An adaptive iterative learning collaborative control method for extrusion motorized beam and extrusion rod

Abstract

The present invention discloses a method for adaptive iterative learning collaborative control of a movable beam and an extrusion rod of an extruder, which relates to the technical field of multi-agent adaptive iterative learning collaborative control and includes the following steps: constructing a dynamic model of the movable beam and the extrusion rod; determining a control target; determining a position error tracking system according to the control target, and designing a controller and a parameter update law based on adaptive iterative learning control theory; and performing theoretical simulation verification. The present invention adopts the above-mentioned method for adaptive iterative learning collaborative control of a movable beam and an extrusion rod of an extruder, regards the movable beam and the extrusion rod of the extruder as intelligent bodies, and combines adaptive iterative learning control theory to effectively realize the collaborative control of the movable beam and the extrusion rod; the method has self-regulating control capabilities, can produce products with higher precision requirements under the influence of nonlinear factors, improve production efficiency and reduce production costs, and is easy to expand and adapt to production needs of different scales.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent adaptive iterative learning collaborative control, and in particular to a method for adaptive iterative learning collaborative control of an extrusion motorized beam and an extrusion rod. Background Art

[0002] Metal extrusion has long played a vital role in industrial development. It enables the production of complex, precisely sized metal parts, effectively reducing the consumption of raw materials such as steel, thereby improving production efficiency, reducing energy consumption and costs, and enhancing product quality. It is widely used in industries such as automotive, aerospace, power electronics, construction, and military manufacturing. Currently, the extrusion process in extruders faces inconsistent performance issues due to manual operator adjustments and traditional control technologies. Industrial extruders are increasingly required to produce high-quality, low-cost products. The moving beam and extrusion rod in an extruder are crucial components in the extrusion process. The moving beam propels the extrusion rod, while the extrusion barrel holds and supports the material being extruded. In short, the performance of key extruder components, such as the moving beam and extrusion rod, directly impacts the overall performance of the extruder, requiring precise control. Furthermore, in practical metal extrusion processes, precise, efficient, and stable control of the moving beam and extrusion rod is essential to improve production efficiency, reduce energy consumption and costs, and enhance product quality. This necessitates the study of coordinated control of the moving beam and extrusion rod.

[0003] An agent is an autonomous, interactive, and responsive entity capable of perceiving its environment, making decisions, and executing actions. In a multi-agent system, multiple agents collaborate and compete to achieve a common goal. Considering the moving beam and extrusion rod as agents, a control strategy is designed to enable these agents to collaborate and achieve precise, efficient, and stable control of the extrusion process in the extruder.

[0004] Iterative learning control is an intelligent control method whose core concept is to repeatedly execute the same task, leveraging information from the previous execution or executions to modify the control inputs in the current and subsequent executions. This allows for complete tracking of the desired trajectory or target over a finite time interval, or for gradual improvement in control performance. Control laws designed using iterative learning control can effectively improve product accuracy and reduce production costs.

[0005] To address these issues, the present invention designs an adaptive iterative learning collaborative control strategy for the movable beam and extrusion rod to achieve precise control of the extrusion process. By utilizing intelligent collaborative control technology to control the position of the movable beam and the speed of the extrusion rod, the extrusion process achieves higher control precision, greater stability, higher production efficiency, and lower production costs. Summary of the Invention

[0006] The purpose of the present invention is to provide an adaptive iterative learning collaborative control method for an extrusion movable beam and an extrusion rod, so as to solve the problem that traditional control methods are difficult to meet the requirements of complex extrusion processes. During the extrusion process, the working states of the movable beam and the extrusion rod are interrelated and affect the stability of the extrusion operation and the quality of the product.

[0007] To achieve the above object, the present invention provides an adaptive iterative learning collaborative control method for an extrusion motorized beam and an extrusion rod, comprising the following steps:

[0008] Step 1: Based on the physical properties of the moving beam and the extrusion rod in the extruder and the working mode of the extrusion rod during the extrusion process, a dynamic model of the moving beam and the extrusion rod is constructed;

[0009] Step 2: Determine the control target based on the constructed dynamic model of the moving beam and the extrusion rod;

[0010] Step 3: Determine the position error tracking system according to the control target, and design the controller and parameter update law based on the adaptive iterative learning control theory;

[0011] Step 4: Conduct theoretical simulation verification.

[0012] Preferably, the dynamic model of the moving beam in step 1 is as follows:

[0013]

[0014] Where k is the number of iterations, which refers to the number of reciprocating motions, θ is the unknown nonlinear perturbation parameter, ξ(x k ,t) is the known local Lipschitz nonlinear function caused by friction, hydraulic oil characteristics and mechanical structure deformation on [0,T], T is the working time of the extrusion rod, x k (t) is the position of the moving beam at the kth iteration, x k ∈R,u k ∈R are the position state and control input of the moving beam respectively.

[0015] Preferably, the dynamic model of the extrusion rod in step 1 is as follows:

[0016]

[0017] Where x0 is the ideal position of the extrusion rod, and f(x0,t) represents the ideal nonlinear function of the extrusion rod pushing the material in the extrusion cylinder to produce a product with a certain precision, satisfying ||f(x0,t)||≤M, Where M is an unknown positive value.

[0018] Preferably, step 2 specifically includes:

[0019] The consistency error of the moving beam and the extruded rod is defined as follows:

[0020] e k (t) = x k (t)-x0(t);

[0021] The control objective is to design the input control law u k (t) and the parameter update law of the unknown parameters θ and M, so that the position of the moving beam tracks the ideal position information of the upper extrusion rod in the sense of the two norm, as shown in the following formula:

[0022]

[0023] Where L2 represents the second norm of the vector.

[0024] Preferably, step 3 specifically includes:

[0025] According to the theory of adaptive iterative learning control, the following assumptions are made:

[0026] Align the initial state of the moving beam at the beginning of each iteration so that x k (0) = x k-1 (T), at the same time, the ideal trajectory of the extrusion rod needs to satisfy the characteristic of being closed in space, so that x0(0)=x0(T), and we get, e k (0) = e k-1 (T);

[0027] The position error tracking system is as follows:

[0028]

[0029] The input control law of the designed system is:

[0030]

[0031] Where c represents an adjustable positive constant;

[0032] and The update law is:

[0033]

[0034] In the formula, the convergent series sequence {Δ k}: Satisfies the given sequence The following inequality holds: Where k∈Z + ,l(∈Z +)≥2,a(∈R)>0;γand r are adjustable design parameters, N represents an unknown positive constant to be estimated, N=M 2 ,

[0035] The initial state of the parameter update law is set to the initial state of the estimated parameters at the beginning of each iteration, as shown in the following formula:

[0036]

[0037] Preferably, in step 4, a composite energy function is used for theoretical simulation verification, as shown in the following formula:

[0038]

[0039] Where γ and r are adjustable design parameters, N represents an unknown positive constant to be estimated, N = M 2 ,

[0040] Therefore, the present invention adopts the above-mentioned adaptive iterative learning collaborative control method of the extrusion movable beam and extrusion rod, combined with the adaptive iterative learning control theory, to effectively realize the collaborative control of the movable beam and the extrusion rod; compared with the traditional control method, it has self-adjusting control capability, can produce products with higher precision requirements under the influence of nonlinear factors, improve production efficiency and reduce production costs, and is easy to expand and adapt to production needs of different scales.

[0041] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The consistency error curve of the moving beam and the extrusion rod as the number of iterations increases is provided for the simulation verification of the adaptive iterative learning cooperative control method of the extrusion moving beam and the extrusion rod of the present invention;

[0043] Figure 2 An input control law curve with increasing iteration number is provided for simulation verification of an adaptive iterative learning cooperative control method for an extrusion motor beam and an extrusion rod of the present invention;

[0044] Figure 3 A comparison diagram of the trajectory curve of the moving beam and the ideal curve of the extrusion rod after the last iteration is provided for the simulation verification of the adaptive iterative learning cooperative control method of the extrusion moving beam and the extrusion rod of the present invention. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0046] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0047] Example

[0048] See also Figure 1-3 The present invention provides an adaptive iterative learning collaborative control method for an extrusion movable beam and an extrusion rod. The control objective of this method is to design a controller for the movable beam to achieve the following in a finite time interval [0, T]:

[0049]

[0050] Among them, x k (t) is the position of the moving beam at the kth iteration, and x0 is the position information of the extrusion rod, that is, the ideal working process in which the extrusion rod can produce high-precision products.

[0051] In order to achieve the above object, the method comprises the following steps:

[0052] Step 1: Construct the dynamic model of the moving beam and extrusion rod. Specifically include:

[0053] Considering a leader-follower agent system, the dynamic model of the follower, i.e. the moving beam, is described as follows:

[0054]

[0055] Among them, k is the number of iterations, θ is the unknown nonlinear perturbation parameter, ξ(x k ,t) is the known local Lipschitz nonlinear function caused by friction, hydraulic oil characteristics and mechanical structure deformation on [0,T], T is the working time of the extrusion rod, x k (t) is the position of the moving beam at the kth iteration, x k ∈R,u k ∈R are the position state and control input of the moving beam respectively.

[0056] The dynamic model of the leader, i.e. the extrusion rod, is described as follows:

[0057]

[0058] Among them, x0 is the ideal position state of the extrusion rod, f(x0,t) represents the ideal unknown nonlinear function that the extrusion rod can use to push the material in the extrusion cylinder to produce a product with a certain precision. The unknown dynamic model that satisfies the leader is bounded, that is, ||f(x0,t)||≤M, Where M is an unknown positive value.

[0059] Step 2: Determine the control objectives based on the constructed dynamic models of the moving beam and extrusion rod. Specifically, it includes:

[0060] The consistency error of the moving beam and the extruded rod is defined as:

[0061] e k (t) = x k (t)-x0(t);

[0062] The control goal of this embodiment is to design a suitable input control law u k (t) and the parameter update law of the unknown parameters θ and M, so that the position of the moving beam can track the ideal position information of the upper extrusion rod in the sense of the two norm, that is:

[0063]

[0064] Where: L2 represents the second norm of the vector.

[0065] Step 3: Determine the position error tracking system based on the control objective, and design the controller and parameter update law based on adaptive iterative learning control theory. Specifically, it includes:

[0066] Align the initial state of the moving beam at the beginning of each iteration, that is, x k (0) = x k-1 (T), at the same time, the ideal trajectory of the extrusion rod needs to satisfy the characteristic of being closed in space, that is, x0(0)=x0(T). It is easy to obtain that e k (0) = e k-1 (T).

[0067] Using the convergent series sequence {Δ k} To deal with the bounds of unknown errors, the convergent series sequence is shown as follows:

[0068]

[0069] Where k∈Z + ,l(∈Z + )≥2,a(∈R)>0.

[0070] For a given sequence where k∈Z + ,l(∈Z + )≥2, satisfying the following inequality:

[0071]

[0072] The position error tracking system is as follows:

[0073]

[0074] The composite energy function is selected as follows:

[0075]

[0076] Among them, γ and r are adjustable design parameters, N represents an unknown positive constant to be estimated, N = M 2 ,

[0077] Taking the derivative of the above formula, we can get:

[0078]

[0079] because Then we have:

[0080]

[0081] in, Here r = Δ k The input control law of the designed system is:

[0082]

[0083] Where c represents an adjustable positive constant;

[0084] Then we have:

[0085]

[0086] Design parameter update law Then we have:

[0087]

[0088] Design parameter update law Then we have:

[0089]

[0090] The initial state of the parameter update law is set to the initial state of the estimated parameters at the beginning of each iteration, that is:

[0091]

[0092] Step 4: Based on the above conclusions, theoretical simulation verification is carried out to prove the conclusion of coordinated control of the moving beam and the extrusion cylinder. Considering the given intelligent system of the moving beam and the extrusion rod, the adaptive iterative learning control law u k (t), parameter update law and It is ensured that when the number of iterations tends to infinity, the movable beam can track the ideal position information of the upper extrusion rod in the sense of the second norm, that is, the coordinated control of the movable beam and the extrusion rod is completed. The specific steps of theoretical simulation verification include:

[0093] Easy to know, ||e k (0)|| 2 =0≤||e k (T)|| 2 ,make

[0094] but

[0095] make The above formula can be rewritten as:

[0096]

[0097] because Then we have:

[0098]

[0099] Therefore, E0(k) is bounded. And since Then we have:

[0100]

[0101] We can get:

[0102]

[0103] This shows that the movable beam and the extrusion rod have achieved the effect of coordinated control. The controller can make the two work together with high precision, improving product quality and production efficiency.

[0104] The numerical simulation verification in this implementation is as follows:

[0105] This embodiment verifies the effectiveness of the designed control strategy through numerical examples. The dynamic trajectory of the follower-moving beam is Leader - The ideal extrusion rod dynamic trajectory is The controller parameters are set to c = 8, γ = 3, r = 0.1, and the initial state of the moving beam is x k (0)=0.92.

[0106] The simulation results are as follows Figure 1-Figure 3 As shown in the figure, the simulation results prove that this method can achieve high-precision coordinated position control of the moving beam and the extrusion rod, and the tracking error converges to a small neighborhood near the zero point with the increase of the number of iterations, and the input control curve is very smooth and bounded.

[0107] Therefore, the present invention adopts the above-mentioned adaptive iterative learning collaborative control method of the extrusion movable beam and extrusion rod, combined with the adaptive iterative learning control theory, to effectively realize the collaborative control of the movable beam and the extrusion rod; compared with the traditional control method, it has self-adjusting control capability, can produce products with higher precision requirements under the influence of nonlinear factors, improve production efficiency and reduce production costs, and is easy to expand and adapt to production needs of different scales.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod, characterized in that: The following steps are involved: Step 1: Based on the physical properties of the moving beam and the extrusion rod in the extruder and the working mode of the extrusion rod during the extrusion process, a dynamic model of the moving beam and the extrusion rod is constructed; Step 2: Determine the control target based on the constructed dynamic model of the moving beam and the extrusion rod; Step 3: Determine the position error tracking system according to the control target, and design the controller and parameter update law based on the adaptive iterative learning control theory; Step 4: Conduct theoretical simulation verification; The dynamic model of the moving beam in step 1 is as follows: ； Where, is the number of iterations, which refers to the number of reciprocating motions. is the unknown nonlinear perturbation parameter, for The known local Lipschitz nonlinear function caused by friction, hydraulic oil characteristics and mechanical structure deformation, is the working time of the extrusion rod, For the dynamic Liang The position at the iteration, are the position state and control input of the moving beam respectively; The dynamic model of the extruded rod in step 1 is as follows: ； Where, is the ideal position of the extrusion rod. It represents an ideal nonlinear function that can produce a product with a certain precision by pushing the material in the extrusion cylinder with the extrusion rod, satisfying ,in, is an unknown positive value; Step 3 specifically includes: According to the theory of adaptive iterative learning control, the following assumptions are made: Align the initial state of the moving beam at the beginning of each iteration so that At the same time, the ideal trajectory of the extrusion rod needs to be closed in space. ,get, ; The position error tracking system is as follows: ； The input control law of the designed system is: ； Where, Indicates an adjustable positive constant; and The update law is: ； ； In the formula, the convergent series sequence : , which satisfies the given sequence , the following inequality holds: ,in, ; and is an adjustable design parameter, represents an unknown positive constant to be estimated, , , ; The initial state of the parameter update law is set to the initial state of the estimated parameters at the beginning of each iteration, as shown in the following formula: ； In step 4, the composite energy function is used for theoretical simulation verification, as shown in the following formula: ； Where, and is an adjustable design parameter, represents an unknown positive constant to be estimated, , , .

2. The adaptive iterative learning collaborative control method for an extrusion motor beam and an extrusion rod according to claim 1 is characterized in that: Step 2 specifically includes: The consistency error of the moving beam and the extruded rod is defined as follows: ； The control objective is to design the input control law and unknown parameters and The parameter update law is used to make the position of the moving beam track the ideal position information of the upper extrusion rod in the sense of the second norm, as shown in the following formula: ； Where, Express Find the binorm.

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