the operation of the multi-motor drive system, due to the proposed synchronous control, each motor will approach the average state Q. id and T id Until the average deviation e is =0 and e iT =0, i=1,…,n, and then the torque synchronization target of the multi-motor drive system is achieved.

[0444] Note 5: In a multi-motor drive system, if assumption 2 holds, then the load tracking performance is solely determined by the tracking control law u. it The values ​​of i = 1, ..., n are determined. However, the acceleration error S i2 and S i3 The convergence process of i = 1, ..., n will still be affected by synchronization control, because and The effects of the proposed synchronization control on load tracking performance are exactly offset. Therefore, the impact of the proposed synchronization control on load tracking performance is very small.

[0445] Stability Analysis: Theorem 2: Based on Assumption 2, for the multi-motor drive system (8), local average deviation coupled synchronous control inputs (60) and (65) are designed. If the parameters and If the appropriate selection is made, the boundedness of the synchronization error is guaranteed. This ensures the synchronization of the torque input of each motor.

[0446] Proof: The Lyapunov function is defined as follows:

[0447] V s =Q t T LQ t +T s T LT s (72)

[0448] V s The derivative is calculated as

[0449]

[0450] To simplify the subsequent proof, we introduce... and Among them B Q and B T It is a positive number. Then (73) is rewritten as

[0451]

[0452] The derivation yields

[0453]

[0454]

[0455] Substituting (75) and (76) into (74) yields

[0456]

[0457] in and and It is a normal number.

[0458] Define the following variables as

[0459]

[0460] Then (77) is rewritten as

[0461]

[0462] The solution to (79) can be further written as:

[0463]

[0464] This demonstrates that the synchronization error of a multi-motor drive system is bounded. In other words, torque synchronization is achieved in the multi-motor drive system. The proof concludes here.

[0465] Simulation experiments on a 50-motor drive system verified the load tracking and torque synchronization performance of the multi-motor drive system under the designed control scheme. The parameters at the motor and load ends are as follows: R i =0.8~1.2Ω, L iq =0.04~0.06H, ψ i =0.08~0.12Wb, J i =0.004~0.006kg·m 2 J0 = 10 kg·m 2 f iv =0.00042~0.00062N·m·s / rad, f 0v =0.2 N·m·s / rad, i = 1,…,50. The reference trajectory is chosen as z. d1 =2sin t+10tanh t and z d2 =12sin t, the parameters of the multi-motor drive system are given as r=10, d e =6, n=50, k=3000, c=1 and χ=0.2. The relevant parameters of the velocity function are T. c =2, φ(t)=1 and The parameters for interference compensation are selected as λ1 = 15, λ2 = 1, λ3 = 40, and λ4 = 4. The parameters for the second-order tracking differentiator are designed as μ1 = 90, μ2 = 30, μ3 = 30, and μ4 = 10. The design parameters for the accelerated inversion tracking controller are selected as c. i1 =300, c i2 =0.5, c i3 =10, B i1 =100, B i2 =1000 and B i3 =100, i=1,…,50. The parameters of the local average deviation coupled synchronization controller are set to... η1 = 8 and η2 = 8. The concentrated disturbance of the multi-motor drive system is as follows, d i =F ip +p i6 sin t, i = 1, ..., 50 and d0 = F 0p +p 06 sin t+d L , where d L =F Lp +p L6sin t+f L ω0, f L =8, and the relevant parameters are as follows: p i1 =2~12, p 01 =100, p L1 =800, p i2 =0.02~0.12, p 02 =1, p L2 =8, p i3 =0.01, p 03 =0.1, p L3 =0.1, p i4 =0.008, p 04 =0.08, p L4 =0.08, p i5 =0.005, p 05 =0.05, p L5 =0.05, p i6 =0.02~0.12, p 06 =0.25, p L6 =3, i=1,…,50.

[0466] Figure 4 Simulation results for load speed tracking are presented, demonstrating the stability of the multi-motor drive system under the proposed control scheme. Zoomed-down figures (a) and (c) show the tracking error e. 0,1 =z0-z d1 and e 0,2 =z0-z d2 As can be seen, the load can track the reference trajectory within 1.5 seconds. Zoomed plots (b) and (d) show that the tracking error converges to ±0.0005 rads during stable operation of the multi-motor drive system.

[0467] Figure 5 The synchronous torque T of 50 motors was demonstrated. s Simulation results show that: ① In scaled plot (a), it is clear that torque synchronization is achieved within 0.2 seconds. ② Scaled plot (b) shows that during stable operation of the multi-motor drive system, the synchronization error converges to ±0.01 N·m. ③ Scaled plots (c)-(e) indicate that the increased synchronization error is caused by some motors reducing their torque input, specifically at t=20s (motor numbers: 5, 7, 8, 14, 28, 32, 41, 46, 48, 49), t=30s (motor numbers: 8, 14, 28, 48, 49), and t=40s (motor numbers: 8, 49). ④ Scaled plot (e) shows that the synchronization torque T... s It oscillates at t=40s and tends to stabilize within 0.5 seconds.

[0468] Figure 6 The actual torque input of motors 1, 7, 14, and 8 is shown. At t = 20s, motor 1 operates normally, while the other three motors operate with reduced torque (T). im =0.5T m ,T m =4.8 N·m, i = 7, 14, 8); at t = 30 s, motors 14 and 8 reduce their operating torque (T im =0.3T m ,T m =4.8 N·m, i = 14, 8); at t = 40 s, motor No. 8 has no torque input (T 8m =0). From the scaled graphs (a)-(d), it can be seen that: ① at t = 20s, T7, T 14 ① T8 decreases and T1 increases. ② At t = 30s, T7 remains constant, T 14 And T8 decreases. ③ At t = 40s, T7 and T... 14 ④ When T8 = 0, the gap nonlinearity causes motor 8 to oscillate. Then, due to the synchronous control, all motors oscillate, and all states tend to stabilize within 0.5 seconds. ⑤ During the stable operation of the multi-motor drive system (t = 46s ~ 49s), T1 performs normally, while T7 and T... 14 T8 remains unchanged, (T 7m =0.5T m ,T 14m =0.3T m ,T 8m =0,T m =4.8 N·m). At this time, motor 8 is driven by the load, and the disturbance torque of motor 8 is distributed to the other motors. In addition, the scaled graph (f) shows that the total torque input of the multi-motor drive system is not affected by the synchronization control until T8 = 0.

[0469] exist Figure 7 The control voltages of motors 1, 7, 14, and 8 are shown in the figure. Scaled plot (a) reveals the stability of the control signal in the first 1.5 seconds. Further experiments in scaled plots (b)-(d) demonstrate that the proposed synchronous control scheme significantly affects the control voltage signal. At t = 20s, u q7 ,u q14 and u q8 Reduce, and u q1 The change is similar at t=30s and t=40s. As can be seen from subplot (d), when T8=0, u... q8 The oscillation caused u q1 ,u q7 and uq14 Oscillations occurred. The above results demonstrate the effectiveness of the proposed torque synchronization control scheme.

[0470] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology, characterized in that: Includes the following steps: S1: Establish a dynamic model of a multi-motor drive system with dead zone, friction and disturbance characteristics; S2: Perform disturbance compensation on the dynamic model of the multi-motor drive system; S3: Utilize the velocity function to accelerate the convergence process of tracking errors; S4: Constrain the system output using a cosine barrier function; S5: Use a second-order tracking differentiator to solve the "complexity term explosion" problem; S6: Use an interference compensator to compensate for concentrated interference in the system; S7: Integrate steps S3-S6 into the inversion control and design an accelerated inversion tracking controller; S8: Design of a local average deviation coupling synchronization control scheme for tracking technology based on accelerated inversion tracking controller; The local average deviation coupling synchronization control scheme described in step S8 specifically includes: In a multi-motor drive system, each motor is treated as an independent intelligent agent. A rule-based communication network is established for information exchange to achieve synchronization between the agents. Within this network, each agent has an equal out-degree, and each agent has... There are two types of agents: one is the connecting node, which connects to the adjacent connecting node and the hidden node; the other is the hidden node, which connects only to the adjacent connecting node. A new agent is selected as a hidden node until an entire row of hidden nodes is transformed into an entire row of connecting nodes. If there is an empty space in a row of hidden nodes, then the adjacent connecting nodes are connected to each other. The torque input of each motor is expressed as follows: The derivative is derived as follows: in It is the first i The total control input for all motors It is tracking and synchronization compensation. It is a torque synchronization control law; The following auxiliary variables are introduced: During the operation of a multi-motor drive system, different This will result in different torque inputs; the synchronization scheme is divided into two parts: Synchronization of the motor and the torque input of each motor; In this local average deviation coupled synchronization control scheme, the reference trajectory is the average state of each motor and its corresponding neighbor. Reference trajectory Given: in It is a node The neighbor set; definition Synchronous torque used solely for information exchange, where It is virtual torque; Reference trajectory Given: The tracking error of local average deviation coupled synchronization control is defined as Step 1: Consider The synchronization error between them and their corresponding neighbors is chosen using the Lyapunov function: in It is an undirected graph The adjacency matrix, It is an undirected graph The Laplace matrix; ; The derivative is calculated to be: in and ; Tracking and Synchronization Compensation Designed as follows: in It is a positive constant; Therefore, we get: Step 2: Introducing Virtual Torque In information exchange; if the first i If a motor requires a reduction in torque input, then... It will continue to increase until the torque input Reduced to the desired state, and excess torque load distributed to other motors via the synchronous controller; if the first i If each motor is running normally, then ; Represented as: in It is the input signal. and It is a positive number. It is a state variable; The desired reduction is in the torque input, where It is the ideal trajectory of the angular velocity at the load end; Selected as , or , It is the rated torque; Considering the torque synchronization error of a multi-motor drive system, the Lyapunov function is defined as: in ; The derivative is calculated as follows: in and ; Torque synchronization control law Designed as follows: in It is a positive constant; Therefore, we get: In multi-motor drive systems, concentrated interference at the motor end Related to the state of the load end; The total torque input setpoint for the multi-motor drive system is: The derivative is calculated as follows: because Then we can deduce that: in ; Integrating both sides of the above equation, we get... ; because Then we can deduce that: because and ,have to: This indicates the total torque input of the multi-motor drive system. Only by tracking control law Decide.

2. The local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology according to claim 1, characterized in that: The dynamic model of the multi-motor drive system with dead zone, friction, and disturbance characteristics described in step S1 includes: n permanent magnet synchronous motors are connected to n pinions through reducers. The n pinions mesh with a large gear, which is connected to a load device, thereby enabling the n permanent magnet synchronous motors to drive a load device together. The controller sends control signals to the actuator based on the reference trajectory and feedback signals. The feedback signals are obtained through an optical encoder, Parker transform, and Clarke transform. The control signals are converted through an inverse Parker transform and then space vector pulse width modulation (SVPWM) technology is used to control the insulated gate bipolar transistor (IGBT) inverter. Finally, the controller is connected to the permanent magnet synchronous motor to drive the motor. The dynamic model of a single, independent permanent magnet synchronous motor is represented as follows: in and yes d shaft and q Stator current of the shaft; and yes d shaft and q Stator voltage of the shaft; and yes d shaft and q Stator inductance of the shaft; , , , and These are stator resistance, number of pole pairs, angular velocity, magnetic flux, and moment of inertia; , and These are friction torque, unknown dynamic term, and transmission torque, respectively. Will d The shaft reference current is set to zero to improve the efficiency of the permanent magnet synchronous motor and to approximately eliminate the coupling effect between angular velocity and current. The model is then rewritten as follows: The friction torque of a multi-motor drive system is approximated using a continuously differentiable friction model, written as: in in It is the coefficient of friction. It is a normal value; during the controller design process, frictional torque pass Compensation is required for unknown dynamic items. It should be categorized into centralized interference for processing; Introduction , , , , , , and ,get: The dynamic model of the load end is given as follows: Where the subscript 0 indicates the load side, the subscript... i Indicates the first i One motor, , It is the angular velocity at the load end. This includes load-side interference, which includes unknown dynamic items and workload. Each motor provides the same transmission torque to the multi-motor drive system, and then the drive burden at the load end is evenly distributed among the n permanent magnet synchronous motors, as follows: in and ; The transmission torque model is expressed as: in in , , , and These are torque coefficient, damping coefficient, half clearance, angular displacement, and transmission ratio; The dynamic model of the entire multi-motor drive system is represented as follows: The ideal trajectory of the load end angular velocity Its derivative is continuous and bounded; Using undirected graphs This describes the information exchange network between n motors and simplifies the design process of the synchronous controller; For a leaderless multi-agent system, information exchange follows an undirected graph. ,in It is a vertex set. It is an edge set, and It is an undirected graph The adjacency matrix; if in the agent i and j There is an edge between them, that is ,So ,otherwise , for ;node The neighbor set is ;node The degree of exit is Undirected graph The degree distribution matrix is undirected graph The Laplace matrix is .

3. The local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology according to claim 2, characterized in that: The interference compensation in step S2 includes: Interference compensation at the load end: An improved second-order tracking differentiator is used to approximate the interference at the load end as follows: in and This is the input signal of this second-order tracking differentiator. and It is a positive number. yes The estimated value, and These are the state variables of this second-order tracking differentiator. It is measurable; Interference compensation at the motor end: Improve the second-order tracking differentiator as follows: in and It is a positive number. yes The estimated value, and These are the state variables of this second-order tracking differentiator.

4. The local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology according to claim 3, characterized in that: The velocity function described in step S3 is expressed as: in It is a positive constant. It is a smooth function that does not decrease to infinity; satisfy as well as , It is a design parameter and satisfies ; It is positive and increasing. And will increase to ; Influence exist The rate of increase during the period express from Increase to The time.

5. The local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology according to claim 4, characterized in that: The cosine barrier function described in step S4 is expressed as: if ,So .

6. The local average deviation coupling synchronization control method for a multi-motor drive system based on accelerated inversion technology according to claim 5, characterized in that: The accelerated inversion tracking controller described in step S7 is constructed as follows: Acceleration error is defined as in , and It is the first i Virtual control law for each motor ; first step: The derivative is derived as follows: in ; Define the first barrier Lyapunov function as: in It is a positive constant and satisfies ; The derivative is calculated to be: in ; Virtual control law Designed as follows: in , It is a positive constant; Therefore, we get: in ; Step Two: The derivative is calculated to be: Introducing a second-order tracking differentiator to approximate the virtual control law The derivative; the second-order tracking differentiator is written as: in It is the input signal. and It is a positive number. and It is the output of the second-order tracking differentiator; the approximation error is defined as... and , , and By selecting appropriate parameters, the value can be reduced to an arbitrarily small level; The second obstacle is the choice of the Lyapunov function: in It is a positive constant and satisfies ; The derivative is: in ; Virtual control law Designed as follows: in It is a positive constant; Therefore, we get: in Step 3: The derivative is: A second-order tracking differentiator is used to approximate the virtual control law. The derivative is written as: in It is the input signal. and It is a positive number. and This is the output of the second-order tracking differentiator; the approximation error is defined as... and , , and By selecting appropriate parameters, the value can be reduced to an arbitrarily small level; The third barrier, the Lyapunov function, is defined as: in It is a positive constant and satisfies ; The derivative is calculated as follows: in ; The tracking control law of the first motor Designed as follows: in It is a positive constant; Therefore, we get: The design process for the acceleration inversion tracking controller for each motor is the same; No. 3n-2 step: The derivative is calculated as follows: No. 3n-2 The Lyapunov function for the obstacle is chosen as follows: in It is a positive constant and satisfies ; The derivative is calculated to be: in ; Virtual control law Selected as: in , It is a positive constant; Therefore, we get: in ; No. 3n-1 step: The derivative is given as: No. 3n-1 The Lyapunov function for each obstacle is defined as: in It is a positive constant and satisfies ; calculate The derivative is: in ; Virtual control law Select as: in It is a positive constant; Therefore, we get: in ; No. 3n step: The derivative is calculated as follows: No. 3n The Lyapunov function for each obstacle is defined as: in It is a positive constant and satisfies ; calculate The derivative is obtained as follows: in ; The tracking control law for the nth motor Designed as follows: in It is a positive constant; Therefore, we get: 。

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