A synchronous control method based on mapping the difference of dual-axis mass damping into unbalanced output

Abstract

The present invention provides a synchronous control method based on mapping the difference of dual-axis mass damping to unbalanced output, which relates to the field of automatic control theory and motor control technology. The method is mainly used in a moving beam gantry motion platform, and uses a dynamic characteristic model of dual-axis mass damping to calculate the unbalanced force that needs to be output by the dual axes to suppress the synchronization error, and performs controller one-to-one mapping parameter design and realizes adaptive adjustment based on the output unbalanced force of the two axes. This method does not need to decouple the dual-axis characteristics (the decoupling calculation amount is large), and does not need to collect the asynchronous error as the control quantity in real time. It directly performs theoretical analysis on the inconsistency of the dual-axis dynamic characteristics, and designs the controller and makes real-time adjustments based on the theoretical analysis. The physical meaning is clear and easy to implement, and the controller parameters can be directly mapped one by one according to the different mechanical characteristics and the active controller design can be realized.

Description

Technical Field

[0001] The present invention relates to the field of automatic control theory and motor control technology, and in particular to a synchronous control method based on mapping dual-axis mass damping difference into unbalanced output. Background Art

[0002] With the development of my country's high-end manufacturing industry, the moving beam dual-drive gantry platform is widely used in semiconductor processing, precision testing, precision assembly, industrial robots, high-end instruments and other fields due to its large span. At present, the dual-axis drive mode generally adopts the same structure and dual-motor electrical drive system. In theory, the mechanical and electrical parameters are consistent, and the two axes are balanced in output. However, during operation, the load on the moving beam changes in real time, which will lead to inconsistent dynamic characteristics of the two axes. If the same controller is designed for the two axes of the dual drive at this time, and the same parameters are used for balanced output, it is bound to cause inconsistent response characteristics of the two axes, and finally produce asynchronous tracking errors, reducing the accuracy of the motion platform.

[0003] At present, there are some studies on the synchronous control method of the moving beam gantry structure at home and abroad. Some studies mainly propose solutions for the gap between the two axes, different friction forces at low speed or high-frequency vibration, but do not analyze the load change on the beam and directly perform synchronous control (Fan Wei. Research on dynamic modeling and synchronous control technology of dual-drive feed system [D]. Wuhan University of Technology, 018.). Some analyze the change of load center of mass, but based on a more complex model, a compensation controller is used to decouple and compensate the control force, such as cross-coupling fuzzy control or neural network-based control (Gao Huijun, Gong Jiansu, Wang Dazhao, et al. High-speed gantry dual-drive synchronous control method and system with disturbance suppression [P]. Heilongjiang Province: CN202211393025.3, 2023-07-25.), and there is also a control strategy in which the deflection torque is obtained by compensating the deflection command according to the deflection angle of the beam, and the deflection torque is used as a cross-coupling parameter to compensate for the asynchronous error. Or take one axis as the reference and use the asynchronous error as the input of the driven axis for synchronous control (Xie Hanjun, Wang Qinruo. GSLQR optimal control and force feedforward decoupling control algorithm based on virtual center of mass [J]. Automation and Information Engineering, 2024, 45(03):16-21+44.; Guo Enzheng, Ren Guiping, Jin Changming, et al. Dual-drive gantry drive control method, system, storage medium and processor [P]. Anhui Province: CN202410532734.8, 2024-06-25.; Wu Chao, Zheng Zhongwei, Zhang Hao. A high-speed and high-precision gantry dual-drive cross-synchronous control system and its control method [P]. Jiangsu Province: CN202211027581.9, 2022-11-04.). Or the pitch error can be compensated by an interferometer (Xie Jingchao, Li Ying, Li Xin, et al. A method for synchronous adjustment of the gantry of a dual-drive system [P]. Sichuan Province: CN202210064135.9, 2023-05-05.).

[0004] The above-mentioned existing gantry structure control technology includes pitch compensation through interferometer, measuring the pitch error of the two axes, and then using the pitch error as the compensation amount for compensation, but it can only compensate for the static error of the two axes, and cannot control the dynamic error of the two axes. Some do not analyze the impact of load changes on the error from the perspective of motion mechanism, and cannot consider the load on the beam as a moving factor. Some consider the impact of center of mass changes, but based on a more complex dynamic model, there are many identification parameters, which are not easy to measure online, and design cross-coupling, neural network, fuzzy control and other controllers, which have a large amount of calculation and high requirements for hardware resources. The designed controller has no one-to-one mapping relationship with the mechanical parameters. Other studies use the measured deflection angle and deflection command as the basis for the calculation of the control command, and perform synchronous error control through indirect physical quantity measurement. The dynamic characteristics of the two axes are not analyzed, and the physical meaning is unclear. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a synchronization control method based on mapping the difference in mass and damping of two axes into unbalanced output, so as to solve the technical problem of asynchronism caused by the different mass and damping characteristics of the two axes in the existing moving beam gantry motion platform.

[0006] In order to achieve the above object, an embodiment of the present invention provides a synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output, characterized in that it includes the following steps:

[0007] The two axes of dual drive are equivalent, and the driving force of the feed axis is controlled by controlling the voltage and current of the motor. Considering the relationship between the control voltage and driving force of the motor, the model of a single axis of the dual drive axis can be obtained, as shown in the following formula (1):

[0008]

[0009] Ignoring the electrical time constant, the relationship between the output acceleration and the input voltage is:

[0010]

[0011] in, , , is the equivalent mass of the feed axis, is the viscous friction coefficient, is the back electromotive force coefficient, is the torque constant, is the motor equivalent resistance, U is the input control voltage, is the external disturbance force, To control the current, is the equivalent inductance, is the driving force, f is the friction force, is the speed of the feed axis, is the acceleration of the feed axis.

[0012] Alternatively, assuming that the electrical parameters of the two axes are the same, that is, the equivalent resistance and inductance of the motors are the same, we can consider the driving force end. If the driving force is adjusted in real time with the different dynamic characteristics of the two axes, and both axes can achieve good control, no deflection will occur. Therefore, the following model expression (3) can be obtained:

[0013]

[0014] in , is the driving force of the two axes, , is the nonlinear friction force on the two axes, , is the cutting interference force of the two axes, , is the viscous damping coefficient of the two axes, representing the linear friction part, , is the equivalent mass of the two axes, , , , It is the speed and acceleration of the two axes of dual drive.

[0015] Optionally, when the influence of friction and interference force is ignored and the driving forces of the two axes are the same,

[0016] That is, the asynchronous error of the two axes can be expressed as shown in formula (4):

[0017] (4)

[0018] When the driving forces of the two axes are consistent, the asynchronous error will change with the change in mass and damping of the two axes, and is related to the form of the input force; mass changes will produce errors related to the system input acceleration, and different damping will produce errors related to the system input speed.

[0019] Alternatively, when the input forces of the two axes are different, that is, , , the asynchronous error can be obtained as shown in formula (5):

[0020] (5)

[0021] It can be seen from formula (5) that the synchronization error between the two axes can be controlled by changing the driving force of the two axes, where the change in the driving force needs to be determined by the mass change and damping difference of the two axes.

[0022] Optionally, when the load moves in real time, the beam is subjected to force analysis, and the moment balance is obtained as shown in equation (6):

[0023]

[0024] in, is the beam mass, is the load mass, is the mass of the guide rails on both sides, is the distance from the equivalent center of gravity to axis 1, is the distance from the equivalent center of gravity to axis 2, is the equivalent pressure on shaft 1, is the equivalent pressure on shaft 2;

[0025] From the moment balance, we can get the following equation (7):

[0026] (7)

[0027] in, is the distance from the equivalent center of gravity to the center of gravity of the beam, is the distance from the spindle load center to the beam center, then

[0028] when hour,

[0029]

[0030] when hour,

[0031]

[0032] in, is the span between the two axes, is the load coordinate position, is the distance from the zero point to axis 1;

[0033] From equations (6) to (9), we can get the equivalent mass distributed on the two axes:

[0034]

[0035] in is the equivalent mass of axis 1, is the equivalent mass of axis 2. When the driving forces of the two axes are the same, the error caused by the different mass distribution of the two axes has a linear relationship with the position movement of the x-axis.

[0036] Optionally, the different damping of the two axes is also the main factor causing the asynchronous error. The damping coefficient is identified by the least square method, as shown in formula (11):

[0037] (11)

[0038] in, is the input thrust command, For the quality to be identified, is the friction viscosity coefficient;

[0039] Using the least squares principle and the batch least squares method, we can get formula (12):

[0040]

[0041] in, , , , , using the recursive least squares method, the principle is: the new estimate = Old estimate + correction term, the algorithm is shown in the following formula (13)

[0042]

[0043] in , By using the step torque signal as the torque input and identifying the relationship between the driving force and the speed under uniform speed, the damping coefficient B can be obtained.

[0044] Optionally, a PI control architecture is adopted, and the gain parameters of the two axes of the dual drive are set to be the same. However, due to the different mechanical characteristics of the two axes, synchronization errors are bound to occur. Therefore, the control parameters need to be designed based on the mass of the dual drive axes and the relationship between the linear damping changes.

[0045] When only considering a single axis, the system has a faster response and no overshoot when PI control is used. Assume that the system damping constant , the velocity transfer function is shown in formula (14):

[0046] (14)

[0047] According to the zero-pole position configuration, we can get the relationship of formula (15):

[0048]

[0049] Available

[0050] It can be seen from equation 15 that in order to make systems with different masses and damping have the same response, it is necessary to change the speed loop gain coefficient and time constant.

[0051] Alternatively, if two feed axes with different dynamic performances are considered, the input-output transfer function of one of the axes is as shown in equation (16):

[0052] (16)

[0053] The dual-axis driving force expression of formula (16) can be obtained as shown in formula (17):

[0054] (17)

[0055]

[0056] If we want to make the performance of axis 2 with different mass and damping equal to that of axis 1, and If it remains unchanged, then we must ensure that:

[0057]

[0058] We can get:

[0059] Then we have: in

[0060] in Compensate for errors caused by changes in mass distribution, Compensate for the error caused by two-axis linear damping;

[0061] In addition, the closed-loop characteristic equation of the system is as shown in formula (19):

[0062] (19)

[0063] According to Routh's criterion, when the system is stable, it must satisfy the following equation (20):

[0064] (20)

[0065] At this time, the driving force of the two axes is shown in formula (21):

[0066]

[0067] The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output provided by the present invention has the following technical effects:

[0068] The control method provided by the present invention uses a dynamic characteristic model of dual-axis mass damping to calculate the unbalanced force that needs to be output by the dual axes to suppress the synchronization error, and performs one-to-one mapping parameter design of the controller according to the output unbalanced force of the two axes and realizes adaptive adjustment. The damping coefficient is identified by a system identification method, and the mass parameters and changes are calculated by physical calculation. After one-to-one mapping with the controller parameters, the controller parameters that can eliminate the synchronization error are designed.

[0069] Compared with the current dual-drive synchronous controller, which mainly targets static error compensation (by measuring the relationship between asynchronous error and gantry axis position), error caused by low-speed nonlinear friction (eliminating low-speed friction), and error caused by high-speed vibration, a cross-coupling control method based on synchronous error measurement is proposed. This method does not need to decouple the dual-axis characteristics (the decoupling calculation is large), and does not need to collect asynchronous errors as control quantities in real time (the storage data is large, and it is impossible to collect and write to closed controllers). It directly conducts theoretical analysis on the inconsistency of dual-axis dynamic characteristics, and designs and adjusts the controller in real time based on the theoretical analysis. The physical meaning is clear and easy to implement. The controller parameters can be directly mapped one by one according to different mechanical characteristics, and active controller design can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0071] Figure 1 It is the force analysis diagram of the double feed shaft;

[0072] Figure 2 It is a dual-drive, dual-axle mechanical model;

[0073] Figure 3 It is a dual-drive single-axle model;

[0074] Figure 4a It is a simplified front view of the mass change analysis when the load moves;

[0075] Figure 4b It is a simplified top view of the mass change analysis when the load moves;

[0076] Figure 5 It is a block diagram of the identification method;

[0077] Figure 6 It is a dual-drive axis PI control structure;

[0078] Figure 7 It is the equivalent relationship of the driving force of the two axes;

[0079] Figure 8 is the mass and linear damping controller design;

[0080] Figure 9a It is the simulation curve of the asynchronous error under the step signal;

[0081] Figure 9bIt is the test true curve of the asynchronous error under the step signal;

[0082] Fig.10a It corresponds to Figure 9a The asynchronous error under the S-curve signal in;

[0083] Fig.10b It corresponds to Figure 9b The asynchronous error under the S-curve signal in. DETAILED DESCRIPTION

[0084] To make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0085] Based on the defects in the prior art, Figure 1-Figure 1 The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output of the present invention is described in detail.

[0086] The specific contents of the synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output provided by the present invention are as follows:

[0087] The reciprocating motion of the load on the beam can be equivalent to the different load masses on the two axes, and the reciprocating motion of the two axes driving the beam is equivalent to the different friction forces on the two axes. The rigidity of the two axes is assumed to be the same, and the mechanical model of the motor screw table of the two axes can be simplified to a structure of equivalent damping and mass. By analyzing the change in the mass borne by the two axes when the spindle load moves, the equivalent damping of the two axes can be identified. Finally, according to the change law, the controller is designed to change the instructions sent to the servo to achieve dual-drive high-precision control.

[0088] Taking the moving beam dual-drive structure as an example, the load will move in the X, Y, and Z axis directions. Figure 1 As shown, the center of gravity of the dual-drive shaft driving beam will also change in real time, resulting in different driving masses of the two shafts. The equivalent mass of the two shaft drives will change, and the positive pressure on the two shafts will be , Different, resulting in the friction characteristics of the two shafts , Different. At the same time, the cutting force In order to make the dual-drive axis run accurately, it is necessary to overcome the friction and interference during processing, rather than the average output of the two axes. Therefore, it is necessary to find the relationship between the dual-axis driving force and the position, speed, and acceleration of the two axes, and then propose a control strategy to change the driving force to control it.

[0089] First, the dual-drive two-axis can be equivalent to Figure 2 As shown, , is the nonlinear friction part, , is the equivalent mass when the Z-axis spindle moves, , is the linear friction damping. , is the actual position value of the two axes. If the two axes are twisted, is the torsional stiffness of the two axes.

[0090] The driving force of the feed axis is controlled by controlling the voltage and current of the motor. Considering the relationship between the control voltage and driving force of the motor, the model of a single axis of the dual-drive axis can be obtained as follows: Figure 3 shown.

[0091] That is, it can be expressed as the following formula (1):

[0092]

[0093] Ignoring the electrical time constant, the relationship between the output acceleration and the input voltage can be obtained as formula (2):

[0094] in ,

[0095] is the equivalent mass of the feed axis, is the viscous friction coefficient, is the back electromotive force coefficient, is the torque constant, is the motor equivalent resistance, U is the input control voltage, is the external disturbance force, To control the current, is the equivalent inductance, is the driving force, f is the friction force, is the speed of the feed axis, is the acceleration of the feed axis.

[0096] Assuming that the electrical parameters of the two axes are the same, that is, the equivalent resistance and inductance of the motors are the same, we can consider the driving force end. If the driving force is adjusted in real time according to the different dynamic characteristics of the two axes, and both axes can be well controlled, no deflection will occur. Therefore, the following model expression (3) can be obtained.

[0097]

[0098] in , is the driving force of the two axes, , is the nonlinear friction force on the two axes, , is the cutting interference force of the two axes, , is the viscous damping coefficient of the two axes, representing the linear friction part, , is the equivalent mass of the two axes, , , , It is the speed and acceleration of the two axes of dual drive.

[0099] Ignoring the influence of friction and interference force, when the driving forces of the two axes are the same,

[0100] That is, the asynchronous error of the two axes can be expressed as shown in formula (4):

[0101] (4)

[0102] It can be seen that when the driving forces of the two axes are the same, the asynchronous error will change with the change of mass and damping of the two axes, and is related to the form of the input force. The change of mass will produce an error related to the input acceleration of the system, and the difference in damping will produce an error related to the input speed of the system.

[0103] When the input forces of the two axes are different, that is, , , the asynchronous error can be obtained as shown in formula (5),

[0104] (5)

[0105] From formula (5), we can see that the synchronization error between the two axes can be controlled by changing the driving force of the two axes. The change in the driving force needs to be determined by the mass change and damping difference of the two axes.

[0106] Model analysis of mass change when the load moves along the X-axis

[0107] When the load moves in real time, the equivalent mass on both sides of the dual-drive shaft will change when the Z-axis load moves along the X-axis. In order to make the driving characteristics of the two axes consistent, the driving force needs to be adjusted. Therefore, it is of great significance to analyze the change in the equivalent mass of the two axis ends when the Z-axis load moves along the X-axis.

[0108] The dual-drive shafts jointly drive the crossbeam and the main shaft load motion to be simplified as shown in FIG4 , where (a) is a simplified front view and (b) is a simplified top view.

[0109] Then the force analysis of the beam is carried out, and the moment balance is used to obtain equation (6):

[0110]

[0111] in is the beam mass, is the load mass, is the mass of the guide rails on both sides, is the distance from the equivalent center of gravity to axis 1, is the distance from the equivalent center of gravity to axis 2, is the equivalent pressure on shaft 1, is the equivalent pressure on axis 2.

[0112] From the moment balance, we can get equation (7):

[0113] (7)

[0114] in is the distance from the equivalent center of gravity to the center of gravity of the beam, is the distance from the spindle load center to the beam center.

[0115] when hour,

[0116]

[0117] when hour,

[0118]

[0119] in is the span between the two axes, is the load coordinate position (can be read directly), is the distance from the zero point to axis 1. From (6) to (9), the equivalent mass distributed on the two axes can be obtained:

[0120]

[0121] in is the equivalent mass of axis 1, is the equivalent mass of axis 2. When the driving forces of the two axes are the same, the error caused by the different mass distribution of the two axes has a linear relationship with the position movement of the x-axis.

[0122] The difference in damping between the two axes is also the main factor causing the asynchronous error. The damping value can be obtained by identification. Figure 5 identification method.

[0123] The damping coefficient is identified by the least square method, and the formula (11)

[0124] (11)

[0125] in is the input thrust command, For the quality to be identified, is the friction viscosity coefficient. Using the least squares principle and batch least squares method, we have formula (12):

[0126]

[0127] in , , , , using the recursive least squares method, the principle is: the new estimate = Old estimate +Correction items,

[0128] The algorithm is shown in formula (13):

[0129]

[0130] in ,

[0131] By using a step torque signal as the torque input and identifying the relationship between the driving force and the speed under uniform speed, the damping coefficient B can be obtained.

[0132] The PI control architecture is adopted, and the gain parameters of the two axes of the dual drive are set the same. However, due to the different mechanical characteristics of the two axes, synchronization errors are bound to occur. Therefore, the control parameters need to be designed according to the relationship between the mass and linear damping changes of the dual drive axes. Figure 6 The control structure of the dual-drive shaft is shown in which the mass m and damping B of the two shafts are different. If the performance of the two shafts is to be consistent, the driving force needs to be changed for control according to the changes in mass and damping.

[0133] When only considering a single axis, when using PI control, we hope that the system has a faster response and no overshoot. Assume that the system damping constant , the velocity transfer function is shown in formula (14):

[0134] (14)

[0135] According to the zero-pole position configuration, we can get the relationship (15):

[0136]

[0137] Available

[0138] It can be seen from equation 15 that in order to make systems with different masses and damping have the same response, it is necessary to change the speed loop gain coefficient and time constant.

[0139] If two feed axes with different dynamic performance are considered, Figure 6 The input-output transfer function of one axis is shown in equation (16):

[0140] (16)

[0141] The dual-axis driving force expression can be obtained as shown in formula (17):

[0142] (17)

[0143]

[0144] The equivalent relationship can be expressed as Figure 7 As shown in , due to the different damping and mass, the driving force must be inconsistent. As shown in formula 17, when the speed and position are required to be the same, the controller parameters and damping coefficient can be changed to achieve the change of control force. Then the consistency of position and speed can be achieved.

[0145] If we want to make the performance of axis 2 with different mass and damping equal to that of axis 1, and remains unchanged, then we must ensure that as shown in formula (18)

[0146]

[0147] We can get:

[0148] Then we have:

[0149] in

[0150] in Compensate for errors caused by changes in mass distribution, Compensate for the error caused by two-axis linear damping.

[0151] The compensation structure adopted is as follows Figure 8 shown.

[0152] In addition, the closed-loop characteristic equation of the system is as follows:

[0153] (19)

[0154] According to Routh's criterion, when the system is stable, it must satisfy the following equation (20):

[0155] (20)

[0156] At this time, the driving force of the two axes is shown in formula (21):

[0157]

[0158] It can be seen that the mechanical properties of the two axes are different. If the system response is to be completely consistent, different driving forces need to be provided for control. The method has a one-to-one mapping relationship with the mass damping of the two axes. When designing the controller, the controller parameters can be directly obtained through the mass and damping coefficients. The physical meaning is clear and it is easy to implement.

[0159] Embodiment 1

[0160] Taking a dual-drive beam gantry structure motion platform as an example, simulation and testing are carried out on it, and the input is a step signal and an S-curve signal. The simulation curve and test results of the step signal are shown in Figure 9 below, and the S-curve is shown in Figure 10 below.

[0161] It can be seen from the results that this control method can effectively reduce the asynchronous error and improve the control accuracy.

[0162] In order to realize the synchronous control of the two axes, including position, speed and acceleration, the output force of the two axes must be unbalanced. The present invention adopts the method of physically calculating the changes in the mass and damping stiffness of the two axes when the load moves on the beam, and then analyzing the response characteristics of the two axes. In order to make the characteristics of the two axes consistent, the unbalanced force required by the two axes is calculated, and then the unbalanced and response characteristics required by the two axes are mapped one by one to determine the set controller parameters. The determined parameters are directly related to the mass change of the load on the beam and the damping change of the two axes. Through computer identification of these two parameters, the controller parameters to be determined can be directly mapped one by one in advance, and the driving force required by the two axes can be calculated, so as to realize the synchronous control of the dynamic characteristics of the two axes in advance. The design parameters are simple and the physical meaning is clear and definite.

[0163] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A synchronous control method based on mapping the difference of dual-axis mass damping into unbalanced output, characterized in that: The following steps are involved: The two axes of dual drive are equivalent, and the driving force of the feed axis is controlled by controlling the voltage and current of the motor. Considering the relationship between the control voltage and driving force of the motor, the model of a single axis of the dual drive axis can be obtained, as shown in the following formula (1): Ignoring the electrical time constant, the relationship between the output acceleration and the input voltage is: in, , , is the equivalent mass of the feed axis, is the viscous friction coefficient, is the back electromotive force coefficient, is the torque constant, is the motor equivalent resistance, U is the input control voltage, is the external disturbance force, To control the current, is the equivalent inductance, is the driving force, f is the friction force, is the speed of the feed axis, is the acceleration of the feed axis; The PI control architecture is adopted, and the gain parameters of the two axes of the dual drive are set the same. However, due to the different mechanical characteristics of the two axes, synchronization errors are bound to occur. Therefore, the control parameters need to be designed according to the relationship between the mass of the dual drive axes and the linear damping change. When only considering a single axis, the system has a faster response and no overshoot when PI control is used. Assume that the system damping constant , the velocity transfer function is shown in formula (14): （14） According to the zero-pole position configuration, we can get the relationship of formula (15): Available in, K v is the speed loop gain coefficient, T v is the time constant, m For the quality to be identified, B is the damping coefficient; It can be seen from equation 15 that in order to make systems with different masses and damping have the same response, it is necessary to change the speed loop gain coefficient and time constant.

2. The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output according to claim 1 is characterized in that: Assuming that the electrical parameters of the two axes are the same, that is, the equivalent resistance and inductance of the motors are the same, we can consider from the driving force end that if the driving force is adjusted in real time with the different dynamic characteristics of the two axes, and both axes can achieve good control, no deflection will occur. Therefore, the following model expression (3) can be obtained: in , is the driving force of the two axes, , is the nonlinear friction force on the two axes, , is the cutting interference force of the two axes, , is the viscous damping coefficient of the two axes, representing the linear friction part, , is the equivalent mass of the two axes, , , , It is the speed and acceleration of the two axes of dual drive.

3. The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output according to claim 2, characterized in that: When the influence of friction and interference force is ignored and the driving forces of the two axes are the same, That is, the asynchronous error of the two axes can be expressed as shown in formula (4): （4） When the driving forces of the two axes are consistent, the asynchronous error will change with the change in mass and damping of the two axes, and is related to the form of the input force; mass changes will produce errors related to the system input acceleration, and different damping will produce errors related to the system input speed.

4. The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output according to claim 2 is characterized in that: When the input forces of the two axes are different, that is, , , the asynchronous error can be obtained as shown in formula (5): （5） It can be seen from formula (5) that the synchronization error between the two axes can be controlled by changing the driving force of the two axes, where the change in the driving force needs to be determined by the mass change and damping difference of the two axes.

5. The synchronous control method based on mapping the dual-axis mass damping difference into unbalanced output according to claim 1, characterized in that: When the load moves in real time, the beam is subjected to force analysis, and the moment balance is obtained as shown in equation (6): in, is the beam mass, is the load mass, is the mass of the guide rails on both sides, is the distance from the equivalent center of gravity to axis 1, is the distance from the equivalent center of gravity to axis 2, is the equivalent pressure on shaft 1, is the equivalent pressure on shaft 2; From the moment balance, we can get the following equation (7): （7） in, is the distance from the equivalent center of gravity to the center of gravity of the beam, is the distance from the spindle load center to the beam center, then when hour, when hour, in, is the span between the two axes, is the load coordinate position, is the distance from the zero point to axis 1; From equations (6) to (9), we can get the equivalent mass distributed on the two axes: in is the equivalent mass of axis 1, is the equivalent mass of axis 2. When the driving forces of the two axes are the same, the error caused by the different mass distribution of the two axes has a linear relationship with the position movement of the x-axis.

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