Dynamic compensation method for yawing angle of double-drive synchronous control of precision motion platform

Abstract

The application relates to a precision motion platform double-drive synchronous control deflection angle dynamic compensation method, and relates to the control field of a double-drive gantry motion platform. The method solves the problem of poor compensation effect of the deflection angle compensation method in the prior art. The precision motion platform double-drive synchronous control deflection angle dynamic compensation method obtains a plurality of synchronous error compensation values of the crossbeam and the guide rail in the local vertical condition at a plurality of positions through an iterative identification method, and adopts a fitting technology to obtain a synchronous error compensation function. The estimated value of the deflection angle is dynamically compensated in real time in the control algorithm operation process, and the dynamic compensation effect is improved. The application is mainly applied to an H-shaped double-drive gantry system.

Description

Technical Field

[0001] This invention relates to the field of control for dual-drive gantry motion platforms. Background Technology

[0002] In the field of high-end equipment manufacturing, precision motion platforms, as core functional carriers, directly determine the technological ceiling of industries such as precision machinery, microelectronics manufacturing, and semiconductor processing. Among precision motion platform structures, the H-type dual-drive gantry system, with its structural symmetry, thrust decoupling characteristics, and motion stability, has become the mainstream structure in the field of precision motion control. For example... Figure 1 As shown, the H-type gantry motion platform has three drive axes: Y1, Y2, and X. Each drive axis includes a linear guide pair, a linear motor, and a grating position sensor. The longitudinal axes Y1 and Y2 are parallel to each other, constraining the axial movement of the crossbeam and providing vertical power. The X drive axis alone provides power for the sliding platform on the crossbeam to move along the crossbeam. The drive units of the three drive axis motors operate in torque mode. The host controller distributes thrust commands to each motor drive unit in real time based on information collected by the corresponding grating position sensors of the three axes, enabling the sliding platform to complete the in-plane motion task comprehensively.

[0003] Depending on the type of equipment, the H-type dual-drive gantry system primarily undertakes two types of precision control tasks: First, high-precision trajectory tracking control, which focuses on equipment such as high-end CNC machine tools and laser cutting machines that have stringent requirements for real-time trajectory or contour accuracy, aiming to ensure accurate tracking of predetermined trajectories. Second, high-precision positioning control, which is mainly for equipment such as high-end pick-and-place machines and high-performance dispensing machines that have extremely high standards in terms of operating speed and end-effector positioning accuracy, striving to achieve precise positioning during high-speed motion. The control tasks of these two types of equipment have different technical focuses: the former emphasizes implementing real-time, high-precision compensation strategies throughout the entire motion process in the face of complex and ever-changing dynamic characteristics (including nonlinear characteristics, coupling effects, and uncertainties); while the latter focuses on effectively suppressing the potential negative impacts of complex nonlinear dynamics on system stability and end-effector positioning accuracy under extreme operating conditions (such as high-speed operation and high acceleration). Although they differ in their control strategies, pursuing ultimate precision in high-speed motion is a common core objective for almost all precision motion platforms.

[0004] However, for H-type gantry motion platforms requiring high-precision control, the synchronous control of their Y1 and Y2 axes is a core challenge. Without solving the problem of dual-drive synchronous control of the H-type gantry motion platform, the platform's accuracy is difficult to improve, and large synchronization errors can even cause the platform to stop or be damaged.

[0005] Cross-decoupling control is a mainstream framework for dual-drive synchronous control algorithms. It decouples the control of the Y1 and Y2 axes into a gantry axis and a yaw axis, respectively. This allows for the consideration of beam flexibility and sliding table movement during modeling, thereby suppressing vibration modes in the beam motion and achieving higher control accuracy. Ideally, cross-decoupling control estimates the yaw axis state using the difference in position readings between the Y1 and Y2 axes and uses the control algorithm to control the yaw angle to zero, meaning the beam and the Y1 and Y2 axis guides are always perpendicular. However, in reality, errors in grating ruler installation and guide rail deformation can cause the estimated yaw angle to be non-zero even when the beam and guide rail are perpendicular. There is an unknown initial error that varies with the beam's position on the guide rail, causing the yaw angle estimate in decoupling synchronous control to deviate significantly from the true value, thus affecting the control effect. Figure 2 As shown, G1 and G2 are linear guides, E1 and E2 are absolute grating position sensors, 1, 2, and 3 represent three different states of the crossbeam, and O and O' are the zero-point positions of the two absolute grating rulers. Minor deformation of the guides and installation errors of the grating rulers cause the readings of the grating heads on both sides to be different when the crossbeam and guides are partially perpendicular, and these readings fluctuate with position changes. The difference in readings is determined by the grating ruler installation error ΔY0 and the distances ΔY1, ΔY2, and ΔY3 between the center positions of the sliders on both sides in the direction of the grating ruler. Without special handling, the yaw angle feedback will never reach zero, resulting in a large yaw axis control output. This causes compression between the guides and sliders, and the Y1 and Y2 axis motor thrusts to reverse, ultimately leading to increased friction and excessive internal force in the crossbeam. This effect is similar to the stall phenomenon of a rotary servo motor, which can damage the mechanical structure and internal circuitry, increase motor energy consumption, and in more severe cases, trigger unstable modes, causing the system to lose stability.

[0006] To address the yaw axis control problem in the cross-decoupling synchronization control of the aforementioned dual-drive motion platform, the existing yaw axis compensation method treats the yaw axis angle compensation value as a constant value, without considering its dynamic changes with position. This results in poor compensation performance during large-scale movements. Therefore, these problems urgently need to be solved. Summary of the Invention

[0007] The purpose of this invention is to solve the problem of poor compensation effect in the existing yaw angle compensation methods; this invention provides a dynamic yaw angle compensation method for dual-drive synchronous control of a precision motion platform.

[0008] A dynamic compensation method for yaw angle in dual-drive synchronous control of a precision motion platform, comprising the following steps:

[0009] S1. Construct the synchronization error compensation function, specifically as follows:

[0010] S11. Based on the collected readings of the Y1-axis and Y2-axis grating rulers of the dual-drive gantry precision motion table when the motor is in a no-thrust state, respectively (y10 and y20), set the initial values ​​of the position compensation estimates for each sampling point.

[0011] An iterative identification method is adopted, with an iteration period T. d Using time as a reference, the estimated position compensation values ​​for each sampling point are iteratively updated, and the estimated position compensation value of that sampling point at the point where the iteration stops is used as the synchronization error compensation value for that sampling point.

[0012] The sampling points are the position information collected on the Y1 axis grating ruler during the process of driving the crossbeam of the dual-drive gantry precision motion table under the thrust state of the Y1 axis and Y2 axis linear motors in historical data.

[0013] This represents the position information of the nth sampling point on the Y1 axis grating ruler, where n = 1, 2, 3...N, and N is the total number of sampling points; for The initial value of the location compensation estimate;

[0014] for The synchronization error compensation value;

[0015] S12. Calculate the mean location compensation value based on all location compensation estimates for all sampling points.

[0016] use right After scaling correction, we obtain in, for The corresponding synchronization error compensation value after scale correction;

[0017] S13. Based on the compensation data of each group Construct the mean function m(y1) of the Gaussian process regression model; y1 is a variable representing any reading within the allowable range of the Y1 axis grating ruler reading;

[0018] S14. Restore the mean function m(y1) of the Gaussian process regression model to its original scale to obtain the synchronization error compensation function. Where 'a' is the amplification factor;

[0019] S2, based on the synchronization error compensation function y comp(y1), and the position information y1(t) and y2(t) generated by the Y1 axis grating ruler and the Y2 axis grating ruler under the current thrust state, determine the current beam sway angle α(t) at time t;

[0020] Then, based on the yaw angle α(t) of the crossbeam, a corresponding dynamic compensation yaw axis control quantity is generated to realize dynamic compensation of the yaw angle of the crossbeam.

[0021] Preferably, in step S11,

[0022] Among them, y dist The initial disturbance bias is given.

[0023] Preferably, in step S11, the iterative update of the position compensation estimate for each sampling point is implemented as follows:

[0024]

[0025] in, When updating during the j-th iteration of the iteration process Location compensation estimate, When updating during the (j+1)th iteration of the iteration process The estimated location compensation value, j = 0, 1, 2, 3...m, where m is an integer greater than or equal to 9, k it For the iterative update rate, ∑u q2 For the (j+1)th iteration period T d In the middle, all control cycles T s The resulting yaw axis control quantity u under non-dynamic compensation q2 sum;

[0026] Among them, the yaw axis control quantity u under non-dynamic compensation generated at each time step during the (j+1)th iteration update. q2 The implementation methods include:

[0027] S111. Let the control error vector e be:

[0028]

[0029] Among them, L e Where T is the length of the beam and T is the transpose.

[0030] A virtual control vector is generated using a PID control algorithm. Andu q =[u q1 ,u q2 ] T ,

[0031] u q1 Indicates the gantry axis control quantity, uq2 This represents the yaw axis control quantity under non-dynamic compensation. K represents the proportionality coefficient matrix. p1 K represents the proportionality coefficient of the gantry shaft. p2 This represents the proportionality coefficient of the yaw axis. Let K represent the coefficient matrix of the integral term. b1 K represents the coefficient of the integral term of the gantry axis. b2 This represents the coefficient of the integral term along the yaw axis. K represents the coefficient matrix of the differential terms. d1 K represents the differential coefficient of the gantry shaft. d2 This represents the coefficient of the differential term of the yaw axis.

[0032] Preferably, in step S11, the condition for stopping the iterative update is:

[0033]

[0034] in,

[0035] max{} and min{} are functions that retrieve the maximum and minimum values, respectively;

[0036] Y stop It is a positive constant, representing the threshold of the range of change within 10 consecutive iteration periods T;

[0037] When updating during the i-th iteration of the iteration process The location compensation estimate is given by , where i is a variable from j-9 to j.

[0038] Preferably, in S12, using right After scaling correction, we obtain The implementation method is as follows:

[0039]

[0040] Preferably, in,

[0041] This indicates any reading y1 within the allowable range of the Y1 axis grating ruler reading. A vector composed of the covariance function values ​​between them;

[0042] K indicates and The matrix formed by the covariance function values ​​between them;

[0043] This provides the position information of the w-th sampling point on the Y1-axis grating ruler.

[0044] This provides the position information of the q-th sampling point on the Y1-axis grating ruler.

[0045] w=1,2,3...N, q=1,2,3...N;

[0046] This is a vector consisting of the synchronization error compensation values ​​after all scale corrections.

[0047] Preferably, p is an integer greater than 2 and less than N.

[0048] Preferably,

[0049]

[0050] p is an integer greater than 2 and less than N.

[0051] Preferably,

[0052] For y1 and The covariance function value between, p is an integer between 2 and N.

[0053] Preferably, the covariance function k(x,x) is... ′ The expression for ) is:

[0054]

[0055] Where x and x ′ All are variables, σ f It is the signal standard deviation, and its value is set to... and for The overall standard deviation;

[0056] σ l It is a length scale, and its value is set to... and for The overall standard deviation.

[0057] The beneficial effects of this invention are as follows:

[0058] This invention presents a dynamic compensation method for the yaw angle in dual-drive synchronous control of a precision motion platform. It obtains synchronization error compensation values ​​at several locations where the crossbeam and guide rail are partially perpendicular through an iterative identification method, and uses a fitting technique to obtain a synchronization error compensation function. During the control algorithm's operation, the estimated yaw angle is dynamically compensated in real time, improving the dynamic compensation effect. Furthermore, this method allows for better cross-decoupling synchronous control of the dual-drive precision motion platform, even in the presence of mechanical installation errors and minor deformations of the linear guide rail. Its main advantages include:

[0059] This solves the problem of excessive yaw axis control torque caused by inaccurate yaw angle feedback.

[0060] To prevent increased friction and mechanical damage caused by the mutual squeezing of the slider and guide rail; because the controller generates less yaw control torque, the thrust generated by the linear motors on both sides is more balanced, eliminating the problem of reverse thrust of the linear motors on both sides caused by inaccurate yaw angle feedback, which can effectively reduce the total energy consumption of the linear motors on both sides and reduce the overcurrent and heat generation inside the linear motors.

[0061] In addition, it saves on overall power consumption. This method is easy to implement and requires minimal online computation, eliminating the need for additional precision measuring instruments such as laser interferometers, yet still effectively improves control performance. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of a typical linear motor dual-drive gantry precision motion platform;

[0063] Figure 2 A schematic diagram showing the installation error of the grating ruler and the minute deformation of the guide rail in a dual-drive motion platform.

[0064] Figure 3 A flowchart of a dynamic compensation method for yaw angle in dual-drive synchronous control of a precision motion platform;

[0065] Figure 4 The graph shows the synchronization error compensation function fitted to the synchronization error compensation values ​​of the sampling points obtained by implementing this method on a dual-drive motion platform.

[0066] Figure 5 The image shows the trajectory tracking effect of the crossbeam (i.e., the gantry shaft) when the crossbeam is controlled to track a sinusoidal trajectory using a control algorithm based on a cross-decoupling framework, with and without the compensation method.

[0067] Figure 6When using a control algorithm based on a cross-decoupling framework to control a crossbeam to track a sinusoidal trajectory, a schematic diagram of the synchronization error represented by the yaw angle error is shown with and without compensation using this method.

[0068] Figure 7 The waveform diagram shows the reverse thrust commands of the linear motors on the Y1 and Y2 axes when the beam is controlled to track a sinusoidal trajectory using a control algorithm based on a cross-decoupling framework, reflecting the situation with and without compensation.

[0069] Figure 8 This paper compares the statistical data of gantry axis tracking error, synchronization error between Y1 and Y2 axes, and total control input of Y1 and Y2 under the conditions of compensation using this method and without compensation using this method. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0072] Detailed Implementation Method 1, see [link / reference] Figure 3 This embodiment describes a dynamic compensation method for the yaw angle of a precision motion platform with dual-drive synchronous control. The method includes the following steps:

[0073] S1. Construct the synchronization error compensation function, specifically as follows:

[0074] S11. Based on the collected readings of the Y1-axis and Y2-axis grating rulers of the dual-drive gantry precision motion table when the motor is in a no-thrust state, respectively (y10 and y20), set the initial values ​​of the position compensation estimates for each sampling point.

[0075] An iterative identification method is adopted, with an iteration period T. d Using time as a reference, the estimated position compensation values ​​for each sampling point are iteratively updated, and the estimated position compensation value of that sampling point at the point where the iteration stops is used as the synchronization error compensation value for that sampling point.

[0076] Specifically, y dist Given the initial disturbance bias;

[0077] The sampling points are the position information collected on the Y1 axis grating ruler during the process of driving the crossbeam of the dual-drive gantry precision motion table under the thrust state of the Y1 axis and Y2 axis linear motors in historical data.

[0078] This provides the position information of the nth sampling point on the Y1 axis grating ruler, where n = 1, 2, 3...N, and N is the total number of sampling points.

[0079] for The initial value of the location compensation estimate;

[0080] for The synchronization error compensation value;

[0081] S12. Calculate the mean location compensation value based on all location compensation estimates for all sampling points.

[0082] use right After scaling correction, we obtain in, for The corresponding synchronization error compensation value after scale correction;

[0083] S13. Based on the compensation data of each group Construct the mean function m(y1) of the Gaussian process regression model; y1 is a variable representing any reading within the allowable range of the Y1 axis grating ruler reading;

[0084] S14. Restore the mean function m(y1) of the Gaussian process regression model to its original scale to obtain the synchronization error compensation function. Where 'a' is the amplification factor;

[0085] S2, based on the synchronization error compensation function y comp (y1), and the position information y1(t) and y2(t) generated by the Y1 axis grating ruler and the Y2 axis grating ruler under the current thrust state, determine the current beam sway angle α(t) at time t;

[0086] Then, based on the beam sway angle α(t), a corresponding dynamic compensation sway axis control quantity is generated to achieve dynamic compensation of the beam sway angle. In practical applications, the process of generating the corresponding dynamic compensation sway axis control quantity based on the beam sway angle α(t) can be achieved using existing technologies.

[0087] The yaw angle dynamic compensation method for dual-drive synchronous control of precision motion platform described in this embodiment obtains the synchronous error compensation value of the crossbeam and guide rail at several positions under local perpendicularity through iterative identification method, and obtains the synchronous error compensation function by fitting technology. During the operation of the control algorithm, the estimated value of the yaw angle is dynamically compensated in real time to improve the dynamic compensation effect.

[0088] Furthermore, the method of this invention mainly includes identifying the synchronization error compensation value of each sampling point based on iterative learning. And obtain the synchronization error compensation function y co,p The process of (y1) involves obtaining the synchronization error compensation function y. comp (y1) is used to determine the difference in position information between the Y1 and Y2 axis grating rulers when the Y1 axis linear motor is in a specific position and there is no squeezing effect between the sliders and guide rails on both sides of the crossbeam. In other words, it represents the synchronization error compensation value corresponding to the Y1 axis linear motor being in that position. The obtained synchronization error compensation function y comp The process (y1) generates a function based on the sampling method to obtain the position reading of the linear motor corresponding to the Y1 axis, which is used to calculate the accurate yaw angle compensation value in real time in the cross-decoupling synchronous control.

[0089] To further specify, in step S11, the method for iteratively updating the estimated location compensation values ​​for each sampling point is as follows:

[0090]

[0091] in, When updating during the j-th iteration of the iteration process Location compensation estimate, When updating during the (j+1)th iteration of the iteration process The estimated location compensation value, j = 0, 1, 2, 3...m, where m is an integer greater than or equal to 9, k it For the iterative update rate, ∑u q2 For the (j+1)th iteration period T, all control periods T s The resulting yaw axis control quantity u under non-dynamic compensation q2 The sum; where u is the yaw axis control quantity under non-dynamic compensation generated at each time step during the (j+1)th iteration update. q2 The implementation methods include:

[0092] S111. Let the control error vector e be:

[0093]

[0094] Among them, L e Where T is the length of the beam and T is the transpose.

[0095] A virtual control vector is generated using a PID control algorithm. Andu q =[u q1 ,u q2 ] T ,

[0096] u q1 Indicates the gantry axis control quantity, u q2 This represents the yaw axis control quantity under non-dynamic compensation. K represents the proportionality coefficient matrix. p1 K represents the proportionality coefficient of the gantry shaft. p2 This represents the proportionality coefficient of the yaw axis. Let K represent the coefficient matrix of the integral term. b1 K represents the coefficient of the integral term of the gantry axis. b2 This represents the coefficient of the integral term along the yaw axis. K represents the coefficient matrix of the differential terms. d1 K represents the differential coefficient of the gantry shaft. d2 This represents the coefficient of the differential term of the yaw axis.

[0097] The condition for stopping iterative updates is:

[0098]

[0099] in,

[0100] max{} and min{} are functions that retrieve the maximum and minimum values, respectively;

[0101] Y stop It is a positive constant representing the threshold of the range of change within 10 consecutive iteration periods T;

[0102] When updating during the i-th iteration of the iteration process The location compensation estimate is given by , where i is a variable from j-9 to j.

[0103] The iterative update method provided in this preferred embodiment is based on the yaw axis control quantity u in the previous iteration cycle. q2 By updating the compensation estimate through an iterative method, the positional compensation estimate that minimizes the squeezing and friction between the sliders at both ends of the crossbeam and the guide rail can be accurately obtained.

[0104] In specific applications, S12 utilizes... right After scaling correction, we obtain The implementation method is as follows:

[0105]

[0106] Furthermore, in step S14 in,

[0107] This indicates any reading y1 within the allowable range of the Y1 axis grating ruler reading. A vector composed of the covariance function values ​​between them;

[0108] K indicates and The matrix formed by the covariance function values ​​between them;

[0109] This provides the position information of the w-th sampling point on the Y1-axis grating ruler.

[0110] This provides the position information of the q-th sampling point on the Y1-axis grating ruler.

[0111] w=1,2,3...N, q=1,2,3...N;

[0112] This is a vector consisting of the synchronization error compensation values ​​after all scale corrections.

[0113] Going further, p is an integer greater than 2 and less than N;

[0114]

[0115] For y1 and The covariance function value between, p is an integer between 2 and N.

[0116] In this preferred embodiment, the following is given K and The specific expression is obtained by calculating the covariance function and the product of the above matrix and vector, so as to obtain the value of the mean function m(y1) of the Gaussian process regression model in real time, and then obtain the synchronous error compensation value. It is easy to program and has a small amount of real-time calculation.

[0117] Furthermore, the covariance function k(x,x) ′ The expression for ) is:

[0118]

[0119] Where x and x ′ All are variables, σ f It is the signal standard deviation, and its value is set to... and for The overall standard deviation;

[0120] σ l It is a length scale, and its value is set to... and for The overall standard deviation.

[0121] In this preferred embodiment, the covariance function k(x,x) is given. ′ The specific expression for ) uses the covariance function k(x,x) ′ The obtained synchronization error compensation function can calculate the synchronization error compensation value more accurately, thereby improving the accuracy of dynamic compensation for yaw angle.

[0122] Verification experiments: The beneficial effects of the present invention were verified using the following embodiments, as detailed below:

[0123] Example 1:

[0124] In such Figure 1 In the linear motor dual-drive gantry motion platform shown, the left and right linear motors are of the same specifications and are each driven by a servo driver operating in torque control mode. The resolution of the grating rulers on both sides is 50nm. The host computer acts as the main controller and communicates with the drivers via an EtherCAT bus. The control cycle of the main control program is T. s =1ms.

[0125] according to Figure 3 Perform the steps shown to compare the effects of using this method for compensation and not using this method under the same conditions.

[0126] During the experiment, the beam motion table was placed at the center of the beam, and the PID parameter was selected as K. p =diag{1000,800}, K b =diag{0,0}, K d =diag{5,6}, the initial perturbation bias y during iteration dist =5×10 -6 The iteration update rate is set to k. it =5×10 -7 The iteration period is set to T. d =0.5s, the threshold for the iteration range is set to Y stop =5×10 -8 Eight sampling points were selected at equal intervals in a direction perpendicular to the crossbeam.

[0127] Choose an amplification factor of a = 4.

[0128] Replace the control error vector in S111 with Among them, y d =0.08·(1-cos(2πt)).

[0129] Depend on Figure 4 It can be seen that the sampled data points are all on the obtained synchronization error compensation function, which initially ensures the reliability of the compensation.

[0130] Depend on Figure 5 It can be seen that when tracking a sinusoidal trajectory, the trajectory tracking accuracy is slightly improved when using this method for compensation compared to not using this method for compensation.

[0131] Depend on Figure 6 It can be seen that, under the same conditions, the synchronization error compensated by this method is greatly reduced.

[0132] Depend on Figure 7 It can be seen that, under the same conditions, when using this method for compensation, the problem of the Y1 and Y2 axis linear motor thrust commands having opposite signs for a certain period of time (e.g., 0.5s-1s) is solved.

[0133] Depend on Figure 8 It can be seen that when using the same control algorithm and parameters to track the same motion trajectory, the maximum tracking error of the crossbeam (i.e., the gantry shaft) is reduced when this method is used for compensation. The maximum value and root mean square value of the synchronization error between the Y1 and Y2 axes are reduced by 76% and 84.25% respectively, and the sum of the root mean square of the control inputs to the Y1 axis linear motor and the Y2 axis linear motor is reduced by 9.33%.

[0134] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform, characterized in that, The method includes the following steps: S1. Construct the synchronization error compensation function, specifically as follows: S11. Based on the collected readings of the Y1-axis and Y2-axis grating rulers of the dual-drive gantry precision motion table when the motor is in a no-thrust state, respectively and Set the initial value of the compensation estimate for each sampling point location. ; ;in, Given the initial disturbance bias; An iterative identification method is adopted, with an iteration period of... Using time as a reference, the estimated position compensation values ​​for each sampling point are iteratively updated, and the estimated position compensation value of that sampling point at the point where the iteration stops is used as the synchronization error compensation value for that sampling point. ; The implementation method for iteratively updating the location compensation estimate of each sampling point is as follows: ； in, For the first iteration in the process During the next iteration update Location compensation estimate, For the first iteration in the process During the next iteration update Location compensation estimate, =0,1,2,3……m, where m is an integer greater than or equal to 9. For the iterative update rate, For the first one iteration cycle In, all control cycles The resulting yaw axis control quantity under non-dynamic compensation sum; Among them, the The yaw axis control quantity generated at each time step during the next iteration update under non-dynamic compensation The implementation methods include: S111, Let the control error vector be... for: ； in, The length of the beam. For transpose; A virtual control vector is generated using a PID control algorithm. ,and , Indicates the gantry shaft control quantity. This represents the yaw axis control quantity under non-dynamic compensation. Represents the proportional term coefficient matrix. This represents the proportionality coefficient of the gantry shaft. This represents the proportionality coefficient of the yaw axis. Represents the coefficient matrix of the integral term. Indicates the coefficient of the integral term of the gantry axis. This represents the coefficient of the integral term along the yaw axis. Represents the coefficient matrix of the differential terms. Represents the differential coefficients of the gantry shaft. Indicates the differential term coefficient of the yaw axis; The sampling points are the position information collected on the Y1 axis grating ruler during the process of driving the crossbeam of the dual-drive gantry precision motion table under the thrust state of the Y1 axis and Y2 axis linear motors in historical data. For the first Position information of each sampling point on the Y1 axis grating ruler =1,2,3……N, where N is the total number of sampling points; for The initial value of the location compensation estimate; for Synchronization error compensation value; S12. Calculate the mean location compensation value based on the estimated location compensation values ​​for all sampling points. ; use right After scaling correction, we obtain ; for The corresponding synchronization error compensation value after scale correction; S13, Based on the compensation data of each group { , Construct the mean function of the Gaussian process regression model. ; Any reading within the allowable range of the Y1 axis grating ruler reading; S14, the Gaussian process regression model By restoring to the original scale, the synchronization error compensation function is obtained. ;in, To amplify the index; S2. Based on the synchronization error compensation function And the position information generated by the Y1-axis and Y2-axis grating rulers under the current thrust state. and Determine the current time Crossbeam yaw angle ; Then, based on the angle of the beam's sway... Generate the corresponding dynamic compensation yaw axis control quantity to achieve dynamic compensation of the yaw angle of the crossbeam.

2. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 1, characterized in that, In step S11, the condition for stopping the iterative update is: ； in, and These are functions for finding the maximum and minimum values, respectively. It is a positive constant, representing 10 consecutive iterations. The threshold for the range of change within; For the first iteration in the process During the next iteration update The estimated location compensation value, and from to One of the variables.

3. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 1, characterized in that, S12, utilizing right After scaling correction, we obtain The implementation method is as follows: 。 4. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 1, characterized in that, ； in, This represents any reading within the allowable range of the Y1 axis grating ruler reading. and A vector composed of the covariance function values ​​between them; express and A matrix formed by function values; For the first Position information of each sampling point on the Y1 axis grating ruler; For the first Position information of each sampling point on the Y1 axis grating ruler; =1,2,3……N, =1,2,3……N; This is a vector consisting of the synchronization error compensation values ​​after all scale corrections.

5. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 4, characterized in that, ， 6. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 4, characterized in that, ； for and less than An integer between [a certain value] and [a certain value].

7. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 4, characterized in that, ； for function value, for and less than An integer between [a certain value] and [a certain value].

8. The method for dynamic compensation of yaw angle in dual-drive synchronous control of a precision motion platform according to claim 4, characterized in that, covariance function The expression is: ； in, All are variables. It is the signal standard deviation, and its value is set to... , for The overall standard deviation; It is a length scale, and its value is set to... ,and The overall standard deviation.

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