Vertical mill hydraulic control method and system based on improved dung beetle optimization algorithm

Abstract

The invention discloses a vertical mill hydraulic control method and system based on an improved dung beetle optimization algorithm, and the method comprises the steps: constructing a vertical mill machine-liquid coupling simulation model, introducing a fusion good point set and reverse learning strategy, a self-adaptive breeding theft strategy and a self-adaptive hybrid variation strategy into the dung beetle algorithm, and obtaining a simulation model; the quantization factor and the scaling factor of the fuzzy PID controller are optimized through IDBO and are applied to the hydraulic control system of the vertical mill. Control parameters can be dynamically adjusted to adapt to different working conditions and disturbances; the longitudinal fluctuation error of the grinding roller is effectively reduced; the good point set and the reverse learning strategy are fused to initialize the population, the quality and diversity of the initial population solution are improved, the premature convergence phenomenon is effectively avoided, the blank area in the search space is reduced, and the algorithm performance is improved; meanwhile, an adaptive reproduction theft strategy is introduced, the diversity of the search range is increased, the global search ability of the algorithm is improved in the earlier stage of iteration, and the algorithm is endowed with stronger local fine search ability in the later stage of iteration.

Description

Technical Field

[0001] The invention belongs to the technical field of hydraulic control of vertical mills, and relates to a hydraulic control method and system of a vertical mill based on an improved dung beetle optimization algorithm. Background Art

[0002] The hydraulic system of the vertical mill provides a buffering effect for its lifting and dropping rollers. However, the instability of the system will induce the loading and unloading impact of the mechanical body, causing unstable vibration of the grinding system, and then causing damage to the mechanical structure and transmission system. In view of the inherent complex mechanical-hydraulic coupling characteristics of the vertical mill, it has complex dynamic characteristics and closed-loop instability in the face of variable working conditions and parameter fluctuations. The targeted control strategy research in this field is still scarce and needs to be deeply explored and optimized. At the same time, the relevant parameters of the fuzzy PID controller in the existing technology are difficult to adjust, and the simulation trial and error method has the problems of blindness, long time consumption, and unsatisfactory control effect. The dung beetle algorithm can solve the optimization target of the problem based on the "rolling-laying eggs-foraging-stealing" simulation framework. It is widely used in the fields of frequency-frequency curve inversion, vibration signal prediction, path planning and fault diagnosis. Although the dung beetle search algorithm performs well in global search ability and convergence speed, when facing complex problem dimensions, the algorithm has problems such as lack of population diversity, weak global search ability, and easy to fall into local optimality. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the research on the control strategy of the hydraulic system of a vertical mill in the prior art is still scarce and needs to be deeply explored and optimized; at the same time, the search efficiency and accuracy of the fuzzy PID controller are low, and the global search ability of the dung beetle algorithm is weak and easy to fall into the local optimum. A vertical mill hydraulic control method and system based on an improved dung beetle optimization algorithm are provided.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention proposes a vertical mill hydraulic control method based on an improved dung beetle optimization algorithm, comprising:

[0006] Based on the structural force data of the vertical mill and the Lagrange equation, the system dynamics differential equations in each generalized coordinate system are obtained;

[0007] Based on the dynamic differential equation, build the ADAMS-AMESim-Simulink joint simulation model;

[0008] Improve the strategy of DBO algorithm and obtain IDBO algorithm;

[0009] The IDBO algorithm is applied to the joint simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill.

[0010] The present invention proposes a vertical mill hydraulic control method based on an improved dung beetle optimization algorithm, comprising:

[0011] An acquisition module, wherein the acquisition module acquires the system dynamics differential equations in each generalized coordinate system based on the structural force data of the vertical mill and the Lagrange equation;

[0012] A building module, wherein the building module builds an ADAMS-AMESim-Simulink joint simulation model based on dynamic differential equations;

[0013] An improvement module, wherein the improvement module performs strategy improvement on the DBO algorithm to obtain the IDBO algorithm;

[0014] The optimization module applies the IDBO algorithm to the joint simulation model, optimizes the quantization factor and the proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] The present invention proposes a vertical mill hydraulic control method based on an improved dung beetle optimization algorithm. By constructing a vertical mill machine-liquid coupling simulation model, the fusion of good point sets and reverse learning strategy, adaptive reproduction stealing strategy and adaptive hybrid mutation strategy are introduced into the dung beetle algorithm, and the quantization factor and proportional factor of the fuzzy PID controller are optimized by IDBO, and applied to the vertical mill hydraulic control system. The present invention can dynamically adjust the control parameters to adapt to different working conditions and disturbances. The longitudinal fluctuation error of the grinding roller is effectively reduced, and the effect of stabilizing the grinding force is achieved by fine-tuning the small-range fluctuation of the gap between the grinding roller and the grinding disc. The present invention integrates the good point set and the reverse learning strategy to initialize the population, improves the quality and diversity of the initial population solution, effectively avoids premature convergence, reduces the blank area in the search space, and improves the algorithm performance; at the same time, the adaptive reproduction stealing strategy is introduced to increase the diversity of the search range, improve the global search ability of the algorithm in the early iteration, and give the algorithm stronger local fine search ability in the later iteration. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0018] Figure 1The figure is a flow chart of the hydraulic control method of a vertical mill based on the improved dung beetle optimization algorithm of the present invention.

[0019] Figure 2 It is a structural schematic diagram of the hydraulic control system of a vertical mill based on the improved dung beetle optimization algorithm of the present invention.

[0020] Figure 3 It is a technical roadmap of the vertical mill hydraulic control method based on the improved dung beetle optimization algorithm of the present invention.

[0021] Figure 4 The model structure diagram of the vertical mill ((a) is a schematic diagram of the dynamic model of the vertical mill; (b) is a schematic diagram of the virtual prototype model of the vertical mill).

[0022] Figure 5 Schematic diagram of the closed-loop model of the vertical mill hydraulic system.

[0023] Figure 6 This is a schematic diagram of the vertical mill control system structure.

[0024] Figure 7 Schematic diagram of the DBO algorithm flow.

[0025] Figure 8 Schematic diagram comparing the population distribution of random initialization and good point set initialization.

[0026] Fig. 9 Schematic diagram of spiral search.

[0027] Fig.10 It is a comparison curve of nonlinear adaptive parameter change trend.

[0028] Fig.11 It is the probability density distribution diagram of Cauchy distribution, Gaussian distribution and t distribution.

[0029] Fig.12 This is the trend diagram of adaptive factor changes.

[0030] Fig.13 A visualization diagram of the Kendall coefficient.

[0031] Fig.14 This is a schematic diagram comparing the convergence curves of IDBO algorithm, DBO algorithm, BOA algorithm, TSA algorithm, SSA algorithm, PSO algorithm and WOA algorithm.

[0032] Fig.15 Schematic diagram of the fitness value change curve of the DBO algorithm and the IDBO algorithm.

[0033] Fig.16 Optimization curve diagram for control parameters.

[0034] Fig.17This is the step signal tracking result diagram.

[0035] Fig.18 This is the step signal control result diagram.

[0036] Fig.19 This is the result diagram of sinusoidal signal control.

[0037] Fig. 20 This is a comparison curve of the grinding roller longitudinal displacement error. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0039] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0041] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0042] See also Figure 1 The present invention proposes a vertical mill hydraulic control method based on an improved dung beetle optimization algorithm, comprising:

[0043] S1: Based on the structural force data of the vertical mill and the Lagrange equation, the system dynamics differential equations in each generalized coordinate system are obtained;

[0044] The vertical mill comprises a rocker arm, a swing arm, a grinding roller, a grinding roller shaft and a hydraulic cylinder; the rocker arm and the swing arm of the vertical mill are connected through the grinding roller shaft; the swing arm of the vertical mill is connected to the grinding roller; the hydraulic cylinder and the rocker arm are connected through a connecting rod.

[0045] Based on the structural force data of the vertical mill and the Lagrange equation, the system dynamics differential equations in each generalized coordinate system are derived, specifically:

[0046] Taking the hydraulic rod as an example, the center of mass is simplified and its kinetic energy T 液Potential energy U 液 for

[0047]

[0048]

[0049] Based on formula (1) and formula (2), the dynamic differential equation under the generalized coordinate q1 is obtained as follows:

[0050]

[0051] Among them, l1 is the length of the hydraulic rod, α is the angle between the rocker arm and the Z axis, β is the angle between the rocker arm and the X axis, δ is the angle between the hydraulic cylinder and the X axis, m1 is the mass of the hydraulic cylinder, m2 is the mass of the rocker arm, m3 is the mass of the rocker arm, m4 is the mass of the grinding roller, and c is the damping of the hydraulic cylinder;

[0052] The system dynamics differential equations in the generalized coordinate systems of q2, q3, θ, and Ψ are as follows:

[0053]

[0054] Among them, the generalized coordinate system q1 is selected in the XOY plane to describe the extension and contraction of the hydraulic rod, θ is selected to describe the rotation angle of the grinding roller, rocker arm and swing arm around the grinding roller axis, q2 and q3 are selected to quantify the bending deformation of the rocker arm in the XOZ plane and YOZ plane respectively, and Ψ is introduced in the XOZ plane to describe the torsional deflection angle of the rocker arm; l2 is the length of the rocker arm, l3 is the length of the swing arm, l4 is the length of the grinding roller, m e2 is the equivalent mass of the rocker arm during bending vibration.

[0055] S2: Based on the dynamic differential equation, build the ADAMS-AMESim-Simulink joint simulation model;

[0056] Based on the dynamic differential equations, the parameters and material properties of each component of the vertical mill, the force and constraint relationship is applied according to the relationship between the relatively fixed and moving parts, and the rigid-flexible coupling dynamic model of the vertical mill is established;

[0057] Based on AMESim and the hydraulic and closed-loop control principles, a vertical mill hydraulic system model was constructed;

[0058] Based on the fuzzy PID controller, the error between the actual and expected displacements and their rate of change are selected as inputs, and the valve electrical signal of the vertical mill is used as output to form a multi-input single-output Mamdani type fuzzy controller.

[0059] Based on the rigid-flexible coupling dynamics model of the mill, the hydraulic system model of the vertical mill and the Mamdani type fuzzy controller with multiple inputs and single outputs, an ADAMS-AMESim-Simulink joint simulation model was constructed.

[0060] S3: Improve the strategy of DBO algorithm and obtain IDBO algorithm;

[0061] Initialize the population based on the fusion of good point set and reverse learning strategy; map the good point set to the solution space to obtain the initialized population, implement reverse learning to generate the initial population, evaluate the fitness after merging, and select N optimal individuals to construct a new initial population;

[0062] The dynamic spiral search shape parameter is introduced in the initial population to give the dung beetle the ability to adjust the diversified paths. In order to prevent premature convergence in the middle and late stages of iteration, a nonlinear weight factor c is introduced. t ; Get the egg balls and stealing dung beetles to update their positions according to local and global optimality;

[0063] For adaptive t-distribution variation, the adaptive factor is used to constrain the degree of variation; and the Kendall rank correlation coefficient is introduced into the selective centroid reverse learning strategy to measure the correlation between two random variables. Negatively correlated and unrelated individuals are selected for reverse learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm.

[0064] Initialize the population based on the fusion of good point set and reverse learning strategy; map the good point set to the solution space to obtain the initialized population, implement reverse learning to generate the initial population, evaluate the fitness after merging, and select N optimal individuals to construct a new initial population, specifically:

[0065] The population is initialized by integrating the good point set and the reverse learning strategy to improve the convergence speed of the DBO algorithm. The reverse learning formula is:

[0066]

[0067] Where k is a 1×D random vector that obeys a normal distribution, Ub and Lb represent the upper and lower bounds of the solution space, and X represents the initial population.

[0068] The dynamic spiral search shape parameter is introduced in the initial population to give the dung beetle the ability to adjust the diversified paths. In order to prevent premature convergence in the middle and late stages of iteration, a nonlinear weight factor c is introduced. t ; Get the egg ball and stealing dung beetle according to the local and global optimal update position, specifically:

[0069] The dynamic spiral search shape parameter p is introduced to give the dung beetle the ability to adjust its path in a variety of ways, and its expression is:

[0070] β=exp(r×p)×cos(2πr) (6)

[0071]

[0072] Where: β is the spiral search factor, r is a random number in [0,1], t is the current iteration number, and T is the maximum iteration number;

[0073] In order to prevent premature convergence in the late iteration, a nonlinear weight factor is introduced to improve the global optimization performance of the algorithm by optimizing the nonlinear adaptive decreasing parameters. The expression is:

[0074]

[0075] Where: c t is the inertia weight of iteration t times, the maximum inertia weight c max =1, minimum inertia weight c min =0.001;

[0076] The egg ball and the stealing dung beetle update their positions according to the local and global optimality as follows:

[0077] B i (t+1)=c t ×X*+β×b1×[B i (t)-Lb*]+β×b2×[B i (t)-Ub*] (9)

[0078] X i (t+1)=c t ×X b +[|X i (t)-X * |+|X i (t)-X b ∣]×β×S×g (10)

[0079] Where: X * is the current local optimal solution, B i (t) is the position of the i-th egg ball of the t-th generation, which is constrained by the independent random vectors b1 and b2 (1×D dimensions) and the optimization dimension D, and is located in the spawning area [Lb*,Ub*], X i (t) is the position of the i-th thieving dung beetle in the t-th generation, X b is the global optimal solution, g is a 1×D normal random vector, and S is a constant.

[0080] For adaptive t-distribution variation, the adaptive factor is used to constrain the degree of variation; the Kendall rank correlation coefficient is introduced into the selective centroid reverse learning strategy to measure the correlation between two random variables, negatively correlated and unrelated individuals are selected for reverse learning, and the optimal individual is subjected to mixed variation disturbance to complete the improvement of the DBO algorithm. Specifically:

[0081] Introduce the adaptive t distribution mutation strategy, the mutation formula is

[0082] X bestnew =X best (1+t(T)) (11)

[0083] The degree of freedom parameter a of the t distribution variation is the number of iterations T. When the T value is small, the curve is a Cauchy distribution C(0,1). When the T value tends to infinity, the curve is a Gaussian distribution N(0,1).

[0084] The adaptive factor α is used to constrain the degree of variation, and the calculation formula is:

[0085]

[0086] The sensitive parameter f = 0.6, which defines the local development accuracy during the iteration process;

[0087] Based on the selective centroid reverse learning strategy, the Kendall rank correlation coefficient is introduced to improve the population variation ability, which is defined as

[0088]

[0089] Where N is the population individual, expressed as {x1, x2, ..., x N}, the search space dimension is D, M d is the value of the group center M in the dth dimension, X id For individual X i The reverse position of the center of gravity in d dimension;

[0090] Kendall's rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables; two D-dimensional random variables Xi = [x i1 , x i2 ...,x iD ] and X j =[x j1 , x j2 ...,x jD The Kendall rank correlation coefficient of ] is defined as

[0091]

[0092] In the formula, x i and x j is the value of the first random variable, y i and j is the value of the second random variable;

[0093] Using the selection probability P S Perform mixed mutation disturbance on the optimal individual; when P S <0.5, adaptive t distribution variation is used for large-scale perturbation; when P SWhen ≥0.5, selective center of gravity reverse learning is used to perform small-scale perturbations; the relevant definitions are as follows:

[0094]

[0095] Where, X best is the optimal dung beetle position before disturbance;

[0096] A greedy selection mechanism is used to replace the mutated solution when its fitness is better than the original solution, ensuring that the algorithm evolves to a better solution space. The definition is as follows

[0097]

[0098] Where X' best The optimal dung beetle position after greedy selection.

[0099] S4, the IDBO algorithm is applied to the joint simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill.

[0100] The scale coefficient of the fuzzy PID controller is changed, thereby changing the weight corresponding to the system error and the error change rate at different stages;

[0101] Based on the minimum integral of the absolute value of time multiplied by the error as the fitness criterion for optimization, the control system parameters are optimized to improve the steady-state accuracy of the hydraulic cylinder; the expression is

[0102]

[0103] Where t is the system operation time, and e(t) represents the amplitude difference between the actual and target displacements.

[0104] See also Figure 2 The present invention discloses a vertical mill hydraulic control system based on an improved dung beetle optimization algorithm, comprising:

[0105] An acquisition module, wherein the acquisition module acquires the system dynamics differential equations in each generalized coordinate system based on the structural force data of the vertical mill and the Lagrange equation;

[0106] A building module, wherein the building module builds an ADAMS-AMESim-Simulink joint simulation model based on dynamic differential equations;

[0107] An improvement module, wherein the improvement module performs strategy improvement on the DBO algorithm to obtain the IDBO algorithm;

[0108] The optimization module applies the IDBO algorithm to the joint simulation model, optimizes the quantization factor and the proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

[0109] Example:

[0110] See also Figure 3 The present invention discloses a hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm, comprising:

[0111] Step 1: Establish a simplified mechanical model of the vertical mill, select a generalized coordinate system, and derive the system dynamics differential equations in each generalized coordinate system based on the Lagrange equation method; use ANSYS software to make the rocker arm flexible, set the combination parameters and material properties of each component of the model in ADAMS / View, apply forces and constraints based on the relationship between the relatively fixed and moving components, and establish a rigid-flexible coupling dynamic model of the vertical mill; use AMESim to build a vertical mill hydraulic system model according to the hydraulic and closed-loop control principles; the fuzzy PID controller uses the error E between the actual and expected displacements and its rate of change EC as input, and the valve electrical signal as output to form a multi-input single-output Mamdani fuzzy controller. Based on this, an ADAMS-AMESim-Simulink joint simulation model is established.

[0112] Step 2: Improve the DBO algorithm strategy:

[0113] A) Initialize the population by integrating the good point set and the reverse learning strategy. Map the good point set to the solution space to obtain the initialized population, implement reverse learning to generate the initial population, evaluate the fitness after merging, and select the best N individuals to construct a new initial population.

[0114] B) Adaptive breeding stealing strategy. The dynamic spiral search shape parameter p is introduced to give the dung beetle the ability to adjust the diversified paths. In order to prevent premature convergence in the middle and late stages of the iteration, a nonlinear weight factor c is introduced. t The egg ball and the stealing dung beetle update their positions according to the local and global optimality;

[0115] C) Adaptive hybrid mutation strategy, using the selection probability P S Alternate between adaptive t-distribution mutation and selective centroid backpropagation learning.

[0116] a. For adaptive t-distribution variation, the adaptive factor α is used to constrain the degree of variation;

[0117] b. For the selective centroid reverse learning strategy, the Kendall rank correlation coefficient is introduced to measure the correlation between two random variables. Then, based on the formula, negatively correlated and unrelated individuals are selected for reverse learning to enhance the algorithm's mutation ability.

[0118] Reuse P S The optimal individuals are subjected to mixed mutation disturbance. The two strategies complement each other, prompting the algorithm to jump out of the local extreme value space and achieve more efficient solution space exploration. The greedy selection mechanism is adopted to replace the mutated solution when its fitness is better than the original solution, ensuring that the algorithm evolves to a better solution space.

[0119] Finally, the CEC2005 benchmark test function set is selected to solve the global optimal solution of the function for performance testing. At the same time, the IDBO algorithm is compared with the DBO algorithm, butterfly algorithm (BOA), tree seed algorithm (TSA), sparrow search algorithm (SSA), particle swarm algorithm (PSO) and whale algorithm (WOA) to verify the convergence speed and accuracy of the IDBO algorithm.

[0120] Step 3: Based on the difference between the actual and target displacement amplitudes, the time multiplied absolute error integral (ITAE) criterion is used as the optimization fitness criterion to update the individual fitness to meet the preset requirements of the fitness criterion; the IDBO algorithm is applied to the joint simulation model to quantize the fuzzy PID controller. E , K EC and the proportionality factor ΔK p , ΔK i , ΔK d Optimize; output the optimal control parameters to adjust the opening of the servo valve; compare this controller with the Fuzzy-PID controller and the PID controller in terms of step tracking test and anti-interference test, observe the fluctuation degree of the hydraulic cylinder rod displacement, and verify the anti-interference ability and steady-state characteristics of the controller. Perform a displacement response test in the joint simulation model to verify its effectiveness and feasibility in responding to the roller displacement.

[0121] 1.1 The steps to establish a simplified mechanical model of the vertical mill are as follows: the vertical mill grinding system consists of a grinding disc, a grinding roller, a rocker arm, a swing arm and a hydraulic cylinder. The system is subjected to complex and changeable forces, and the interaction between the components is significant. The bending deformation and torsional vibration of the rocker arm, the feed motion of the hydraulic cylinder, the vibration of the grinding disc, and the friction of the material will all affect the motion state of the grinding roller.

[0122] In order to construct the mechanical model, the system components are simplified as follows: 1) Each component is linearized; 2) The hydraulic cylinder is simplified to a mass-spring-damper element; 3) The rocker arm and the swing arm are regarded as mass elastic bodies, and the grinding roller is simplified to a concentrated mass; 4) The constant force and static displacement terms in the linear system are ignored; 5) F1 is set as the grinding force of the grinding roller on the material, that is, the exciting force on the grinding roller, and F2 is the sliding friction between the material and the grinding roller.

[0123] Build as Figure 4In the simplified dynamic model shown in (a), the generalized coordinate system q1 is selected in the XOY plane to describe the extension and contraction of the hydraulic rod, θ is selected to describe the rotation angle of the grinding roller, rocker arm and swing arm around the grinding roller axis, q2 and q3 are selected to quantify the bending deformation of the rocker arm in the XOZ plane and the YOZ plane respectively, and Ψ is introduced in the XOZ plane to describe the torsional deflection of the rocker arm. Among them, α is the angle between the rocker arm and the Z axis, β is the angle between the swing arm and the X axis, δ is the angle between the hydraulic cylinder and the X axis, m1 is the mass of the hydraulic cylinder, m2 is the mass of the rocker arm, m3 is the mass of the swing arm, m4 is the mass of the grinding roller, k is the stiffness of the hydraulic cylinder, and c is the damping of the hydraulic cylinder.

[0124] Taking the hydraulic rod as an example, the center of mass is simplified to the center of the rod, and its kinetic energy T 液 Potential energy U 液 for

[0125]

[0126] According to equations (1) and (2), the dynamic differential equation under the generalized coordinate q1 can be obtained as

[0127]

[0128] Where l1 is the length of the hydraulic rod.

[0129] By analogy, the system dynamics differential equations in the generalized coordinate systems of q2, q3, θ, and Ψ are shown in formula (4):

[0130]

[0131] Where: l2 is the length of the rocker arm, l3 is the length of the swing arm, l4 is the length of the grinding roller, m e2 is the equivalent mass of the rocker arm during bending vibration.

[0132] According to equations (3) and (4), the rocker arm is made flexible through ANSYS software. The combination parameters and material properties of each component of the model are set in ADAMS / View. Forces and constraints are applied according to the relationship between the relatively fixed and moving components. The virtual prototype model of the vertical mill is as follows: Figure 4 (b).

[0133] 1.2 Construction of hydraulic system closed-loop model

[0134] According to the hydraulic and closed-loop control principle of the vertical mill, the AMESim hydraulic system model is established and the software interface is set up. The hydraulic system model is as follows: Figure 5 Based on the load conditions and grinding pressure, the hydraulic cylinder module parameters are detailed in Table 1.

[0135] Table 1AMEsim simulation parameters

[0136]

[0137] The control process based on the ADAMS-AMESim-Simulink joint simulation platform is as follows: the displacement target is preset, and the AMESim hydraulic position model outputs the force signal Vf to the ADAMS mechanical model; it feeds back the hydraulic rod displacement Vx to the control system; the deviation is processed by the controller as the current input signal Vi, which drives the opening degree of the electro-hydraulic proportional valve, adjusts the hydraulic cylinder to push and pull the grinding roller load, and realizes the closed-loop control strategy.

[0138] The vertical mill grinding system is a nonlinear system with complex dynamic characteristics and closed-loop instability. In order to adapt to different working conditions and disturbances, the fuzzy controller is combined with the PID controller, and the fuzzy reasoning is performed based on the displacement deviation of the hydraulic cylinder and its rate of change, and the PID parameter increment ΔK is dynamically adjusted. p , ΔK i , ΔK d , realizing intelligent parameter setting. The structure of the control system is as follows Figure 6 shown.

[0139] In view of the significant influence of the quantization and proportional factors of the fuzzy controller on the control performance, the artificial experience method is time-consuming and the accuracy error of the determined parameters is large. The quantization and proportional factors are optimized by improving the dung beetle algorithm to ensure the optimal control performance.

[0140] The fuzzy PID controller drives the electro-hydraulic proportional valve by adjusting the output current to achieve roller displacement control. The present invention adopts two inputs (error E and its rate of change EC) and three outputs (PID parameter correction value ΔK p , ΔK i , ΔK d ) of the Mamdani type fuzzy controller. The fuzzy domain of the controller variable is [-6 -4-2 0 2 4 6], the fuzzy subset is {NB, NM, NS, ZO, PS, PM, PB}, corresponding to {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}, and the membership function adopts the triangular function. The output variable rule table is shown in Table 2.

[0141] The mathematical model of the fuzzy PID controller can be expressed as

[0142]

[0143] Where: K p , K i , K d is the initial setting value, U(t) is the output of fuzzy PID, and e(t) is the input of fuzzy PID.

[0144] Table 2 Fuzzy rules table

[0145]

[0146] 2.DBO optimization strategy

[0147] See also Figure 7 , Figure 7 The specific algorithm flow chart for the DBO optimization strategy includes the following specific steps:

[0148] a) Initialize the algorithm parameters, determine the number of dung beetle individuals N, the upper and lower limits of the position, and the maximum number of iterations T;

[0149] b) Map the good point set to the solution space to obtain the initial population, and perform reverse learning according to formula (13) to generate the initial population;

[0150] c) Calculate the fitness value of each dung beetle individual and record the global optimal position Xb and the global worst position X w and the local optimal position X*;

[0151] d) The rolling dung beetle updates its position using formula (6), the dancing dung beetle updates its position using formula (7), and the dancing foraging dung beetle updates its position using formula (10);

[0152] e) updating the dynamic spiral search shape parameter p of the breeding and stealing dung beetles, and the positions of the breeding and stealing dung beetles are updated according to equations (17) and (18);

[0153] f) The optimal dung beetle is selected according to the probability P S Update the position according to formula (25), compare the fitness values ​​of the dung beetle individuals before and after the update, and retain the dung beetle individuals with large fitness values;

[0154] g) The number of iterations t=t+1, if it is less than the maximum number of iterations, return to step b);

[0155] h) Otherwise, the iteration ends and the global optimal value and optimal path are output. At the same time, the optimal control parameter K is output. E , K EC , ΔK p , ΔK i , ΔK d .

[0156] 2.1 First, let’s introduce the DBO algorithm. The local search and global search of the dung beetle algorithm are mainly achieved by simulating the rolling, dancing, foraging, breeding and stealing behaviors of the dung beetle group. Assume that the position of the i-th dung beetle is X i =[x i1 , x i2 ...,x iD ], where i = 1, 2, 3, ..., N, and D are the dimensions of the search space. The dung beetle uses celestial information to navigate during its rolling process, and its position update formula is:

[0157]

[0158] Where t is the current number, Xi(t) is the position information of the i-th dung beetle at the t-th iteration, k is a constant value in (0,0.2] indicating the deflection coefficient; b is a constant value in (0,1); α is the natural coefficient, which is 1 or -1; Δx is the environmental change; X W is the global worst position.

[0159] When a dung beetle encounters an obstacle and cannot move forward, it will obtain a new route through dancing behavior. DBO uses the tangent function to imitate this behavior. Its position update formula is:

[0160] X i (t+1)=X i (t)+tanθX i (t)-X i (t-1)| (7)

[0161] Where θ is the deflection angle, θ∈[0,Π]. If θ is 0, Π / 2, or Π, the position of the dung beetle is not updated.

[0162] When breeding dung beetles roll dung balls to a safe area to provide a safe and protective environment for their offspring, DBO proposes a boundary selection strategy to simulate the egg-laying area of ​​breeding dung beetles, which is defined as:

[0163]

[0164] Where, X * is the current local optimal position; Lb * , Ub * are the lower and upper limits of the spawning area respectively; R = 1-t / T max , represents the dynamic selection factor; T max is the maximum number of iterations; t is the current number of iterations; Lb and Ub are the lower and upper limits of the optimization problem respectively.

[0165] From R, we can know that the area where the breeding dung beetles lay eggs is dynamically adjusted with the number of iterations, and the iterative dynamic change process of the egg ball position is:

[0166] B i (t+1)=X*+b1×[B i (t)-Lb*]+b2×[B i (t)-Ub*] (9)

[0167] In the formula, B i (t) is the position information of the i-th egg ball at the t-th iteration; b1 and b2 are independent random vectors of 1×D respectively; D is the dimension of the optimization problem.

[0168] Foraging dung beetles will look for the best foraging area. DBO proposes a boundary selection strategy to simulate the foraging area, which is defined as:

[0169]

[0170] Where, Lb b , Ub b are the lower and upper limits of the optimal foraging area, respectively, and X b is the global best position.

[0171] From R, we can see that the optimal foraging area is dynamically adjusted with the number of iterations, so the position update process of the foraging dung beetle is:

[0172] X i (t+1)=X i (t)+C1×[X i (t)-Lb b ]+C2×[X i (t)-Ub b ] (11)

[0173] Where C1 is a random number that follows a normal distribution; C2 is a random number between (0, 1).

[0174] As a competitor, the stealing dung beetle usually appears in the global optimal place, and its position is updated as follows:

[0175] X i (t+1)=X b +S×g×[|X i (t)-X * |+|X i (t)-X b ∣] (12)

[0176] Among them, X i (t) is the position information of the i-th thieving dung beetle at the t-th iteration; g is a 1×D independent random vector that obeys a normal distribution; D is the dimension of the optimization problem; S is a constant value.

[0177] 2.2 Good Point Set and Reverse Learning Strategy

[0178] The DBO algorithm is prone to premature convergence to the local optimum due to the high randomness and uncertainty of individual generation. The good point set method can efficiently use a small number of sample points to achieve uniform coverage of the search space. The present invention integrates the good point set and the reverse learning strategy to initialize the population and improve the convergence speed of the DBO algorithm. Figure 8As shown in the figure, the population size is 500, the dimension is 2, and the upper and lower bounds of the position are 1 and 100. The optimal point set method can achieve a better uniform distribution of individual positions, improve the quality and diversity of the initial population solution, effectively avoid premature convergence, and reduce the blank area in the search space to improve the algorithm's optimization performance.

[0179] Map the good point set to the solution space to get the initial population, and implement reverse learning to generate the initial population. After merging, evaluate the fitness and select the best N individuals to construct a new initial population. The reverse learning formula is

[0180]

[0181] Where k is a 1×D random vector that obeys a normal distribution, Ub and Lb represent the upper and lower bounds of the solution space, and X represents the initial population.

[0182] 2.3 Adaptive reproductive stealing strategy

[0183] The egg ball and the stealing dung beetle update their positions according to the local and global optimal respectively. The algorithm has a wide search range at the beginning, but it is easy to fall into the local optimal when accelerating convergence.

[0184] Based on the whale optimization algorithm, the present invention proposes a variable spiral search strategy and introduces a dynamic spiral search shape parameter p to endow dung beetles with diversified path adjustment capabilities. Fig. 9 This is a schematic diagram of spiral search. The expression is:

[0185] β=exp(r×p)×cos(2πr) (14)

[0186]

[0187] Where: β is the spiral search factor, r is a random number in [0,1], t is the current iteration number, and T is the maximum iteration number.

[0188] In order to prevent premature convergence in the late iteration, a nonlinear weight factor is introduced. By optimizing the nonlinear adaptive decreasing parameter, the global optimization performance of the algorithm is improved. The expression is:

[0189]

[0190] Where: c t is the inertia weight of iteration t times, the maximum inertia weight c max =1, minimum inertia weight c min =0.001.

[0191] Comparison of nonlinear adaptive parameter change trends Fig.10As shown in the figure, the nonlinear adaptive parameters show a nonlinear change trend that is fast at first and then slow. The inertia weight factor adjusts the inertia weight with a higher value and a faster decreasing rate at the beginning, which improves the global search ability of the algorithm. In the later stage, the weight is reduced to a lower level and maintains a slow decline trend, giving the algorithm a stronger local fine search ability.

[0192] The egg ball and the stealing dung beetle update their positions according to the local and global optimality as follows:

[0193] B i (t+1)=c t ×X*+β×b1×[B i (t)-Lb*]+β×b2×[B i (t)-Ub*] (17)

[0194] X i (t+1)=c t ×X b +[|X i (t)-X * |+|X i (t)-X b ∣]×β×S×g (18)

[0195] Where: X * is the current local optimal solution, B i (t) is the position of the i-th egg ball of the t-th generation, which is constrained by the independent random vectors b1 and b2 (1×D dimensions) and the optimization dimension D, and is located in the spawning area [Lb*,Ub*], X i (t) is the position of the i-th thieving dung beetle in the t-th generation, X b is the global optimal solution, g is a 1×D normal random vector, and S is a constant.

[0196] 2.4 Adaptive Hybrid Mutation

[0197] When the DBO algorithm iteratively updates the optimal solution, it is easy to fall into the local extreme value space due to the lack of a perturbation mechanism for the optimal individual. The present invention proposes an adaptive hybrid mutation strategy, which includes adaptive t-distribution mutation and selective centroid reverse learning, and perturbs the optimal solution after iteration.

[0198] Introduce the adaptive t distribution mutation strategy, the mutation formula is

[0199] X bestnew =X best (1+t(T)) (19)

[0200] The Cauchy distribution and Gaussian distribution are special cases of the t distribution. The degree of freedom parameter a of the t distribution variation is the number of iterations T. When the T value is small, the curve is a Cauchy distribution C(0,1). When the T value tends to infinity, the curve is a Gaussian distribution N(0,1). The function graphs of the three are as follows: Fig.11 As shown in the figure, with the increase of the degree of freedom parameter, the variation near the origin is significant, and the probability of large-scale disturbances is higher in the early iteration, which is conducive to global exploration; the probability of small-scale disturbances increases in the later iteration, which strengthens the local development ability of the algorithm and achieves balanced optimization of global and local search capabilities.

[0201] The application of t-distribution mutation requires the regulation of the degree of mutation. In the early stage of iteration, the mutation is strengthened to facilitate global search, and in the later stage of iteration, it is gradually reduced to improve local development. The adaptive factor α is used to constrain the degree of mutation. The calculation formula is:

[0202]

[0203] The sensitive parameter f=0.6 in the formula defines the local development accuracy during the iteration process.

[0204] The iterative curve of the adaptive factor α is as follows: Fig.12 As shown in the figure, α shows a nonlinear decreasing trend. When the number of iterations is small, α is close to 1, which is conducive to global search; when the number of iterations is large, α is close to 0, which is conducive to local search, thereby accurately balancing the search strategy.

[0205] In the later stages of algorithm iteration, the reverse learning strategy often leads to the solution space being concentrated in a small area, and the algorithm is prone to fall into a local optimal solution. Therefore, a selective centroid reverse learning strategy is proposed, and the Kendall rank correlation coefficient is introduced to improve the population variation ability, which is defined as

[0206]

[0207] Where: N is the population individual, expressed as {x1, x2, ..., x N}, the search space dimensions are D, M d is the value of the group center M in the dth dimension, X id For individual X i The reverse position of the center of gravity in d dimension.

[0208] Kendall's rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables. i1 , x i2 ...,x iD ] and X j =[x j1 , x j2 ...,x jDThe Kendall rank correlation coefficient of ] is defined as

[0209]

[0210] Where: x i and x j is the value of the first random variable, y i and j is the value of the second random variable.

[0211] Suppose a 100×5 random data matrix is ​​generated and the Kendall coefficient matrix is ​​visualized as follows: Fig.13 As shown. The τ value reveals the correlation between random variables. When τ = 1, it indicates that the two random variables are completely positively correlated and their changing trends are the same; when τ = -1, it indicates that the two random variables are negatively correlated and their changing trends are completely opposite; and when τ tends to 0, it indicates that there is no correlation between the two variables.

[0212] When the Kendall rank correlation coefficient is applied to the dung beetle optimization algorithm, the coefficient is used to measure the correlation between individuals and the best individual, and negatively correlated and unrelated individuals are selected for reverse learning strategy to enhance the algorithm's mutation ability.

[0213] Using the selection probability P S Perform mixed mutation disturbance on the optimal individuals. S <0.5, adaptive t distribution variation is used for large-scale perturbation; when P S When ≥0.5, selective center of gravity reverse learning is used to perform small-scale perturbations. The two strategies complement each other, prompting the algorithm to jump out of the local extreme value space and achieve more efficient solution space exploration. The relevant definitions are as follows:

[0214]

[0215] Where X best is the optimal dung beetle position before disturbance.

[0216] A greedy selection mechanism is used to replace the mutated solution when its fitness is better than the original solution, ensuring that the algorithm evolves to a better solution space. The definition is as follows

[0217]

[0218] Where X' best The optimal dung beetle position after greedy selection.

[0219] 2.5 Algorithm Testing

[0220] The CEC2005 benchmark test set is used to evaluate the performance of the IDBO algorithm in solving the global optimal solution, and compared with the DBO algorithm, the butterfly algorithm (BOA), the tree seed algorithm (TSA), the sparrow search algorithm (SSA), the particle swarm algorithm (PSO) and the whale algorithm (WOA) to verify the convergence speed and accuracy. It covers single-peak (F4, F7), multi-peak (F8, F10), and fixed multi-peak (F15, F23) function types.

[0221] Fig.14 is the iterative convergence curve of each test function. In test functions F4 and F10, the IDBO algorithm provides a favorable initial state for the population by relying on the good point set and reverse learning strategy, and combines the adaptive hybrid mutation strategy to quickly and accurately converge to the global optimum, effectively avoiding the local extreme value space. In F7 and F8, the adaptive breeding stealing strategy enables the IDBO algorithm to intelligently adjust the search path, and can jump out of the local extreme value space with fewer iterations. In F15, the iteration curve of the IDBO algorithm steadily approaches the global optimal solution, effectively avoiding falling into the local optimal solution and obtaining the optimal fitness value. In F23, although the convergence accuracy of the IDBO algorithm is slightly worse, it can quickly jump out of the local optimum, and the convergence speed is faster than that of the DBO algorithm. In summary, the three strategies significantly improve the convergence performance and accuracy of the DBO algorithm, and the IDBO algorithm has a strong generalization ability.

[0222] 3. IDBO algorithm optimizes controller parameters The control performance of the fuzzy PID controller depends on the internal parameters of the controller. The present invention uses the IDBO algorithm to optimize the quantization factor K E , K EC and the proportionality factor ΔK p , ΔK i , ΔK d to ensure optimal control performance.

[0223] 3.1 Optimization variables

[0224] By changing the scale coefficient of the fuzzy PID controller, the error of the system at different stages and the weight corresponding to the error change rate can be changed. The value range of each optimization variable is shown in Table 3.

[0225] Table 3 Upper and lower limits of optimization variables

[0226]

[0227] 3.2 Fitness Function

[0228] The minimum ITAE is used as the fitness criterion for optimization. The basis is that the grinding force fluctuation period is short and the amplitude is large during the grinding process. Therefore, the hydraulic system needs to have a fast transient response to buffer the impact between the grinding roller and the grinding disc. This algorithm aims to optimize the control system parameters and improve the steady-state accuracy of the hydraulic cylinder. The expression is

[0229]

[0230] Where: t is the system operation time, and e(t) represents the amplitude difference between the actual and target displacements.

[0231] 3.3 Control parameter optimization process

[0232] In order to reflect the objectivity of the comparison, the IDBO algorithm and the DBO algorithm are iteratively optimized with the same number of iterations, population size and performance indicators. The fitness value change curve is shown in Fig.15 , the control parameter optimization curve is shown in Fig.16 , specific parameter values ​​are shown in Table 4.

[0233] During the iteration process, the DBO algorithm fell into the local solution space too early, causing the premature phenomenon of the population, and converged to the optimal solution of 4.9758 after 87 iterations. The IDBO algorithm continued to jump out of the local solution space with the increase in the number of iterations, and converged to the optimal solution of 4.9749 after 25 iterations, and obtained better control parameters, which improved the performance of the system. This shows that the IDBO algorithm has a good convergence speed and optimization ability in the parameter tuning process of this controller.

[0234] Table 4 Comparison of iterative optimization results

[0235]

[0236] 4 Simulation analysis and results

[0237] In order to verify the control effect of IDBO-Fuzzy-PID controller on the hydraulic system of the vertical mill, a comparative simulation was carried out with the Fuzzy-PID controller and the PID controller. The simulation time was set to 20s and the simulation step size was set to 0.01.

[0238] 4.1 System step tracking test

[0239] When the grinding pressure of the system is constant and the working displacement of the equilibrium point is set to 50mm, the simulation experiment uses a step input signal and introduces a step external load signal at the 10th second to simulate the sudden increase in grinding pressure caused by the presence of hard materials during the grinding process, resulting in a sudden increase in the displacement of the hydraulic rod. The step response curves of the three controllers are shown in Figure 1. Fig.13 The comparison of the response results is shown in Table 5.

[0240] from Fig.17 It can be seen from Table 5 that the adjustment time of the PID controller is as long as 5.294s, and the overshoot is 8.568%, indicating that the PID controller is not suitable for this parameter time-varying system. The overshoot and adjustment time of the Fuzzy-PID controller are better than those of the PID controller. In contrast, the adjustment time of the IDBO-Fuzzy-PID controller is 0.743s, and it can basically reach the target displacement without overshoot. For step external load disturbances, the IDBO-Fuzzy-PID controller has the best anti-interference ability, followed by the Fuzzy-PID controller, and the PID controller has the worst anti-interference effect. In summary, the IDBO-Fuzzy-PID controller has an absolute advantage in response speed and control accuracy, and has strong robustness.

[0241] Table 5 Comparison of simulation results of three controllers

[0242]

[0243] 4.2 System Anti-interference Test

[0244] The hydraulic control system of the vertical mill is accompanied by many interference factors in the actual process, such as component aging, hard material adhesion during the grinding process, causing grinding pressure fluctuations, or noise interference in the sensor feedback signal. In order to verify the feasibility of the controller, it is necessary to conduct anti-interference tests on this system to ensure its stable operation under complex working conditions.

[0245] 4.2.1 Step signal simulation

[0246] When the grinding pressure of the system is constant and the working displacement of the equilibrium point is 50 mm, the simulation results obtained by applying random white noise to the feedback are as follows: Fig.18 After the controller is disturbed, the displacement oscillation amplitude of the hydraulic rod of the PID controller is 0.879 mm, the displacement oscillation amplitude of the Fuzzy-PID controller is 0.463 mm, and that of the IDBO-Fuzzy-PID controller is significantly reduced to 0.252 mm. The anti-interference ability is greatly improved, thereby improving the longitudinal displacement error of the grinding roller.

[0247] 4.2.2 Sinusoidal signal simulation

[0248] The above object is a linear model based on a step signal, which is limited to performance testing near a specific working point. Given that the system parameters change dynamically with the grinding process under actual working conditions, it is necessary to conduct anti-interference testing on the nonlinear model. The experimental results obtained by applying random white noise to the feedback using a sinusoidal input signal are as follows: Fig.19Compared with the fuzzy-PID controller and the PID controller, the stability of the IDBO-Fuzzy-PID controller is not significantly affected under disturbance, and its sine wave tracking performance is optimal. This shows that it has significant advantages in steady-state accuracy, good robustness, and meets the high standard requirements of the control system.

[0249] 4.3 Displacement response test

[0250] The actual working conditions require that the hydraulic system of the vertical mill achieves self-stabilization and balance, and maintains a constant grinding force during the grinding process. The fluctuation of the grinding force triggers the response of the hydraulic system, which in turn affects the dynamic change of the gap between the grinding roller and the grinding disc. The gap needs to be within a reasonable range to avoid the violent fluctuation of the grinding roller and affect the stability of the grinding process. The designed controller is applied to the joint simulation model of the vertical mill to verify its effectiveness and feasibility in responding to the displacement of the grinding roller.

[0251] like Fig. 20 As shown in the figure, the displacement error generated by the Fuzzy-PID controller is 0.3mm, while the IDBO-Fuzzy-PID controller reduces the displacement error to 0.1mm, indicating that the IDBO-Fuzzy-PID controller effectively suppresses the longitudinal fluctuation of the grinding roller, and at the same time achieves the stabilization of the grinding force by fine-tuning the slight fluctuation of the gap between the grinding roller and the grinding disc.

[0252] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A vertical mill hydraulic control method based on an improved dung beetle optimization algorithm, characterized in that: include: Based on the structural force data of the vertical mill and the Lagrange equation, the system dynamics differential equations in each generalized coordinate system are obtained; Based on the dynamic differential equation, build the ADAMS-AMESim-Simulink joint simulation model; Improve the strategy of DBO algorithm and obtain IDBO algorithm; The IDBO algorithm is applied to the joint simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill.

2. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The vertical mill comprises a rocker arm, a swing arm, a grinding roller, a grinding roller shaft and a hydraulic cylinder; the rocker arm of the vertical mill is connected to the swing arm; the swing arm of the vertical mill is connected to the grinding roller; the hydraulic cylinder is connected to the rocker arm through a connecting rod.

3. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: Based on the structural force data of the vertical mill and the Lagrange equation, the system dynamics differential equations in each generalized coordinate system are derived, which are specifically: The center of mass of the hydraulic rod is simplified, and its kinetic energy T 液 Potential energy U 液 for: Based on formula (1) and formula (2), the dynamic differential equation under the generalized coordinate q1 is: Among them, l1 is the length of the hydraulic rod, α is the angle between the rocker arm and the Z axis, β is the angle between the rocker arm and the X axis, δ is the angle between the hydraulic cylinder and the X axis, m1 is the mass of the hydraulic cylinder, m2 is the mass of the rocker arm, m3 is the mass of the rocker arm, m4 is the mass of the grinding roller, and c is the damping of the hydraulic cylinder; The system dynamics differential equations in the generalized coordinate systems of q2, q3, θ, and Ψ are shown in formula (4): Among them, the generalized coordinate system q1 is selected in the XOY plane to describe the extension and contraction of the hydraulic rod, θ is selected to describe the rotation angle of the grinding roller, rocker arm and swing arm around the grinding roller axis, q2 and q3 are selected to quantify the bending deformation of the rocker arm in the XOZ plane and YOZ plane respectively, and Ψ is introduced in the XOZ plane to describe the torsional deflection angle of the rocker arm; l2 is the length of the rocker arm, l3 is the length of the swing arm, l4 is the length of the grinding roller, m e2 is the equivalent mass of the rocker arm during bending vibration.

4. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The ADAMS-AMESim-Simulink joint simulation model is constructed based on the dynamic differential equation, specifically: Based on the dynamic differential equations, the parameters and material properties of each component of the vertical mill, the force and constraint relationship is applied according to the relationship between the relatively fixed and moving parts, and the rigid-flexible coupling dynamic model of the vertical mill is established; Based on AMESim and the hydraulic and closed-loop control principles, a vertical mill hydraulic system model was constructed; Based on the fuzzy PID controller, the error between the actual and expected displacements and their rate of change are selected as inputs, and the valve electrical signal of the vertical mill is used as output to form a multi-input single-output Mamdani type fuzzy controller. Based on the rigid-flexible coupling dynamics model of the mill, the hydraulic system model of the vertical mill and the Mamdani type fuzzy controller with multiple inputs and single outputs, an ADAMS-AMESim-Simulink joint simulation model was constructed.

5. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The strategy improvement of the DBO algorithm is performed to obtain the IDBO algorithm, specifically: Initialize the population based on the fusion of good point set and reverse learning strategy; map the good point set to the solution space to obtain the initialized population, implement reverse learning to generate the initial population, evaluate the fitness after merging, and select N optimal individuals to construct a new initial population; The dynamic spiral search shape parameter is introduced in the initial population to give the dung beetle the ability to adjust the diversified paths. In order to prevent premature convergence in the middle and late stages of iteration, a nonlinear weight factor c is introduced. t ; Get the egg balls and stealing dung beetles to update their positions according to local and global optimality; For adaptive t-distribution variation, the adaptive factor is used to constrain the degree of variation; and the Kendall rank correlation coefficient is introduced into the selective centroid reverse learning strategy to measure the correlation between two random variables. Negatively correlated and unrelated individuals are selected for reverse learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm.

6. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The method of initializing the population based on the fusion of the good point set and the reverse learning strategy; mapping the good point set to the solution space to obtain the initialized population, performing reverse learning to generate the initial population, evaluating the fitness after merging, and selecting N optimal individuals to construct a new initial population is as follows: The population is initialized by integrating the good point set and the reverse learning strategy to improve the convergence speed of the DBO algorithm. The reverse learning formula is: Where k is a 1×D random vector that obeys a normal distribution, Ub and Lb represent the upper and lower bounds of the solution space, and X represents the initial population.

7. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The dynamic spiral search shape parameter is introduced into the initial population to give the dung beetle a diversified path adjustment capability; in order to prevent premature convergence in the middle and late stages of iteration, a nonlinear weight factor c is introduced t ; Get the egg ball and stealing dung beetle to update the position according to the local and global optimal, specifically: The dynamic spiral search shape parameter p is introduced to give the dung beetle the ability to adjust its path in a variety of ways. The expression is: β=exp(r×p)×cos(2πr) (6) Where: β is the spiral search factor, r is a random number in [0,1], t is the current iteration number, and T is the maximum iteration number; In order to prevent premature convergence in the middle and late stages of iteration, a nonlinear weight factor is introduced to improve the global optimization performance of the algorithm by optimizing the nonlinear adaptive decreasing parameters. The expression is: Where: c t is the inertia weight of iteration t times, the maximum inertia weight c max =1, minimum inertia weight c min =0.001; The egg ball and the stealing dung beetle update their positions according to the local and global optimality as follows: B i (t+1)=c t ×X*+β×b1×[B i (t)-Lb*]+β×b2×[B i (t)-Ub*] (9) X i (t+1)=c t ×X b +[|X i (t)-X * |+|X i (t)-X b ∣]×β×S×g (10) Where: X * is the current local optimal solution, B i (t) is the position of the i-th egg ball of the t-th generation, which is constrained by the independent random vectors b1 and b2 (1×D dimensions) and the optimization dimension D, and is located in the spawning area [Lb*,Ub*], X i (t) is the position of the i-th thieving dung beetle in the t-th generation, X b is the global optimal solution, g is a 1×D normal random vector, and S is a constant.

8. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: For the adaptive t-distribution variation, the adaptive factor is used to constrain the variation degree; and the Kendall rank correlation coefficient is introduced into the selective centroid reverse learning strategy to measure the correlation between two random variables, negatively correlated and unrelated individuals are selected for reverse learning, and the optimal individual is subjected to mixed variation disturbance to complete the improvement of the DBO algorithm, specifically: An adaptive t-distribution mutation strategy is introduced, and the mutation formula is: X bestnew =X best (1+t(T)) (11) The degree of freedom parameter a of the t distribution variation is the number of iterations T. When the T value is small, the curve is a Cauchy distribution C(0,1). When the T value tends to infinity, the curve is a Gaussian distribution N(0,1). The adaptive factor α is used to constrain the degree of variation, and the calculation formula is: The sensitive parameter f = 0.6, which defines the local development accuracy during the iteration process; Based on the selective centroid reverse learning strategy, the Kendall rank correlation coefficient is introduced to improve the population variation ability, which is defined as: Where N is the population individual, expressed as {x1, x2, ..., x N }, the search space dimension is D, M d is the value of the group center M in the dth dimension, X id For individual X i The reverse position of the center of gravity in d dimension; Kendall's rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables; two D-dimensional random variables Xi = [x i1 , x i2 ...,x iD ] and X j =[x j1 , x j2 ...,x jD The Kendall rank correlation coefficient of ] is defined as: In the formula, x i and x j is the value of the first random variable, y i and j is the value of the second random variable; Using the selection probability P S Perform mixed mutation disturbance on the optimal individual; when P S <0.5, adaptive t distribution variation is used for large-scale perturbation; when P S When ≥0.5, selective center of gravity reverse learning is used to perform small-scale perturbations; the relevant definitions are as follows: Where, X best is the optimal dung beetle position before disturbance; A greedy selection mechanism is used to replace the mutated solution when its fitness is better than the original solution, ensuring that the algorithm evolves to a better solution space. The definition is as follows: Where X' best The optimal dung beetle position after greedy selection.

9. The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to claim 1 is characterized in that: The quantization factor and the proportional factor of the fuzzy PID controller are optimized, the optimal control parameters are output, and the hydraulic control system of the vertical mill is optimized, specifically: The scale coefficient of the fuzzy PID controller is changed, thereby changing the weight corresponding to the system error and the error change rate at different stages; Based on the minimum integral of the absolute value of time multiplied by the error as the fitness criterion for optimization, the control system parameters are optimized to improve the steady-state accuracy of the hydraulic cylinder; the expression is: Where t is the system operation time, and e(t) represents the amplitude difference between the actual and target displacements.

10. A vertical mill hydraulic control method based on an improved dung beetle optimization algorithm is characterized in that: include: An acquisition module, wherein the acquisition module acquires the system dynamics differential equations in each generalized coordinate system based on the structural force data of the vertical mill and the Lagrange equation; A building module, wherein the building module builds an ADAMS-AMESim-Si mulink joint simulation model based on dynamic differential equations; An improvement module, wherein the improvement module performs strategy improvement on the DBO algorithm to obtain the IDBO algorithm; The optimization module applies the IDBO algorithm to the joint simulation model, optimizes the quantization factor and the proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

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