An adaptive friction compensation control method and system for a dual-drive tracking platform

Abstract

The invention discloses an adaptive friction compensation control method and system for a dual-drive tracking platform, and relates to the technical field of radar seeker testing. The method comprises: establishing a dynamic model of the dual-drive tracking platform; obtaining an asymptotically stable target system with a lower dimension than the dual-drive tracking platform according to the dynamic model; determining an immersion mapping in the target system according to the target system; obtaining an implicit manifold according to the immersion mapping in the target system; obtaining a control law according to the implicit manifold; the control law is used to make the image of the dynamic trajectory under the immersion mapping in the target system remain unchanged and attract the manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law; establishing a LuGre friction model of nonlinear friction of the dual-drive tracking platform; and using the control law to perform adaptive friction compensation control on the LuGre friction model. The invention can improve the tracking accuracy and synchronization accuracy of the dual-drive tracking platform.

Description

Technical Field

[0001] The invention relates to the technical field of radar seeker testing, and in particular to an adaptive friction compensation control method and system for a dual-drive tracking platform. Background Art

[0002] The moving target simulator is one of the key components in the field of radar seeker testing. The existing moving target simulator mainly performs dynamic tracking based on infrared imaging. In the dynamic tracking process, a two-axis stable tracking platform is generally used to simulate the motion characteristics of space targets in space, thereby testing and evaluating the comprehensive performance of the guidance subsystem of guided weapons. The moving target simulator can carry infrared / microwave characteristic signal devices to perform two-dimensional motion in the seeker field of view. It generally uses two orthogonal online motion servo systems, namely, a two-axis stable tracking platform.

[0003] The traditional driving mode of servo motion system (motion servo system) is single-axis single drive, but due to the heavy load weight and large range of target motion rate, the driving mode based on single motor is difficult to meet the needs of target motion characteristic simulation. Therefore, dual motor synchronous drive is often used in online servo motion system, and the dynamic performance of servo system is more superior. In the dual drive tracking platform, that is, the dual drive synchronous servo motion system, the motor output force of the dual axis is small during low speed motion, and the nonlinear factors such as axis friction are large, so there are unstable jitter, creeping and slow response, which reduces the tracking accuracy and synchronization accuracy of the dual drive tracking platform. Summary of the invention

[0004] The object of the present invention is to provide an adaptive friction compensation control method and system for a dual-drive tracking platform, so as to improve the tracking accuracy and synchronization accuracy of the dual-drive tracking platform.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] An adaptive friction compensation control method for a dual-drive tracking platform, the method comprising:

[0007] Establish the dynamic model of the dual-drive tracking platform;

[0008] According to the dynamic model, an asymptotically stable target system with lower dimension than the dual-drive tracking platform is obtained;

[0009] determining an immersion map in the target system according to the target system;

[0010] Obtaining an implicit manifold according to an immersion map in the target system;

[0011] A control law is obtained according to the implicit manifold; the control law is used to make the image of the dynamic trajectory under the immersion mapping in the target system remain unchanged in the attracting manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law;

[0012] Establish the LuGre friction model of nonlinear friction of dual-drive tracking platform;

[0013] The control law is used to perform adaptive friction compensation control on the LuGre friction model.

[0014] Optionally, the kinetic model is expressed as:

[0015]

[0016]

[0017]

[0018] Wherein, X1 is the displacement of the first motor; X2 is the displacement of the second motor; the first motor is the motor equipped for the first guide rail in the dual-drive tracking platform; the second motor is the motor equipped for the second guide rail in the dual-drive tracking platform; M1 is the mass of the beam in the dual-drive tracking platform; M2 is the mass of the slider on the beam; L is the length of the beam; Y is the distance from the center of gravity of the slider to the center of gravity of the beam; I1 is the moment of inertia of the beam; f(v) is the function form of the nonlinear friction of the dual-drive tracking platform; μ is the viscous friction coefficient between the contact surfaces in the dual-drive tracking platform at a macroscopic level; M is the inertia matrix; U is the inverse of the coefficient of the matrix inertia matrix M.

[0019] Optionally, the target system is represented as:

[0020]

[0021] Where ξ1 is a point in the target system; x is an unknown number in the target system expression; and λ is a positive parameter.

[0022] Optionally, the immersion map is expressed as:

[0023]

[0024] Where β1 is the immersion map of a point in the target system; β2 is the immersion map of the target system.

[0025] Optionally, the control law is expressed as:

[0026]

[0027] Where, F1 is the force of the first motor acting on the first guide rail; K0 is 1; χ is a constant, χ∈[0.5,1]; Δx is the tracking error of the dual-drive tracking platform, Δx=x1-x; θ 11 is the first row and first column of the inertia matrix; η is any constant greater than zero; k is a positive coefficient greater than zero; x1 represents the displacement of the first guide rail; x3 represents the running speed of the first guide rail; z represents the unknown parameter estimation error in the friction compensation controller; θ m It means that when the dual-drive tracking platform faces m uncertain parameters, it still has a global asymptotic equilibrium stable point at the desired position.

[0028] Optionally, the implicit manifold is expressed as:

[0029] Q={x|π(x)=x3-β3=0}

[0030] Where Q represents the implicit manifold; π(x) is the implicit manifold expression; β3 is a mapping point on the implicit manifold.

[0031] Optionally, the LuGre friction model is expressed as:

[0032]

[0033]

[0034]

[0035] Where, f represents the static friction term in the LuGre friction model; g(v) represents the dynamic friction term in the LuGre friction model; f s is the maximum static friction; f c is the Coulomb friction force; Z is the uniform elastic deformation of the bristle; Ω is the critical stribeck velocity; σ1 is the equivalent stiffness of the bristle; σ2 is the microscopic damping coefficient between the contact surfaces; v is the instantaneous velocity between the contact surfaces; δ is an empirical value.

[0036] The present invention also provides the following solution:

[0037] An adaptive friction compensation control system for a dual-drive tracking platform, the system comprising:

[0038] A dynamic model building module is used to build a dynamic model of the dual-drive tracking platform;

[0039] A target system obtaining module, used for obtaining an asymptotically stable target system with lower dimension than the dual-drive tracking platform according to the dynamic model;

[0040] An immersion mapping determination module, configured to determine an immersion mapping in the target system according to the target system;

[0041] An implicit manifold obtaining module, used for obtaining an implicit manifold according to an immersion map in the target system;

[0042] A control law obtaining module is used to obtain a control law according to the implicit manifold; the control law is used to make the image of the dynamic trajectory under the immersion mapping in the target system remain unchanged in the attracting manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law;

[0043] LuGre friction model building module, used to build the LuGre friction model of nonlinear friction of dual-drive tracking platform;

[0044] The adaptive friction compensation control module is used to perform adaptive friction compensation control on the LuGre friction model by using the control law.

[0045] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0046] The adaptive friction compensation control method and system of the dual-drive tracking platform disclosed in the present invention obtain an asymptotically stable target system with lower dimension than the dual-drive tracking platform based on the established dynamic model of the dual-drive tracking platform, obtain an implicit manifold based on the immersion mapping in the target system, and obtain a control law based on the implicit manifold. The control law can make the image of the dynamic trajectory of the dual-drive tracking platform under the control law remain unchanged under the immersion mapping, and can also make the dynamic trajectory bounded. The control law is used to perform adaptive friction compensation control on the LuGre friction model, thereby improving the tracking accuracy and synchronization accuracy of the dual-drive tracking platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] 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 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 labor.

[0048] Figure 1 It is a flow chart of an embodiment of an adaptive friction compensation control method of a dual-drive tracking platform of the present invention;

[0049] Figure 2 This is a schematic diagram of the structure of the dual-drive tracking platform of the present invention;

[0050] Figure 3 It is the principle diagram of the control system of the present invention;

[0051] Figure 4It is a structural diagram of an embodiment of the adaptive friction compensation control system of the dual-drive tracking platform of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] The object of the present invention is to provide an adaptive friction compensation control method and system for a dual-drive tracking platform, so as to improve the tracking accuracy and synchronization accuracy of the dual-drive tracking platform.

[0054] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] Figure 1 Flow chart of an embodiment of the adaptive friction compensation control method of the dual-drive tracking platform of the present invention. Figure 1 , the adaptive friction compensation control method of the dual-drive tracking platform includes:

[0056] Step 101: Establish a dynamic model of the dual-drive tracking platform.

[0057] In step 101, the dynamic model of the dual-drive tracking platform, that is, the dynamic model of the dual-drive servo system is expressed as:

[0058]

[0059]

[0060] U=M2 2 Y 2 +2M1M2Y 2 +I1(M1+M2) (3)

[0061] Wherein, X1 is the displacement of the first motor; X2 is the displacement of the second motor; the first motor is the motor equipped for the first guide rail in the dual-drive tracking platform; the second motor is the motor equipped for the second guide rail in the dual-drive tracking platform; M1 is the mass of the beam in the dual-drive tracking platform; M2 is the mass of the slider on the beam; L is the length of the beam; Y is the distance from the center of gravity of the slider to the center of gravity of the beam; I1 is the moment of inertia of the beam; f(v) is the function form of the nonlinear friction of the dual-drive tracking platform; μ is the viscous friction coefficient between the contact surfaces in the dual-drive tracking platform at a macroscopic level, that is, the viscous friction coefficient of the dual-drive servo system; M is the inertia matrix; U is the inverse of the coefficient of the matrix inertia matrix M.

[0062] Take the state of the X1 axis (first guide rail) under low-speed motion of the dual-drive servo system as a reference:

[0063]

[0064] Where: K0 = 1; μ is the viscous friction coefficient; θ 11 is the first row and first column of the inertia matrix; F1 is the force acting on the X1 axis by the motor; ε1 is one of the state variables of the system disturbance model, T is the transpose; θ1 is the unknown parameter.

[0065] Define the adaptive estimate of θ1:

[0066]

[0067] Where: is the adaptive estimate of θ1, is a dynamic adaptive function; The introduction of the auxiliary compensation function increases the flexibility of the design of the adaptive estimation value of the disturbance parameter and defines the unknown parameter estimation error:

[0068]

[0069] Where: z1 is the unknown parameter estimation error.

[0070] Figure 2 This is a schematic diagram of the dual-drive tracking platform structure of the present invention. Figure 2 A represents the intersection of the left guide rail and the left end of the beam, y represents the horizontal direction, O represents the center of gravity of the beam, and θ represents the angle between the beam and the Y-axis. Figure 2 A simplified model of a moving target simulator is shown. Figure 2The dual-drive tracking platform (dual-drive synchronous servo motion system) is mainly composed of three parts: the first is the motion target simulator platform base; the motion simulator is composed of two guide rails (X1 axis and X2 axis) and a crossbeam (Y axis), and the crossbeam is driven by two parallel linear motors. The X1 axis and the X2 axis (the second guide rail) are each equipped with a motor of exactly the same model; the second is the crossbeam moving along the X direction; and the third is the slider moving along the crossbeam. Specifically, the first motor X1 and the second motor X2 are both linear motors.

[0071] Step 102: Obtain an asymptotically stable target system with lower dimension than the dual-drive tracking platform according to the dynamic model.

[0072] In step 102, a target system with a lower dimension than the original system is designed based on the dynamic model of the system. In step 102, the target system is represented as:

[0073]

[0074] Where ξ1 is a point in the target system; x is an unknown number in the target system expression; λ is a positive parameter. The system under consideration has ξ * =x as the only globally asymptotically stable equilibrium.

[0075] Step 103: Determine an immersion map in the target system according to the target system.

[0076] In step 103, an immersion map is designed to obtain the dynamic trajectory of the original system under the control law and the image of the immersion map in the target system. In step 103, the immersion map is expressed as:

[0077]

[0078] Where β1 is the immersion map of a point in the target system; β2 is the immersion map of the target system.

[0079] Step 104: Obtain an implicit manifold according to the immersion mapping in the target system.

[0080] In step 104, the implicit manifold is represented as:

[0081] Q={x|π(x)=x3-β3=0} (9)

[0082] Where Q represents the implicit manifold; π(x) is the implicit manifold expression; β3 is a mapping point on the implicit manifold.

[0083] Step 105: Obtain the control law according to the implicit manifold; the control law is used to make the image of the dynamic trajectory immersed in the target system under the mapping remain unchanged in the attracting manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law.

[0084] This step 105 derives the implicit manifold Q = {x|π(x) = x3 - β3 = 0} and obtains the control law.

[0085] The system tracking error is defined as: Δx = x1-x; if the above implicit flow form exists, the position tracking error can converge to zero asymptotically; substitute formula (4) and formula (8) into formula (9), and take the derivative to get:

[0086]

[0087] In the formula, c is the restriction law; For auxiliary functions.

[0088] At this time, the axis controller expression selection is as follows:

[0089]

[0090] In the formula, is an auxiliary function; to meet the system stability requirements, the constant χ must satisfy χ∈[0.5,1].

[0091] In step 105, the control law is expressed as:

[0092]

[0093] Where F1 is the force of the first motor acting on the first guide rail; K0 is 1; χ is a constant, χ∈[0.5,1]; Δx is the tracking error of the dual-drive tracking platform, Δx=x1-x; θ 11 is the first row and first column of the inertia matrix; η is any constant greater than zero; k is a positive coefficient greater than zero; x1 represents the displacement of the first guide rail (X1 axis); x3 represents the running speed of the first guide rail (X1 axis); z represents the unknown parameter estimation error in the friction compensation controller; θ m It means that when the dual-drive tracking platform faces m uncertain parameters, it still has a global asymptotic equilibrium stable point at the desired position.

[0094] Ensure that this control law can keep the image of the target system as an invariant attracting manifold and the trajectory is bounded:

[0095] In order to make the parameter estimation error approach zero, the parameter error formula, that is, formula (6), is derived to obtain:

[0096]

[0097] Where ω1 is the adaptive function; In order to seek partial guidance.

[0098] We can further obtain the adaptive update law of unknown parameters:

[0099]

[0100] Substituting formula (13) into formula (14):

[0101]

[0102] Design function V(z1), and in satisfying Solve the auxiliary compensation function under the condition of:

[0103]

[0104] Where V is the designed function,

[0105] The partial derivative of the auxiliary compensation function is selected as:

[0106]

[0107] In the formula, when η is any constant greater than zero, then:

[0108]

[0109] The auxiliary compensation function can be obtained by formula (18):

[0110]

[0111] Substituting formula (11) and formula (19) into formula (14), we can obtain the adaptive update law of the unknown parameter θ1: Denoted as ω1:

[0112]

[0113] Where p is the auxiliary function.

[0114] At this time, substituting formula (19) and formula (20) into formula (14) can obtain the position loop adaptive control law:

[0115]

[0116] Where: ∫ is the integral; k is a positive coefficient greater than zero; since Δx = x1-x, the complete nonlinear disturbance immersion and invariant adaptive control law are finally obtained, as shown in formula (12).

[0117] Rewrite formula (12):

[0118]

[0119] Where: f(·) is a time-varying nonlinear function containing disturbance state variables; F1' represents the derivative of F1.

[0120] The rewritten formula (22) is actually an extension of the adaptive expression of the classic PID control, in which the three PID terms are expressed as:

[0121]

[0122] The rewritten control law has one more item than the three items of the basic PID, which is the feedforward control law in which the position command of the dual-drive synchronous servo motion system directly acts on the input end of the control system. This item is still in the form of adaptive expression.

[0123] The above parameters (kp, ki, kd) are updated and changed by the time-varying nonlinear adaptive function composed of the state variables that affect the disturbance, so that the control output of the control law changes in real time. Adaptive feedforward control combined with feedback control can quickly eliminate the position deviation caused by friction and realize high-precision position servo of the synchronous servo motion system.

[0124] Step 106: Establish a LuGre friction model of the nonlinear friction of the dual-drive tracking platform.

[0125] The nonlinear friction of the system adopts the LuGre friction model. In step 106, the LuGre friction model is expressed as:

[0126]

[0127] Where, f represents the static friction term in the LuGre friction model; g(v) represents the dynamic friction term in the LuGre friction model; f s is the maximum static friction; f c is the Coulomb friction force; Z is the mean elastic deformation of the bristle; Ω is the critical stribeck velocity; σ1 is the equivalent stiffness of the bristle; σ2 is the microscopic damping coefficient between the contact surfaces; μ is the macroscopic viscous friction coefficient between the contact surfaces; v is the instantaneous velocity between the contact surfaces; δ is an empirical value, generally taken as 2.

[0128] When the system is in a steady state and enters the incomplete lubrication stage and the complete lubrication stage, there are but:

[0129]

[0130] Wherein, σ3 is the friction reference coefficient; sgn(v) is the step function; and e is the e-index.

[0131] In the formulas involved in the present invention, the parameter with “·” on the top represents the first-order derivative of the parameter with respect to time, and the parameter with “··” on the top represents the second-order derivative of the parameter with respect to time.

[0132] Step 107: Use the control law to perform adaptive friction compensation control on the LuGre friction model.

[0133] The present invention provides an adaptive friction compensation control design scheme for a dual-drive tracking platform, which relates to a motion target simulator system, specifically a dual-drive synchronous servo motion system and a control method, so as to improve the tracking accuracy and synchronization accuracy of the system. Since the tracking accuracy and synchronization accuracy of the tracking platform are reduced due to the large influence of the nonlinear friction of the system when the tracking platform moves in a low-speed unidirectional manner, the present invention adopts a nonlinear immersed invariant adaptive position controller to compensate the nonlinear friction of the system online; the control method provided by the present invention can estimate and compensate the friction disturbance online during the low-speed operation of the dual-drive synchronous servo motion system, including the following steps: (1) establishing a dynamic model of the motion system tracking platform; (2) designing a target system with a lower dimension than the original system and tending to be stable according to the dynamic model of the system; (3) designing an immersed mapping so that the dynamic trajectory of the original system under the control law is the image of the target system under the immersed mapping; (4) deriving the implicit flow and obtaining the control law; (5) ensuring that the control law can keep the image of the target system as an invariant attracting manifold and the trajectory is bounded.

[0134] Figure 3 is the principle diagram of the control system of the present invention, Figure 3 Where X represents the input value, and s represents the derivative of the input value. represents the equivalent stiffness of the bristle in the LuGre friction model, represents the damping coefficient of the microscopic contact surface in the LuGre friction model, It represents the viscous friction damping coefficient of the macroscopic lower contact surface in the LuGre friction model. Figure 3 The present invention can quickly eliminate the position deviation caused by friction through adaptive feedforward control combined with feedback control, and realize high-precision position servo of the synchronous servo motion system. When the synchronous servo motion system has position deviation during position tracking, the extended adaptive feedback PID control law will always act on the synchronous servo motion system to continuously eliminate the influence caused by disturbance; and the synchronous servo motion system always has uncertain nonlinear time-varying interference during the motion process, then the extended adaptive feedforward control law directly produces a correction effect without the need for control through position deviation. The control law designed by the present invention effectively combines the timeliness of feedforward control, the accuracy of feedback control and the target of adaptive control.

[0135] Compared with the prior art, the advantages of the present invention are as follows:

[0136] 1. After calculation, the complete control law is obtained, which is actually equivalent to the rewriting and expansion of PID because of the increase of uncertain unknowns.

[0137] 2. According to the nonlinear friction model in the tracking platform, a control law is obtained through this controller, which is then fed back to the nonlinear friction, and then feedforward compensation is performed before the friction.

[0138] 3. Only the parameter estimator needs to be designed. The control law is derived from the fixed object model and parameter estimator using the nonlinear immersion invariant implicit manifold.

[0139] Compared with the prior art, the present invention has the following beneficial effects:

[0140] (1) The present invention collects the dual-axis guide rails, dual-axis speeds, LuGre friction model and the force generated by the motor current to jointly estimate the friction parameters in real time. When nonlinear friction occurs in the dual-axis, the friction parameters can be estimated online. As the signal input, the dual-axis low-speed motion instructions can be accurately and quickly responded to, and the LuGre model can be compensated online, thereby improving the synchronization and tracking accuracy of the synchronous servo motion system.

[0141] (2) It can realistically simulate the motion characteristics of space targets in space, thereby testing and evaluating the comprehensive performance of guided weapon guidance subsystems, reducing the cost of failure and the consumption of resources.

[0142] Figure 4 FIG. 1 is a structural diagram of an embodiment of an adaptive friction compensation control system of a dual-drive tracking platform of the present invention. Figure 4 , the adaptive friction compensation control system of the dual-drive tracking platform includes:

[0143] The dynamic model building module 401 is used to build the dynamic model of the dual-drive tracking platform.

[0144] The target system obtaining module 402 is used to obtain an asymptotically stable target system with lower dimension than the dual-drive tracking platform according to the dynamic model.

[0145] The immersion mapping determination module 403 is used to determine the immersion mapping in the target system according to the target system.

[0146] The implicit manifold obtaining module 404 is used to obtain the implicit manifold according to the immersion map in the target system.

[0147] The control law obtaining module 405 is used to obtain the control law according to the implicit manifold; the control law is used to make the image of the dynamic trajectory immersed in the target system remain unchanged in the attracting manifold under the mapping, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law.

[0148] The LuGre friction model building module 406 is used to build a LuGre friction model of the nonlinear friction of the dual-drive tracking platform.

[0149] The adaptive friction compensation control module 407 is used to perform adaptive friction compensation control on the LuGre friction model using a control law.

[0150] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0151] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. An adaptive friction compensation control method for a dual-drive tracking platform, characterized in that: The method comprises: Establish the dynamic model of the dual-drive tracking platform; According to the dynamic model, an asymptotically stable target system with lower dimension than the dual-drive tracking platform is obtained; determining an immersion map in the target system according to the target system; Obtaining an implicit manifold according to an immersion map in the target system; A control law is obtained according to the implicit manifold; the control law is used to make the image of the dynamic trajectory under the immersion mapping in the target system remain unchanged in the attracting manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law; Establish the LuGre friction model of nonlinear friction of dual-drive tracking platform; Using the control law to perform adaptive friction compensation control on the LuGre friction model; The kinetic model is expressed as: <h2 style=";text-align:left;direction:ltr">U=M2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> Y<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2M1M2Y<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +I1(M1+M2) Wherein, X1 is the displacement of the first motor; X2 is the displacement of the second motor; the first motor is the motor equipped for the first guide rail in the dual-drive tracking platform; the second motor is the motor equipped for the second guide rail in the dual-drive tracking platform; M1 is the mass of the beam in the dual-drive tracking platform; M2 is the mass of the slider on the beam; L is the length of the beam; Y is the distance from the center of gravity of the slider to the center of gravity of the beam; I1 is the moment of inertia of the beam; f(v) is the function form of the nonlinear friction of the dual-drive tracking platform; μ is the viscous friction coefficient between the contact surfaces in the dual-drive tracking platform under macroscopic conditions; M is the inertia matrix; U is the inverse of the coefficient of the matrix inertia matrix M; The target system is represented as: In the formula, ξ1 is a point in the target system; x is an unknown number in the target system expression; λ is a positive parameter; The immersion map is expressed as: Where β1 is the immersion mapping of a point in the target system; β2 is the immersion mapping of the target system; The control law is expressed as: Where, F1 is the force of the first motor acting on the first guide rail; K0 is 1; χ is a constant, χ∈[0.5,1]; Δx is the tracking error of the dual-drive tracking platform, Δx=x1-x; θ 11 is the first row and first column of the inertia matrix; η is any constant greater than zero; k is a positive coefficient greater than zero; x1 represents the displacement of the first guide rail; x3 represents the running speed of the first guide rail; z represents the unknown parameter estimation error in the friction compensation controller; θ m It means that when the dual-drive tracking platform faces m uncertain parameters, it still has a global asymptotic equilibrium stable point at the desired position; The LuGre friction model is expressed as: Where, f represents the static friction term in the LuGre friction model; g(v) represents the dynamic friction term in the LuGre friction model; f s is the maximum static friction; f c is the Coulomb friction force; Z is the uniform elastic deformation of the bristle; Ω is the critical stribeck velocity; σ1 is the equivalent stiffness of the bristle; σ2 is the microscopic damping coefficient between the contact surfaces; v is the instantaneous velocity between the contact surfaces; δ is an empirical value.

2. The adaptive friction compensation control method of the dual-drive tracking platform according to claim 1, characterized in that: The implicit manifold is expressed as: Q={x|π(x)=x3-β3=0} Where Q represents the implicit manifold; π(x) is the implicit manifold expression; β3 is a mapping point on the implicit manifold.

3. An adaptive friction compensation control system for a dual-drive tracking platform, characterized in that: Based on the adaptive friction compensation control method of the dual-drive tracking platform according to claim 1, the system comprises: A dynamic model building module is used to build a dynamic model of the dual-drive tracking platform; A target system obtaining module, used for obtaining an asymptotically stable target system with lower dimension than the dual-drive tracking platform according to the dynamic model; An immersion mapping determination module, configured to determine an immersion mapping in the target system according to the target system; An implicit manifold obtaining module, used for obtaining an implicit manifold according to an immersion map in the target system; A control law obtaining module is used to obtain a control law according to the implicit manifold; the control law is used to make the image of the dynamic trajectory under the immersion mapping in the target system remain unchanged in the attracting manifold, and is also used to make the dynamic trajectory bounded; the dynamic trajectory is the dynamic trajectory of the dual-drive tracking platform under the action of the control law; LuGre friction model building module, used to build the LuGre friction model of nonlinear friction of dual-drive tracking platform; The adaptive friction compensation control module is used to perform adaptive friction compensation control on the LuGre friction model by using the control law.

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