FSW joint mechanical property model-free adaptive control method

Abstract

The invention belongs to the field of welding quality control of friction stir welding, and relates to a model-free self-adaptive control method for mechanical properties of an FSW joint. The FSW process is described as a disturbance-containing multiple-input-multiple-output discrete time nonlinear system, and the disturbance-containing multiple-input-multiple-output discrete time nonlinear system is converted into a tight-format dynamic linearization data model; a model-free adaptive controller is constructed according to a control input criterion function, and online estimation of control law parameters is realized in combination with a pseudo Jacobian matrix estimator; estimating the disturbance of the FSW system by using the FNNDO, and carrying out feed-forward compensation on the disturbance; and the joint mechanical property obtained through prediction serves as input of an FNNDO-MFAC controller, welding process parameters are dynamically adjusted through real-time feedback, and therefore precise control over the mechanical property of the FSW joint is achieved. The method does not need to depend on model parameters in the FSW process, through disturbance estimation and compensation of the FNNDO, the disturbance processing capacity of the MFAC is remarkably improved, and the self-adaptability of the system is effectively enhanced.

Description

Technical Field

[0001] The invention belongs to the field of friction stir welding (FSW) welding quality control, and in particular relates to a model-free adaptive control method for mechanical properties of a FSW joint. Background Art

[0002] The FSW process technology uses a rotating stirring head to form a weld under the forging action of heat and force coupling. It has the advantages of high weld joint strength, few welding defects, small welding deformation, no need for filling materials, and environmental protection. It is especially suitable for the welding of light metal materials such as aluminum alloys and magnesium alloys.

[0003] With the increasing requirements for welding quality in high-end manufacturing industries such as aerospace, shipbuilding, and rail transit, how to accurately control the mechanical properties of FSW joints has become a key issue for technological innovation and quality improvement. In view of the fact that welding temperature and welding force affect the mechanical properties of welded joints, experts have conducted a lot of research on the control of welding temperature and upsetting force during the FSW process. Taysom et al. from Brigham Young University in the United States developed a FSW model predictive control method based on the first-order delay plus pure hysteresis (FOPDT) model to effectively control the temperature change during welding. Bachmann et al. from the Technical University of Munich in Germany designed an L1 adaptive controller based on a semi-analytical model to achieve precise control of the FSW interface temperature. De Backer et al. from the University of Western Sweden developed a proportional integral (PI) controller based on a first-order model, and successfully achieved stable control of the welding temperature by adjusting the speed of the stirring head. Zhao Sheng from Shanghai Jiaotong University designed an upsetting force tracking controller that integrates feedforward compensation, stabilization compensation, and servo compensation by establishing a nonlinear empirical model of FSW, and used a linear quadratic regulator to achieve high-precision control of the upsetting force. Wang et al. from Donghua University developed a multi-level fuzzy proportional integral differential (PID) controller to effectively control the upsetting force in the FSW process. Davis et al. from Purdue University proposed an adaptive robust control method based on a state observer, which significantly reduced the change of upsetting force under process disturbance.

[0004] Studies have shown that existing FSW process control methods mainly rely on technologies such as model predictive control, fuzzy control and adaptive robust control, and achieve stable control of temperature or force during welding by adjusting process parameters such as stirring head speed and welding speed in real time. However, it is difficult to fully guarantee the welding quality by only controlling the welding temperature or upsetting force. It is urgent to develop a control strategy with the mechanical properties of the FSW joint as the control target. In addition, the above-mentioned FSW control strategy usually relies on an accurate model of the controlled system, while the strong nonlinearity and multi-physical field coupling characteristics of the FSW system and the existence of random disturbances make it difficult to accurately model the system, making it difficult to achieve precise control of the mechanical properties of the FSW joint.

[0005] The model-free adaptive control (MFAC) method has the significant advantage of not relying on the precise model of the system. It can adaptively adjust the control strategy in a real-time data-driven manner, which is particularly suitable for complex nonlinear systems. Although the MFAC method has been widely used in welding quality control fields such as plasma welding, gas metal welding, and arc welding, its application in FSW process control has not been reported. Summary of the invention

[0006] In view of the difficulty in establishing an accurate mathematical model for the complex nonlinear FSW process and the difficulty in predicting and suppressing the disturbances and uncertainties in the system, the present invention provides a model-free adaptive control method for the mechanical properties of FSW joints based on a fuzzy neural network disturbance observer (FNNDO) (abbreviated as FNNDO-MFAC), which aims to accurately control the tensile strength and microhardness of FSW joints. As a data-driven control strategy, MFAC has good adaptability and portability. It only requires the input and output data of the controlled system, and does not rely on an accurate mathematical model, thereby overcoming the limitations of traditional model-based control methods in the FSW process. Considering the factors such as unstable operation, changes in the geometric parameters of the butt surface, and external interference in the actual welding process, which will affect the stability of the FSW system, the present invention improves the MFAC algorithm, uses FNNDO to dynamically estimate the disturbances and uncertainties inside and outside the system, and compensates them to the control input, thereby further enhancing the robustness and accuracy of the control of the mechanical properties of the FSW joint. The present invention introduces the MFAC method into the mechanical property control of FSW joints, combines the pseudo-Jacobian matrix estimator and the fuzzy neural network disturbance observer, and provides an innovative research idea and solution for solving the complex, nonlinear, and multi-disturbance FSW process control problem.

[0007] This method does not rely on any model parameters related to the FSW process. Instead, it uses FNNDO to dynamically estimate the total disturbance of the system based on the welding process parameter input data and the joint mechanical properties output data, effectively overcoming the shortcomings of the existing MFAC in dealing with disturbances and the poor adaptive ability. Through this method, the control accuracy and system robustness of the mechanical properties of the FSW joint are significantly improved, ensuring the stability and consistency of the welding quality.

[0008] The technical solution of the present invention:

[0009] A model-free adaptive control method for mechanical properties of FSW joints, comprising the following steps:

[0010] Step 1: The dynamic data model of the FSW process is constructed based on the compact dynamic linearization (CFDL) model, and the MFAC control law algorithm of the mechanical properties of the FSW joint based on CFDL is designed according to the control input criterion function.

[0011] Considering the influence of system disturbance on the control effect, the FSW process is described as the following discrete time nonlinear system:

[0012]

[0013] Among them, f(…) is an unknown nonlinear function, which represents the nonlinear dynamic system of the FSW process; k is the sampling time; U(k) and Y(k) represent the input welding process parameters and output joint mechanical properties of the system at the current moment, respectively; u1(k) is the stirring head speed of the system at the current moment, and u2(k) is the welding speed at the current moment; y1(k) is the joint tensile strength of the system at the current moment, and y2(k) is the joint microhardness at the current moment; d(k) represents the total disturbance of the system at the current moment; n y , n u , n d are three unknown positive integers, representing the order of system output, input and total disturbance.

[0014] When the total disturbance d(k) of the system is bounded, the function f(…) satisfies the continuity of partial derivatives of any variable of the FSW system and satisfies the generalized Lipschitz continuity condition, the discrete-time nonlinear system of the FSW process in equation (1) can be equivalent to the following CFDL data model:

[0015] ΔY(k+1)=Φ c (k)ΔU(k)+r(k) (2)

[0016] In the formula, is the pseudo-Jacobian matrix of the FSW system, which is given by the partial derivative φ ij The diagonally dominant matrix is ​​bounded at any time, where R 2×2 represents a 2-dimensional real matrix space; r(k) is the total disturbance of the system; ΔY(k+1)=Y(k+1)-Y(k); ΔU(k)=U(k)-U(k-1), and ΔU(k)≠0.

[0017] The control input criterion function J(U(k)) of the FSW system is defined as:

[0018] J(U(k))=||Y * (k+1)-Y(k+1)|| 2 +λ||U(k)-U(k-1)|| 2 (3)

[0019] Among them, λ>0 is a weight factor, which is used to limit the change of control input, reduce the system steady-state error, and ensure the smoothness of control input; Y * (k+1) is the expected output signal of the system at the next moment; Y(k+1) is the actual output signal of the system at the next moment; U(k) is the input control quantity of the system at the current moment; U(k-1) is the input control quantity of the system at the previous moment.

[0020] Substituting the equivalent CFDL data model of equation (2) into the control input criterion function of equation (3), taking the derivative of U(k) and setting it equal to zero, we can obtain:

[0021]

[0022] Where I is the identity matrix.

[0023] Formula (4) contains a matrix inversion operation. When the input and output dimensions of the system are large, the matrix inversion operation is very time-consuming. Therefore, the single-input single-output model-free adaptive control law algorithm can be expanded to obtain a multi-input multi-output model-free adaptive control law algorithm of formula (5):

[0024]

[0025] Among them, ρ1∈(0,1], ρ2∈(0,1] are the operation step factors of the control law.

[0026] In the control law algorithm of formula (5), the pseudo-Jacobian matrix Φ c (k) and the total system disturbance r(k) are unknown, so they need to be estimated.

[0027] Step 2: Use the pseudo-Jacobian matrix estimator to calculate the pseudo-Jacobian matrix Φ in the control law algorithm c The parameters of (k) are estimated online.

[0028] The estimation criterion function of the pseudo-Jacobian matrix J(Φ c (k)):

[0029]

[0030] Among them, μ>0 is a weight factor used to penalize excessive changes in the pseudo-Jacobian matrix estimate; is Φ c (k) is the estimated value; r(k-1) is the total interference of the system at the previous moment.

[0031] Minimizing equation (6), according to the inverse matrix lemma, we can obtain the pseudo-Jacobian matrix Φ c (k) estimation algorithm:

[0032]

[0033] Among them, η∈(0,2] is the operation step factor of the estimation algorithm; is the estimated value of r(k-1).

[0034] In order to make the online estimation algorithm have stronger time-varying tracking ability and ensure that the pseudo-Jacobian matrix can maintain high accuracy and stability when facing parameter changes, the reset mechanism shown in formula (8) is introduced to reset the value of the pseudo-Jacobian matrix:

[0035]

[0036] Among them, ε is a sufficiently small positive number.

[0037] Step 3: Use FFNDO to estimate the total disturbance r(k) of the system and perform feed-forward compensation on the disturbance to generate the FNNDO-MFAC controller.

[0038] From the CFDL data model of formula (2), we can get:

[0039] r(k-1)=Y(k)-Y(k-1)-Φ c (k-1)ΔU(k-1) (9)

[0040] Therefore, the input of the fuzzy neural network is defined as X = [Y(k), Y(k-1), U(k-1), Uk(-2), and the output is

[0041] Using Gauss function as membership function, the final output of fuzzy neural network is It can be expressed as:

[0042]

[0043] Where W is the weight matrix; is the fuzzy basis function vector; c and σ represent the center value vector and width vector of the membership function respectively.

[0044] Using the total disturbance of the FNNDO real-time observation system, the following dynamic observer is constructed:

[0045]

[0046] Among them, α is the state variable of the observer; the constant γ>0 is the gain of the observer; is the estimated value of the total disturbance; is the estimated value of the weight matrix; is the estimated value of the central value vector of the membership function; is the estimated value of the membership function width vector; is the estimated value of the fuzzy basis function vector.

[0047] Define the optimal values ​​of the weight matrix, membership function center value vector and width vector as W * 、c * and σ * , then the true value of the total disturbance can be expressed as:

[0048]

[0049] Among them, τ is the approximation error, and its upper bound is

[0050] Define the tracking error of the observer as e = X-α, then Combining equation (11) and equation (12), we can get:

[0051]

[0052] Will exist Taking the first-order Taylor expansion as the first-order one and ignoring the higher-order expansion terms, equation (13) can be rearranged as:

[0053]

[0054] On this basis, the adaptive law of FNNDO parameters is selected as:

[0055]

[0056] Among them, δ W ,δ c and δ σ is a positive definite parameter matrix;

[0057] Combining equations (5), (7), (8) and (11), the FNNDO-MFAC controller algorithm for the mechanical properties of the FSW joint is obtained as follows:

[0058]

[0059] Step 4: Based on the real-time collected welding temperature and upsetting force signals, an intelligent prediction model for the mechanical properties of the FSW joint is constructed, and the predicted joint mechanical properties Y(k) are used as the input of the FNNDO-MFAC controller in step 3. The welding process parameters are dynamically adjusted through real-time feedback, thereby achieving precise control of the mechanical properties of the FSW joint.

[0060] As a preferred implementation, an intelligent prediction model for the mechanical properties of FSW joints is established with welding temperature and upsetting force as input variables and joint tensile strength and microhardness as output variables.

[0061] As a preferred embodiment, an infrared thermal imager and a piezoelectric dynamometer are used to collect the weldment surface temperature and upsetting force signals in real time during the FSW process, and the data are transmitted to a main control computer for processing.

[0062] As a preferred embodiment, the main control computer is embedded with an intelligent prediction model for the mechanical properties of the FSW joint. The time axis of the temperature and force signals are aligned by downsampling, and these signals are used as inputs of the prediction model to output the predicted values ​​of the tensile strength and microhardness of the joint in real time.

[0063] As a preferred embodiment, the tensile strength and microhardness prediction values ​​Y(k) obtained by the intelligent prediction model of joint mechanical properties are combined with the set target value Y * (k+1), calculate the deviation Y between the predicted value and the target value * (k+1)-Y(k), and the deviation is input into the FNNDO-MFAC controller in step 3 to calculate the required stirring head speed and welding speed adjustment. The actuator is driven by the servo system of the FSW machine tool to adjust the process parameters during the welding process, and finally the closed-loop control of the mechanical properties of the FSW joint is achieved.

[0064] Beneficial effects of the present invention:

[0065] The present invention provides a model-free adaptive control method suitable for the mechanical properties of FSW joints. The FNNDO is used to estimate the interference and uncertainty in the system, the stirring head rotation speed and the welding speed are used as the control variables, and the tensile strength and microhardness of the joint are used as the control targets to achieve precise control of the mechanical properties of the FSW joint. In view of the fact that it is difficult to establish an accurate mathematical model for the FSW process, the present invention designs an MFAC controller that does not rely on the welding process model. By jointly adjusting the stirring head rotation speed and the welding speed, the control accuracy is improved, and the limitation of the control effect by the complex modeling process and the model accuracy is avoided. The advantage of this method is that it only relies on the input and output data in the FSW process, and there is no need for complex mathematical modeling, thereby ensuring the adaptability of the system in complex environments. Compared with other MFAC methods, the FNNDO-MFAC controller designed by the present invention has stronger anti-disturbance ability, which significantly enhances the adaptability and overall control performance of the FSW joint mechanical properties controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is the working principle diagram of the model-free adaptive control method of the mechanical properties of FSW joints;

[0067] Figure 2 It is the FNNDO-MFAC control structure diagram of the mechanical properties of FSW joints;

[0068] Figure 3 It is the simulation flow chart of FNNDO-MFAC control scheme for mechanical properties of FSW joints;

[0069] Figure 4 It is the tracking curve diagram of the FSW joint mechanical property control simulation;

[0070] Figure 5 It is the input curve diagram of the FSW joint mechanical property control simulation. DETAILED DESCRIPTION

[0071] The specific implementation of the present invention is described in detail below in conjunction with the technical scheme and the accompanying drawings, but the present invention is not limited to this embodiment.

[0072] In this embodiment, a FSW joint experiment is carried out on a static gantry friction stir welding machine to provide input and output sample data for controller design. The experimental material is a 2219-T8 aluminum alloy thick plate with a size of 300mm×120mm×18mm. By designing the FNNDO-MFAC controller, the stirring head speed and welding speed are jointly adjusted to achieve adaptive control of the tensile strength and microhardness of the FSW joint considering process disturbances.

[0073] The input and output data required by the model-free adaptive control method for the mechanical properties of the FSW joint described in the present invention are collected online through the FSW experimental platform. The main equipment models and uses of the FSW experimental platform are as follows:

[0074] The infrared thermal imager, model FLIR A615, is mainly used to measure the surface temperature of the weldment; the piezoelectric dynamometer, composed of four piezoelectric force measuring units, is mainly used to collect the upsetting force during the welding process; the charge amplifier, model Kistler5018, is mainly used to amplify the weak charge signal generated by the piezoelectric force measuring unit; the data acquisition card, model USB 61902, is mainly used to convert the collected force signal into a readable digital voltage signal; the FSW machine tool, model FSW-SD1015, is used to complete the welding of 2219-T8 aluminum alloy plates; the main control computer, model Lenovo Y7000, is mainly used to pre-process the welding temperature and upsetting force signals, predict the mechanical properties of the joint in real time and execute the control algorithm.

[0075] The FSW experimental platform is used to obtain the required input and output data sets {R(k), V(k), UTS(k), HV(k)}, where R(k) is the stirring head speed value, V(k) is the welding speed value, UTS(k) is the joint tensile strength value, and HV(k) is the joint microhardness value.

[0076] Combination Figure 1The working process of the model-free adaptive control method for the mechanical properties of FSW joints based on FNNDO is as follows:

[0077] The infrared thermal imager and piezoelectric dynamometer are used to collect the surface temperature and upsetting force signals of the weldment in the FSW process in real time, and the data are transmitted to the main control computer. The main control computer is embedded with an intelligent prediction model for the mechanical properties of the joint. First, the time axis of the temperature and force signals are aligned by downsampling, and these signals are used as the input of the prediction model to output the predicted values ​​of the tensile strength and microhardness of the joint. According to the set tensile strength and microhardness target values, the system calculates the deviation between the predicted value and the target value, and transmits the deviation to the CNC system of the FSW machine tool through the bus. The CNC system of the FSW machine tool consists of three parts: the upper processor, the lower processor and the servo driver. The upper processor integrates the FNNDO-MFAC controller, which generates the adjustment amount of the stirring head speed and welding speed by calculating the deviation, and transmits the adjustment amount as a control signal to the lower processor. The lower processor, as the control unit of the actuator, drives the servo system according to the control signal, and the servo driver controls the movement of the spindle motor and the worktable lead screw, thereby adjusting the stirring head speed and welding speed during the welding process, and finally realizing the closed-loop control of the mechanical properties of the FSW joint.

[0078] Next, the FNNDO-MFAC controller is designed.

[0079] like Figure 2 As shown, the FNNDO-MFAC control structure diagram embodies the control method of the example of the present invention, including a compact dynamic linearization model-free adaptive controller, a pseudo-Jacobi matrix estimator, and a fuzzy neural network disturbance observer. This method can effectively deal with the influence of interference and uncertainty on the control effect during the welding process.

[0080] The FSW process is described as a discrete-time nonlinear system with a total disturbance:

[0081]

[0082] Among them, f(…) is an unknown nonlinear function, which represents the nonlinear dynamic system of the FSW process; k is the sampling time; U(k) and Y(k) represent the input welding process parameters and output joint mechanical properties of the system at the current moment, respectively; u1(k) is the stirring head speed of the system at the current moment, and u2(k) is the welding speed at the current moment; y1(k) is the joint tensile strength of the system at the current moment, and y2(k) is the joint microhardness at the current moment; d(k) represents the total disturbance of the system at the current moment, including unmodeled dynamics, internal and external disturbances, and other uncertain factors; n y , n u , n dare three unknown positive integers, representing the order of system output, input and total disturbance.

[0083] When the total disturbance d(k) of the system is bounded, the function f(…) satisfies the continuity of partial derivatives of any variable of the FSW system and satisfies the generalized Lipschitz condition, the discrete-time nonlinear system of the FSW process in equation (1) can be equivalent to the following CFDL data model:

[0084] ΔY(k+1)=Φ c (k)ΔU(k)+r(k) (2)

[0085] In the formula, is the pseudo-Jacobian matrix of the FSW system, where φ ij is the partial derivative φ ij , R 2×2 represents a 2-dimensional real matrix space; r(k) is the total disturbance of the system; ΔY(k+1)=Y(k+1)-Y(k); ΔU(k)=U(k)-U(k-1), and ΔU(k)≠0.

[0086] The control input criterion function J(U(k)) of the FSW system is defined as:

[0087] J(U(k))=||Y * (k+1)-Y(k+1)|| 2 +λ||U(k)-U(k-1)|| 2 (3)

[0088] Among them, λ>0 is a weight factor; Y * (k+1) is the expected output signal of the system at the next moment; Y(k+1) is the actual output signal of the system at the next moment; U(k) is the input control quantity of the system at the current moment; U(k-1) is the input control quantity of the system at the previous moment.

[0089] Substituting the equivalent CFDL data model of equation (2) into the control input criterion function of equation (3), taking the derivative of U(k) and setting it equal to zero, we can obtain:

[0090]

[0091] Where I is the identity matrix.

[0092] Formula (4) contains a matrix inversion operation, which expands the single-input single-output model-free adaptive control law algorithm to obtain the following multi-input multi-output model-free adaptive control law algorithm:

[0093]

[0094] Among them, ρ1∈(0,1], ρ2∈(0,1] are the step factors.

[0095] Next, the pseudo-Jacobian matrix Φ in the control law is calculated in the pseudo-Jacobian matrix estimator. c The parameters of (k) are estimated online.

[0096] The estimation criterion function of the pseudo-Jacobian matrix J(Φ c (k)):

[0097]

[0098] Among them, μ>0 is a weight factor; is Φ c (k) is the estimated value; r(k-1) is the total interference of the system at the previous moment.

[0099] Minimizing equation (6), according to the inverse matrix lemma, we can obtain the pseudo-Jacobian matrix Φ c (k) estimation algorithm:

[0100]

[0101] Among them, η∈(0,2] is the step size factor; is the estimated value of r(k-1).

[0102] In order to make the online estimation algorithm have stronger time-varying tracking ability, the following reset mechanism is introduced to reset the value of the pseudo-Jacobian matrix:

[0103]

[0104] Among them, ε is a sufficiently small positive number.

[0105] Next, the FFNDO is used to estimate the total disturbance r(k) of the system and feed-forward compensate the disturbance to generate the FNNDO-MFAC controller.

[0106] From the CFDL data model of formula (2), we can get:

[0107] r(k-1)=Y(k)-Y(k-1)-Φ c (k-1)ΔU(k-1) (9)

[0108] Therefore, the input of the fuzzy neural network is defined as X = [Y(k), Y(k-1), U(k-1), Uk(-2), and the output is

[0109] Select Gauss function as the membership function, and the fuzzy neural network will output It can be expressed as:

[0110]

[0111] Where W is the weight matrix; is the fuzzy basis function vector; c and σ represent the center value vector and width vector of the membership function respectively.

[0112] Using the total disturbance of the FNNDO real-time observation system, the following dynamic observer is constructed:

[0113]

[0114] Among them, α is the state variable of the observer; the constant γ>0 is the gain of the observer; is the estimated value of the total disturbance; is the estimated value of the weight matrix; is the estimated value of the central value vector of the membership function; is the estimated value of the membership function width vector; is the estimated value of the fuzzy basis function vector.

[0115] Define the optimal values ​​of the weight matrix, membership function center value vector and width vector as W * , c * and σ * , then the true value of the total disturbance can be expressed as:

[0116]

[0117] Among them, τ is the approximation error, and its upper bound is

[0118] Define the tracking error of the observer as e = X-α, then Combining equation (11) and equation (12), we can get:

[0119]

[0120] Will exist Taking the first-order Taylor expansion as the first-order one and ignoring the higher-order expansion terms, equation (13) can be rearranged as:

[0121]

[0122] On this basis, the adaptive law of FNNDO parameters is selected as:

[0123]

[0124] Among them, δ W ,δ c and δ σ is a positive definite parameter matrix;

[0125] Combining equations (5), (7), (8) and (11), the FNNDO-MFAC controller algorithm for the mechanical properties of the FSW joint is obtained as follows:

[0126]

[0127] Finally, the controller was simulated and verified using MATLAB / Simulink software, which proved the effectiveness of the model-free adaptive control method of the mechanical properties of FSW joints based on FNNDO proposed in this paper.

[0128] Combination Figure 3 , the simulation process of the FNNDO-MFAC control scheme for the mechanical properties of FSW joints is as follows:

[0129] First, the simulation starts from T = 0s. Using the observed input and output data set {R(k-1), V(k-1), UTS(k), HV(k)} and the pseudo-Jacobian matrix estimation algorithm, the pseudo-Jacobian matrix Φ is calculated. c The value of (k) According to the target values ​​of joint tensile strength and microhardness, the deviation at the current moment is obtained; then the total disturbance of the system is estimated through the FNNDO algorithm. Then, based on the MFAC control algorithm, the stirring head speed R(k) and welding speed V(k) that should be applied to the FSW process at the current moment are calculated; the obtained R(k) and V(k) are applied to the current FSW process to obtain the input and output data set {R(k), V(k), UTS(k+1), HV(k+1)} at the next moment. By looping the above steps, the simulation will continue until the set time T0=20s ends.

[0130] In the simulation, the output parameters are the tensile strength and microhardness of the joint, and the input parameters are the stirring head rotation speed and welding speed. The target values ​​are set to 305MPa tensile strength and 100HV microhardness, respectively.

[0131] The simulation parameters of the MFAC controller are set by trial and error, as follows: ρ1 = 0.8, ρ2 = 0.6, η = 0.9, λ = 1, μ = 1.5, ε = 10 -5 , the initial value of the pseudo-Jacobian matrix of the given system is: The initial value of the given system control input is: U(0) = [300,50] T .

[0132] In the simulation, an unmeasurable step interference signal d(k) = 0.05 is added to simulate the disturbance in actual operation. FNNDO takes X = [UTS(k), HV(k), UTS(k-1), HV(k-1), R(k-1), V(k-1), R(k-2), V(k-2)] as input, and the input vector dimension m = 8. Set the number of FNNDO fuzzy rules n = 3. Set the specific simulation parameters of FNNDO as: γ = 1000, δ W =300,δ c =100,δ σ =50, Where m = 1, 2, ..., 8 and n = 1, 2, 3.

[0133] Figure 4 and Figure 5 The simulation results of the control tracking curve and input curve of the mechanical properties of the FSW joint are shown respectively.

[0134] The results show that the FNNDO-MFAC control algorithm of the present invention can effectively meet the requirements of FSW joint mechanical property control, and the control curve is smooth and stable. For the control of joint tensile strength and microhardness, the adjustment time of the controller is 6.2 seconds and 4.8 seconds respectively, the maximum overshoot is 6.12% and 4.32% respectively, and the steady-state error is 2.54MPa and 1.08HV. The above simulation results verify the effectiveness of the FNNDO-based model-free adaptive control method proposed in the present invention in adjusting the mechanical properties of FSW joints.

Claims

1. A model-free adaptive control method for mechanical properties of FSW joints, characterized in that: The following steps are involved: Step 1: Based on the compact dynamic linearization model CFDL, the dynamic data model of the FSW process is constructed, and the MFAC control law algorithm of the mechanical properties of the FSW joint based on CFDL is designed according to the control input criterion function; Considering the influence of system disturbance on the control effect, the FSW process is described as the following discrete time nonlinear system: Among them, f(…) is an unknown nonlinear function, which represents the nonlinear dynamic system of the FSW process; k is the sampling time; U(k) and Y(k) represent the input welding process parameters and output joint mechanical properties of the system at the current moment, respectively; u1(k) is the stirring head speed of the system at the current moment, and u2(k) is the welding speed at the current moment; y1(k) is the joint tensile strength of the system at the current moment, and y2(k) is the joint microhardness at the current moment; d(k) represents the total disturbance of the system at the current moment; n y , n u , n d are three unknown positive integers, representing the order of the system output, input and total disturbance; When the total disturbance d(k) of the system is bounded, the function f(…) satisfies the continuity of partial derivatives of any variable of the FSW system and satisfies the generalized Lipschitz continuity condition, the discrete-time nonlinear system of the FSW process in equation (1) can be equivalent to the following CFDL data model: ΔY(k+1)=Φ c (k)∆U(k)+r(k) (2) In the formula, is the pseudo-Jacobian matrix of the FSW system, which is given by the partial derivative φ ij The diagonally dominant matrix is ​​bounded at any time, where R 2×2 represents a 2-dimensional real matrix space; r(k) is the total disturbance of the system; ΔY(k+1)=Y(k+1)-Y(k); ΔU(k)=U(k)-U(k-1), and ΔU(k)≠0; The control input criterion function J(U(k)) of the FSW system is defined as: J(U(k))=||Y * (k+1)-Y(k+1)|| 2 +λ||U(k)-U(k-1)|| 2 (3) Among them, λ>0 is a weight factor, which is used to limit the change of control input, reduce the system steady-state error, and ensure the smoothness of control input; Y * (k+1) is the expected output signal of the system at the next moment; Y(k+1) is the actual output signal of the system at the next moment; U(k) is the input control quantity of the system at the current moment; U(k-1) is the input control quantity of the system at the previous moment; Substituting the equivalent CFDL data model of equation (2) into the control input criterion function of equation (3), taking the derivative of U(k) and setting it equal to zero, we can obtain: Where I is the identity matrix; Formula (4) contains a matrix inversion operation. When the input and output dimensions of the system are large, the matrix inversion operation is very time-consuming. Therefore, the single-input single-output model-free adaptive control law algorithm can be expanded to obtain a multi-input multi-output model-free adaptive control law algorithm of formula (5): Among them, ρ1∈(0,1], ρ2∈(0,1] are the operation step factors of the control law; In the control law algorithm of formula (5), the pseudo-Jacobian matrix Φ c (k) and the total system disturbance r(k) are unknown, so they need to be estimated; Step 2: Use the pseudo-Jacobian matrix estimator to calculate the pseudo-Jacobian matrix Φ in the control law algorithm c The parameters of (k) are estimated online; The estimation criterion function of the pseudo-Jacobian matrix J(Φ c (k)): Among them, μ>0 is a weight factor used to penalize excessive changes in the pseudo-Jacobian matrix estimate; Φ c (k) is the estimated value; r(k-1) is the total interference of the system at the previous moment; Minimizing equation (6), according to the inverse matrix lemma, we can obtain the pseudo-Jacobian matrix Φ c (k) estimation algorithm: Among them, η∈(0,2] is the operation step factor of the estimation algorithm; is the estimated value of r(k-1); In order to make the online estimation algorithm have stronger time-varying tracking ability and ensure that the pseudo-Jacobian matrix can maintain high accuracy and stability when facing parameter changes, the reset mechanism shown in formula (8) is introduced to reset the value of the pseudo-Jacobian matrix: if or |ΔU(k-1)|≤ε or So Among them, ε is a sufficiently small positive number; Step 3: Use FFNDO to estimate the total disturbance r(k) of the system and perform feed-forward compensation on the disturbance to generate the FNNDO-MFAC controller. From the CFDL data model of formula (2), we can get: r(k-1)=Y(k)-Y(k-1)-Φ c (k-1)ΔU(k-1) (9) Therefore, the input of the fuzzy neural network is defined as The output is Using Gauss function as membership function, the final output of fuzzy neural network is It can be expressed as: Where W is the weight matrix; is the fuzzy basis function vector; c and σ represent the center value vector and width vector of the membership function respectively; Using the total disturbance of the FNNDO real-time observation system, the following dynamic observer is constructed: Among them, α is the state variable of the observer; the constant γ>0 is the gain of the observer; is the estimated value of the total disturbance; is the estimated value of the weight matrix; is the estimated value of the central value vector of the membership function; is the estimated value of the membership function width vector; is the estimated value of the fuzzy basis function vector; Define the optimal values ​​of the weight matrix, membership function center value vector and width vector as W * 、c * and σ * , then the true value of the total disturbance can be expressed as: Among them, τ is the approximation error, and its upper bound is Define the tracking error of the observer as e = X-α, then Combining equation (11) and equation (12), we can get: Will exist Taking the first-order Taylor expansion as the first-order one and ignoring the higher-order expansion terms, equation (13) can be rearranged as: On this basis, the adaptive law of FNNDO parameters is selected as: Among them, δ W ,δ c and δ σ is a positive definite parameter matrix; Combining equations (5), (7), (8) and (11), the FNNDO-MFAC controller algorithm for the mechanical properties of the FSW joint is obtained as follows: Step 4: Based on the real-time collected welding temperature and upsetting force signals, an intelligent prediction model for the mechanical properties of the FSW joint is constructed, and the predicted joint mechanical properties Y(k) are used as the input of the FNNDO-MFAC controller in step 3. The welding process parameters are dynamically adjusted through real-time feedback, thereby achieving precise control of the mechanical properties of the FSW joint.

2. A model-free adaptive control method for mechanical properties of FSW joints according to claim 1, characterized in that: An intelligent prediction model for the mechanical properties of FSW joints was established with welding temperature and upsetting force as input variables and joint tensile strength and microhardness as output variables.

3. A model-free adaptive control method for mechanical properties of FSW joints according to claim 2, characterized in that: Infrared thermal imager and piezoelectric dynamometer are used to collect the weldment surface temperature and upsetting force signals in real time during the FSW process, and the data are transmitted to the main control computer for processing.

4. A model-free adaptive control method for mechanical properties of FSW joints according to claim 3, characterized in that: The main control computer is embedded with an intelligent prediction model for the mechanical properties of FSW joints. It aligns the time axes of temperature and force signals by downsampling, and uses these signals as inputs to the prediction model to output the predicted values ​​of tensile strength and microhardness of the joint in real time.

5. A model-free adaptive control method for mechanical properties of FSW joints according to claim 1, characterized in that: According to the tensile strength and microhardness prediction values ​​Y(k) obtained by the intelligent prediction model of joint mechanical properties, combined with the set target value Y * (k+1), calculate the deviation Y between the predicted value and the target value * (k+1)-Y(k), and the deviation is input into the FNNDO-MFAC controller in step 3 to calculate the required stirring head speed and welding speed adjustment; the actuator is driven by the servo system of the FSW machine tool to adjust the process parameters during the welding process, and finally the closed-loop control of the mechanical properties of the FSW joint is achieved.

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