Speed tracking self-adaptive iterative learning control method for extrusion rod of extruder

Abstract

The invention belongs to the technical field of intelligent control, and discloses a speed tracking self-adaptive iterative learning control method for an extrusion rod of an extruding machine, which comprises the following steps of: determining a dynamic model of the extrusion rod and a control target according to the physical property and the motion mode of the extrusion rod; based on an approximation theory, establishing a neural network model for an uncertain part in the extrusion rod motion model, and determining a speed tracking error system of the extrusion rod; designing virtual control input and actual control input based on a self-adaptive iterative learning control theory; based on the Lyapunov stability theorem, the stability of the controller is analyzed and designed. According to the speed tracking self-adaptive iterative learning control method for the extrusion rod of the extruding machine, limited time speed tracking of the extrusion rod can be effectively controlled, accurate motion control over the extrusion rod is achieved, and the size precision, the surface quality and the production efficiency of products are ensured.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control technology, in particular to a speed tracking adaptive iterative learning control method for an extrusion rod of an extruder. Background Art

[0002] Smart manufacturing is a key engine driving high-quality economic development in China. Extruders play a crucial role in smart manufacturing, directly impacting product dimensional accuracy, surface quality, and production efficiency. Precise speed tracking ensures uniform material flow during the extrusion process, avoiding defects and improving overall product quality. However, various interfering factors in the extrusion process, such as temperature fluctuations, changes in material properties, and die wear, can cause fluctuations in the extruder rod speed. Therefore, achieving precise speed control is a major challenge in extruder rod speed tracking.

[0003] Finite-time speed tracking control refers to the process of quickly and accurately tracking and maintaining the speed of the extrusion rod at a set reference speed within a given time range. Therefore, traditional control methods for finite-time speed tracking control of the extrusion rod mainly include PID control, open-loop control, and simple closed-loop control. PID control has limited effectiveness in controlling nonlinear, time-varying, and uncertain extrusion processes, and may not be able to quickly and accurately track changes in the speed of the extrusion rod. Open-loop control has poor accuracy and stability and is easily affected by factors such as the extrusion material, die, and extrusion temperature. Although simple closed-loop control has a feedback mechanism, its control algorithm is relatively simple and may not be able to respond quickly and accurately to changes in the speed of the extrusion rod. When faced with complex and changing working conditions, traditional control solutions often lack intelligence and adaptability, and are unable to automatically adjust control parameters and strategies according to changes in working conditions.

[0004] To address these issues, the present invention designs an adaptive iterative learning control method for tracking the speed of an extruder rod. This method implements tracking control of the rod's speed over a finite time interval. This method utilizes adaptive iterative learning control technology based on a radial basis function neural network to control the rod's speed, achieving higher speed control accuracy and precise motion control of the rod, ensuring product dimensional accuracy, surface quality, and production efficiency. Summary of the Invention

[0005] The purpose of the present invention is to provide an adaptive iterative learning control method for speed tracking of an extrusion rod of an extruder, and to provide a finite-time speed tracking control strategy for the extrusion rod. Based on the adaptive iterative learning control theory and combined with the Fourier series-radial basis function neural network approximation method, the finite-time high-precision speed tracking control of the extrusion rod is achieved.

[0006] To achieve the above object, the present invention provides a speed tracking adaptive iterative learning control method for an extrusion rod of an extruder, comprising the following steps: Step S1: Determine a dynamic model of the extrusion rod and a control target based on the physical properties of the extrusion rod and the movement mode of the extrusion rod; Step S2: Based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model, and a speed tracking error system of the extrusion rod is determined; Step S3: designing virtual control input and actual control input based on adaptive iterative learning control theory; Step S4: Based on the Lyapunov stability theorem, analyze the stability of the designed controller.

[0007] Preferably, in step S1, a dynamic model of the extrusion rod is constructed based on the physical properties of the extrusion rod and the movement mode of the extrusion rod to determine the control target. The specific process is as follows: Under uncertain working conditions, due to various external disturbances, the basic dynamic equation of the extruded rod is as follows: ; in, is the effective mass of the extruded rod and the metal inside it; is the acceleration of the squeeze rod; is the damping coefficient, representing the energy dissipation during the extrusion process; is the speed of the squeeze rod; is the stiffness coefficient; is the displacement of the extrusion rod; is the squeezing force; is friction; is the external interference force; The above extrusion rod dynamics model is transformed into an uncertain nonlinear parameterized system, and the finite time high precision velocity tracking control problem of the extrusion rod is regarded as a finite time high precision velocity tracking control problem of an uncertain nonlinear parameterized system. Through the dynamics study of the extrusion rod of the extruder, the dynamic model is established as follows: ; in, are the two state variables of the nonlinear parameterized extruded rod system—displacement and velocity; is the extrusion pressure control input of the nonlinear parameterized extrusion rod system; Contains unknown time-varying parameters The unmodeled dynamics of the model, including model uncertainties and unknown time-varying disturbances; is an unknown bounded external disturbance; is the displacement output of the system, Indicates the number of iterations.

[0008] Preferably, in step S2, based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model, and the velocity tracking error system of the extrusion rod and its corresponding displacement tracking error system of the extrusion rod are determined. The specific process is as follows: The velocity tracking error system of the extrusion rod is as follows: ; in, For the System speed output at iteration Target velocity trajectory The error, that is, Velocity tracking error at iteration 1; The corresponding displacement tracking error system of the extrusion rod is as follows: ; in, For the The system displacement output at the iteration With target trajectory The error, that is, Displacement tracking error at iterations; Step S21: in the extruded rod model, processing the uncertain time-varying parameter items; In a finite time interval, the uncertain time-varying parameter term is a periodic signal, They are expanded into Fourier series as follows: ; in, It is a matrix of trigonometric functions about time; is the corresponding weight matrix; is the truncation error after expansion, and its upper bound is ; Step S22: Establish a new Fourier series expansion-radial basis function neural network approximator, and Model them separately as follows: ; ; ; in, is a newly constructed approximator used to approximate the nonlinear parameterized terms that are not modeled in the system ; It's about parameters and Neural network Gaussian basis function vector; weight matrix and is bounded, satisfied , ; is the corresponding upper bound of the unknown, and its value is a positive number; , express The upper bound of and is the unknown weight vector and estimates; and Respectively and The estimated error between the estimated value and the actual value; is the approximation error when a simple neural network approximates an unknown non-parametric term; ; in, is the basis function Neural network basis functions when contains unknown parameter estimates; yes The derivative of represents the sum of higher-order terms in the Taylor series expansion; The total approximation error of the approximator is as follows: ; ; in, , , ; Remainder The boundary is ; Step S23: design of error function and processing of unknown bounds; A typical convergent series sequence is introduced to deal with the unknown upper bound of each error term as follows: , ,satisfy ; At the beginning of each iteration, the initial error value should satisfy , ,in, is a convergent series sequence; Construct a new error function , as shown below: ; in, The saturation function is: ; in, It is an improved time-varying layer boundary.

[0009] Preferably, in step S3, based on the adaptive iterative learning control theory, the virtual control input and the actual control input are designed to obtain a finite time high-precision displacement tracking control strategy for the extrusion rod. The specific process is as follows: Step S31: Design virtual control input and parameter adaptive law , ; Select a new error function and , as shown below: ; ; The first subsystem for the extruded rod model is shown below: ; According to the position tracking error, the Lyapunov function is selected as follows: ; In order to make Negative semidefinite, design a virtual controller as follows: ; The parameter adaptation law is: ; ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed; Step S32: Design actual control input and parameter adaptation law , ; Designing a new error function , as shown below: ; Select the Lyapunov function as shown below: ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed; Taking its derivative we get: ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed; Design the actual controller as follows: ; Select the parameter update law as: .

[0010] Therefore, the present invention adopts the above-mentioned speed tracking adaptive iterative learning control method for the extrusion rod of the extruder, and the beneficial effects are as follows: (1) Compared with the prior art, the present invention takes the extruder rod as the control object, whose motion is reciprocating, and models it as a nonlinear parameterized system. Combined with the adaptive iterative learning control theory, it effectively realizes high-precision speed tracking control of the extruder rod in a limited time interval; (2) Compared with traditional control methods, the finite time control method can accurately track the speed of the extruder rod and meet the requirements of high-precision processing; (3) The control method proposed in this paper can cope with various uncertainties, such as changes in extrusion pressure, uncertainty in friction, differences in material properties, and possible external interference, which is conducive to maintaining the stability and performance of the system.

[0011] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is an overall flow chart of a speed tracking adaptive iterative learning control method for an extrusion rod of an extruder according to the present invention; Figure 2 is a curve showing the change of the maximum value of the displacement error with the number of iterations in Example 2 of the present invention; Figure 3 is a curve showing the change of the maximum value of the speed error with the number of iterations in Example 2 of the present invention; Figure 4 is a curve showing the change of the norm of the control input with the number of iterations in Example 2 of the present invention. DETAILED DESCRIPTION

[0013] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0014] like Figure 1 As shown, the present invention provides a speed tracking adaptive iterative learning control method for an extruder extrusion rod, comprising the following steps: Step S1: Determine a dynamic model of the extrusion rod and a control target based on the physical properties of the extrusion rod and the movement mode of the extrusion rod; Step S2: Based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model of the extruder, and a speed tracking error system of the extrusion rod is determined; Step S3: designing virtual control input and actual control input based on adaptive iterative learning control theory; Step S4: Based on the Lyapunov stability theorem, analyze the stability of the designed controller.

[0015] Example 1 Step S1: construct a dynamic model of the extrusion rod according to the physical properties of the extruder extrusion rod and the movement mode of the extrusion rod, and determine the control target.

[0016] Under uncertain working conditions, since many factors need to be considered, such as the change in extrusion pressure, the uncertainty of friction, the difference in material properties, and possible external interference, the basic dynamic equation of the extrusion rod is as follows: ; in, is the effective mass of the extruded rod and the metal inside it; is the acceleration of the squeeze rod; is the damping coefficient, representing the energy dissipation during the extrusion process; is the speed of the squeeze rod; is the stiffness coefficient, reflecting the elasticity of the extruded rod and its supporting structure; is the displacement of the extrusion rod; is the squeezing force, which varies with time; is the friction force, including the friction between the extrusion rod and the die, extrusion pad and other components, which also changes with time; It is an external interference force, which may include uncertain factors such as vibration and impact.

[0017] The above extruder rod dynamics model is converted into an uncertain nonlinear parameterized system. Then the finite time high precision speed tracking control problem of the extruder rod can be regarded as the finite time high precision speed tracking control problem of the uncertain nonlinear parameterized system. Through the dynamics study of the extruder rod, the dynamic model is established as follows: ; in, are the two state variables of the nonlinear parameterized extruded rod system—displacement and velocity; is the extrusion pressure control input of the nonlinear parameterized extrusion rod system; Contains unknown time-varying parameters The unmodeled dynamics of the model, including model uncertainties and unknown time-varying disturbances; is an unknown bounded external disturbance; is the displacement output of the system, Indicates the number of iterations.

[0018] Step S2: Based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model of the extruder, and the speed tracking error system of the extrusion rod and its corresponding displacement tracking error system of the extrusion rod are determined.

[0019] Among them, the speed tracking error system of the extrusion rod is as follows: ; in, For the System speed output at iteration Target velocity trajectory The error, that is, Velocity tracking error at iterations.

[0020] The corresponding displacement tracking error system of the extrusion rod is as follows: ; in, For the The system displacement output at the iteration With target trajectory The error, that is, The displacement tracking error at the iteration.

[0021] Step S21: In the extruder rod model, the uncertain time-varying parameter items are processed.

[0022] In a finite time interval, the uncertain time-varying parameter term is a periodic signal, They are expanded into Fourier series as follows: ; in, It is a matrix of trigonometric functions about time; is the corresponding weight matrix; is the truncation error after expansion, which is bounded, and its upper bound is .

[0023] Step S22: Establish a new Fourier series expansion-radial basis function neural network approximator, and Model them separately as follows: ; ; ; in, is a newly constructed approximator used to approximate the nonlinear parameterized terms that are not modeled in the system ; It's about parameters and Neural network Gaussian basis function vector; weight matrix and is bounded, satisfied , ; is the corresponding upper bound of the unknown, and its value is a positive number; , express The upper bound of and is the unknown weight vector and estimates; and Respectively and The estimated error between the estimated value and the actual value; is the approximation error when a simple neural network approximates the unknown non-parametric term.

[0024] ; in, is the basis function Neural network basis functions when contains unknown parameter estimates; yes The derivative of represents the sum of higher-order terms in the Taylor series expansion.

[0025] The total approximation error of the approximator is as follows: ; ; in, , , ; Remainder The boundary is .

[0026] Step S23: Design of error function and processing of unknown bounds.

[0027] A typical convergent series sequence is introduced to deal with the unknown upper bound of each error term as follows: , ,satisfy ; At the beginning of each iteration, the initial error value should satisfy , ,in, is a convergent series sequence.

[0028] Construct a new error function , as shown below: ; in, The saturation function is: ; in, It is an improved time-varying layer boundary.

[0029] Step S3: Based on the adaptive iterative learning control theory, the virtual control input and the actual control input are designed to obtain a finite-time high-precision speed tracking control strategy for the extrusion rod.

[0030] Step S31: Design virtual control input and parameter adaptive law , .

[0031] Select a new error function and , as shown below: ; ; The first subsystem for the extruded rod model is shown below: ; According to the position tracking error, the Lyapunov function is selected as follows: ; In order to make Negative semidefinite, design a virtual controller as follows: ; The parameter adaptation law is: ; ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed.

[0032] Step S32: Design actual control input and parameter adaptation law , .

[0033] Designing a new error function , as shown below: ; Select the Lyapunov function as shown below: ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed.

[0034] Taking its derivative we get: ; in, is an approximation to an unknown function The neural network weights Estimates and weights The estimation error of is an unknown parameter Estimates, is the gain value that needs to be designed; 、 、 、 is the gain matrix that needs to be designed.

[0035] Design the actual controller as follows: ; Select the parameter update law as: ; Step S4: Based on the Lyapunov stability theorem, analyze the stability of the designed extrusion rod high-precision speed tracking control system.

[0036] According to hypothesis 1, , take the Lyapunov function as: ; in, ; ; ; ; ; ; available, .

[0037] definition , so the above formula can be rewritten as: ; According to the properties of convergent series, we know that ,therefore is bounded, and has ,therefore .

[0038] It is arbitrary, for , can be obtained, ; in, It is bounded.

[0039] Through the concept of convergent series sequence, is bounded, and has , so we can get, It is also bounded.

[0040] for , , and , for any ,Can is bounded. Therefore, we can get: It is bounded.

[0041] Most importantly, for any , is bounded, so we have , , , and They are all bounded, There are also boundaries, bounded; and by It is uniformly continuous, so it can be proved that in a finite time interval and under uncertain working conditions, the position tracking error of the extrusion rod system can converge to zero as the number of iterations increases, that is, the task of high-precision position tracking is completed, thereby meeting the corresponding high-precision velocity tracking requirements.

[0042] Example 2 In order to verify the effectiveness of the method of the present invention, simulation verification is carried out.

[0043] The effectiveness of the designed control strategy is verified by numerical examples. The model description of the extruder extrusion rod is as follows: ; ; ; in, ; and are the displacement and velocity variables of the extruded rod, respectively; is the extrusion pressure control input variable. The target output satisfies the following reference output model: ; ; ; in, and is a state variable. From the above formula The ideal tracking trajectory generated when .

[0044] Select the following virtual control law and actual control strategy: ; ; ; ; The parameter update law is: ; ; ; The specific parameter selections are as follows: , , , , , , , , , , .

[0045] The maximum displacement error changes with the number of iterations, such as Figure 2 As shown in the figure, the maximum value of the speed error changes with the number of iterations, as shown in the figure. Figure 3 As shown; the curve of the change of the norm of the control input with the number of iterations is as follows Figure 4 As shown. Figure 2-Figure 4 It can be seen that with the increase of the number of iterations, the extruder extrusion rod can achieve high-precision speed tracking in a limited time interval.

[0046] Therefore, the present invention adopts the above-mentioned adaptive iterative learning control method for speed tracking of the extrusion rod of an extruder, combines the approximation theoretical knowledge with the adaptive iterative learning control method, and realizes high-precision speed tracking control of the extrusion rod in a limited time interval, ensuring that the speed trajectory of the extrusion rod is consistent with the set speed curve, quickly responding to process requirements, meeting the requirements of high-precision extrusion process, and improving production efficiency.

[0047] 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 speed tracking adaptive iterative learning control method for an extruder extrusion rod, characterized in that: The following steps are involved: Step S1, determining a dynamic model of the extrusion rod and a control target according to the physical properties of the extrusion rod of the extruder and the movement mode of the extrusion rod; Step S2: Based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model, and a speed tracking error system of the extrusion rod is determined; Step S3: designing virtual control input and actual control input based on adaptive iterative learning control theory; Step S4: Analyze the stability of the designed controller based on the Lyapunov stability theorem.

2. The speed tracking adaptive iterative learning control method for an extruder extrusion rod according to claim 1 is characterized in that: In step S1, according to the physical properties of the extrusion rod and the movement mode of the extrusion rod, a dynamic model of the extrusion rod is constructed and the control target is determined. The specific process is as follows: Under uncertain working conditions, due to various external disturbances, the basic dynamic equation of the extruded rod is as follows: ； in, is the effective mass of the extruded rod and the metal inside it; is the acceleration of the squeeze rod; is the damping coefficient, representing the energy dissipation during the extrusion process; is the speed of squeezing the rod; is the stiffness coefficient; is the displacement of the extrusion rod; It is the squeezing force; is the friction force; It is an external disturbance force; The above extrusion rod dynamics model is transformed into an uncertain nonlinear parameterized system, and the finite time high precision velocity tracking control problem of the extrusion rod is regarded as the finite time high precision velocity tracking control problem of the uncertain nonlinear parameterized system. Through the dynamics study of the extrusion rod of the extruder, the dynamic model is established as follows: ； in, They are the two state variables of the nonlinear parameterized extruded rod system—displacement and velocity; is the extrusion pressure control input of the nonlinear parameterized extrusion rod system; For unknown time-varying parameters The unmodeled dynamics of the model, including model uncertainties and unknown time-varying disturbances; is an unknown bounded external disturbance; is the displacement output of the system, Indicates the number of iterations.

3. The speed tracking adaptive iterative learning control method for an extruder extrusion rod according to claim 1, characterized in that: In step S2, based on the approximation theory, a neural network model is established for the uncertain part of the extrusion rod model, and the velocity tracking error system of the extrusion rod and its corresponding displacement tracking error system of the extrusion rod are determined. The specific process is as follows: The velocity tracking error system of the extrusion rod is as follows: ； in, For the The system speed output at the iteration With the target speed trajectory The error, that is, Velocity tracking error at the iteration; The corresponding displacement tracking error system of the extrusion rod is as follows: ； in, For the The system displacement output at the iteration With target trajectory The error, that is, Displacement tracking error at iterations; Step S21, in the extruded rod model, processing the uncertain time-varying parameter item; In a finite time interval, the uncertain time-varying parameter term is a periodic signal, They are expanded into Fourier series as follows: ； in, It is a matrix of trigonometric functions about time; is the corresponding weight matrix; is the truncation error after expansion, and its upper bound is ; Step S22: Establish a new Fourier series expansion-radial basis function neural network approximator. and Model them separately as follows: ； ； ； in, is a newly constructed approximator used to approximate the unmodeled nonlinear parameterized terms in the system ; It's about parameters and Neural network Gaussian basis function vector; weight matrix and is bounded, satisfies , ; is the corresponding upper bound of the unknown, and its value is a positive number; , express The upper bound of and is the unknown weight vector and estimates; and Respectively and The estimated error between the estimated value and the actual value; The approximation error when a simple neural network approximates unknown non-parametric terms; ； in, is the basis function Neural network basis functions when contains unknown parameter estimates; yes The derivative of represents the sum of higher-order terms in the Taylor series expansion; The total approximation error of the approximator is as follows: ； ； in, , , ; Remainder The boundary is ; Step S23, design of error function and processing of unknown bounds; A typical convergent series sequence is introduced to deal with the unknown upper bound of each error term as follows: , ,satisfy ; At the beginning of each iteration, the initial error value should satisfy , ,in, is a convergent series sequence; Construct a new error function , as shown below: ； in, The saturation function is: ； in, It is an improved time-varying layer boundary.

4. The speed tracking adaptive iterative learning control method for an extruder extrusion rod according to claim 1, characterized in that: In step S3, based on the adaptive iterative learning control theory, the virtual control input and the actual control input are designed to obtain the finite time high-precision displacement tracking control strategy of the extrusion rod. The specific process is as follows: Step S31: Design virtual control input and parameter adaptation law , ; Choose a new error function and , as shown below: ； ； The first subsystem for the extruded rod model is shown below: ； According to the position tracking error, the Lyapunov function is selected as follows: ； In order to make Negative semi-definite, design a virtual controller as follows: ； The parameter adaptation law is: ； ； in, is an approximation to the unknown function The neural network weights Estimates With weight The estimation error of is an unknown parameter The estimate, is the gain value that needs to be designed; , , , is the gain matrix that needs to be designed; Step S32: Design actual control input And parameter adaptation law , ; Designing a new error function , as shown below: ； Select the Lyapunov function as follows: ； in, is an approximation to the unknown function The neural network weights Estimates With weight The estimation error of is an unknown parameter The estimate, is the gain value that needs to be designed; , , , is the gain matrix that needs to be designed; Taking its derivative we get: ； in, is an approximation to the unknown function The neural network weights Estimates With weight The estimation error of is an unknown parameter The estimate, is the gain value that needs to be designed; , , , is the gain matrix that needs to be designed; Design the actual controller as follows: ； Select the parameter update law as: 。

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