Adaptive iterative learning cooperative control method for movable beam and extrusion rod of extrusion machine

Abstract

The invention discloses a self-adaptive iterative learning cooperative control method for a movable beam and an extrusion rod of an extrusion machine, and relates to the technical field of multi-agent self-adaptive iterative learning cooperative control, and the method comprises 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 a control target, and designing a controller and a parameter updating law based on an adaptive iterative learning control theory; and theoretical simulation verification is carried out. According to the adaptive iterative learning cooperative control method for the movable beam and the extrusion rod of the extruding machine, the movable beam and the extrusion rod of the extruding machine are regarded as intelligent agents, and cooperative control over the movable beam and the extrusion rod is effectively achieved in combination with the adaptive iterative learning control theory; the device has a self-adjusting control capability, can produce products with higher precision requirements under the influence of non-linear factors, improves the production efficiency, reduces the production cost, is easy to expand, and meets the production requirements of different scales.

Description

Technical Field

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

[0002] The metal extrusion process has always played an important role in the development of industry. Using it, metal parts with complex shapes and precise dimensions can be produced in industrial production, which can effectively reduce the consumption of raw materials such as steel, improve production efficiency, reduce energy consumption and costs, and enhance product quality. It is widely used in industries such as the automotive industry, aerospace, power electronics, construction, and military manufacturing. At present, the extrusion process of the extruder faces the problem of poor consistency due to manual adjustment by operators and traditional control technologies. In industry, extruders are increasingly required to produce high-quality and low-cost products. The moving beam and the extrusion rod in the extruder are important equipment in the extrusion process. The moving beam is responsible for pushing the extrusion rod to perform the extrusion operation, while the extrusion cylinder is a container for accommodating and supporting the material to be extruded. In short, the working performance of key components such as the moving beam and the extrusion rod of the extruder directly affects the overall working performance of the extruder, and precise control of them is required. At the same time, in the actual metal extrusion process, in order to improve production efficiency, reduce energy consumption and costs, and enhance product quality, precise, efficient, and stable control of the moving beam and the extrusion rod needs to be achieved, and for this, the cooperative control of the moving beam and the extrusion rod must be studied.

[0003] An agent is an entity with autonomy, interactivity, and reactivity, capable of perceiving the environment, making decisions, and performing actions. In a multi-agent system, multiple agents achieve common goals through cooperation and competition. Regarding the moving beam and the extrusion rod as agents, by designing control strategies, the agents can cooperate with each other to jointly complete the precise, efficient, and stable control during the extrusion process of the extruder.

[0004] Iterative learning control is an intelligent control method. Its core idea is to continuously repeat the execution of the same task, and use the information in the previous execution or previous several executions to correct the control input in the current and subsequent executions, so as to achieve complete tracking of the desired trajectory or target or gradual improvement of control performance in a finite time interval. The control law designed using iterative learning control can effectively improve the precision of the produced products and reduce production costs.

[0005] Aiming at the above problems, the present invention designs an adaptive iterative learning cooperative control strategy for the moving beam and the extrusion rod to achieve precise control of the extrusion process. Using intelligent cooperative control technology to control the position of the moving beam and the speed of the extrusion rod, the control accuracy of the extrusion process is higher, the stability is stronger, the production efficiency is higher, and the production cost is lower. Summary of the Invention

[0006] The object of the present invention is to provide a self - adaptive iterative learning cooperative control method for the moving beam and extrusion rod of an extruder, 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 moving 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 a self - adaptive iterative learning cooperative control method for the moving beam and extrusion rod of an extruder, including the following steps:

[0008] Step 1: Construct a dynamic model of the moving beam and the extrusion rod according to 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;

[0009] Step 2: Determine the control objective according to the constructed dynamic model of the moving beam and the extrusion rod;

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

[0011] Step 4: Conduct theoretical simulation verification.

[0012] Preferably, the dynamic model of the moving beam in Step 1 is shown as the following formula:

[0013]

[0014] In the formula, k is the number of iterations, here referring to the number of reciprocating motions, θ is an unknown non - linear disturbance parameter, ξ(x k ,t) is a known locally Lipschitz non - linear function on [0,T] brought by friction, hydraulic oil characteristics and mechanical structure deformation, T is the working time of the extrusion rod, x k (t) is the position of the moving beam at the k - th iteration, x k ∈R, u k ∈R are respectively the position state and control input of the moving beam.

[0015] Preferably, the dynamic model of the extrusion rod in Step 1 is shown as the following formula:

[0016]

[0017] In the formula, x 0 is the ideal position state of the extrusion rod, f(x 0 ,t) represents an ideal non - linear function for the extrusion rod to push the material in the extrusion barrel to produce a product with a certain specific accuracy, satisfying ||f(x 0 ,t)||≤M, where M is an unknown positive value.

[0018] Preferably, step 2 specifically includes:

[0019] Define the consistency error between the moving beam and the extrusion rod as shown in the following formula:

[0020] e k (t) = x k (t) - x 0 (t);

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

[0022]

[0023] In the formula, L 2 represents taking the two-norm of this vector.

[0024] Preferably, step 3 specifically includes:

[0025] Make the following assumptions according to the theory of adaptive iterative learning control:

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

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

[0028]

[0029] Design the input control law of the system as:

[0030]

[0031] In the formula, c represents an adjustable positive constant;

[0032] and The update laws of are:

[0033]

[0034] In the formula, the convergent series sequence {Δ k}: Satisfy the following inequality for the given sequence The following inequality holds: where \(k\in Z\) + , \(l\in Z\) + )\(\geq2\), \(a\in R\gt0\); \(\gamma\) and \(r\) are adjustable design parameters, \(N\) represents an unknown positive constant to be estimated, \(N = M\) 2 ,

[0035] The setting of the initial state of the parameter update law is the initial state of the estimated parameter 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 \(\gamma\) 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 cooperative control method for the moving beam and the extrusion rod of an extruder, combines the adaptive iterative learning control theory, and effectively realizes the cooperative control of the moving beam and the extrusion rod; compared with the traditional control method, it has self-adjusting control ability, can produce products with higher precision requirements under the influence of non-linear factors, improve production efficiency and reduce production costs, and is easy to expand and adapt to different scales of production requirements.

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Brief Description of the Drawings

[0042] Figure 1 The curve of the consistency error between the moving beam and the extrusion rod with the increase of the iteration number provided for the simulation verification of an adaptive iterative learning cooperative control method for the moving beam and the extrusion rod of an extruder according to the present invention;

[0043] Figure 2 The input control law curve with the increase of the iteration number provided for the simulation verification of an adaptive iterative learning cooperative control method for the moving beam and the extrusion rod of an extruder according to the present invention;

[0044] Figure 3 The comparison diagram of the moving beam trajectory curve and the ideal curve of the extrusion rod after the end of the last iteration provided for the simulation verification of an adaptive iterative learning cooperative control method for the moving beam and the extrusion rod of an extruder according to the present invention. Detailed Embodiment

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

[0046] Unless otherwise defined, the technical terms or scientific terms used in this invention shall have the ordinary meanings as understood by those of ordinary skill in the art to which this invention pertains. The terms "first", "second" and similar terms used in this invention do not denote any order, quantity or importance, but are only used to distinguish different components. Words such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to indicate relative position relationships, and when the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0047] Embodiment

[0048] Please refer to Figures 1-3 , the present invention provides a collaborative control method for adaptive iterative learning of the moving beam and the extrusion rod of an extrusion machine. The control objective of this method is to design a controller for the moving beam to achieve the following within a finite time interval [0, T]:

[0049]

[0050] where, x k (t) is the position of the moving beam at the k-th iteration, and x 0 is the position information of the extrusion rod, that is, the ideal working process for the extrusion rod to produce high-precision products.

[0051] To achieve the above objective, this method includes the following steps:

[0052] Step 1: Construct the dynamic models of the moving beam and the extrusion rod. Specifically, it includes:

[0053] Considering the leader-follower agent system, the dynamics model of the follower - that is, the moving beam - is described as follows:

[0054]

[0055] where, k is the iteration number, θ is the unknown non-linear perturbation parameter, ξ(x k , t) is a known locally Lipschitz non-linear function on [0, T] brought by friction, hydraulic oil characteristics and mechanical structure deformation, T is the working time of the extrusion rod, x k (t) is the position of the moving beam at the k-th iteration, and x k ∈ R, u k ∈ R are respectively the position state and control input of the moving beam.

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

[0057]

[0058] where x 0 is the ideal position state of the extrusion rod, and f(x 0 , t) represents an ideal unknown nonlinear function for the extrusion rod to push the material in the extrusion cylinder to produce a product with a certain specific precision. It satisfies that the unknown dynamic model of the leader is bounded, i.e., ||f(x 0 , t)|| ≤ M, where M is an unknown positive value.

[0059] Step 2: According to the constructed dynamic models of the moving beam and the extrusion rod, determine the control objectives. Specifically, it includes:

[0060] Define the consistency error between the moving beam and the extrusion rod as:

[0061] e k (t) = x k (t) - x 0 (t);

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

[0063]

[0064] In the formula: L 2 represents taking the two-norm of this vector.

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

[0066] Align the initial state of the moving beam at the beginning of each iteration, i.e., 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, i.e., x 0 (0) = x 0 (T). It is easy to obtain that e k (0) = e k-1 (T).

[0067] Use the convergent series sequence {Δ k} to handle the bound of the unknown error. The convergent series sequence is shown as follows:

[0068]

[0069] where \(k\in Z\) + , \(l(\in Z\) + ) \(\geq 2\), \(a(\in R)>0\).

[0070] For a given sequence where \(k\in Z\) + , \(l(\in Z\) + ) \(\geq 2\), the following inequality is satisfied:

[0071]

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

[0073]

[0074] Select the composite energy function as follows:

[0075]

[0076] where \(\gamma\) and \(r\) are adjustable design parameters, \(N\) represents a positive constant to be estimated and unknown, \(N = M\) 2 ,

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

[0078]

[0079] Since then we have:

[0080]

[0081] where, Here \(r=\Delta\) 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] The design parameter update law Then we have:

[0087]

[0088] The 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, i.e.:

[0091]

[0092] Step 4: According to the above conclusions, conduct theoretical simulation verification to give a proof of the collaborative control conclusion of the moving beam and the extrusion cylinder. Considering the given agent system of the moving beam and the extrusion rod, the adaptive iterative learning control law u k (t), the parameter update law and guarantee that when the number of iterations tends to infinity, the moving beam can track the ideal position information of the extrusion rod in the sense of the two-norm, that is, the collaborative control of the moving beam and the extrusion rod is completed The specific steps of the theoretical simulation verification include:

[0093] It is easy to know that ||e k (0)|| 2 = 0 ≤ ||e k (T)|| 2 Let

[0094] Then

[0095] Let Then the above formula can be rewritten as:

[0096]

[0097] Since Then there is:

[0098]

[0099] Therefore, it can be obtained that E 0 (k) is bounded. And since Then there is:

[0100]

[0101] It can be obtained that:

[0102]

[0103] This shows that the moving beam and the extrusion rod achieve the effect of collaborative control, and 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 - the moving beam is The dynamic trajectory of the leader - the ideal extrusion rod is The controller parameters are set as 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 Figures 1-3 shown. The simulation results prove that the proposed method can achieve high - precision cooperative position control of the moving beam and the extrusion rod, and the tracking error converges to a small neighborhood near zero as the number of iterations increases. The input control curve is very smooth and bounded.

[0107] Therefore, the present invention adopts the above - mentioned adaptive iterative learning cooperative control method for the moving beam and the extrusion rod of an extruder, combines the theory of adaptive iterative learning control, and effectively realizes the cooperative control of the moving beam and the extrusion rod. Compared with the traditional control method, it has self - adjusting control ability, can produce products with higher precision requirements under the influence of non - linear factors, improve production efficiency and reduce production costs, and is easy to expand and adapt to different scales of production requirements.

[0108] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements do not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An adaptive iterative learning collaborative control method for an extrusion motor beam and an extrusion rod, characterized in that: The following steps are involved: Step 1: According to 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 according to 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.

2. The method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod according to claim 1, characterized in that: The dynamic model of the moving beam in step 1 is as follows: 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 factors such as 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.

3. The method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod according to claim 2, characterized in that: The dynamic model of the extruded rod in step 1 is as follows: 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 Where M is an unknown positive value.

4. The method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod according to claim 3 is characterized in that: Step 2 specifically includes: Define the consistency error of the moving beam and the extruded rod as shown in the following equation: yes k (t)=x k (t)-x0(t); 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 second norm, as shown in the following formula: In the formula, L2 represents the second norm of the vector.

5. The method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod according to claim 4, characterized in that: 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 x k (0) = x k-1 (T), and 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); The position error tracking system is as follows: The input control law of the designed system is: In the formula, c represents an adjustable positive constant; and The update law is: 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;γ and r are adjustable design parameters, N represents an unknown positive constant to be estimated, N=M 2 , 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:

6. The method for adaptive iterative learning collaborative control of an extrusion motor beam and an extrusion rod according to claim 5, characterized in that: In step 4, a composite energy function is used for theoretical simulation verification, as shown in the following formula: In the formula, γ and r are adjustable design parameters, N represents an unknown positive constant to be estimated, and N = M 2 ,

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