A Synchronous Control Method for All-Drive of H-Type Motion Platform Based on Adaptive Switching Model

Abstract

This invention discloses a full-drive synchronous control method for an H-type motion platform based on an adaptive switching model, belonging to the fields of precision machining, motion control, and mechatronics servo control. This invention solves the problems of platform vibration, poor control stability, and low precision caused by asynchronous motion on both sides of the H-type motion platform. Based on the physical constraints of the H-type motion platform, this invention establishes a dynamic model of the crossbeam's center of mass displacement-synchronization error and constructs adaptive model switching parameters, enabling adaptive model switching between tilt angle adjustment and tilt angle saturation conditions. Then, a differential-mode and common-mode decoupling control method is designed to decouple the model into a full-drive synchronous system model. Based on the full-drive synchronous system model, a full-drive error dynamic model is derived. Finally, based on the full-drive error dynamic model, the differential-mode and common-mode control quantities of the two motors are obtained, and the H-type motion platform is synchronously controlled based on these differential-mode and common-mode control quantities. This invention can be applied to high-precision synchronous control tasks of H-type motion platforms.

Description

Technical Field

[0001] This invention belongs to the fields of precision machining, motion control and mechatronics servo control, and specifically relates to a full-drive synchronous control method for an H-type motion platform based on an adaptive switching model. Background Technology

[0002] The H-type motion platform is a servo system capable of positioning and tracking control in the XY plane. It features a simple and efficient structure, with the central section comprising an H-shaped servo structure consisting of a crossbeam and an actuator, while thrust devices on either side provide power. In industrial control, the control input is converted into current or voltage by a driver to drive the thrust devices on either side. These thrust devices can be linear motors or combinations of rotary motors and ball screws. Due to its simple structure, high reliability, and large thrust, the H-type motion platform is widely used in automated measurement, large-span gantry cranes, laser processing, surface mounting, and wafer inspection systems.

[0003] The control challenge of the H-type motion platform lies in the coupled synchronous control of the two motors. Because the two motors of the H-type motion platform are coupled together through a crossbeam, and there is a gap at the connection between the crossbeam and the guide rail, the motion of the two motors is mutually coupled and affects each other, generating synchronization errors. This leads to problems such as vibration, reduced control stability, and decreased accuracy of the H-type motion platform. Currently, there is considerable research on the decoupling and synchronous control of the H-type motion platform, including master-slave synchronous control and cross-coupling synchronous control methods. However, existing synchronous control methods focus on the synchronous control process while neglecting the coupled synchronous dynamics of the H-type motion platform. Therefore, the improvement in the synchronous control performance of the H-type motion platform by existing methods remains relatively limited, and control stability and accuracy need further improvement. Summary of the Invention

[0004] The purpose of this invention is to improve the synchronous control performance of an H-type motion platform and solve the problems of platform vibration, poor control stability and low accuracy caused by asynchronous movement on both sides. A full-drive synchronous control method for an H-type motion platform based on an adaptive switching model is proposed. By improving the synchronous control performance, the accuracy of tracking and positioning is improved.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for all-drive synchronous control of an H-type motion platform based on an adaptive switching model, the method specifically includes the following steps:

[0007] Step 1: Based on the physical constraints of the H-type motion platform, establish a bilateral position-angle synchronization dynamic model based on the beam deflection angle. Then, transform the established bilateral position-angle synchronization dynamic model based on the beam deflection angle into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides.

[0008] Step 2: For the model switching between the two working conditions of tilt angle adjustment and tilt angle saturation of the H-type motion platform beam, design adaptive model switching parameters, and transform the model in Step 1 into a beam centroid displacement-synchronization error dynamic model based on the adaptive model switching parameters.

[0009] Step 3: Design a decoupling control method for the differential mode and common mode of the H-type motion platform, decoupling the dynamic model of the beam centroid displacement-synchronization error based on the adaptive model switching parameters into an all-drive synchronization system model; and then derive the all-drive error dynamic model based on the all-drive synchronization system model.

[0010] Step 4: Obtain the differential mode control quantity and common mode control quantity of the two motors based on the full drive error dynamic model, and perform synchronous control of the H-type motion platform based on the differential mode control quantity and common mode control quantity of the two motors.

[0011] Furthermore, the establishment of a bilateral position-angle synchronization dynamic model based on the beam deflection angle according to the physical constraints of the H-shaped motion platform is specifically as follows:

[0012] The physical constraints of the H-type motion platform are:

[0013]

[0014] In the formula, θ is the rotation angle of the middle crossbeam, y1 is the displacement of linear motor 1, y2 is the displacement of linear motor 2, and L is the length of the crossbeam.

[0015] Under physical constraints, the bilateral position-deflection angle synchronous dynamic model of the crossbeam connection of the H-shaped motion platform is as follows:

[0016]

[0017] In the formula, m1 is the equivalent inertial mass of linear motor 1, m2 is the equivalent inertial mass of linear motor 2, m is the average mass of linear motor 1 and linear motor 2, and K θ1 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 1. θ1 K is the damping coefficient produced by the beam rotation angle on linear motor 1. θ2 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 2. θ2 The damping coefficient produced by the beam rotation angle on linear motor 2. The first derivative of θ The second derivative of y1, The second derivative of y² Let F1 be the second derivative of θ, F2 be the control thrust of linear motor 1, and F3 be the control thrust of linear motor 2. f1 F is the frictional force acting on linear motor 1. f2 This refers to the frictional force experienced by linear motor 2;

[0018] The frictional force F fi for:

[0019]

[0020] In the formula, i = 1, 2, y i It is the displacement of linear motor i. y i The first derivative, g is the acceleration due to gravity, sgn(·) is the sign function, and m i Let μ be the equivalent inertial mass of the linear motor i. k The constant coefficient of friction, k, represents the macroscopic motion of an object. v The coefficient of kinetic friction represents the macroscopic motion of an object.

[0021] Furthermore, the established bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides, specifically as follows:

[0022] The bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a dynamic model based on the position deviation Δy of the two motors:

[0023]

[0024] In the formula, Δy = y1 - y2 is the synchronization error of the H-type motion platform. Let Δy be the first derivative. K is the second derivative of Δy. Δ =(K θ1 +K θ2 ) / L, C Δ =(C θ1 +C θ2 ) / L, K i =K θi / L,C i =C θi / L, i = 1, 2;

[0025] The dynamic model based on the positional deviation Δy of the two motors is transformed into a dynamic model based on the displacement of the center of mass of the beam and the positional deviation of the two motors, namely, the displacement of the center of mass of the beam and the synchronization error.

[0026]

[0027] In the formula, y = (y1 + y2) / 2, K is the second derivative of y. y = (K1-K2) / 2, C y = (C1-C2) / 2.

[0028] Furthermore, the specific process of transforming the model from step one into a dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters is as follows:

[0029] When the beam inclination angle reaches saturation, The dynamic model of beam centroid displacement-synchronization error is transformed into:

[0030]

[0031] The dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters is as follows:

[0032]

[0033] In the formula, k(Δy) is the switching parameter of the designed adaptive model;

[0034] The model can be switched between equations (5) and (6) based on the adaptive model switching parameters designed.

[0035] Furthermore, the adaptive model switching parameter k(Δy) is:

[0036]

[0037] In the formula, Δy max χ is the maximum value of the guide rail clearance, e is the base of the natural logarithm, χ > 0, δ > 0, and δ represents the parameter of the adaptive term.

[0038] Furthermore, a decoupling control method for the differential and common modes of the H-type motion platform is designed, which decouples the dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters into a full-drive synchronous system model, specifically:

[0039]

[0040] Where u c For common-mode control of the all-drive synchronization system, u d Differential mode control for all-drive synchronization systems;

[0041]

[0042] Furthermore, in order to achieve the desired state of the all-drive synchronization system, the all-drive error dynamics model is as follows:

[0043]

[0044] In the formula, y r The second derivative of y r For the desired tracking signal of the all-drive synchronization system, For e y The second derivative, e y This is the positional deviation.

[0045] Furthermore, the differential mode control quantity and common mode control quantity of the two motors are:

[0046]

[0047] in, This is the common-mode control quantity for the motors on both sides. These are the differential control quantities for the two motors, where a0, a1, b0, and b1 are coefficients required for pole configuration.

[0048] Furthermore, the synchronous control of the H-shaped motion platform based on the differential mode control and common mode control of the two motors specifically involves:

[0049]

[0050] In the formula, F1 is the calculated control thrust of linear motor 1, and F2 is the calculated control thrust of linear motor 2.

[0051] Furthermore, the coefficients a0, a1, b0, and b1 required for the pole placement are calculated as follows:

[0052] Based on the all-drive theory control method, the pole positions are set as follows:

[0053]

[0054] In the formula, λ c1 and λ c2 Indicates positional deviation e y The locations of the two dominant poles of the subsystem, λ d1 and λ d2 Indicates the positions of the two dominant poles of the synchronization subsystem;

[0055] Derive k j ,l j If j = 0,1, then pole placement is performed, i.e., parameters a0, a1, b0, and b1 are respectively:

[0056]

[0057] The beneficial effects of this invention are:

[0058] 1. In view of the synchronous motion characteristics of the H-type motion platform, this invention designs an adaptive model switching parameter. The dynamic model of beam centroid displacement-synchronization error constructed based on the adaptive model switching parameter can not only meet the actual physical system constraints of the H-type motion platform, but also realize continuous model switching between the two working conditions of tilt angle adjustment and tilt angle saturation.

[0059] 2. Based on the adaptive switching model, this invention proposes a general differential mode and common mode decoupling control method, which can decouple the dynamic model of beam centroid displacement-synchronization error into a full-drive synchronous system model, and further obtain the full-drive error dynamic model, which facilitates the full-drive synchronous control of H-type motion platform, and has important research significance and practical value.

[0060] 3. Based on the all-drive error dynamic model, this invention proposes an all-drive synchronous control method for an H-type motion platform. It designs an all-drive system control method based on differential mode control and common mode control to improve the synchronous control performance of the H-type motion platform. This method can solve the problems of platform vibration, poor control stability and low accuracy caused by the asynchronous movement of the motors on both sides, and achieves a highly efficient and stable all-drive synchronous control effect. Attached Figure Description

[0061] Figure 1 This is a block diagram of the all-drive synchronous control system for an H-type motion platform;

[0062] Figure 2 This is a diagram showing the dynamic identification results of the synchronization error of the H-type motion platform;

[0063] Figure 3 This is a comparison chart of the tracking performance of the crossbeam's center of mass displacement under sinusoidal signal input.

[0064] Figure 4 This is a comparison chart of the tracking error of the crossbeam's center of mass displacement under sinusoidal signal input;

[0065] Figure 5 This is a comparison chart of the synchronization errors of an H-shaped motion platform under sinusoidal signal input. Detailed Implementation

[0066] Specific Implementation Method 1: The H-type motion platform all-drive synchronous control method based on an adaptive switching model described in this implementation method specifically includes the following steps:

[0067] Step 1: Based on the physical constraints of the H-type motion platform, establish a bilateral position-angle synchronization dynamic model based on the beam deflection angle. Then, transform the established bilateral position-angle synchronization dynamic model based on the beam deflection angle into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides.

[0068] Step 2: For the model switching between the beam tilt angle adjustment condition and the tilt angle saturation condition of the H-type motion platform, design adaptive model switching parameters, and transform the model from Step 1 into a beam centroid displacement-synchronization error dynamic model based on the adaptive model switching parameters.

[0069] Step 3: Design a decoupling control method for the differential mode and common mode of the H-type motion platform, decoupling the dynamic model of the beam centroid displacement-synchronization error based on the adaptive model switching parameters into an all-drive synchronization system model; and then derive the all-drive error dynamic model based on the all-drive synchronization system model.

[0070] Step 4: Obtain the differential mode control quantity and common mode control quantity of the two motors based on the full drive error dynamic model, and perform synchronous control of the H-type motion platform based on the differential mode control quantity and common mode control quantity of the two motors.

[0071] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the establishment of a bilateral position-angle synchronization dynamic model based on the beam deflection angle according to the physical constraints of the H-shaped motion platform is as follows:

[0072] The physical constraints of the H-type motion platform are:

[0073]

[0074] In the formula, θ is the rotation angle of the middle crossbeam, y1 is the displacement of linear motor 1, y2 is the displacement of linear motor 2, and L is the length of the crossbeam.

[0075] Under physical constraints, the bilateral position-deflection angle synchronous dynamic model of the crossbeam connection of the H-shaped motion platform is as follows:

[0076]

[0077] In the formula, m1 is the equivalent inertial mass of linear motor 1, m2 is the equivalent inertial mass of linear motor 2, m is the average mass of linear motor 1 and linear motor 2, and K θ1 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 1. θ1 K is the damping coefficient produced by the beam rotation angle on linear motor 1. θ2 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 2. θ2 The damping coefficient produced by the beam rotation angle on linear motor 2. The first derivative of θ The second derivative of y1, The second derivative of y² Let F1 be the second derivative of θ, F2 be the control thrust of linear motor 1, and F3 be the control thrust of linear motor 2. f1 F is the frictional force acting on linear motor 1. f2 This refers to the frictional force experienced by linear motor 2;

[0078] The frictional force F fi for:

[0079]

[0080] In the formula, i = 1, 2, y i It is the displacement of linear motor i. y i The first derivative, g is the acceleration due to gravity, sgn(·) is the sign function, and m i Let μ be the equivalent inertial mass of the linear motor i. k The constant coefficient of friction, k, represents the macroscopic motion of an object. v The coefficient of kinetic friction represents the macroscopic motion of an object.

[0081] The other steps and parameters are the same as in Specific Implementation Method 1.

[0082] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the established bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides. The specific process is as follows:

[0083] Considering practical industrial control applications, the bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a dynamic model based on the position deviation Δy of the two motors:

[0084]

[0085] In the formula, Δy = y1 - y2, Let Δy be the first derivative. K is the second derivative of Δy. Δ =(K θ1 +K θ2 ) / L, C Δ =(C θ1 +C θ2 ) / L, K i =K θi / L,C i =C θi / L, i = 1, 2;

[0086] Without considering the model deviation of the two motors, the next optimization step is to transform the dynamic model based on the position deviation Δy of the two motors into a dynamic model of the displacement of the center of mass of the beam and the synchronization error:

[0087]

[0088] In the formula, y = (y1 + y2) / 2, K is the second derivative of y. y =(K1-K2) / 2,C y = (C1-C2) / 2.

[0089] Other steps and parameters are the same as in specific implementation method one or two.

[0090] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the model in Step One is transformed into a dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters. The specific process is as follows:

[0091] Since the motor models on both sides are quite similar, K y C y ≈0, frictional force F f1 ,F f2 The model is now complete, as it provides damping for the system.

[0092] In engineering, due to the tolerances in the production of mechanical structures, the cause of synchronization error is the guide rail clearance. Since the guide rail clearance is finite, a system model under extreme positions is considered, that is, when the guide rail clearance approaches its maximum value Δy→Δy. max When the beam's tilt angle reaches saturation, the tilt angle of the entire beam becomes fixed. The dynamic model of beam centroid displacement-synchronization error is transformed into:

[0093]

[0094] The dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters is as follows:

[0095]

[0096] In the formula, k(Δy) is the switching parameter of the designed adaptive model;

[0097] The model can be switched between equations (5) and (6) based on the adaptive model switching parameters designed.

[0098] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0099] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the adaptive model switching parameter k(Δy) is:

[0100]

[0101] In the formula, Δy max χ is the maximum value of the guide rail clearance, e is the base of the natural logarithm, χ > 0, δ > 0, and δ represents the parameter of the adaptive term.

[0102] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0103] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that it designs a decoupling control method for the differential and common modes of the H-type motion platform. Specifically, it decouples the dynamic model of the beam centroid displacement-synchronization error based on adaptive model switching parameters into a full-drive synchronization system model.

[0104]

[0105] Where u c For common-mode control of the all-drive synchronization system, directly drive the position y subsystem, u d Differential mode control for the all-drive synchronization system is used to control the synchronization error Δy subsystem;

[0106]

[0107] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0108] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in order to further achieve the desired state of the all-drive synchronization system, the all-drive error dynamics model is as follows:

[0109]

[0110] In the formula, y r The second derivative of y r For the desired tracking signal of the all-drive synchronization system, For e y The second derivative, e y This is the positional deviation.

[0111] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0112] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the differential mode control quantity and common mode control quantity of the two motors are:

[0113]

[0114] in, This is the common-mode control quantity for the motors on both sides. These are the differential control quantities for the two motors, where a0, a1, b0, and b1 are coefficients required for pole configuration.

[0115] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0116] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the synchronous control of the H-shaped motion platform based on the differential mode control and common mode control of the two side motors is specifically as follows:

[0117]

[0118] In the formula, F1 is the calculated control thrust of linear motor 1, and F2 is the calculated control thrust of linear motor 2.

[0119] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0120] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the calculation method for the coefficients a0, a1, b0, and b1 required for pole placement is as follows:

[0121] Based on the all-drive theory control method, the pole positions are set as follows:

[0122]

[0123] In the formula, λ c1 and λ c2 Indicates positional deviation e y The locations of the two dominant poles of the subsystem, λ d1 and λ d2 This indicates the positions of the two dominant poles of the synchronization subsystem. These two sets of poles need to be tuned according to the parameters.

[0124] Based on the two selected poles, k can be derived. j ,l j If j = 0,1, then pole placement is performed, i.e., parameters a0, a1, b0, and b1 are respectively:

[0125]

[0126] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0127] Example

[0128] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the implementation of the present invention is not limited thereto.

[0129] This embodiment provides a tracking and synchronization control method for an H-type motion platform based on an all-drive system model. The algorithm is verified using a dual-drive linear motor platform.

[0130] like Figure 1 The image shows an H-shaped motion platform in this embodiment. The thrust devices on both sides are linear motors and linear motor drivers. The thrust devices provide power to the system. The thrust devices on both sides are coupled and connected through a middle crossbeam to form an H-shaped motion platform. Figure 1 The coordinate transformation, all-drive error dynamic model, elimination of nonlinear terms, pole reconfiguration, and derivation of differential and common mode control quantities are the steps in this embodiment of the proposed all-drive synchronous control method for an H-type motion platform based on an adaptive switching model. Specifically, the method includes the following steps:

[0131] Step 1: Establish dynamic models for the H-shaped motion platform under two working conditions: beam tilt angle adjustment and tilt angle saturation. When the beam tilt angle has not reached saturation, i.e., under the tilt angle adjustment condition, the dynamic model of beam centroid displacement-synchronization error is as follows:

[0132]

[0133] In the formula, y = (y1 + y2) / 2, K is the second derivative of y. y = (K1-K2) / 2, C y = (C1-C2) / 2.

[0134] Since the motor models on both sides are quite similar, K y C y ≈0, frictional force F f1 ,F f2 The model is now complete, as it provides damping for the system.

[0135] In engineering, due to the tolerances in the production of mechanical structures, the cause of synchronization error is the guide rail clearance. Since the guide rail clearance is finite, a system model under extreme positions is considered, that is, when the guide rail clearance approaches its maximum value Δy→Δy. max When the beam's tilt angle reaches saturation, the tilt angle of the entire beam becomes fixed. Therefore, when the beam inclination angle reaches saturation, i.e., under the inclination angle saturation condition, the dynamic model of beam centroid displacement-synchronization error transforms into:

[0136]

[0137] Step 2, the dynamic model of beam centroid displacement-synchronization error based on adaptive model parameter switching is as follows:

[0138]

[0139] In the formula, k(Δy) is the switching parameter of the designed adaptive model;

[0140] The switching parameter k(Δy) of the designed adaptive model is expressed in the following form:

[0141]

[0142] In the formula, parameter δ>0, Δy max Depending on the specific system design, χ > 0 is used to prevent the denominator of the synchronization control input from being 0.

[0143] Step 3: Establish the system structure, determine the main parameters of the system, and verify the accuracy of the model.

[0144] Based on the control method of the all-drive system model, a decoupling control method for differential mode and common mode of H-type motion platform is designed. The control input is linearly transformed to convert the system into an all-drive system, that is, the linear transformation is as follows:

[0145]

[0146] Where u c This represents the common-mode input of the system, which directly drives the position y subsystem. d This represents the differential input of the system, which is used to control the Δy subsystem. Therefore, the common-mode signal, u, is obtained from the thrust of the motors on both sides of y1 and y2. c and u d This represents the all-drive synchronous control of an H-type motion platform based on an adaptive switching model. To verify the accuracy of the above model, a u-type motion platform is established. d →Δy transfer function relationship, and use the frequency sweep method to identify the synchronization error dynamics of the H-type motion platform, such as Figure 2 As shown. The parameters for the adaptive term are determined as δ = 2.81, χ = 0.05, and Δy. max =35.5μm, K Δ =1.627×10 5 C Δ =171.41.

[0147] Step 4: Let the desired tracking signal of the system be y. r , Given the second derivative of the desired tracking signal or the desired acceleration signal, the following error dynamics equation is obtained:

[0148]

[0149] Step 5: Obtain the differential mode control quantity and common mode control quantity of the two motors based on the full drive error dynamic model, and perform nonlinear term elimination and pole reconfiguration.

[0150] Derived control variables:

[0151]

[0152] Based on the all-wheel drive theory control method, the pole positions are set as follows:

[0153]

[0154] In the formula, λ c1,2 Indicates positional deviation e y The locations of the two dominant poles of the subsystem, λ d1,2 This indicates the positions of the two dominant poles of the synchronization subsystem, and different k values ​​are chosen. j ,l j (j=0,1) can be pole placement.

[0155] Then the solution is calculated and parameter a j ,b j (j = 0, 1) takes the following form:

[0156] a0 = -mk0

[0157] a1 = -mk1

[0158] b0 = ml0 / k(Δy)

[0159] b0 = ml1 / k(Δy)

[0160] Step Six: Calculate the thrust on both sides using the method from Step Four:

[0161]

[0162] F1 and F2 represent the thrust on both sides of the H-shaped motion platform, which can simultaneously control tracking error and synchronization error.

[0163] Experiments were conducted on the above design process. The input reference signal was a sinusoidal signal. The proposed all-drive synchronous control method based on an adaptive switching model and the traditional parallel synchronous control method were used to control the bilateral motors of the H-type motion platform to track the reference signal, yielding the following results: Figures 3 to 5 The test results. Figure 3 The image shows a comparison of the tracking performance of the crossbeam's center of mass displacement under a sinusoidal signal input. The angular frequency of the input signal is π rad / s, and the amplitude is 40 mm. Figure 4This is a comparison chart of the tracking error of the crossbeam's center of mass displacement under sinusoidal signal input. According to the results in the chart, compared with the traditional control method, the control method proposed in this invention has a better tracking effect, and the peak error is reduced by about 50μm. Figure 5 The figure shows a comparison of the synchronization errors of the H-type motion platform under sinusoidal signal input. According to the results in the figure, the peak synchronization error of the control method proposed in this invention is about 5μm, which is only one-third of that of the traditional control method, thus significantly improving the synchronization control performance of the H-type motion platform.

[0164] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for all-drive synchronous control of an H-type motion platform based on an adaptive switching model, characterized in that, The method specifically includes the following steps: Step 1: Based on the physical constraints of the H-type motion platform, establish a bilateral position-angle synchronization dynamic model based on the beam deflection angle. Then, transform the established bilateral position-angle synchronization dynamic model based on the beam deflection angle into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides. The establishment of a bilateral position-deflection angle synchronous dynamic model based on the beam deflection angle, according to the physical constraints of the H-shaped motion platform, is as follows: The physical constraints of the H-type motion platform are: In the formula, θ is the rotation angle of the middle crossbeam, y1 is the displacement of linear motor 1, y2 is the displacement of linear motor 2, and L is the length of the crossbeam. Under physical constraints, the bilateral position-deflection angle synchronous dynamic model of the crossbeam connection of the H-shaped motion platform is as follows: In the formula, m1 is the equivalent inertial mass of linear motor 1, m2 is the equivalent inertial mass of linear motor 2, m is the average mass of linear motor 1 and linear motor 2, and K θ1 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 1. θ1 K is the damping coefficient produced by the beam rotation angle on linear motor 1. θ2 C is the stiffness coefficient produced by the beam rotation angle relative to linear motor 2. θ2 The damping coefficient produced by the beam rotation angle on linear motor 2. The first derivative of θ The second derivative of y1, The second derivative of y² Let F1 be the second derivative of θ, F2 be the control thrust of linear motor 1, and F3 be the control thrust of linear motor 2. f1 F is the frictional force acting on linear motor 1. f2 This refers to the frictional force experienced by linear motor 2; The frictional force F fi for: In the formula, i = 1, 2, y i It is the displacement of linear motor i. For y i The first derivative, g is the acceleration due to gravity, sgn(·) is the sign function, and m i Let μ be the equivalent inertial mass of the linear motor i. k The constant coefficient of friction, k, represents the macroscopic motion of an object. v The coefficient of kinetic friction represents the macroscopic motion of an object. The established bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a beam centroid displacement-synchronization error dynamic model based on the beam centroid displacement and the position deviation of the motors on both sides. Specifically: The bilateral position-angle synchronization dynamic model based on the beam deflection angle is transformed into a dynamic model based on the position deviation Δy of the two motors: In the formula, Δy = y1 - y2, Let Δy be the first derivative. K is the second derivative of Δy. Δ =(K θ1 +K θ2 ) / L, C Δ =(C θ1 +C θ2 ) / L, K i =K θi / L,C i =C θi / L, i = 1, 2; The dynamic model based on the positional deviation Δy of the two motors is transformed into a dynamic model of the displacement of the crossbeam's center of mass and the synchronization error: In the formula, y = (y1 + y2) / 2, K is the second derivative of y. y = (K1-K2) / 2, C y = (C1-C2) / 2; Step 2: For the model switching between the two working conditions of beam tilt angle adjustment and tilt angle saturation of the H-type motion platform, design adaptive model switching parameters, and transform the model in Step 1 into a beam centroid displacement-synchronization error dynamic model based on the adaptive model switching parameters. The specific process of transforming the model from step one into a dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters is as follows: When the beam inclination angle reaches saturation, The dynamic model of beam centroid displacement-synchronization error is transformed into: The dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters is as follows: In the formula, k(Δy) is the switching parameter of the designed adaptive model; The model can be switched between equations (5) and (6) based on the adaptive model switching parameters designed; Step 3: Design a decoupling control method for the differential mode and common mode of the H-type motion platform, decoupling the dynamic model of the beam centroid displacement-synchronization error based on the adaptive model switching parameters into an all-drive synchronization system model; and then derive the all-drive error dynamic model based on the all-drive synchronization system model. Step 4: Obtain the differential mode control quantity and common mode control quantity of the two motors based on the full drive error dynamic model, and perform synchronous control of the H-type motion platform based on the differential mode control quantity and common mode control quantity of the two motors.

2. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 1, characterized in that, The adaptive model switching parameter k(Δy) is: In the formula, Δy max χ is the maximum value of the guide rail clearance, e is the base of the natural logarithm, χ > 0, δ > 0, and δ represents the parameter of the adaptive term.

3. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 2, characterized in that, The design of the differential mode and common mode decoupling control method for the H-type motion platform decouples the dynamic model of beam centroid displacement-synchronization error based on adaptive model switching parameters into a full-drive synchronous system model, specifically: In the formula, u c For common-mode control of the all-drive synchronization system, u d Differential mode control for all-drive synchronization systems; 4. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 3, characterized in that, The dynamic model of the all-drive error is as follows: In the formula, For y r The second derivative of y r For the desired tracking signal of the all-drive synchronization system, For e y The second derivative, e y This is the positional deviation.

5. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 4, characterized in that, The differential mode control quantity and common mode control quantity of the two motors are: in, This is the common-mode control quantity for the motors on both sides. These are the differential control quantities for the two motors, where a0, a1, b0, and b1 are coefficients required for pole configuration.

6. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 5, characterized in that, The synchronous control of the H-type motion platform based on the differential mode control and common mode control of the two motors is specifically as follows: In the formula, F1 is the calculated control thrust of linear motor 1, and F2 is the calculated control thrust of linear motor 2.

7. The all-drive synchronous control method for an H-type motion platform based on an adaptive switching model according to claim 6, characterized in that, The calculation method for the coefficients a0, a1, b0, and b1 required for pole placement is as follows: Based on the all-drive theory control method, the pole positions are set as follows: In the formula, λ c1 and λ c2 Indicates positional deviation e y The locations of the two dominant poles of the subsystem, λ d1 and λ d2 Indicates the positions of the two dominant poles of the synchronization subsystem; Derive k j ,l j If j = 0,1, then pole placement is performed, i.e., parameters a0, a1, b0, and b1 are respectively:

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