A position tracking control method for extrusion mobile beam based on adaptive iterative learning

Abstract

The present invention discloses a method for position tracking and controlling a movable beam of an extrusion machine based on adaptive iterative learning, and belongs to the technical field of position control. The method for position tracking and controlling a movable beam of an extrusion machine based on adaptive iterative learning comprises the following steps: according to the physical properties of the movable beam, by analyzing the movement mode of the movable beam, a dynamic model of a nonlinear parameterized movable beam system is constructed; a fuzzy model is established for the unknown part of the dynamic model, and the position tracking error system of the movable beam is determined; based on the adaptive iterative learning control theory, a finite-time high-precision position tracking control strategy of the movable beam of an extrusion machine is designed; and the stability of the controller is analyzed. The method for position tracking and controlling a movable beam of an extrusion machine based on adaptive iterative learning realizes finite-time high-precision position tracking and controlling of the movable beam based on adaptive iterative learning control theory and the Fourier series-fuzzy approximation method.

Description

Technical Field

[0001] The invention relates to the technical field of position control, and in particular to a method for position tracking and controlling an extrusion motor beam based on adaptive iterative learning. Background Art

[0002] Extruders play a vital role in intelligent manufacturing. Extruders have gradually transformed from traditional mechanical operations to highly intelligent production equipment. The extruder dynamic beam is an important component of the extruder equipment. The extrusion system uses the rotation and propulsion of the screw to heat, melt and plasticize the material in the barrel, and then extrude it through the die. By controlling the precise movement of the dynamic beam, the stability and efficiency of the extrusion process are ensured. In the process of metal extrusion, forging and other processes, the position control of the extruder dynamic beam is crucial to ensure product quality. The dynamic beam needs to reach the specified position accurately during the extrusion process to ensure the accuracy and consistency of the extrusion. Slight position deviations may lead to deviations in product size or changes in shape. Factors such as material flow, friction and temperature changes in the extrusion process have nonlinear characteristics, which makes it difficult for the control system to establish an accurate mathematical model and increases the difficulty of control. Traditional position control systems are often based on mechanical or hydraulic control, which makes it difficult to achieve high-precision position tracking within a limited time interval.

[0003] Traditional control schemes often use classic control algorithms, such as PID control. When faced with complex and changeable working conditions, the PID control algorithm has an unsatisfactory control effect on nonlinear and time-varying systems, which can easily lead to system overshoot, oscillation and other problems, thus affecting the high-precision position tracking of the extrusion mobile beam. Traditional control schemes often lack intelligence and adaptive capabilities, and cannot automatically adjust control parameters and strategies according to changes in working conditions. This results in the inability of traditional control schemes to achieve the best control effect under complex and changeable working conditions. In order to overcome these defects, it is necessary to study advanced control algorithms and technical means such as intelligent and adaptive control strategies to improve the accuracy and stability of position tracking. Summary of the invention

[0004] The purpose of the present invention is to provide a method for position tracking control of an extrusion moving beam based on adaptive iterative learning, based on adaptive iterative learning control theory and combined with Fourier series-fuzzy approximation method to achieve finite time high-precision position tracking control of the moving beam.

[0005] The control objective of the present invention is to design a high-precision position tracking adaptive iterative learning controller for the moving beam. , in a limited time interval Implementation:

[0006] ;

[0007] That is, the moving beam can move accurately in a limited time under the action of the controller, realizing high-precision position tracking control. The specified position track.

[0008] Indicates the position status information of the moving beam. represents the output displacement of the moving beam, Indicates the number of iterations.

[0009] To achieve the above object, the present invention provides a method for position tracking control of an extrusion motor beam based on adaptive iterative learning, comprising the following steps:

[0010] S1. According to the physical properties of the moving beam, the dynamic model of the nonlinear parameterized moving beam system is constructed by analyzing the movement mode of the moving beam;

[0011] S2. Establish a fuzzy model for the unknown part of the dynamic model and determine the position tracking error system of the moving beam;

[0012] S3. Based on adaptive iterative learning control theory, a finite time high-precision position tracking control strategy for the extrusion motor beam is designed;

[0013] S4. Analyze the stability of the controller.

[0014] Preferably, in S1, the dynamic model of the nonlinear parameterized moving beam system is:

[0015] ;

[0016] in, For the nonlinear parameterized moving beam system The first reciprocating motion state variables, For the nonlinear parameterized moving beam system The control input during the reciprocating motion is is the dynamic dimension of the system, For unknown time-varying parameters The unmodeled dynamics of is an uncertain bounded external disturbance, . For the dynamic beam Output displacement during reciprocating motion, is the number of iterations, which here refers to the number of reciprocating motions.

[0017] Preferably, in S2, the specific process of establishing the fuzzy model includes:

[0018] S21, processing unknown time-varying parameters in the dynamic model;

[0019] The unknown time-varying parameters Expanded into a Fourier series

[0020] ;

[0021] in, It is a matrix of trigonometric functions about time; is the weight matrix; is the residual error after Fourier series expansion, which is bounded by ;

[0022] S22, establishing a Fourier series-fuzzy approximator;

[0023] ;

[0024] ;

[0025] in,

[0026] ;

[0027] is the new approximation function constructed, is the unknown function being approximated, It is about the state parameter and of The order basis function vector, is the approximation error, the weight matrix and is bounded, satisfies , , is the unknown normal number bound, m Weight The subscript of the upper bound, a Weight The subscript of the upper bound;

[0028] , express The upper bound of

[0029] ,in , They are the unknown weight vectors and The estimate, , Respectively and The estimated error between the estimated value and the actual value; represents the sum of higher-order terms in the Taylor series expansion;

[0030] S23, design error function;

[0031] ;

[0032] in, Indicates the moving beam Output displacement during reciprocating motion, is the reference output trajectory;

[0033] At the beginning of each iteration, the initial error value , ,in is a convergent series sequence;

[0034] Construct a new error function for

[0035] ;

[0036] in, is a saturation function, expressed as

[0037] ;

[0038] in, is an improved time-varying layer boundary function, is a tunable parameter whose value is greater than zero.

[0039] Preferably, in S22, the approximation error of the Fourier series-fuzzy approximator is:

[0040] ;

[0041] In the above formula,

[0042] ;

[0043] in, , , , is the parameter variable set; the remainder The boundary is .

[0044] Preferably, in S3, the specific steps of tracking control strategy design include:

[0045] S31. Design virtual control input

[0046] Choose a new error function and :

[0047] ;

[0048] ;

[0049] First subsystem for the extruded motorized beam model:

[0050] ;

[0051] According to the position tracking error, the Lyapunov function is selected as ;

[0052] In order to make Negative semi-definite, the virtual controller is designed as follows:

[0053] ;

[0054] in, is an unknown parameter The estimate, , is the gain value;

[0055] S32. Design actual control input And parameter adaptation law ;

[0056] The actual controller is

[0057] ;

[0058] ;

[0059] Select the parameter update law as

[0060] ;

[0061] ;

[0062] The new error function for:

[0063] ;

[0064] ;

[0065] ;

[0066] , ;

[0067] ;

[0068] ;

[0069] Among them, the subscript g is the uncertain function in the system The subscript f is the uncertain function in the system. Mark.

[0070] The advantages and positive effects of the position tracking control method of the extrusion movable beam based on adaptive iterative learning described in the present invention are: the present invention models the extrusion movable beam as a particle system as a nonlinear parameterized system, and combines the adaptive iterative learning control theory to effectively realize the high-precision position tracking control of the movable beam in a limited time interval. The adaptive iterative learning control method described in the present invention can realize the accurate tracking of the position of the movable beam and meet the requirements of high-precision processing. At the same time, the method has the ability to cope with various uncertain factors, such as load changes, friction changes, etc., to maintain the stability and performance of the system.

[0071] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a flow chart of the method for position tracking and controlling the extrusion motor beam based on adaptive iterative learning of the present invention;

[0073] Figure 2 It is the displacement error curve of the extrusion motor beam without iteration provided by the simulation verification of the present invention;

[0074] Figure 3 It is the displacement error curve of the extruded motor beam at 30 iterations provided by the simulation verification of the present invention;

[0075] Figure 4 It is a curve showing the change of the control input of the extrusion motor beam with the number of iterations provided by the simulation verification of the present invention. DETAILED DESCRIPTION

[0076] like Figure 1 A method for position tracking control of an extrusion motor beam based on adaptive iterative learning comprises the following steps:

[0077] S1. According to the physical properties of the moving beam, the dynamic model of the nonlinear parameterized moving beam system is constructed by analyzing the movement mode of the moving beam.

[0078] The kinematic model of the moving beam can usually be described using the method of particle system kinematics. In the model, the moving beam can be regarded as a particle system, and its motion state is determined by the position and velocity of each particle. By establishing the motion equation of the particle system, the overall motion state of the moving beam, such as displacement, velocity, acceleration, etc., can be described. In addition, the rigid body motion characteristics of the moving beam, such as rotation and translation, can also be considered. When establishing the model, many factors need to be considered, such as the nonlinearity of the material, the friction and clearance between the components, the nonlinear characteristics of the hydraulic system, etc. These factors will increase the complexity of the model and the difficulty of solving, making precise motion control more difficult. Considering these factors, the kinematic model of the moving beam can be modeled as a nonlinear parameterized system.

[0079] The extrusion movable beam is regarded as a mass point system. Under uncertain working conditions (such as load changes and hydraulic pressure fluctuations), the dynamic model is established through the dynamic study of the movable beam as follows:

[0080] ;

[0081] in, For the nonlinear parameterized moving beam system The first reciprocating motion state variables, For the nonlinear parameterized moving beam system The control input during the reciprocating motion is is the dynamic dimension of the system, For unknown time-varying parameters The unmodeled dynamics of is an uncertain bounded external disturbance, . For the dynamic beam Output displacement during reciprocating motion, is the number of iterations, which here refers to the number of reciprocating motions. n =2.

[0082] S2. Establish a fuzzy model for the unknown part of the dynamic model and determine the position tracking error system of the moving beam.

[0083] The specific process of establishing the fuzzy model includes:

[0084] S21, processing unknown time-varying parameters in the dynamic model;

[0085] In a finite time interval, it is considered as a periodic signal, so the unknown time-varying parameters Expanded into a Fourier series

[0086] ;

[0087] in, It is a matrix of trigonometric functions about time; is the weight matrix; is the residual error after Fourier series expansion, which is bounded by .

[0088] S22, establishing a Fourier series-fuzzy approximator;

[0089] ;

[0090] ;

[0091] in,

[0092] ;

[0093] is the new approximation function constructed, is the unknown function being approximated, It is about the state parameter and of The order basis function vector, is the approximation error, the weight matrix and is bounded, satisfies , , is the unknown normal number bound, m Weight The subscript of the upper bound, a Weight Subscript of the upper bound.

[0094] , express The upper bound of .

[0095] ,in , They are the unknown weight vectors and The estimate, , Respectively and The estimated error between the estimated value and the actual value; represents the sum of higher-order terms in the Taylor series expansion.

[0096] The approximation error of the Fourier series-fuzzy approximator is:

[0097] ;

[0098] In the above formula,

[0099] ;

[0100] in, , , , is the parameter variable set; the remainder The boundary is .

[0101] S23, design error function;

[0102]

[0103] in, Indicates the moving beam Output displacement during reciprocating motion, is the reference output trajectory;

[0104] For the treatment of unknown upper bounds of each error term, the following typical convergent series sequence is introduced:

[0105] , ,satisfy .

[0106] At the beginning of each iteration, the initial error value , ,in is a convergent series sequence.

[0107] Construct a new error function for

[0108] ;

[0109] in, is a saturation function, expressed as

[0110] ;

[0111] in, is an improved time-varying layer boundary function, is a tunable parameter whose value is greater than zero.

[0112] S3. Based on the adaptive iterative learning control theory, a finite-time high-precision position tracking control strategy for the extrusion mobile beam is designed.

[0113] The specific steps of tracking control strategy design include:

[0114] S31. Design virtual control input

[0115] Choose a new error function and :

[0116] ;

[0117] ;

[0118] First subsystem for the extruded motorized beam model:

[0119] ;

[0120] According to the position tracking error, the Lyapunov function is selected as ;

[0121] In order to make Negative semi-definite, the virtual controller is designed as follows:

[0122] ;

[0123] in, is an unknown parameter The estimate, , is the gain value.

[0124] S32. Design actual control input And parameter adaptation law ;

[0125] Select ;

[0126] , ;

[0127] ;

[0128] ;

[0129] Designing a new error function for:

[0130] ;

[0131] Select the Lyapunov function

[0132] ;

[0133] Taking its derivative, we get

[0134] ;

[0135] The actual controller is designed as

[0136] ;

[0137] ;

[0138] Select the parameter update law as

[0139] ;

[0140] ;

[0141] Among them, the subscript g is the uncertain function in the system The mark, subscript f is the uncertain function in the system Mark.

[0142] S4. Analyze the stability of the controller.

[0143] Assumption 1: When , for any number of iterations ,have ; ; ; .

[0144] According to hypothesis 1, . Take the Lyapunov function as ,have

[0145] ;

[0146] in, , , , , .

[0147] ;

[0148] definition , so the above formula can be rewritten as

[0149] ;

[0150] According to the properties of convergent series, we know that ,therefore, is bounded, and has ,therefore

[0151] ;

[0152] is arbitrary, for , can be obtained

[0153] ;

[0154] is bounded. Through the concept of convergent series sequence, is bounded, and has , so we can get is also bounded. , , and , for any , can be obtained is bounded, so we can get is bounded. Most importantly, for any , is bounded, so we have , , , and They are all bounded. is also bounded. 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 mobile beam system can converge to zero as the number of iterations increases, that is, the task of high-precision tracking is completed.

[0155] In order to verify the effectiveness of the method described in the present invention, a simulation verification is carried out

[0156] The effectiveness of the designed control strategy is verified by numerical examples. The state equation of the extrusion mobile beam system is:

[0157] ;

[0158] ;

[0159] ;

[0160] in, .

[0161] The reference model of the system is:

[0162] ;

[0163] ;

[0164] ;

[0165] In the formula, is the displacement of the extrusion motor beam, is the velocity of the squeeze maneuvering beam, and the desired target trajectory given by the reference model is .

[0166] The adaptive iterative learning control strategy is selected as follows

[0167] ;

[0168] ;

[0169] ;

[0170] And determine the parameter update law

[0171] ;

[0172] ;

[0173] ;

[0174] In the formula , , , , , , , , .

[0175] First, define six fuzzy flags , they evenly cover the input domain. Corresponding to the four inputs of the system. Indicates the six fuzzy sets corresponding to a certain input of the system. When using fuzzy logic to approximate the function, take the following six membership functions:

[0176] For input , choose the membership function as:

[0177] , , , , , .

[0178] For input , choose the membership function as:

[0179] , , , , , .

[0180] For input , choose the membership function as:

[0181] ;

[0182] ;

[0183] ;

[0184] ;

[0185] ;

[0186] .

[0187] For the uncertain items in the system, the fuzzy IF-THEN rules are selected as follows:

[0188] ;

[0189] in , , .

[0190] You can get:

[0191] ;

[0192] in is a matrix A parameter in . Introducing vector , the above formula can be written as:

[0193] ;

[0194] in is a 216-dimensional vector, where The elements are:

[0195] ;

[0196] The displacement error curve without iteration is as follows: Figure 2 As shown, the displacement error curve of the 30th iteration is as follows Figure 3 As shown, the curve of control input changing 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 iteration number, the extrusion motorized beam can achieve high-precision position tracking.

[0197] Therefore, the method for position tracking control of the extrusion moving beam based on adaptive iterative learning described in the present invention is adopted, based on the adaptive iterative learning control theory and combined with the Fourier series-fuzzy approximation method, to realize the finite time high-precision position tracking control of the moving beam.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. 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 solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for position tracking control of an extrusion motor beam based on adaptive iterative learning, characterized in that: The following steps are involved: S1. According to the physical properties of the moving beam, the dynamic model of the nonlinear parameterized moving beam system is constructed by analyzing the movement mode of the moving beam; S2. Establish a fuzzy model for the unknown part of the dynamic model and determine the position tracking error system of the moving beam; S3. Based on adaptive iterative learning control theory, a finite time high-precision position tracking control strategy for the extrusion motor beam is designed; S4. Analyze the stability of the controller; In S1, the dynamic model of the nonlinear parameterized moving beam system is: ； in, For the nonlinear parameterized moving beam system The first reciprocating motion state variables, For the nonlinear parameterized moving beam system The control input during the reciprocating motion is is the dynamic dimension of the system, For unknown time-varying parameters The unmodeled dynamics of is an uncertain bounded external disturbance, , For the dynamic beam Output displacement during reciprocating motion, is the number of reciprocating motions; In S2, the specific process of establishing the fuzzy model includes: S21, processing unknown time-varying parameters in the dynamic model; The unknown time-varying parameters Expanded into a Fourier series ， in, It is a matrix of trigonometric functions about time; is the weight matrix; is the residual error after Fourier series expansion, which is bounded by ; S22, establishing a Fourier series-fuzzy approximator; ； ； in, ； is the new approximation function, is the unknown function being approximated, It is about the state parameter and of The order basis function vector, is the approximation error, the weight matrix and is bounded, satisfies , , is the unknown normal number bound, m Weight The subscript of the upper bound, Weight The subscript of the upper bound; , express The upper bound of ,in , They are the unknown weight vectors and The estimate, , Respectively and The estimated error between the estimated value and the actual value; represents the sum of higher-order terms in the Taylor series expansion; S23, design error function; ； in, Indicates the moving beam Output displacement during reciprocating motion, is the reference output trajectory; At the beginning of each iteration, the initial error value , ,in is a convergent series sequence; Construct a new error function for ； in, is a saturation function, expressed as ； in, is an improved time-varying layer boundary function, is an adjustable parameter whose value is greater than zero; In S3, the specific steps of tracking control strategy design include: S31. Design virtual control input ; Choose a new error function and : ； ； First subsystem for the extruded motorized beam model: ； According to the position tracking error, the Lyapunov function is selected as ; In order to make Negative semi-definite, the virtual controller is designed as follows: ； in, is an unknown parameter The estimate, , is the gain value; S32. Design actual control input And parameter adaptation law ; The actual controller is ； ； Select the parameter update law as ； ； The new error function for: ； ； ； ， ； ； ， Among them, the subscript g is the uncertain function in the system The mark, subscript f is the uncertain function in the system Mark.

2. The method for position tracking control of an extrusion motor beam based on adaptive iterative learning according to claim 1 is characterized in that: In S22, the approximation error of the Fourier series-fuzzy approximator is: ； In the above formula, ； in, , , , is the parameter variable; the remainder The boundary is .

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