Mirror image milling system sliding mode control method based on neural network disturbance observer

Abstract

The invention belongs to the technical field of intelligent control of mirror image milling processing systems, and discloses a sliding mode control method of a mirror image milling system based on a neural network disturbance observer. The method comprises the following steps: firstly, establishing a mirror image milling system nonlinear dynamic model containing parameter uncertainty and unknown disturbance; then designing a radial basis function neural network disturbance observer, and carrying out real-time accurate estimation and compensation on lumped disturbance in the system; designing a composite control law in combination with a non-singular fast terminal sliding mode control method, and ensuring that the system state is quickly converged in finite time; and finally, strictly proving the stability of the closed-loop system through a Lyapunov method. According to the method, vibration and deformation in the mirror image milling process can be effectively restrained, the trajectory tracking precision, disturbance rejection capacity and robustness of a machining system are remarkably improved, and the method is suitable for the high-precision and high-stability machining requirements of the aviation skin.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent control of mirror milling processing systems, and relates to a mirror milling system sliding mode control method based on a neural network disturbance observer. BACKGROUND

[0002] Mirror milling processing technology is a new type of flexible processing technology developed for thick and weakly rigid parts such as aircraft large skins, and has the characteristics of no pollution, high flexibility and high consistency. It is one of the key processes to replace traditional chemical milling and realize green manufacturing and intelligent manufacturing. With the development of China's C919 large passenger aircraft from the research and development stage to the batch production stage, and the development of MA700 and other regional passenger aircraft, the requirements for skin processing efficiency, quality and stability are increasing.

[0003] However, mirror milling processing still faces significant control problems in actual application, especially under mass production conditions. Due to the ultra-thin thickness and extremely weak structural rigidity of the skin, vibration and deformation are easily excited by cutting force during processing, resulting in loss of wall thickness precision and instability of the cutting process. The existing control methods mostly use traditional PID strategies with fixed parameters, lack real-time accurate observation ability of the internal state and external disturbance of the system, and are difficult to adaptively adjust according to nonlinear, time-varying disturbances and model uncertainties in processing. Therefore, when facing complex working conditions such as changes in skin curvature, release of material residual stress, and dynamic interaction between tool and workpiece, the control precision and stability are difficult to guarantee.

[0004] Some related research has tried to improve control performance. For example, Zhao Lele et al. (2023, CN202311299420.X) proposed an adaptive machine tool motion control method based on an improved genetic algorithm, which improved the trajectory tracking accuracy and robustness by optimizing PID parameters; Wei Wenlong et al. (2021, CN202110452285.2) disclosed a fuzzy sliding mode position control method based on a proportional integral sliding surface, which improved the dynamic response performance of the system. However, these methods do not estimate and compensate for internal and external disturbances, friction and other nonlinear disturbances in the processing process in real time, so there are still limitations in processing accuracy and stability when dealing with complex and variable working conditions of mirror milling.

[0005] Therefore, it is urgent to develop an intelligent control method that can estimate and compensate disturbances in real time, while having strong robustness and fast response capability, to realize high precision and high stability control of the mirror milling processing process. SUMMARY

[0006] To solve the above technical problems, the application provides a mirror milling system sliding mode control method based on a neural network disturbance observer.

[0007] The technical scheme of the application is as follows:

[0008] A mirror milling system sliding mode control method based on a neural network disturbance observer comprises the following steps:

[0009] Step S1: a nonlinear dynamics model of a mirror milling system containing parameter uncertainty and internal and external unknown disturbances is established.

[0010] According to Newton's second law and the rigid body fixed-axis rotation law, a torque balance equation of the mirror milling system is established.

[0011]

[0012] wherein, is a motor torque, is a load torque, and are an equivalent rotational inertia and an equivalent viscous damping coefficient of a ball screw feeding system respectively, is a motor rotation angle; wherein the equivalent rotational inertia of the ball screw feeding system is composed of multiple parts.

[0013]

[0014]

[0015] wherein, is a lead of the screw, and are the mass of the workbench and the workpiece respectively, and are the mass and the diameter of the screw respectively, , and represent the rotational inertia of the bearing, the coupling and the motor shaft respectively, is a screw damping, is a coupling damping, is a bearing damping;

[0016] Laplace transformation is performed on the formula to obtain:

[0017]

[0018] where, is the Laplace transform operator;

[0019] Therefore, the worktable displacement is related to the motor torque by the transfer function :

[0020]

[0021] where, and are the Laplace transforms of the worktable displacement and the input torque , respectively;

[0022] The current loop and the torque loop of the servo motor are simplified as the motor current constant and the torque constant ; then the motor torque is expressed as:

[0023]

[0024] where, is the control voltage;

[0025] Finally, according to the equation and the equation , and letting , the rigid-body transfer function between the control voltage and the worktable displacement is expressed as:

[0026]

[0027] where, is the Laplace transform of the control voltage ;

[0028] The actual displacement of the worktable is defined as the system state variable , and the actual velocity of the worktable is defined as the system state variable . Further considering that the mirror milling machining system is affected by parameter uncertainty and unknown internal and external disturbances during operation, the nonlinear dynamics model of the mirror milling machining system is written as:

[0029]

[0030] where, The total disturbance of the mirror milling machining system, including parameter uncertainty and internal and external unknown disturbances is a real number and has an upper bound, there exists , is the upper bound of the total disturbance , is a real set, satisfying ;

[0031] Step S2: Based on the nonlinear dynamics model of the mirror milling machining system, a RBF neural network disturbance observer is designed to estimate and compensate the total disturbance of the mirror milling machining system in real time;

[0032] The total disturbance of the mirror milling machining system is estimated by RBF neural network is:

[0033]

[0034]

[0035] wherein, is the ideal weight value of the RBF neural network; is the approximation error of the RBF neural network, satisfying , is the upper bound of the absolute value of the approximation error of the RBF neural network; and are the center and width of the jth Gaussian kernel function, respectively; is the output value of the jth radial basis kernel function; is an m-dimensional column vector composed of all ; m is the number of hidden layer radial basis kernel functions in the RBF neural network; The actual output of the RBF neural network is:

[0036]

[0037]

[0038] wherein, is the estimated weight value of the RBF neural network;

[0039] The approximation error of the RBF neural network satisfies the following:

[0040]

[0041]

[0042] wherein,​ weight error of ideal weight value and estimated weight value of RBF neural network weight;

[0043] Step S3: design a non-singular fast terminal sliding mode surface to ensure the fast finite time convergence of the mirror milling system state, and combine the non-singular fast terminal sliding mode surface with the actual output of the RBF neural network in step S2 , output the final control voltage;

[0044] Define the tracking error of the mirror milling system 、 as follows:

[0045]

[0046] wherein, and are the actual displacement and actual speed of the workbench respectively, and are the reference displacement and reference speed respectively, and are the derivatives of and respectively;

[0047] The non-singular fast terminal sliding mode surface is designed as follows:

[0048]

[0049] wherein, 、 、 are normal numbers, 、 are all positive odd numbers, and ;

[0050] The derivative of the non-singular fast terminal sliding mode surface is:

[0051]

[0052] Substitute equation (13) and equation (14) into equation (12) , and obtain:

[0053] The compound reaching law is designed as follows:

[0054]

[0055]

[0056] ​In the formula, 、 、 is a normal number, ;

[0057] In order to ensure the stability of the mirror milling system, the control voltage is designed as follows:

[0058]

[0059] Step S4: constructing Lyapunov function, and analyzing the stability of the closed loop system composed of the disturbance observer and the non-singular fast terminal sliding mode surface;

[0060] 1) finite time reachable analysis of the non-singular fast terminal sliding mode surface:

[0061] The Lyapunov function equation is constructed as follows: And the RBF neural network weight adaptive update rate is designed as follows: Wherein ; the Lyapunov function is designed as follows: The first order derivative of the Lyapunov function with respect to time t is The non-singular fast terminal sliding mode surface is bounded, and the weight error is bounded;

[0062] According to the finite time convergence theorem, the mirror milling system converges to in finite time :

[0063]

[0064] In the formula, ;

[0065] 2) error convergence analysis:

[0066] The Lyapunov function equation is defined as follows: ;

[0067] According to the finite time convergence theorem, the tracking error of the mirror milling system converges to 0 in finite time ;

[0068]

[0069] In the formula, , .

[0070] The beneficial effects of the present application are:

[0071] Strong disturbance estimation and compensation capability: the application designs a disturbance observer based on RBF neural network, which can estimate the complex lumped disturbance (including model uncertainty, cutting force variation, external disturbance) in the mirror milling process with high precision and self-adaptation. Compared with the traditional fixed gain observer or linear disturbance observer, the application has stronger approximation ability and estimation accuracy for nonlinear and time-varying disturbance.

[0072] High control precision and stability: by combining the neural network disturbance observer with the nonsingular fast terminal sliding mode control, the composite controller constructed by the application can actively offset the disturbance effect, significantly reducing the sensitivity of the system to disturbance. This method not only ensures the rapid convergence of the system state in a limited time and effectively eliminates the steady-state error of the traditional linear sliding mode, but also avoids the singularity problem that may occur in the terminal sliding mode, thereby realizing higher precision trajectory tracking and more stable processing of the mirror milling system. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 Fig. 1 is a schematic diagram of the mirror milling system sliding mode control method based on the neural network disturbance observer of the embodiment of the application;

[0074] Figure 2 Fig. 2 is a schematic diagram of the displacement response trajectory of the mirror milling system tracking the sinusoidal reference signal of the embodiment of the application; wherein (a) is the displacement tracking curve of the workbench, and (b) is the tracking error curve;

[0075] Figure 3 Fig. 3 is a schematic diagram of the displacement response trajectory of the mirror milling system tracking the step reference signal of the embodiment of the application; wherein (a) is the displacement tracking curve of the workbench, and (b) is the tracking error curve. DETAILED DESCRIPTION

[0076] The specific embodiments of the application will be further described in combination with the drawings and technical solutions.

[0077] A mirror milling system sliding mode control method based on a neural network disturbance observer, comprising the following steps:

[0078] Step S1: establishing a nonlinear dynamic model of the mirror milling system containing parameter uncertainty and internal and external unknown disturbance.

[0079] Step S2: based on the nonlinear dynamic model of the mirror milling system, designing an RBF neural network disturbance observer for real-time estimation and compensation of the total disturbance of the mirror milling system;

[0080] Step S3: design a non-singular fast terminal sliding mode surface to ensure the fast finite time convergence of the mirror milling system state, and combine the non-singular fast terminal sliding mode surface with the actual output of the RBF neural network in step S2 , output the final control voltage;

[0081] Step S4: construct a Lyapunov function to analyze the stability of the closed-loop system composed of the disturbance observer and the non-singular fast terminal sliding mode surface, and strictly prove the stability and convergence of the mirror milling system, so as to ensure the high-precision and high-stability motion control of the mirror milling system.

[0082] Step S1 specifically includes:

[0083] The mirror milling system is a typical ball screw feeding system. The controller outputs a control voltage to act on the servo motor, so that the servo motor generates a torque to drive the screw to rotate, and then the rotation is converted into linear motion of the workbench by the nut. In addition, the workbench will also be affected by external disturbances during operation, including cutting force along the screw axis and nonlinear friction. According to Newton's second law and the rigid body fixed axis rotation law, the torque balance equation of the mirror milling system is established as follows:

[0084]

[0085] wherein, is the motor torque, is the load torque, and are the equivalent rotational inertia and equivalent viscous damping coefficient of the ball screw feeding system, respectively, is the motor angle; wherein the equivalent rotational inertia of the ball screw feeding system has multiple parts:

[0086]

[0087]

[0088] wherein, is the lead of the screw, and are the mass of the workbench and the workpiece, respectively, and are the mass and diameter of the screw, respectively, , and represent the rotational inertia of the bearing, coupling and motor shaft, respectively, is the screw damping, is the coupling damping, is the bearing damping;

[0089] Taking Laplace transform of equation (22), we have

[0090]

[0091] where, is the complex frequency domain variable, and L is the Laplace transform operator;

[0092] Therefore, the worktable displacement is related to the motor torque by the transfer function :

[0093]

[0094] where, and are the Laplace transforms of the worktable displacement and the input torque , respectively;

[0095] The current loop and the torque loop of the servo motor are simplified as the motor current constant and the torque constant ; then the motor torque is expressed as:

[0096]

[0097] where, is the control voltage;

[0098] According to and , and let , then the rigid body transfer function between the control voltage and the worktable displacement is expressed as:

[0099]

[0100] where, is the Laplace transform of the control voltage ;

[0101] The actual displacement of the worktable is defined as the system state variable , and the actual velocity of the worktable is defined as the system state variable . Further considering the influence of parameter uncertainty and external unknown disturbance on the mirror milling system during operation, the nonlinear dynamics model of the mirror milling system is written as:

[0102]

[0103] in, The total disturbance of the mirror milling system includes parameter uncertainties and unknown internal and external disturbances; For real numbers and with an upper bound, there exists , For total disturbance The upper realm, Let be the set of real numbers, satisfying .

[0104] Step S2 specifically includes:

[0105] In practice, the total disturbance of a mirror milling system The upper bound of the disturbance is unknown and it is a nonlinear function, therefore an observer needs to be designed to estimate the disturbance of the mirror milling system. RBF neural networks have strong learning and approximation capabilities for nonlinear functions and have been widely used in pattern recognition, signal processing, modeling, and online control systems. Therefore, RBF neural networks are used to estimate the total disturbance of the mirror milling system. It can be described as:

[0106]

[0107]

[0108] In the formula, These are the ideal weight values ​​for an RBF neural network; The approximation error of the RBF neural network satisfies , This is the upper bound of the absolute value of the approximation error of the RBF neural network; and The first The center and width of a Gaussian kernel function; Let be the output value of the j-th radial basis kernel function; For is by all The m-dimensional column vector is formed; m is the number of hidden radial basis kernel functions in the RBF neural network.

[0109] The actual output of the RBF neural network is:

[0110]

[0111] The actual output of the RBF neural network is:

[0112] The approximation error of the RBF neural network satisfies the following equation:

[0113]

[0114]

[0115] wherein, is the weight error of the ideal weight value of the RBF neural network weight and the estimated weight value.

[0116] Step S3 specifically comprises:

[0117] The non-singular fast terminal sliding mode control avoids the singularity problem that may occur in the terminal sliding mode, and a compound approach rate that can converge in a finite time is designed, so as to realize higher-precision trajectory tracking and more stable processing of the mirror milling system.

[0118] The tracking error of the mirror milling system is defined as , :

[0119]

[0120] wherein, and are the actual displacement and actual speed of the workbench respectively, and are the reference displacement and reference speed respectively, and are the derivatives of and respectively;

[0121] The non-singular fast terminal sliding surface is designed as follows:

[0122]

[0123] wherein, , , are normal numbers, , are all positive odd numbers, and ;

[0124] The derivative of the non-singular fast terminal sliding surface is:

[0125]

[0126] Substituting into , the following equation can be obtained:

[0127]

[0128] The compound approaching law is designed as:

[0129]

[0130] In the formula, , , is a constant number, .

[0131] In order to ensure the stability of the mirror milling machining system, the control voltage is designed as:

[0132]

[0133] The step S4 specifically comprises:

[0134] For the designed non-singular fast terminal sliding mode control based on the neural network disturbance observer, the convergence and stability of the closed-loop system are analyzed by using the Lyapunov method.

[0135] In order to ensure the stability of the mirror milling machining system, the control voltage is designed as:

[0136] The Lyapunov function equation is constructed as: , and the RBF neural network weight adaptive update rate is designed as , then

[0137]

[0138] In the formula, ; the , then the Lyapunov function The first order derivative of time t , the non-singular fast terminal sliding surface is bounded, and the weight error is bounded;

[0139] And since , it is obtained that , substitute :

[0140]

[0141] In the formula, .

[0142] According to the finite time convergence theorem, the mirror milling system converges to in finite time :

[0143]

[0144] 2) Error convergence analysis:

[0145] The mirror milling system state reaches the nonsingular fast terminal sliding mode surface in finite time, and maintains on the nonsingular fast terminal sliding mode surface, that is, At this time,

[0146]

[0147] where, , , is a constant, and .

[0148] Define the Lyapunov function equation as:

[0149]

[0150] Let , ,

[0151]

[0152] where, , . According to the finite time convergence theorem, the system converges to 0 in finite time .

[0153]

[0154] In order to further illustrate the effectiveness of the mirror milling system sliding mode control method based on the neural network disturbance observer of the application, simulation verification is carried out on the Matlab / Simulink platform.

[0155] The specific simulation results are shown in Figure 2 and Figure 3 . Figure 2 is the workbench displacement response trajectory of the mirror milling system; Figure 3 is the tracking error response trajectory of the mirror milling system.

[0156] AsFigure 2 and Figure 3 As shown in FIG. 9, in the presence of external disturbances, the worktable displacement response of the mirror milling system can still quickly and accurately track the reference signal and quickly suppress the influence of disturbances. This fully verifies that the mirror milling system sliding mode control method based on the neural network disturbance observer proposed in the present application has high response speed, high control accuracy and strong robustness, and can meet the control requirements of high precision and high stability of the mirror milling system.

Claims

1. A sliding mode control method for a mirror milling system based on a neural network perturbation observer, characterized in that, Includes the following steps: Step S1: Establish a nonlinear dynamic model of the mirror milling system that includes parameter uncertainties and unknown internal and external disturbances; Step S2: Based on the nonlinear dynamic model of the mirror milling system, design an RBF neural network perturbation observer to estimate and compensate for the total perturbation of the mirror milling system in real time; Step S3: Design a non-singular fast terminal sliding surface to ensure fast finite-time convergence of the mirror milling system state, and combine the non-singular fast terminal sliding surface with the actual output of the RBF neural network in step S2. The final control voltage is output. Step S4: Construct the Lyapunov function and perform stability analysis on the closed-loop system consisting of a perturbation observer and a non-singular fast terminal sliding surface.

2. The sliding mode control method for a mirror milling system based on a neural network perturbation observer according to claim 1, characterized in that, The specific implementation process of the first step is as follows: Based on Newton's second law and the law of rigid body rotation about a fixed axis, the torque balance equation for the mirror milling system is established as follows: in, This is the motor torque. For load torque, and These are the equivalent moment of inertia and equivalent viscous damping coefficient of the ball screw feed system, respectively. The rotation angle is the motor angle; the equivalent moment of inertia of the ball screw feed system consists of multiple parts: In the formula, For the lead screw, and The masses of the worktable and the workpiece are respectively. and These are the mass and diameter of the lead screw, respectively. , and These represent the moments of inertia of the bearing, coupling, and motor shaft, respectively. For lead screw damping, For coupling damping, For bearing damping; Pair Performing the Laplace transform, we get: in, For variables in the complex frequency domain, use the Laplace transform operator; Therefore, the table displacement With motor torque The transfer function is : In the formula, and These are the table displacements. With input torque Laplace transform; The current loop and torque loop of the servo motor are simplified to the motor current constant. and torque constant Therefore, the motor torque is expressed as: in, To control the voltage; Finally, according to the formula Japanese style and order At this point, the rigid body transfer function between the control voltage and the table displacement is expressed as: In the formula, To control voltage Laplace transform; Define the actual displacement of the worktable System state variables Its actual speed System state variables Considering the influence of parameter uncertainties and unknown internal and external disturbances on the mirror milling system during operation, the nonlinear dynamic model of the mirror milling system is written as follows: in, The total disturbance of the mirror milling system includes parameter uncertainties and unknown internal and external disturbances; For real numbers and with an upper bound, there exists , For total disturbance The upper realm, Let be the set of real numbers, satisfying .

3. The sliding mode control method for a mirror milling system based on a neural network perturbation observer according to claim 2, characterized in that, The specific implementation process of the second step is as follows: The total disturbance of the mirror milling system is estimated using an RBF neural network. ,for: In the formula, These are the ideal weight values ​​for an RBF neural network; The approximation error of the RBF neural network satisfies , This is the upper bound of the absolute value of the approximation error of the RBF neural network; and The first The center and width of a Gaussian kernel function; Let be the output value of the j-th radial basis kernel function; For is by all The m-dimensional column vector is formed; m is the number of hidden radial basis kernel functions in the RBF neural network. The actual output of the RBF neural network is: In the formula, These are the estimated weight values ​​for the RBF neural network; The approximation error of the RBF neural network satisfies the following: In the formula, The weight error is the difference between the ideal weight value and the estimated weight value of the RBF neural network.

4. The sliding mode control method for a mirror milling system based on a neural network perturbation observer according to claim 3, characterized in that, The specific implementation process of the third step is as follows: Define the tracking error of the mirror milling system , for: in, and These represent the actual displacement and actual velocity of the worktable, respectively. and These are the reference displacement and reference velocity, respectively. and They are respectively and The derivative; Design the following non-singular fast terminal sliding surface: In the formula, , , For positive integers, , All are positive odd numbers, and ; The derivative of the non-singular fast terminal sliding surface is: The formula Substitution of formula (14) ,have to: The composite convergence law is designed as follows: In the formula, , , For positive integers, ; To ensure the stability of the mirror milling system, the control voltage is designed. for: 。 5. The sliding mode control method for a mirror milling system based on a neural network perturbation observer according to claim 1, characterized in that, The specific implementation process of the fourth step is as follows: 1) Finite-time reachability analysis of non-singular fast terminal sliding surfaces: The Lyapunov function equations are constructed as follows: And design an RBF neural network with an adaptive weight update rate. ,in ;design Then the Lyapunov function First derivative with respect to time t Non-singular fast terminal sliding surface Bounded, weighted error Bounded; According to the finite-time convergence theorem, the mirror milling system converges in a finite time... converged to : In the formula, ; 2) Error convergence analysis: Define the Lyapunov function equation as follows: ; According to the finite-time convergence theorem, the tracking error of a mirror milling system converges within a finite time. Converging to 0; In the formula, , .

Images