Dynamic model analysis method for multi-motor belt conveyor

Abstract

The invention relates to the field of belt conveyor control model analysis, in particular to a multi-motor belt conveyor dynamic model analysis method, which comprises the following steps of: dispersing a belt conveyor system into a generation unit; establishing a system dynamics model; proposing constraint expectation; decomposing an uncertainty part in the kinetic model, and identifying matched and unmatched components in the uncertainty part; the influence of unmatched components on the belt conveyor system in the uncertainty part is verified; establishing a robustness control model based on the nominal part, the system error and the uncertainty part of the dynamic model of the belt conveyor; and the model is verified through dynamics simulation to achieve expected time and change trend. According to the method, modeling is carried out for the long-distance large-dip-angle belt conveyor, and the mismatching uncertainty of an under-actuated system is specifically decomposed; a self-adaptive robust controller is designed, and the speed of the conveyor is restrained by controlling the coordinated driving current of multiple motors; and the action effect of the controller is verified through dynamic simulation of dynamics.

Description

Technical Field

[0001] This invention relates to the field of control model analysis for belt conveyors, and in particular to a dynamic model analysis method for multi-motor belt conveyors. Background Technology

[0002] In the operation of belt conveyors, inappropriate control forces can shorten their service life and increase energy losses, problems exacerbated by their nonlinear characteristics. In recent years, the control problems of such uncertain nonlinear systems have received increasing attention.

[0003] The start-up and shutdown phases are crucial aspects of belt conveyor dynamics analysis. During these phases, the rapid torque response and precise speed control of the permanent magnet synchronous motor are essential for effectively preventing problems such as belt breakage. Therefore, the controller needs to consider the coordination between motors and calculate the precise current required by each motor. Furthermore, in the performance analysis of the conveyor, multiple motors provide load torque to ensure accuracy. In engineering practice, considering long distances and viscoelasticity, belt conveyors often need to be divided into several subsystems for detailed analysis. These systems typically have fewer control inputs than degrees of freedom, classifying them as underactuated systems. Given the widespread existence of underactuated systems, considerable research has been dedicated to their study in recent years.

[0004] In practice, nonlinear belt conveyor systems exhibit uncertainties in mass, stiffness, damping, and moment of inertia. For underactuated systems, these uncertainties may be mismatched. Many scholars have conducted extensive research on this issue. However, current control methods often assume that mismatch uncertainties are negligible or nonexistent, highlighting the need for further research into controlling these mismatch uncertainties. Summary of the Invention

[0005] This invention aims to solve the above problems and provides a dynamic model analysis method for multi-motor belt conveyors. The technical solution adopted is as follows: A dynamic model analysis method for a multi-motor belt conveyor includes the following steps: S1. Discretize the belt conveyor system into multiple drive motor units, tensioning devices, and multiple belt subsystems, wherein the belt subsystem includes a first belt subsystem directly connected to the drive motor and a second belt subsystem not directly connected to the drive motor; S2. For each belt subsystem, a dynamic model is established based on the permanent magnet synchronous motor model; S3. Based on the dynamic model, a constraint expectation is proposed to enable the belt conveyor to provide the expected displacement, velocity and acceleration at a certain time. S4. Decompose the uncertainties in the dynamic model and identify the matching and mismatching components. The matching components are in the same direction as the desired constraint in the vector space, and the mismatching components are perpendicular to the desired constraint. S5. Verify the impact of the mismatched components on the belt conveyor system in the uncertainty section; S6. Establish a robust control model based on the nominal part, system error, and uncertainty part of the belt conveyor dynamics model; S7. Based on actual engineering project parameters, establish a dynamic model, constraint expectations, and robust control model under actual working conditions, and verify the time and trend of the model to achieve the expected results through dynamic simulation.

[0006] Based on the above scheme, step S2 includes, S2-1. Define the number of belt subsystems as 20. Sequentially arrange the belt subsystems. Define the first to tenth belt subsystems as the conveyor belt downstream of the tail drive motor, the eleventh to thirteenth belt subsystems as the conveyor belt between the tail drive motor and the steering wheel, the fourteenth and fifteenth belt subsystems as the conveyor belt adjacent to the tension wheel in the tensioning device, and the seventeenth, eighteenth and nineteenth belt subsystems as the conveyor belt adjacent to the two head drive motors. S2-2. Establish the dynamic equations for each belt subsystem. (2-1) Where l takes values ​​of 2, 3, ..., 10, 12, 13, 16, 17; Where i represents the sequence number of each belt subsystem, and the value of i ranges from 1, 2, ..., 20. The coefficient of friction, For the quality of each belt subsystem, It is the acceleration due to gravity. ( ) represents a sign function; if the value in parentheses is positive, then... ( ) = 1, if the value in parentheses is negative, then ( ) = -1; For the stiffness of each belt subsystem, For the damping of each belt subsystem, For the displacement of each belt subsystem, For the speed of each belt subsystem, The acceleration of each belt subsystem; This indicates the tension of the first head drive motor on the 19th belt subsystem. This indicates the tension of the second head drive motor on the 18th belt subsystem. This indicates the tension of the tail drive motor on the 11th belt subsystem. Denote the tension of the tension pulley on the 14th and 15th belt subsystems; S2-3. Use a permanent magnet synchronous motor as the drive motor. Based on the above dynamic equations, add the permanent magnet synchronous motor model, then (2-2) (2-3) where is the driving force provided by the drive motor, is the motor drive current, and l takes values of 1, 2, 3; is the number of pole pairs of the drive motor, is the permanent magnetic flux linkage, is the friction coefficient, r is the radius of the motor drum, is the angular acceleration of the motor, is the angular velocity of the motor, is the motor torque.

[0007] Preferably, the step S3 includes S3-1. Rearrange the dynamic model of the belt conveyor system into a matrix form, then (3-1) where is the input matrix of the belt subsystem, M is the inertia matrix of the belt subsystem, C is the damping coefficient matrix of the belt subsystem, K is the stiffness coefficient matrix of the belt subsystem, and f is the friction resistance matrix of the belt subsystem; is the uncertain time-varying parameter vector, where k is the dimension of the matrix R, and where [[ID=4​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ but (3-6) (3-7) S3-4. Then equation (3-3) can be expressed as (3-8) in Let be a column vector consisting of quantities that are independent of velocity and displacement after taking the second derivative of each constraint in the system. Expressed in matrix form (3-9) in , ,and (3-10) S3-5. Then equation (3-2) can be expressed as (3-11) Expressed in matrix form (3-12) in .

[0008] Based on the above scheme, step S4 includes, S4-1. Decompose equation (3-1) as follows: (4-1) in Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The part that is determined in the middle, namely the nominal part. Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The uncertain part; S4-2. Without considering the uncertainties, the dynamic model can be described as follows: (4-2) definition: ,but (4-3) Equation (3-9) can be rewritten as follows: (4-4) in ; S4-3. Assumption 1: There is control. , making all If the constraints satisfy equation (4-4), then the dynamic system (4-3) is considered to be servo-constrained controllable with respect to constraint (4-4). definition , ,but (4-5) in unknown; S4-4. Assumption 2: Control Consistent with equation (4-5), one solution to equation (4-5) is: ,but (4-6) Make all .

[0009] Based on the above scheme, step S5 includes S5-1. Regarding the constraints as shown in equation (4-4), for the dynamic system (4-2) under the assumption... Servo constraints consistent with equation (4-5) if and only if (5-1) And all ,control for (5-2) Where any depends on vectors express; S5-2. Assume that for any , ,but The MP inverse always exists, therefore (5-3) Utilizing the inverse property of MP, i.e. ; S5-3. Assumption 1 ensures the feasibility of constraints by eliminating self-contradictory or unrealistic constraints; Assumption 2 ensures that the control task is consistent with the nature of the system. Equation (5-1) shows that... Each line is with Each column is orthogonal, which allows for control. exist A certain amount of component is projected into the middle; S5-4. Let , , Where I is the identity matrix, then (5-4) S5-5. Assumption 3: For each , It is reversible, making (5-5) The above formula provides a basis for E. The decomposition divides E into two parts: the matching part. ,lie in Within the value range space; the mismatched part ,lie in Outside the range space; definition and These are the matching and non-matching parts, specifically... (5-6) (5-7) Refer to equations (5-6) and (5-7); S5-6. Definition The part that does not match, that is ,matrix Each column lies within the null space of AD, that is ,but (5-8) Based on the above scheme, step S6 includes S6-1. Based on hypothesis 3, hypothesis 4 is proposed: Let ; Assume there exists a constant This makes all ,but (6-1) in Represents the smallest eigenvalue of the matrix. The largest eigenvalue of the matrix; S6-2. In the absence of uncertainty in M, then ,therefore and ;like There is no uncertainty of no match in it, that is ,but Therefore, choose Assumption 3 is satisfied; S6-3. Assumption 5-1: There exists a constant vector and a function This makes all ,but (6-2) in (6-3) Assumption 5-2: For each ,function It is a first-order continuously differentiable function and is concave; therefore, for any ,exist (6-4) And its parameters Each component does not decrease; Due to assumption 4 being applied Conditions, functions This can be interpreted as an uncertain boundary, where Possibly related to boundary set Related; S6-4. Assumption Given that, then according to The value determines whether the assumption is satisfied. ; make (6-5) (6-6) in , ; It is an adjustable parameter, and its value is greater than 0. The value is negatively correlated with the control effect and control force. parameter Simulating unknown parameters ,and It is governed by the following adaptive laws: (6-7) ,in for The i-th vector, , , where each term of L is nonnegative; S6-5. Since the goal of the control model is to make the dynamic system comply with the constraints proposed in equation (3-12), therefore... As a direct indicator of system performance, considering that equation (3-9) is a second-order form of constraints, then (6-8) S6-6. Assumption Given that, let (6-9) (6-10) in If it is a constant scalar, then control Defined as (6-11).

[0010] Preferably, step S7 includes dynamic analysis of the start-up phase and dynamic analysis of the shutdown phase; The dynamic analysis of the startup phase includes: S7-1-1. Design the desired S-shaped starting curve, including the displacement curve, velocity curve, and acceleration curve; S7-1-2. Analyze the approach trend, speed and error of the belt conveyor dynamic model under the action of robust control model and PID control, and compare the results of the two models. S7-1-3. Calculate the initial static tension and tension changes during the start-up process of each belt subsystem under the action of the robust control model and PID control. The tension changes include the tension fluctuation amplitude and the tension stability value. Compare the results of the two models. S7-1-4. Calculate the total power of multiple drive motor units under the action of robust control model and PID control respectively; The dynamic analysis of the parking phase includes: S7-2-1. Design the desired S-shaped stopping curve, including the displacement curve, velocity curve, and acceleration curve; S7-2-2. Analyze the difference between the actual stopping speed and the desired stopping speed, the speed fluctuation during the actual stopping process, and the difference between the results of the two control models under the action of the robust control model and PID control, respectively, for the dynamic model of the belt conveyor. S7-2-3. Analyze the calculation content of step S7-2-2 under the four working conditions of full-load free stop, no-load free stop, full-load emergency stop and no-load emergency stop respectively; S7-2-4. Calculate the stopping tension curve, tension stability value, and fluctuation amplitude of each second belt subsystem under different temperature conditions under the action of robust control model and PID control, and compare the results of the two models. S7-2-5. Calculate the slip ratio variation curves of the belt subsystem under the robust control model and PID control respectively, and compare the results of the two models.

[0011] The beneficial effects of this invention are as follows: This solution models a long-distance, large-angle belt conveyor and specifically decomposes the mismatch uncertainty of the front drive system; it designs an adaptive robust controller with underactuated constraint following, which constrains the speed of the conveyor by controlling the coordinated drive current of multiple motors; it verifies the effect of the controller through dynamic simulation, and performs dynamic analysis on factors such as speed, tension, temperature, and slip ratio to prove that the controller has good performance in terms of control speed, stability, and stability. Attached Figure Description

[0012] Figure 1 : Flowchart of the method of this invention; Figure 2 : Schematic diagram of the belt conveyor model of the present invention. Detailed Implementation

[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments: In this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0014] like Figure 1 and Figure 2 As shown, a dynamic model analysis method for a multi-motor belt conveyor includes the following steps: S1. Discretize the belt conveyor system into multiple drive motor units, tensioning devices, and multiple belt subsystems, wherein the belt subsystem includes a first belt subsystem directly connected to the drive motor and a second belt subsystem not directly connected to the drive motor; S2. For each belt subsystem, a dynamic model is established based on the permanent magnet synchronous motor model; S3. Based on the dynamic model, a constraint expectation is proposed to enable the belt conveyor to provide the expected displacement, velocity and acceleration at a certain time. S4. Decompose the uncertainties in the dynamic model and identify the matching and mismatching components. The matching components are in the same direction as the desired constraint in the vector space, while the mismatching components are perpendicular to the desired constraint. The uncertainties mainly include internal system parameters and external disturbances. Internal parameters are generally caused by measurement errors, wear during operation, etc.; external disturbances include some unpredictable environmental changes, etc. S5. Verify the impact of the mismatched components on the belt conveyor system in the uncertainty section; S6. Establish a robust control model based on the nominal part, system error, and uncertainty part of the belt conveyor dynamics model; S7. Based on actual engineering project parameters, establish a dynamic model, constraint expectations, and robust control model under actual working conditions, and verify the time and trend of the model to achieve the expected results through dynamic simulation.

[0015] Specifically, step S2 includes, S2-1. Define the number of belt subsystems as 20. Sequentially arrange the belt subsystems. Define the first to tenth belt subsystems as the conveyor belt downstream of the tail drive motor, the eleventh to thirteenth belt subsystems as the conveyor belt between the tail drive motor and the steering wheel, the fourteenth and fifteenth belt subsystems as the conveyor belt adjacent to the tension wheel in the tensioning device, and the seventeenth, eighteenth and nineteenth belt subsystems as the conveyor belt adjacent to the two head drive motors. S2-2. Establish the dynamic equations for each belt subsystem. (2-1) Where l takes values ​​of 2, 3, ..., 10, 12, 13, 16, 17; Where i represents the sequence number of each belt subsystem, and the value of i ranges from 1, 2, ..., 20. The coefficient of friction, For the quality of each belt subsystem, It is the acceleration due to gravity. ( ) represents a sign function; if the value in parentheses is positive, then... ( ) = 1, if the value in parentheses is negative, then ( ) = -1; For the stiffness of each belt subsystem, For the damping of each belt subsystem, For the displacement of each belt subsystem, For the speed of each belt subsystem, The acceleration of each belt subsystem; This indicates the tension of the first head drive motor on the 19th belt subsystem. This indicates the tension of the second head drive motor on the 18th belt subsystem. This indicates the tension of the tail drive motor on the 11th belt subsystem. This indicates the tension exerted by the tension pulley on the 14th and 15th belt subsystems; S2-3. Using a permanent magnet synchronous motor as the drive motor, and adding a permanent magnet synchronous motor model to the above dynamic equations, then... (2-2) (2-3) where is the driving force provided to the drive motor, is the motor drive current, where l takes values of 1, 2, 3; is the number of pole pairs of the drive motor, is the permanent magnetic flux linkage, is the friction coefficient, r is the radius of the motor drum, is the angular acceleration of the motor, is the angular velocity of the motor, is the motor torque.

[0016] The step S3 includes S3-1. Rearrange the dynamic model of the belt conveyor system into matrix form, then (3-1) where is the input matrix of the belt subsystem, M is the inertia matrix of the belt subsystem, C is the damping coefficient matrix of the belt subsystem, K is the stiffness coefficient matrix of the belt subsystem, and f is the friction resistance matrix of the belt subsystem; is the vector of uncertain time-varying parameters, where k is the dimension of the matrix R, where is unknown but compact, representing the potential boundary of; represents the expected designed controller, m represents the number of system inputs, and n is the degree of freedom of the system; when m = n, the system is fully actuated, and when m < n, the system is underactuated; S3-2. Considering the desired constraints, the first-order form after differentiating the desired constraints can be expressed as (3-2) where is the i-th vector of, and is obtained by differentiating the matrix C with respect to the first order. The desired constraints may be non-integrable or non-holonomic.

[0017] Differentiating the above equation with respect to t gives (3-3) where (3-4) (3-5) then (3-6) (3-7) ​​ (3-8) in Let be a column vector consisting of quantities that are independent of velocity and displacement after taking the second derivative of each constraint in the system. Expressed in matrix form (3-9) in , ,and (3-10) S3-5. Then equation (3-2) can be expressed as (3-11) Expressed in matrix form (3-12) in .

[0018] For a given A and b, if constraint (3-9) has at least one solution, then it is considered consistent.

[0019] Let constraint (3-9) be relative to If they are consistent, it means that, in principle, tasks that comply with constraints are manageable, and in mathematical relations, they need to satisfy... , where + represents the Moore-Penrose (MP) generalized inverse.

[0020] Step S4 includes, S4-1. Decompose equation (3-1) as follows: (4-1) in Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The part that is determined in the middle, namely the nominal part. Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The uncertain part; S4-2. Without considering the uncertainties, the dynamic model can be described as follows: (4-2) definition: ,but (4-3) Equation (3-9) can be rewritten as follows: (4-4) in ; S4-3. Assumption 1: There is control. This makes all If the constraints satisfy equation (4-4), then the dynamic system (4-3) is considered to be servo-constrained controllable with respect to constraint (4-4). definition , ,but (4-5) in unknown; S4-4. Assumption 2: Control Consistent with equation (4-5), one solution to equation (4-5) is: ,but (4-6) Make all .

[0021] Step S5 includes S5-1. Regarding the constraints as shown in equation (4-4), for the dynamic system (4-2) under the assumption... Servo constraints consistent with equation (4-5) if and only if (5-1) And all ,control for (5-2) Where any depends on vectors express; S5-2. Assume that for any , ,but The MP inverse always exists, therefore (5-3) Utilizing the inverse property of MP, i.e. ; S5-3. Assumption 1 ensures the feasibility of constraints by eliminating self-contradictory or unrealistic constraints; Assumption 2 ensures that the control task is consistent with the nature of the system. Equation (5-1) shows that... Each line is with Each column is orthogonal, which allows for control. exist A certain amount of component is projected into the middle; S5-4. Let , , Where I is the identity matrix, then (5-4) S5-5. Assumption 3: For each , It is reversible, making (5-5) The above formula provides a basis for E. The decomposition divides E into two parts: the matching part. ,lie in Within the value range space; the mismatched part ,lie in Outside the range space; definition and These are the matching and non-matching parts, specifically... (5-6) (5-7) Refer to equations (5-6) and (5-7); S5-6. Definition The part that does not match, that is ,matrix Each column lies within the null space of AD, that is ,but (5-8) To prove the above equation, we will use For example, we can obtain the following from equation (5-7): (5-9) The described uncertainty decomposition always places the mismatched parts within the null space of the Algebraic Array (AD). Therefore, these mismatched parts remain invisible, and only the matching parts in the range space of the AD are relevant.

[0022] Step S6 includes S6-1. Based on hypothesis 3, hypothesis 4 is proposed: Let ; Assume there exists a constant This makes all ,but (6-1) in Represents the smallest eigenvalue of the matrix. The largest eigenvalue of the matrix; S6-2. In the absence of uncertainty in M, then ,therefore and ;like There is no uncertainty of no match in it, that is ,but Therefore, choose Assumption 3 is satisfied; S6-3. Assumption 5-1: There exists a constant vector and a function This makes all ,but (6-2) in (6-3) Assumption 5-2: For each ,function It is a first-order continuously differentiable function and is concave; therefore, for any ,exist (6-4) And its parameters Each component does not decrease; Due to assumption 4 being applied Conditions, functions This can be interpreted as an uncertain boundary, where Possibly related to boundary set Related; S6-4. Assumption Given that, then according to The value determines whether the assumption is satisfied. ; make (6-5) (6-6) in , ; It is an adjustable parameter, and its value is greater than 0. The value is negatively correlated with the control effect and control force. parameter Simulating unknown parameters ,and It is governed by the following adaptive laws: (6-7) ,in for The i-th vector, , , where each term of L is nonnegative; S6-5. Since the goal of the control model is to make the dynamic system comply with the constraints proposed in equation (3-12), therefore... As a direct indicator of system performance, considering that equation (3-9) is a second-order form of constraints, then (6-8) S6-6. Assumption Given that, let (6-9) (6-10) in If it is a constant scalar, then control Defined as (6-11).

[0023] The above scheme takes into account All system matrices, namely M, C, K, f and And constant matrices A, c, and b, therefore the proposed constraints are of a general form. In the current research, The function is expressed by a single continuous law, which is about The derivative is also continuous.

[0024] Step S7 includes dynamic analysis of the start-up phase and dynamic analysis of the stop phase; The dynamic analysis of the startup phase includes: S7-1-1. Design the desired S-shaped starting curve, including the displacement curve, velocity curve, and acceleration curve; S7-1-2. Analyze the approach trend, speed and error of the belt conveyor dynamic model under the action of robust control model and PID control, and compare the results of the two models. S7-1-3. Calculate the initial static tension and tension changes during the start-up process of each belt subsystem under the action of the robust control model and PID control. The tension changes include the tension fluctuation amplitude and the tension stability value. Compare the results of the two models. S7-1-4. Calculate the total power of multiple drive motor units under the action of robust control model and PID control respectively; The dynamic analysis of the parking phase includes: S7-2-1. Design the desired S-shaped stopping curve, including the displacement curve, velocity curve, and acceleration curve; S7-2-2. Analyze the difference between the actual stopping speed and the desired stopping speed, the speed fluctuation during the actual stopping process, and the difference between the results of the two control models under the action of the robust control model and PID control, respectively, for the dynamic model of the belt conveyor. S7-2-3. Analyze the calculation content of step S7-2-2 under the four working conditions of full-load free stop, no-load free stop, full-load emergency stop and no-load emergency stop respectively; S7-2-4. Calculate the stopping tension curve, tension stability value, and fluctuation amplitude of each second belt subsystem under different temperature conditions under the action of robust control model and PID control, and compare the results of the two models. S7-2-5. Calculate the slip ratio variation curves of the belt subsystem under the robust control model and PID control respectively, and compare the results of the two models.

[0025] The present invention has been described above by way of example, but the present invention is not limited to the specific embodiments described above. Any modifications or variations made based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A dynamic model analysis method for a multi-motor belt conveyor, characterized in that, Includes the following steps: S1. Discretize the belt conveyor system into multiple drive motor units, tensioning devices, and multiple belt subsystems, wherein the belt subsystem includes a first belt subsystem directly connected to the drive motor and a second belt subsystem not directly connected to the drive motor; S2. For each belt subsystem, a dynamic model is established based on the permanent magnet synchronous motor model; S3. Based on the dynamic model, a constraint expectation is proposed to enable the belt conveyor to provide the expected displacement, velocity and acceleration at a certain time. S4. Decompose the uncertainties in the dynamic model and identify the matching and mismatching components. The matching components are in the same direction as the desired constraint in the vector space, and the mismatching components are perpendicular to the desired constraint. S5. Verify the impact of the mismatched components on the belt conveyor system in the uncertainty section; S6. Establish a robust control model based on the nominal part, system error, and uncertainty part of the belt conveyor dynamics model; S7. Based on actual engineering project parameters, establish a dynamic model, constraint expectations, and robust control model under actual working conditions, and verify the time and trend of the model to achieve the expected results through dynamic simulation.

2. The dynamic model analysis method for a multi-motor belt conveyor according to claim 1, characterized in that, Step S2 includes, S2-1. Define the number of belt subsystems as 20. Sequentially arrange the belt subsystems. Define the first to tenth belt subsystems as the conveyor belt downstream of the tail drive motor, the eleventh to thirteenth belt subsystems as the conveyor belt between the tail drive motor and the steering wheel, the fourteenth and fifteenth belt subsystems as the conveyor belt adjacent to the tension wheel in the tensioning device, and the seventeenth, eighteenth and nineteenth belt subsystems as the conveyor belt adjacent to the two head drive motors. S2-2. Establish the dynamic equations for each belt subsystem. （2-1） Where l takes values ​​of 2, 3, ..., 10, 12, 13, 16, 17; Where i represents the sequence number of each belt subsystem, and the value of i ranges from 1, 2, ..., 20. The coefficient of friction, For the quality of each belt subsystem, It is the acceleration due to gravity. ( ) represents a sign function; if the value in parentheses is positive, then... ( ) = 1, if the value in parentheses is negative, then ( ) = -1; For the stiffness of each belt subsystem, For the damping of each belt subsystem, For the displacement of each belt subsystem, For the speed of each belt subsystem, The acceleration of each belt subsystem; This indicates the tension of the first head drive motor on the 19th belt subsystem. This indicates the tension of the second head drive motor on the 18th belt subsystem. This indicates the tension of the tail drive motor on the 11th belt subsystem. This indicates the tension exerted by the tension pulley on the 14th and 15th belt subsystems; S2-3. Using a permanent magnet synchronous motor as the drive motor, and adding a permanent magnet synchronous motor model to the above dynamic equations, then... （2-2） （2-3） in The driving force provided to the drive motor The value of l is the motor drive current, and l takes the values ​​1, 2, and 3. This represents the number of pole pairs of the drive motor. It is a permanent magnet flux chain. Where is the coefficient of friction, and r is the radius of the motor drum. For the angular acceleration of the motor, The angular velocity of the motor. This represents the motor torque.

3. The dynamic model analysis method for a multi-motor belt conveyor according to claim 1, characterized in that, Step S3 includes S3-1. Rearrange the dynamic model of the belt conveyor system into matrix form, then （3-1） Among them is the input matrix of the belt subsystem, M is the inertia matrix of the belt subsystem, C is the damping coefficient matrix of the belt subsystem, K is the stiffness coefficient matrix of the belt subsystem, and f is the friction resistance matrix of the belt subsystem; is an uncertain time-varying parameter vector, where k is the dimension of matrix R, and among them is unknown but compact, representing the potential boundary of; represents the expected designed controller, m represents the number of system inputs, and n is the degree of freedom of the system; when m = n, the system is fully actuated, and when m < n, the system is in an underactuated state; S3-2. Considering the expectation constraint, the first-order form after differentiating the expectation constraint can be expressed as: （3-2） in for The i-th vector, and This is obtained by taking the first derivative of matrix C. S3-3. Differentiating the above equation with respect to t yields... （3-3） in （3-4） （3-5） but （3-6） （3-7） S3-4. Then equation (3-3) can be expressed as （3-8） in Let be a column vector consisting of quantities that are independent of velocity and displacement after taking the second derivative of each constraint in the system. Expressed in matrix form （3-9） in , ,and （3-10） S3-5. Then equation (3-2) can be expressed as （3-11） Expressed in matrix form （3-12） in .

4. The dynamic model analysis method for a multi-motor belt conveyor according to claim 3, characterized in that, Step S4 includes, S4-1. Decompose equation (3-1) as follows: （4-1） in Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The part that is determined in the middle, namely the nominal part. Let M represent the inertia matrix, C the damping coefficient matrix, K the stiffness coefficient matrix, f the friction drag matrix, and the input matrix, respectively. The uncertain part; S4-2. Without considering the uncertainties, the dynamic model can be described as follows: （4-2） definition: ,but （4-3） Equation (3-9) can be rewritten as follows: （4-4） in ; S4-3. Assumption 1: There is control. , making all If the constraints satisfy equation (4-4), then the dynamic system (4-3) is considered to be servo-constrained controllable with respect to constraint (4-4). definition , ,but （4-5） in unknown; S4-4. Assumption 2: Control Consistent with equation (4-5), one solution to equation (4-5) is: ,but （4-6） Make all .

5. The dynamic model analysis method for a multi-motor belt conveyor according to claim 4, characterized in that, Step S5 includes S5-1. Regarding the constraints as shown in equation (4-4), for the dynamic system (4-2) under the assumption... Servo constraints consistent with equation (4-5) if and only if （5-1） And all ,control for （5-2） Where any depends on vectors express; S5-2. Assume that for any , ,but The MP inverse always exists, therefore （5-3） Utilizing the inverse property of MP, i.e. ; S5-3. Assumption 1 ensures the feasibility of constraints by eliminating self-contradictory or unrealistic constraints; Assumption 2 ensures that the control task is consistent with the nature of the system. Equation (5-1) shows that... Each line is with Each column is orthogonal, which allows for control. exist A certain amount of component is projected into the middle; S5-4. Let , , Where I is the identity matrix, then （5-4） S5-5. Assumption 3: For each , It is reversible, making （5-5） The above formula provides a basis for E. The decomposition divides E into two parts: the matching part. ,lie in Within the value range space; the mismatched part ,lie in Outside the range space; definition and These are the matching and non-matching parts, specifically... （5-6） (5-7) Refer to equations (5-6) and (5-7); S5-6. Definition The part that does not match, that is ,matrix Each column lies within the null space of AD, that is ,but （5-8）。 6. The dynamic model analysis method for a multi-motor belt conveyor according to claim 5, characterized in that, Step S6 includes S6-1. Based on hypothesis 3, hypothesis 4 is proposed: Let ; Assume there exists a constant This makes all ,but （6-1） in Represents the smallest eigenvalue of the matrix. The largest eigenvalue of the matrix; S6-2. In the absence of uncertainty in M, then ,therefore and ;like There is no uncertainty of no match in it, that is ,but Therefore, choose Assumption 3 is satisfied; S6-3. Assumption 5-1: There exists a constant vector and a function This makes all ,but （6-2） in （6-3） Assumption 5-2: For each ,function It is a first-order continuously differentiable function and is concave; therefore, for any ,exist （6-4） And its parameters Each component does not decrease; Due to assumption 4 being applied Conditions, functions This can be interpreted as an uncertain boundary, where Possibly related to boundary set Related; S6-4. Assumption Given that, then according to The value determines whether the assumption is satisfied. ; make （6-5） （6-6） in , ; It is an adjustable parameter, and its value is greater than 0. The value is negatively correlated with the control effect and control force. parameter Simulating unknown parameters ,and It is governed by the following adaptive laws: （6-7） ,in for The i-th vector, , , where each term of L is nonnegative; S6-5. Since the goal of the control model is to make the dynamic system comply with the constraints proposed in equation (3-12), therefore... As a direct indicator of system performance, considering that equation (3-9) is a second-order form of constraints, then （6-8） S6-6. Assumption Given that, let （6-9） （6-10） in If it is a constant scalar, then control Defined as （6-11）。 7. The dynamic model analysis method for a multi-motor belt conveyor according to claim 1, characterized in that, Step S7 includes dynamic analysis of the start-up phase and dynamic analysis of the stop phase; The dynamic analysis of the startup phase includes: S7-1-1. Design the desired S-shaped starting curve, including the displacement curve, velocity curve, and acceleration curve; S7-1-2. Analyze the approach trend, speed and error of the belt conveyor dynamic model under the action of robust control model and PID control, and compare the results of the two models. S7-1-3. Calculate the initial static tension and tension changes during the start-up process of each belt subsystem under the action of the robust control model and PID control. The tension changes include the tension fluctuation amplitude and the tension stability value. Compare the results of the two models. S7-1-4. Calculate the total power of multiple drive motor units under the action of robust control model and PID control respectively; The dynamic analysis of the parking phase includes: S7-2-1. Design the desired S-shaped stopping curve, including the displacement curve, velocity curve, and acceleration curve; S7-2-2. Analyze the difference between the actual stopping speed and the desired stopping speed, the speed fluctuation during the actual stopping process, and the difference between the results of the two control models under the action of the robust control model and PID control, respectively, for the dynamic model of the belt conveyor. S7-2-3. Analyze the calculation content of step S7-2-2 under the four working conditions of full-load free stop, no-load free stop, full-load emergency stop and no-load emergency stop respectively; S7-2-4. Calculate the stopping tension curve, tension stability value, and fluctuation amplitude of each second belt subsystem under different temperature conditions under the action of robust control model and PID control, and compare the results of the two models. S7-2-5. Calculate the slip ratio variation curves of the belt subsystem under the robust control model and PID control respectively, and compare the results of the two models.

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