Laser processing reflector predictive control method based on dimension expansion mapping dynamical model

Abstract

The invention provides a laser processing reflector predictive control method based on a dimension expansion mapping dynamical model, and belongs to the field of laser processing reflector motion control, and the method comprises the following steps: S1, providing a dynamical model based on neural network dimension expansion mapping in combination with a neural network and a linear model, so as to describe the double-axis dynamic characteristics of a laser processing reflector; s2, identifying parameters in the dimension expansion mapping dynamical model by solving an optimization problem based on input and output data; s3, designing a linear quadratic programming problem based on the dimension expansion mapping dynamical model and the control target; and S4, solving a quadratic programming problem to obtain a predictive controller with nonlinear feed-forward compensation capability. The method mainly solves the problem of trajectory tracking of the biaxial laser processing reflector under high-frequency sampling, and can solve the problem of insufficient tracking precision caused by nonlinearity of a reflector driver and the problem of difficulty in solving the nonlinear optimization problem under rapid sampling.

Description

Technical Field

[0001] The present invention belongs to the field of motion control of laser processing mirrors, and particularly relates to a predictive control method for laser processing mirrors based on an extended-dimensional mapping dynamics model. Background Art

[0002] Laser processing mirrors play an important role in the field of industrial manufacturing. They can achieve precise laser pointing motion control by tracking specific yaw trajectories, which is of great significance for intelligent manufacturing fields such as semiconductor lithography. However, the driver of the laser processing mirror has a non-linear dynamics that is difficult to characterize, and its action mechanism is complex. In addition, since the motion mode of the mirror is two-axis yaw, its internal structure determines that there must be coupling caused by installation or processing accuracy problems between the two axes. Both the complex non-linear dynamics and the coupling between the two axes pose difficulties for the construction of the laser processing mirror dynamics model, further restricting the improvement of the mirror control accuracy. On the other hand, even if the dynamics characteristics of the mirror are characterized by a non-linear model, the difficulty of solving the control input will inevitably increase due to the introduction of non-linearity, which further restricts the deployment of the control algorithm on fast-sampling hardware.

[0003] Some existing methods fit the non-linear dynamics through neural networks and apply them to the linear model structure in a parallel manner. Subsequently, the non-linear optimal problem is transformed into a linear optimal problem through compensation. The control input obtained in this way is not optimal, and there is room for further improvement in performance. For the modeling method that applies the neural network output in a cascaded form to the linear model structure, the solution of its non-linear optimization problem is very cumbersome, and the contradiction between the calculation time and the sampling frequency is very significant in practical applications. Summary of the Invention

[0004] In order to solve the non-linear dynamics of the mirror driver and the coupling between the two-axis mechanical structures of the mirror, the present invention provides a predictive control method for laser processing mirrors based on an extended-dimensional mapping dynamics model. The historical input and output data are used as the network input of the neural network, and the output of the neural network is used as the non-linear mapping state, so as to construct a new state of the dynamics model based on the neural network extended-dimensional mapping. The parameter identification process of this extended-dimensional mapping dynamics model is based on a linear structure, which is convenient for subsequent quadratic programming problem solving, and solves the contradiction between the high-speed sampling hardware conditions and the control input solution time. The present invention is mainly used to deal with the non-linear characteristics of the laser processing mirror driver itself and the problem of mutual coupling between the two axes of the mirror during the motion process, and also solves the problem of implementing the optimal control algorithm of the non-linear system under high-frequency sampling hardware.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model, comprising the following steps:

[0007] S1. Combining a neural network and a linear model to propose a dynamics model based on neural network extended dimension mapping to characterize the dynamic characteristics of the two axes of the laser processing mirror;

[0008] S2. Identifying the parameters in the extended dimension mapping dynamics model by solving an optimization problem based on input-output data;

[0009] S3. Designing a linear quadratic programming problem based on the extended dimension mapping dynamics model and the control objective;

[0010] S4. Solving the linear quadratic programming problem to obtain a predictive controller with non-linear feedforward compensation ability for predictive control.

[0011] The beneficial effects of the present invention are as follows:

[0012] 1. The method of the present invention includes a dynamics model based on neural network extended dimension mapping for characterizing the dynamics of the laser processing mirror. The present invention characterizes the non-linear dynamics of the actuator and the coupling between the two axes through the mapping relationship of the neural network, makes full use of historical input-output data, and improves the accuracy of the dynamics model.

[0013] 2. Aiming at the problem of difficult quadratic programming solution caused by the non-linear model structure, the dynamics model based on neural network extended dimension mapping constructed by the present invention has the advantages of a linear model structure in controller solution, and transforms the solution of complex non-linear optimization problems into off-line linear model structure parameter identification and linear quadratic programming problem solution.

[0014] 3. In order to ensure the tracking accuracy of the laser processing mirror for different types of reference trajectories, the present invention designs a cost function in a finite time domain based on the extended dimension mapping dynamics model and the control objective, and obtains an analytical predictive controller with non-linear feedforward compensation ability through the solution of the linear quadratic programming problem, ensuring that the control algorithm can be effectively deployed on a hardware platform with fast sampling characteristics. Description of the Drawings

[0015] Figure 1 is a flow chart of the predictive control method for a laser processing mirror based on the extended dimension mapping dynamics model of the present invention;

[0016] Figure 2 is a structure and identification schematic diagram of the extended dimension mapping dynamics model of the laser processing mirror;

[0017] Figure 3 is a two-axis scanning trajectory diagram of the laser processing mirror after inputting the reference trajectory;

[0018] Figure 4 Tracking diagram of the X-axis output rotation angle of the laser processing mirror after inputting the reference trajectory;

[0019] Figure 5 Tracking error diagram of the X-axis of the laser processing mirror after inputting the reference trajectory;

[0020] Figure 6 Tracking diagram of the Y-axis output rotation angle of the laser processing mirror after inputting the reference trajectory;

[0021] Figure 7 Tracking error diagram of the Y-axis of the laser processing mirror after inputting the reference trajectory. Specific implementation manner

[0022] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific implementation examples described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0023] As Figure 1 shown, the present invention proposes a predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model, including the following steps:

[0024] Step S1: Combine a neural network and a linear model to propose a dynamics model based on neural network extended dimension mapping to characterize the dynamic characteristics of the two axes of the laser processing mirror, including:

[0025] Establish the system state vector at the

[0026] moment according to the historical input and output data of the laser processing mirror as:

[0027] where represents at the moment, is used to define variables, and the subscript corresponds to the th axis of the laser processing mirror, is the rotation angle output of the th axis of the laser processing mirror at the moment, is the control input of the th axis of the laser processing mirror at the moment, Represents the model order of a single axis of the laser processing mirror. In the present invention, it is assumed that the orders of the two axes are the same. Represents taking the transpose of a vector or matrix. Denotes the set of real numbers.

[0028] For convenience of representation, The control input of the laser processing mirror at time Is represented as:

[0029] ,

[0030] The Angle output of the laser processing mirror at time is represented as:

[0031] ,

[0032] In order to characterize the non - linear characteristics brought by the actuator in the laser processing mirror and the coupling characteristics between the two axes, a non - linear mapping state vector as shown below is established based on neural network technology :

[0033] ,

[0034] Wherein, Represents the mapping neural network output with As the input and As the neural network parameters. The original system state vector is augmented according to the non - linear mapping state vector generated by this neural network to obtain The state vector of the dimension - expanded mapping dynamic model of the laser processing mirror at time :

[0035] ,

[0036] Wherein, Indicates that several internal vectors are stacked in sequence into a column vector. Then, the dynamic model of the laser processing mirror based on neural network dimension - expanded mapping is:

[0037] ,

[0038] Wherein, Is the Prediction of the state vector of the dimension - expanded mapping dynamic model at time , Is the Angle output vector of the two axes at time predicted by the dimension - expanded mapping dynamic model, Represents a zero matrix matching the dimension of the matrix where it is located, Is the matrix to be identified related to the non - linear mapping state vector Parameter intermediate matrix Satisfy:

[0039] ,

[0040] Among them, the parameter intermediate matrix of the i-th axis is in the form of:

[0041] ,

[0042] ,

[0043] ;

[0044] Among them, is the parameter to be identified related to the historical output of the -th axis of the laser processing mirror, is the parameter to be identified related to the historical input of the -th axis of the laser processing mirror.

[0045] Step S2: Identify the parameters in the extended dimension mapping dynamics model by solving the optimization problem based on the input-output data, including:

[0046] First, input sinusoidal sweep signals with rich spectra to the two axes of the laser processing mirror respectively, record the corresponding angular output of the two axes under this sweep signal, and identify according to the following linear model structure:

[0047] ,

[0048] In the above linear system identification process, select different model orders, compare the differences between the identification results and the actual data, and select the and with the best fitting effect, and then obtain the in the dynamics model of the laser processing mirror based on the neural network extended dimension mapping;

[0049] Subsequently, represent the input-output data recorded in the above identification process as the following data tuple :

[0050] ,

[0051] To ensure the sufficiency of the data and the effectiveness of the extended dimension mapping dynamics model, is divided into two parts. Most of them are used for the tuples to train the model, denoted as , and the other part is used for the tuples to evaluate the identification results, denoted as . For , Figure 2Schematic diagram of the structure and identification of the dimensional expansion mapping dynamic model for the laser processing mirror. In the model, and can be obtained by solving the following optimization problem:

[0052] ,

[0053] where, represents minimizing the cost function by adjusting . The loss in Figure 2 represents the cost function in this optimization problem. is the number of tuples in . represents the square of the vector norm. is a positive constant for increasing sparsity. is the time in the optimization problem. In the above optimization process, obtained according to the linear model structure identification remains unchanged. By changing the network structure and parameters to minimize the one-step prediction error in the optimization problem, and are determined, and then the dimensional expansion mapping-based dynamic model of the neural network is obtained.

[0054] Step S3: Design a linear quadratic programming problem based on the dimensional expansion mapping dynamic model and the control objective, including:

[0055] To make the angular output of the laser processing mirror match the reference trajectory exactly, the following optimization problem is designed:

[0056] ,

[0057] where, is the reference trajectory vector at time . A positive constant. Based on the solution requirements of the above optimization problem, the following cost function in the finite-time form is designed :

[0058] ,

[0059] where, is the optimal control input sequence to be solved. is the prediction step. is the angular output of the laser processing mirror predicted time instants forward from time is the angular output of the laser processing mirror predicted The reference trajectory of the laser processing mirror at a certain moment, is the control input of the laser processing mirror predicted for is the control input increment of the laser processing mirror predicted for

[0060] Based on the above cost function, combined with the dynamic model of neural network dimensionality expansion mapping, the following linear quadratic programming problem is designed:

[0061] ,

[0062] satisfying: ,

[0063] ,

[0064] ,

[0065] ,

[0066] ;

[0067] wherein, is the solution of the quadratic programming problem, represents solving for the that minimizes the cost function, represents the state parameter intermediate matrix of the dimensionality expansion mapping dynamic model predicted for , , .

[0068] Step S4: Solve the quadratic programming problem to obtain a predictive controller with non-linear feedforward compensation ability, including:

[0069] First, express the linear quadratic programming problem in S3 in the following compact form:

[0070] ,

[0071] wherein, is the control input sequence predicted from 0 to for , represents the optimal value of, represents solving for the ; The specific forms of the remaining intermediate variables are as follows:

[0072] ,

[0073] ,

[0074] ,

[0075] ,

[0076] ,

[0077] , ,

[0078] , , ;

[0079] Since is a positive definite matrix, solving the linear quadratic programming problem can be transformed into solving , then the optimal control input sequence of the laser processing mirror is , take the first element in as the optimal control input of the optical processing mirror at

[0080] ,

[0081] where represents the matrix formed by the first and second rows of

[0082] Example:

[0083] To train the dimension-expanded mapping dynamics model, a sine excitation signal with an amplitude of 0 volts to 8 volts and a frequency of 1 Hz to 300 Hz is input to the laser processing mirror, and 1 million sample data are collected at a sampling frequency of 20 kHz. 90% of them are used as the training set, and the remaining 10% are used to evaluate the identification results. The neural network structure adopts a two-layer network structure with 30 single-layer nodes. The activation function uses Leaky ReLU. The training process uses the Adam optimizer. The number of samples used each time is 200, the learning rate is 0.005, and the number of repeated training times is 20.

[0084] (1) Closed-loop tracking simulation:

[0085] Reference trajectory: ,

[0086] where represents the sampling time, is the frequency of the reference trajectory signal, which is selected as 10 in this simulation, and the remaining parameters are selected as: controller parameters , prediction step size .

[0087] The simulation results are as Figures 3 to 7 shown, where Figure 3 is the biaxial scanning trajectory diagram of the laser processing mirror after inputting the above reference trajectory. Figure 4 is the X-axis output rotation angle tracking diagram of the laser processing mirror after inputting the above reference trajectory, Figure 5 is the tracking error diagram of the X-axis of the laser processing mirror after inputting the above reference trajectory, Figure 6 is the Y-axis output rotation angle tracking diagram of the laser processing mirror after inputting the above reference trajectory, Figure 7 is the tracking error diagram of the Y-axis of the laser processing mirror after inputting the above reference trajectory. The maximum steady-state tracking error of the X-axis does not exceed 4 micro-radians, and the maximum steady-state tracking error of the Y-axis does not exceed 2.5 micro-radians.

[0088] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model, characterized in that It includes the following steps: S1. Combine a neural network with a linear model to propose a dynamic model based on neural network dimensionality expansion mapping to characterize the dynamic characteristics of the two axes of a laser processing mirror; S2. Identify the parameters in the dimensionality expansion mapping dynamic model by solving an optimization problem based on input-output data; S3. Design a linear quadratic programming problem based on the dimensionality expansion mapping dynamic model and the control objective; S4. Solve the linear quadratic programming problem to obtain a predictive controller with non-linear feedforward compensation ability for predictive control.

2. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 1, wherein The S1 includes: Establish based on the historical input and output data of the laser processing mirror The system state vector at the moment is , is The control input of the laser processing mirror at the moment, is The rotation angle output of the laser processing mirror at the moment.

3. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 1, characterized in that The S1 also includes: To characterize the nonlinear characteristics brought by the actuator in the laser processing mirror and the coupling characteristics between the two axes, a nonlinear mapping state vector is established based on neural network technology , where represents the mapping neural network output with as the input and as the neural network parameters 4. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 3, characterized in that, The S1 also includes: The state vector of the original system is augmented according to the non-linear mapping state vector generated by the neural network to obtain the state vector of the dimension-expanded mapping dynamic model of the laser processing mirror at time, where means stacking a number of internal vectors in sequence into a column vector. Then, the dynamic model of the laser processing mirror based on neural network dimension-expanded mapping is: ， Among them, is the prediction of the state vector of the time-expanded mapping dynamics model . is the output vector of the rotation angles of the two axes at the time predicted by the expanded mapping dynamics model. represents the zero matrix matching the dimension of the matrix where it is located. is the matrix to be identified related to the non-linear mapping state vector . is the parameter intermediate matrix.

5. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 4, wherein The S2 includes: Input sinusoidal sweep signals with rich spectra to the two axes of the laser processing mirror respectively, record the corresponding angular output of the two axes under this sweep signal, select different model orders during the linear system identification process, compare the differences between the identification results and the actual data, select the system parameters with the best fitting effect, and then obtain the .

6. The predictive control method for a laser processing mirror based on the extended dimension mapping dynamics model according to claim 5, characterized in that The S2 also includes: Represent the input and output data recorded in the above identification process in the form of tuples , to ensure the sufficiency of the data and the effectiveness of the dimension-expanded mapping dynamic model is divided into two parts. One part is the tuples used to train the model, denoted as , and the other part is the tuples used to evaluate the identification results, denoted as ; for , in the dynamic model based on the neural network dimension-expanded mapping and are obtained by solving the following optimization problem: ， Among them, denotes minimizing the cost function by adjusting , is the number of tuples in , represents the 1-norm of the matrix, represents the square of the vector norm, is a positive constant for increasing sparsity; in the above optimization process, the obtained according to the linear model structure identification remains unchanged. By changing the network structure and parameters to minimize the one-step prediction error in the optimization problem, determine and . After that, obtain the determined dynamic model based on the neural network extended dimension mapping.

7. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamic model according to claim 6, characterized in that The S3 includes: Design the cost function in the following finite-time form : ， Among them, is the optimal control input sequence to be solved, is the prediction step length, is the angular output of the laser processing mirror predicted for time instants ahead, is the reference trajectory of the laser processing mirror predicted for time instants ahead, is the control input of the laser processing mirror predicted for time instants ahead, and is the control input increment of the laser processing mirror predicted 8. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 7, characterized in that The S3 also includes: Based on the above cost function, combined with the dynamic model based on neural network dimensionality expansion mapping, design the following linear quadratic programming problem: ， Satisfy: , ， ， ， ； Among them, is the solution of the quadratic programming problem, represents solving for the that minimizes the cost function, represents predicting forward time steps of the state parameter intermediate matrix of the extended mapping dynamics model, , , .

9. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 8, wherein The S4 includes: Express the linear quadratic programming problem in S3 in the following compact form: ， Among them, , represents its optimal value, , , , , are all intermediate variables; means stacking several internal vectors into a column vector in sequence; means solving for the that minimizes the parameter; means at the moment of, represents the prediction step size, is the control input of the laser processing mirror predicted forward time instants at the moment of, .

10. The predictive control method for a laser processing mirror based on an extended dimension mapping dynamics model according to claim 9, wherein The S4 also includes: Due to the intermediate variable being a positive definite matrix, solving the linear quadratic programming problem is transformed into solving , then the optimal control input sequence of the laser processing mirror is . Taking the first element in as the optimal control input of the optical processing mirror at the moment

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