A method and device for controlling preset time of a flexible link robotic arm

Abstract

The present invention provides a preset time control method and device for a flexible linkage manipulator, relating to the field of robotics. The method comprises: constructing a dynamic model of the flexible manipulator; performing a dual-time-scale model decomposition of the flexible manipulator dynamic model based on singular perturbation theory to obtain a slow-varying subsystem and a fast-varying subsystem; designing a preset time trajectory tracking controller based on the slow-varying subsystem using a composite learning algorithm based on a neural network and a disturbance observer, using a time transformation function and a state transformation function; designing a vibration suppression controller based on the fast-varying subsystem by constructing sliding mode variables; and obtaining control inputs for the flexible linkage manipulator based on the preset time trajectory tracking controller and the vibration suppression controller. This method can effectively suppress flexible vibrations and improve the robustness and adaptability of the system.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, and in particular to a method and device for controlling preset time of a flexible link robot arm. Background Art

[0002] Flexible linkage manipulators play an important role in the medical, industrial manufacturing, and aerospace fields due to their advantages such as light weight, energy saving, and high load-to-weight ratio. As the application fields continue to expand, many application scenarios that require precise operations have placed extremely high demands on the system's convergence speed. In order to improve the response speed of the system, finite-time stable control methods and fixed-time stable control methods have been proposed successively; the finite-time stable control method can ensure that the system state converges to the desired value within a finite time, but the stabilization time is affected by the system's initial state and control parameters; the fixed-time stable control method allows the system state to converge to the desired value within a fixed time, and the stabilization time is independent of the system's initial state, but there is a complex numerical relationship between the stabilization time and the control parameters of this method. Although the above two methods can improve the system's response speed to a certain extent, they still have limitations when facing application scenarios that require flexible setting of the stabilization time.

[0003] The preset time stabilization control method allows users to set the system's stabilization time based on their needs, independent of the initial state or control parameters. This method has high research and application value, especially in applications with strict stabilization time requirements. However, existing research results are often difficult to directly apply to complex flexible linkage robotic arm systems.

[0004] To address the complex dynamics of flexible-link manipulators, a control scheme based on rigid-flexible coupling dynamics attempts to simultaneously address trajectory tracking and vibration suppression. However, within this control framework, increasing system response speed often results in increased vibration amplitude, leading to a conflict between rapid system convergence and effective vibration suppression. As the system response speed increases, the amplitude of the flexible vibration also increases, compromising system accuracy and increasing control difficulty. Summary of the Invention

[0005] In order to solve the technical problem of the existing technology that it is impossible to simultaneously achieve the preset time trajectory tracking control of the system and good vibration suppression, the embodiment of the present invention provides a method and device for preset time control of a flexible link robot arm. The technical solution is as follows:

[0006] In one aspect, a method for controlling a preset time of a flexible link manipulator is provided. The method is implemented by a device for controlling a preset time of a flexible link manipulator, and the method comprises:

[0007] S1. Construct a dynamic model of the flexible robotic arm;

[0008] S2. Based on the singular perturbation theory, the flexible manipulator dynamics model is decomposed into a dual-time-scale model to obtain the slow-changing subsystem and the fast-changing subsystem;

[0009] S3. According to the slowly varying subsystem, a composite learning algorithm based on a neural network and a disturbance observer is used to design a preset time trajectory tracking controller based on a time transformation function and a state transformation function;

[0010] S4. Designing a vibration suppression controller by constructing a sliding mode variable according to the fast-changing subsystem;

[0011] S5. Obtaining a control input of the flexible link manipulator arm according to the preset time trajectory tracking controller and the vibration suppression controller.

[0012] On the other hand, a flexible link manipulator preset time control device is provided, which is applied to a flexible link manipulator preset time control method, and the device includes:

[0013] A construction unit for constructing a dynamic model of a flexible robotic arm;

[0014] The first acquisition unit is used to perform a dual-time-scale model decomposition on the flexible manipulator dynamics model based on the singular perturbation theory to obtain a slow-changing subsystem and a fast-changing subsystem;

[0015] A first design unit is configured to design a preset time trajectory tracking controller based on the slowly varying subsystem by adopting a composite learning algorithm based on a neural network and a disturbance observer and based on a time transformation function and a state transformation function;

[0016] A second design unit is configured to design a vibration suppression controller by constructing a sliding mode variable according to the fast-changing subsystem;

[0017] The second acquisition unit is used to obtain the control input of the flexible link manipulator according to the preset time trajectory tracking controller and the vibration suppression controller.

[0018] On the other hand, a flexible-link robotic arm preset time control device is provided, which includes: a processor; a memory, on which computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, any one of the above-mentioned flexible-link robotic arm preset time control methods is implemented.

[0019] On the other hand, a computer-readable storage medium is provided, wherein the storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement any one of the above-mentioned flexible link robot arm preset time control methods.

[0020] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0021] The embodiment of the present invention first constructs a dynamic model of a flexible manipulator; based on the singular perturbation theory, the dynamic model of the flexible manipulator is decomposed into a dual-time-scale model to obtain a slow-varying subsystem and a fast-varying subsystem; based on the slow-varying subsystem, a composite learning algorithm based on a neural network and a disturbance observer is used to design a preset time trajectory tracking controller based on a time transformation function and a state transformation function; based on the fast-varying subsystem, a vibration suppression controller is designed by constructing a sliding mode variable; based on the preset time trajectory tracking controller and the vibration suppression controller, a control input of the flexible link manipulator is obtained. The embodiment of the present invention can solve the preset time trajectory tracking control problem of a flexible link manipulator under system uncertainty and external time-varying disturbances; compared with existing control schemes through simulation experiments, the control scheme proposed by the present invention can achieve trajectory tracking within any preset time by the user and has a good vibration suppression effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. 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 creative work.

[0023] Figure 1 This is a flow chart of a method for controlling preset time of a flexible link manipulator provided by an embodiment of the present invention;

[0024] Figure 2 is a comparison curve diagram of the actual position and the expected position of the angle of joint 1 provided by an embodiment of the present invention;

[0025] Figure 3 is a comparison curve diagram of the actual position and the expected position of the joint 2 angle provided by an embodiment of the present invention;

[0026] Figure 4 is a graph showing the change in tracking error of the angular position of joint 1 over time, provided by an embodiment of the present invention;

[0027] Figure 5 is a graph showing the change in tracking error of the angular position of joint 2 over time, provided by an embodiment of the present invention;

[0028] Figure 6 is a graph showing changes in different flexible modes over time provided by an embodiment of the present invention;

[0029] Figure 7This is a block diagram of a preset time control device for a flexible link mechanical arm provided by an embodiment of the present invention;

[0030] Figure 8 It is a structural schematic diagram of a flexible link robot arm preset time control device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0032] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as an "exemplary" in the present invention should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of the word "exemplary" is intended to present concepts in a concrete manner. Furthermore, in the embodiments of the present invention, "and / or" can mean both or either of the two.

[0033] In the embodiments of the present invention, the terms "image" and "picture" may be used interchangeably. It should be noted that, when the distinction between them is not emphasized, their intended meanings are the same. The terms "of," "corresponding," and "corresponding" may be used interchangeably. It should be noted that, when the distinction between them is not emphasized, their intended meanings are the same.

[0034] In the embodiments of the present invention, sometimes a subscript such as W1 may be written as a non-subscript such as W1. When the difference is not emphasized, the meanings to be expressed are the same.

[0035] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0036] The embodiment of the present invention provides a method for controlling the preset time of a flexible link manipulator, which can be implemented by a device for controlling the preset time of a flexible link manipulator, and the device for controlling the preset time of a flexible link manipulator can be a terminal or a server. Figure 1 The flowchart of the method for controlling the preset time of the flexible link manipulator shown in FIG. 1 may include the following steps:

[0037] S1. Construct a dynamic model of the flexible robotic arm.

[0038] Among them, the planar n-link flexible link manipulator is taken as the research object, the flexible link is discretized based on the hypothetical modal method, and the dynamic model of the flexible manipulator is obtained according to the Lagrangian method; wherein, the dynamic model of the flexible manipulator can be expressed by the following formula (1):

[0039]

[0040] Among them, θ(t)=[θ1(t),...,θ n (t)] T ∈R n represents the joint angle position of the flexible manipulator; assuming the flexible modal order is m, then δ(t)=[δ 1,1 (t),...,δ 1,m (t),...,δ n,1 (t),...,δ n,m (t)] T ∈R nm , where δ i,j (t) represents the jth flexible modal variable of the i-th link; M∈R (n+nm)×(n+nm) is the inertia matrix of the robot, B1∈R n represents the Coriolis force matrix; B2∈R nm Denotes the centrifugal force matrix, D1∈R n×n represents the first damping matrix; D2∈R nm×nm Represents the second damping matrix, S2∈R nm×nm represents the stiffness matrix, u(t)∈R n represents the control input, f d (t)∈R n represents a bounded external time-varying disturbance.

[0041] According to the dynamic characteristics of the manipulator, the inverse matrix of the inertia matrix M is defined and can be expressed by the following formula (2):

[0042]

[0043] Among them, it is known that the inertia matrix M is positive definite and reversible; According to formula (1) and formula (2), the dynamic model of the flexible manipulator is further obtained, which can be expressed by the following formula (3) and formula (4):

[0044]

[0045] S2. Based on the singular perturbation theory, the flexible manipulator dynamics model is decomposed into a dual-time-scale model to obtain the slow-changing subsystem and the fast-changing subsystem.

[0046] Among them, the singular perturbation theory is used to decompose the dynamic model into a dual-time scale model. The specific process includes:

[0047] (1) Define singular perturbation parameters; obtain the singular perturbation model of the flexible manipulator system;

[0048] The singular perturbation variable φ = δ / ρ and the singular perturbation matrix β = ρS2 are defined. According to the singular perturbation parameters, formula (3) and formula (4) are further processed to obtain the following formulas (5) to (6):

[0049]

[0050] Where ρ = 1 / k s represents the singular perturbation parameter; k s represents the minimum stiffness coefficient; wherein, the process of dividing the control input into the slow-changing subsystem control input and the fast-changing subsystem control input based on the singular perturbation theory can be expressed by the following formula (7):

[0051] u(t)=u s (t)+u f (t),(7)

[0052] Where u(t) represents the control input; u s (t) represents the control input of the slow-varying subsystem; u f (t) represents the fast-changing subsystem control input;

[0053] (2) According to the singular perturbation dynamics model of the flexible manipulator, the influence of the high-frequency vibration of the system is neglected to obtain the slow-varying subsystem. In order to establish the slow-varying subsystem model, the influence of the high-frequency vibration of the system is neglected, and the singular perturbation parameter ρ is set to 0. Formula (5)-Formula (6) is further processed to obtain the following formulas (8)-Formula (9):

[0054]

[0055] The symbol subscript s represents that the above variables are all obtained under the condition of slow time variation. Substituting formula (9) into formula (8) to obtain the slow-varying subsystem model, it can be expressed by the following formula (10):

[0056]

[0057] Where η1(t)=θ s (t), ζ(t)=-r(t)(B 1s (t)+D 1s (t)η2(t)), r0 is the nominal value of r,

[0058] (3) Define the fast-changing time scale and the fast-changing subsystem variables; among them, define the fast-changing time scale Compared with fast variables, the rate of change of slow variables is close to zero, so in the fast variable time scale The slow variable can be regarded as a constant, which can be expressed by the following formulas (11) and (12):

[0059]

[0060] In one feasible implementation, define the fast-changing subsystem variables According to the fast-changing subsystem variables, based on formula (6) and formula (9), the fast-changing subsystem model is obtained, which can be expressed by the following formula (13):

[0061]

[0062] where ψ = [ψ1, ψ2] T represents the fast-changing subsystem variable; where, represents the first system matrix of the fast-changing subsystem; where Q f =[0,H 21s ] T Represents the second system matrix of the fast-changing subsystem.

[0063] S3. According to the slowly varying subsystem, a composite learning algorithm based on neural network and disturbance observer is adopted to design a preset time trajectory tracking controller based on time transformation function and state transformation function.

[0064] Optionally, a preset time trajectory tracking control scheme in the time domain t enables the joint positions of the flexible link manipulator to track a desired trajectory within any user-preset time.

[0065] In a feasible implementation, the present application designs a preset time trajectory tracking controller u based on the slow-varying subsystem. s (t), so that the joint position of the flexible link manipulator can track the desired trajectory within any user-preset time, which can be expressed by the following formulas (14) and (15):

[0066]

[0067] Where T>0 represents any user-preset time; η 1d (t) represents the desired trajectory to be tracked.

[0068] Optionally, the specific implementation process of S3 may include S31-S39:

[0069] S31. Using radial basis function neural network to approximate the uncertainty of dynamic model in slow-varying subsystem.

[0070] In one feasible implementation, assuming that the desired trajectory η of the flexible manipulator system is 1d (t), expected speed and the expected acceleration are all known and bounded; the dynamic uncertainty part can be expressed by the following formula (16):

[0071] ζ(t)=w T (t)R(η(t))+ε(t),(16)

[0072] in, is the input vector of the neural network, w(t)∈R p×n is the optimal weight of the neural network, R(η(t))=[R1(η(t)),R2(η(t)),...,R p (η(t))] T is the neural network basis function, ε(t)∈R n is the approximation error of the neural network, and p is the number of nodes in the neural network. The basis function can be expressed by the following formula (17):

[0073]

[0074] Among them, C i is the center vector of the i-th neuron, b i is the width parameter of the i-th neuron; Substituting formula (16) into the slow-varying subsystem model, the expression of the slow-varying subsystem model is obtained, which can be expressed by the following formula (18):

[0075]

[0076] Among them, Ω(t)=b(t)+ε(t) represents the composite disturbance term, represents the composite disturbance consisting of external time-varying disturbance and system dynamics uncertainty;

[0077] represents the uncertainty of system dynamics;

[0078] S32. Define a time transformation function and a state transformation function; expand the slowly varying subsystem from a finite stable period t∈[0,T) to an infinite time domain τ∈[0,+∞); design a control scheme in the transformed new time domain τ, and perform a state transformation on the tracking error variable according to the state transformation function to obtain a transformation error;

[0079] The time transformation function can be expressed by the following formula (19):

[0080]

[0081] Wherein, ι(t) increases monotonically at t∈[0,T); wherein, according to formula (19), the time period t∈[0,T) can be extended to an infinite time domain τ∈[0,+∞), and the inverse function of the time transformation function ι(t) can be expressed by the following formula (20):

[0082]

[0083] The derivative of formula (20) is obtained, and the derivative result is expressed by the following formula (21):

[0084]

[0085] To illustrate the process of time transformation, consider the nonlinear control system represented by the following formula (22):

[0086]

[0087] Where x(t) represents the system state variable; x0 is the initial state of the system; based on the time transformation function, we define Where ι(τ) is a strictly increasing continuous differentiable function, and the following formula (23) holds:

[0088]

[0089] The tracking error variable can be expressed by the following formula (24)-formula (25):

[0090] x1(t)=η1(t)-η 1d (t),(24)

[0091]

[0092] in, represents the corresponding position tracking error variable in the time domain τ; represents the corresponding velocity tracking error variable in the time domain τ; wherein, in order to ensure that the system tracking error can converge to the origin, the process of state transformation of the tracking error variable in the time domain τ can be expressed by the following formula (26):

[0093]

[0094] in, represents the state transition coefficient, To ensure tracking error A control scheme needs to be designed to make the conversion error Asymptotically bounded.

[0095] S33, defining a virtual control variable; defining a synchronization error in the time domain τ according to the virtual control variable and the conversion error;

[0096] The synchronization error can be expressed by the following formula (27):

[0097]

[0098] in, represents the synchronization error; η 2d (τ) represents the virtual control variable to be designed; according to formulas (22)-(23), formula (27) is derived, and the derivative result can be expressed by the following formula (28); among which, the virtual control variable can be expressed by the following formula (29):

[0099]

[0100] η 2d (τ)=-K1e1(τ)(29)

[0101] Among them, η 2d (τ) represents the virtual control variable; where 0<K1∈R n×n Represents the first control gain matrix. According to formula (27), the conversion error is obtained The derivative of can be expressed by the following formula (30):

[0102]

[0103] S34, constructing a velocity observer in the time domain τ and defining a velocity observation error;

[0104] Among them, the speed observer in the time domain τ can be expressed by the following formula (31)-formula (32):

[0105]

[0106] in, Represents the optimal weight of the neural network The estimated value of k p is a positive number; Composite perturbation estimated value.

[0107] S35. Construct a composite disturbance observer in the time domain τ, define a composite disturbance observation error; define a neural network optimal weight estimation error;

[0108] The composite disturbance observer can be expressed by the following formula (33)-formula (34):

[0109]

[0110] Where, l is the first positive constant; r z is the second positive constant; the neural network optimal weight estimation error and the composite disturbance observation error can be expressed by the following formulas (35) and (36), respectively:

[0111]

[0112] in, Represents the error in estimating the optimal weights of the neural network; represents the composite perturbation observation error; wherein, according to formula (34), the process of deriving (33) in the time domain τ can be expressed by the following formula (37):

[0113]

[0114] S36. Deriving the composite disturbance observation error, the velocity observation error, and the neural network optimal weight estimation error in the time domain τ; designing a trajectory tracking controller and a neural network weight update law in the time domain τ;

[0115] The process of deriving the composite disturbance observation error, velocity observation error, and neural network optimal weight estimation error can be expressed by the following formulas (38) to (40):

[0116]

[0117] Alternatively, the trajectory tracking controller in the time domain τ is expressed by the following formula (41):

[0118]

[0119] in, represents the trajectory tracking controller in the time domain τ; 0<K2∈R n×n is the second control gain matrix, γ is the first positive constant; σ is the second positive constant; represents the corresponding conversion error in the time domain τ; represents the corresponding synchronization error in the time domain τ; Represents a dummy control variable; 0<K1∈R n×n is the first control gain matrix; τ represents the time variable of the conversion time domain; represents the state transition coefficient; represents the corresponding position tracking error variable in the time domain τ; represents the corresponding velocity tracking error variable in the time domain τ; represents the corresponding composite disturbance observation in the time domain τ; Represents the corresponding expected trajectory acceleration variable in the time domain τ.

[0120] The neural network weight update law in the time domain τ is expressed by the following formula (42):

[0121]

[0122] in, represents the neural network weight update law in the time domain τ; represents the derivative of the inverse function of the time transformation function with respect to the time variable τ; Represents the input vector of the corresponding neural network in the time domain τ; r z >0 indicates the observation gain parameter; represents the corresponding system velocity observation error in the time domain τ; Represents the corresponding neural network basis function in the time domain τ; Represents the estimated value of the optimal weight of the neural network corresponding to the time domain τ.

[0123] S37, according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ, the composite disturbance observation error, the velocity observation error, the neural network optimal weight estimation error, the conversion error, and the synchronization error are made to converge to a small neighborhood near the origin in the time domain τ, and the trajectory tracking error converges asymptotically to the origin in the time domain τ;

[0124] Among them, based on Lyapunov theory, the following stability conclusions can be obtained: under the action of the trajectory tracking controller, the neural network weight update law and the disturbance observer in the time domain τ, the trajectory tracking error of the slowly varying subsystem converges asymptotically to the origin in the time domain τ, that is,

[0125] S38, obtaining a preset time trajectory tracking control scheme in the time domain t according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ;

[0126] Optionally, according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ, the process of obtaining the preset time trajectory tracking control scheme in the time domain t is expressed by the following formulas (43) to (49):

[0127]

[0128] t∈[0,T),(49)

[0129] Among them, u s(t) represents the preset time trajectory tracking controller in the time domain t; I represents the identity matrix of appropriate dimension; T represents the preset stable time parameter; K1 represents the first control gain matrix; K2 represents the second control gain matrix; R represents the neural network basis function; η(t) represents the input vector of the neural network; represents the synchronization error variable; x1(t) represents the position tracking error; x2(t) represents the velocity tracking error; k N (t) represents the system velocity observation error; represents the estimated value of the optimal weight of the neural network; η2(t) represents the system speed variable; represents the observed value of the system velocity variable; represents the composite perturbation observation; represents the desired trajectory acceleration variable; represents the neural network weight update law; r0(t) represents the nominal value of the system matrix; k p >0 indicates the first observation gain; l>0 indicates the second observation gain; z(t) indicates the intermediate variable of the composite disturbance observer; Represents the rate of change of the intermediate variable of the composite disturbance observer.

[0130] S39. According to the preset time trajectory tracking control scheme in the time domain t, the composite disturbance observation error, velocity observation error, neural network optimal weight estimation error, conversion error and synchronization error are converged to a small neighborhood near the origin in the time domain t, and the trajectory tracking error converges to the origin at the preset time in the time domain t.

[0131] Among them, based on the time transformation relationship, the following stability conclusions can be obtained: under the action of the preset time stability control scheme, the trajectory tracking error of the slow-varying subsystem converges to the origin at the preset time in the time domain t, that is,

[0132] Optionally, based on the time transformation relationship, a takeover control scheme is designed when t ≥ T, which is expressed by the following formulas (50) to (56):

[0133]

[0134] t∈[T,+∞),(56)

[0135] Where e3(t)=K5x1(t)+x2(t) represents the linear combination of position tracking error and velocity tracking error; 0<K3∈R n×n Represents the third control gain matrix; 0<K4∈R n×n Represents the fourth control gain matrix; 0<K5∈R n×n Represents the fifth control gain matrix; when t≥T, the control scheme can maintain the stability of the flexible link manipulator system.

[0136] S4. Based on the fast-changing subsystem, a vibration suppression controller is designed by constructing sliding mode variables.

[0137] The fast-changing subsystem can be expressed by the following formula (57); the sliding mode variable can be expressed by the following formula (58):

[0138]

[0139] Among them, Λ f =P f ψ+(Q f -Q f0 )u f , Q f0 It's Q f The nominal value of

[0140] z1=γψ,(58)

[0141] Among them, 0<γ∈R nm×2nm is the gain matrix.

[0142] Optionally, the process of designing the vibration suppression controller in S4 is expressed by the following formula (59)-formula (61):

[0143]

[0144] Among them, (γQ f0 ) + γQ f0 Pseudo-inverse matrix; 0<K fi ∈R nm×nm , i=1,2,3,4 is the control gain matrix; sign(·) represents the sign function; 0<γ∈R nm×2nm represents the gain matrix; Q f0 Denotes the system matrix Q f The nominal value of z1 represents the sliding mode variable; u f represents the vibration suppression controller; z2 represents the intermediate state variable of the vibration suppression controller; represents the rate of change of the intermediate state variable of the vibration suppression controller. In order to avoid potential controller chattering problems, the sign function sign(·) in the above formula (61) can be replaced by a saturation function, which can be expressed by the following formula (62):

[0145]

[0146] in, Is a positive number.

[0147] S5. Obtain control input of the flexible link manipulator arm according to the preset time trajectory tracking controller and vibration suppression controller.

[0148] In a feasible implementation, the effectiveness of the dual-time-scale preset time trajectory tracking control scheme proposed in this application is verified by simulation experiments. In the simulation experiment, the expected trajectory is set as: η 1d (t) = [cos(t), sin(t)] T The number of nodes p of the neural network is set to 256, and the initial value of the neural network weight is set to zero; the control parameters of the slow-changing subsystem are selected as: K1 = 4I 2×2 ,K2=4I 2×2 ,K3=64I 2×2 ,K4=48I 2×2 ,K5=4I 2×2 ,k p =0.5,γ=20,r z =100, σ=1 and l=10; the control parameters of the fast-changing subsystem are selected as: ρ=0.02, K f1 =0.5I 4×4 , K f2 =4I 4×4 , K f3 =4I 4×4 , K f4 =2I 4×4 and γ=[0.2I 4×4 ,I 4×4 ]. The nominal value of the system matrix r is selected as r0=diag(0.5,0.5), and the time-varying external disturbance is set to f d (t) = [sin(t), sin(t)] T To verify the performance of the control scheme, the stabilization time parameter T was set to 0.8s and 1s respectively, and the simulation results were compared with the neural network adaptive control scheme proposed based on rigid-flexible coupling dynamics. The control parameters in the neural network adaptive control scheme were selected as follows: p = 256, σ = 0.0002, Γ = 100I 256×256 , K1=6I 6×6 and K2=24I 6×6 ; The simulation results are as follows Figure 2-Figure 6 As shown, Figure 2 and Figure 3 The trajectory tracking performance of the flexible link manipulator is shown in the figure. As can be seen from the figure, the flexible link manipulator successfully tracks the desired trajectory within the preset stabilization time T. The tracking error between the system state and the desired trajectory is shown in the figure. Figure 4 and Figure 5As shown in the figure, it can be seen that the tracking error converges to the origin within the preset stabilization time T. By setting a smaller stabilization time parameter T, the joint angle position of the robot arm can converge to the expected value at a faster speed. Figure 6 The convergence curve of the flexible mode of the manipulator is shown. Experimental results show that compared with the neural network adaptive control scheme, the control scheme proposed in this application effectively reduces the amplitude of flexible vibration while ensuring faster system response speed, accelerates the vibration convergence process, and has a good vibration suppression effect.

[0149] Among them, simulation experimental results show that the control scheme proposed by the present invention significantly reduces the amplitude of flexible vibration and accelerates the speed of vibration convergence while ensuring faster response speed. The effectiveness of the present invention in vibration suppression is particularly outstanding in applications requiring high precision and fast response. This application has important significance and broad application prospects in practical applications, especially in the fields of medicine, industrial manufacturing, and aerospace, showing great potential.

[0150] The embodiment of the present invention first constructs a dynamic model of a flexible manipulator; based on the singular perturbation theory, the dynamic model of the flexible manipulator is decomposed into a dual-time-scale model to obtain a slow-varying subsystem and a fast-varying subsystem; according to the slow-varying subsystem, a composite learning algorithm based on a neural network and a disturbance observer is adopted to design a preset time trajectory tracking controller based on a time transformation function and a state transformation function; according to the fast-varying subsystem, a vibration suppression controller is designed by constructing a sliding mode variable; according to the preset time trajectory tracking controller and the vibration suppression controller, the control input of the flexible link manipulator is obtained. The embodiment of the present invention can solve the preset time trajectory tracking control problem of a flexible link manipulator under system uncertainty and external time-varying disturbances. Compared with the existing control scheme through simulation experiments, the control scheme proposed by the present invention can realize trajectory tracking within any preset time of the user and has a good vibration suppression effect.

[0151] Figure 7 This is a block diagram of a flexible link manipulator preset time control device according to an exemplary embodiment, which is used in a flexible link manipulator preset time control method. Figure 7 The device includes a construction unit 810, a first acquisition unit 820, a first design unit 830, a second design unit 840, and a second acquisition unit 850.

[0152] A construction unit 810 is used to construct a dynamic model of the flexible robotic arm;

[0153] The first acquisition unit 820 is configured to perform a dual-time-scale model decomposition on the flexible manipulator dynamics model based on the singular perturbation theory to obtain a slow-varying subsystem and a fast-varying subsystem;

[0154] A first design unit 830 is configured to design a preset time trajectory tracking controller based on the slowly varying subsystem by adopting a composite learning algorithm based on a neural network and a disturbance observer, and based on a time transformation function and a state transformation function;

[0155] A second design unit 840 is configured to design a vibration suppression controller by constructing a sliding mode variable according to the fast-changing subsystem;

[0156] The second acquisition unit 850 is configured to obtain a control input of the flexible link manipulator according to the preset time trajectory tracking controller and the vibration suppression controller.

[0157] Optionally, the first design unit 830 is configured to:

[0158] Using radial basis function neural network to approximate the uncertainty of dynamic model in slow-varying subsystem;

[0159] Define the time transformation function and the state transformation function; expand the slowly varying subsystem from the finite stable period t∈[0,T) to the infinite time domain τ∈[0,+∞); design the control scheme in the new time domain τ after the transformation, and transform the tracking error variable according to the state transformation function to obtain the conversion error;

[0160] Define a dummy control variable; define the synchronization error in the time domain τ based on the dummy control variable and the conversion error;

[0161] Construct a velocity observer in the time domain τ and define the velocity observation error;

[0162] Construct a composite disturbance observer in the time domain τ and define the composite disturbance observation error; define the neural network optimal weight estimation error;

[0163] Derivatives of composite disturbance observation error, observation error, and neural network optimal weight estimation error are obtained in the time domain τ; a trajectory tracking controller and a neural network weight update law are designed in the time domain τ;

[0164] According to the trajectory tracking controller, neural network weight update law and disturbance observer in the time domain τ, the composite disturbance observation error, velocity observation error, neural network optimal weight estimation error, conversion error and synchronization error are made to converge to a small neighborhood near the origin in the time domain τ, and the trajectory tracking error converges asymptotically to the origin in the time domain τ;

[0165] According to the trajectory tracking controller, neural network weight update law and disturbance observer in the time domain τ, a preset time trajectory tracking control scheme in the time domain t is obtained;

[0166] According to the preset time trajectory tracking control scheme in the time domain t, the composite disturbance observation error, velocity observation error, neural network optimal weight estimation error, conversion error and synchronization error converge to a small neighborhood near the origin in the time domain t, and the trajectory tracking error converges to the origin at the preset time in the time domain t.

[0167] Optionally, the trajectory tracking controller in the time domain τ is expressed by the following formula (1):

[0168]

[0169] in, represents the trajectory tracking controller in the time domain τ; 0<K2∈R n×n is the second control gain matrix, γ is the first positive constant; σ is the second positive constant; represents the corresponding conversion error in the time domain τ; represents the corresponding synchronization error in the time domain τ; Represents a dummy control variable; 0<K1∈R n×n is the first control gain matrix; τ represents the time variable of the conversion time domain; represents the state transition coefficient; represents the corresponding position tracking error variable in the time domain τ; represents the corresponding velocity tracking error variable in the time domain τ; represents the corresponding composite disturbance observation in the time domain τ; Represents the corresponding expected trajectory acceleration variable in the time domain τ.

[0170] The neural network weight update law in the time domain τ is expressed by the following formula (2):

[0171]

[0172] in, represents the neural network weight update law in the time domain τ; represents the derivative of the inverse function of the time transformation function with respect to the time variable τ; Represents the input vector of the corresponding neural network in the time domain τ; r z >0 indicates the observation gain parameter; represents the corresponding system velocity observation error in the time domain τ; Represents the corresponding neural network basis function in the time domain τ; Represents the estimated value of the optimal weight of the neural network corresponding to the time domain τ.

[0173] Optionally, the preset time trajectory tracking control scheme in the time domain t enables the joint positions of the flexible link manipulator to track a desired trajectory within any user-preset time.

[0174] Optionally, the process of obtaining a preset time trajectory tracking control scheme in the time domain t according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ is expressed by the following formulas (3) to (9):

[0175]

[0176] t∈[0,T),(9)

[0177] Among them, u s (t) represents the preset time trajectory tracking controller in the time domain t; I represents the identity matrix of appropriate dimension; T represents the preset stable time parameter; K1 represents the first control gain matrix; K2 represents the second control gain matrix; R represents the neural network basis function; η(t) represents the input vector of the neural network; represents the synchronization error variable; x1(t) represents the position tracking error; x2(t) represents the velocity tracking error; k N (t) represents the system velocity observation error; represents the estimated value of the optimal weight of the neural network; η2(t) represents the system speed variable; represents the observed value of the system velocity variable; represents the composite perturbation observation; represents the desired trajectory acceleration variable; represents the neural network weight update law; r0(t) represents the nominal value of the system matrix; k p >0 indicates the first observation gain; l>0 indicates the second observation gain; z(t) indicates the intermediate variable of the composite disturbance observer; Represents the rate of change of the intermediate variable of the composite disturbance observer.

[0178] Optionally, the design of the takeover control scheme when t≥T based on the time transformation relationship is expressed by the following formulas (10)-(16):

[0179]

[0180] t∈[T,+∞),(16)

[0181] Where e3(t)=K5x1(t)+x2(t) represents the linear combination of position tracking error and velocity tracking error; 0<K3∈R n×n Represents the third control gain matrix; 0<K4∈R n×n Represents the fourth control gain matrix; 0<K5∈R n×n Denotes the fifth control gain matrix.

[0182] Optionally, the process of designing the vibration suppression controller in S4 is expressed by the following formulas (17) to (19):

[0183]

[0184]

[0185] Among them, (γQ f0 ) + γQ f0 Pseudo-inverse matrix; 0<K fi ∈R nm×nm , i=1,2,3,4 is the control gain matrix; sign(·) represents the sign function; 0<γ∈R nm×2nm represents the gain matrix; Q f0 Denotes the system matrix Q f The nominal value of z1 represents the sliding mode variable; u f represents the vibration suppression controller; z2 represents the intermediate state variable of the vibration suppression controller; Represents the rate of change of the intermediate state variable of the vibration suppression controller.

[0186] The embodiment of the present invention first constructs a dynamic model of a flexible manipulator; based on the singular perturbation theory, the dynamic model of the flexible manipulator is decomposed into a dual-time-scale model to obtain a slow-varying subsystem and a fast-varying subsystem; based on the slow-varying subsystem, a composite learning algorithm based on a neural network and a disturbance observer is used to design a preset time trajectory tracking controller based on a time transformation function and a state transformation function; based on the fast-varying subsystem, a vibration suppression controller is designed by constructing a sliding mode variable; based on the preset time trajectory tracking controller and the vibration suppression controller, a control input of the flexible link manipulator is obtained. The embodiment of the present invention can solve the preset time trajectory tracking control problem of a flexible link manipulator under system uncertainty and external time-varying disturbances; compared with existing control schemes through simulation experiments, the control scheme proposed by the present invention can achieve trajectory tracking within any preset time by the user and has a good vibration suppression effect.

[0187] Figure 8 : is a structural diagram of a flexible link manipulator preset time control device provided by an embodiment of the present invention, such as Figure 8 As shown, the flexible link manipulator preset time control device may include the above Figure 7 Optionally, the flexible link manipulator preset time control device 910 may include a first processor 2001 .

[0188] Optionally, the flexible link robotic arm preset time control device 910 may further include a memory 2002 and a transceiver 2003 .

[0189] The first processor 2001, the memory 2002 and the transceiver 2003 may be connected via a communication bus.

[0190] The following combination Figure 8 The various components of the flexible link robot arm preset time control device 910 are specifically introduced:

[0191] The first processor 2001 is the control center of the flexible link manipulator preset time control device 910 and can be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 can be one or more central processing units (CPUs), or an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement an embodiment of the present invention, such as one or more microprocessors (digital signal processors, DSPs) or one or more field programmable gate arrays (FPGAs).

[0192] Optionally, the first processor 2001 can execute various functions of the flexible link robot arm preset time control device 910 by running or executing a software program stored in the memory 2002 and calling data stored in the memory 2002.

[0193] In a specific implementation, as an embodiment, the first processor 2001 may include one or more CPUs, such as Figure 8 CPU0 and CPU1 are shown in FIG.

[0194] In a specific implementation, as an embodiment, the flexible link manipulator preset time control device 910 may also include multiple processors, such as Figure 8 1 and 2. The first processor 2001 and the second processor 2004 are shown in FIG. Each of these processors can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). A processor herein can refer to one or more devices, circuits, and / or processing cores for processing data (e.g., computer program instructions).

[0195] The memory 2002 is used to store the software program for executing the solution of the present invention, and is controlled by the first processor 2001 for execution. The specific implementation method can refer to the above method embodiment and will not be repeated here.

[0196] Alternatively, the memory 2002 may be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compact disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 2002 may be integrated with the first processor 2001 or exist independently and preset the interface circuit ( Figure 8 (not shown) is coupled to the first processor 2001, which is not specifically limited in this embodiment of the present invention.

[0197] The transceiver 2003 is used to communicate with a network device or a terminal device.

[0198] Optionally, the transceiver 2003 may include a receiver and a transmitter ( Figure 8 (not shown separately in the figure). The receiver is used to implement a receiving function, and the transmitter is used to implement a sending function.

[0199] Optionally, the transceiver 2003 may be integrated with the first processor 2001 or may exist independently and preset the interface circuit of the time control device 910 through the flexible link manipulator ( Figure 8 (not shown) is coupled to the first processor 2001, which is not specifically limited in this embodiment of the present invention.

[0200] It should be noted that Figure 8 The structure of the flexible link robot arm preset time control device 910 shown in the figure does not constitute a limitation on the router. The actual knowledge structure recognition device may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0201] In addition, the technical effects of the flexible-link robotic arm preset time control device 910 can refer to the technical effects of the flexible-link robotic arm preset time control method described in the above method embodiment, and will not be repeated here.

[0202] It should be understood that the first processor 2001 in the embodiment of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0203] It should also be understood that the memory in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0204] The above embodiments can be implemented in whole or in part through software, hardware (such as circuits), firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, the processes or functions described in accordance with the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired method (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, or magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0205] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0206] In this disclosure, "at least one" means one or more, and "plurality" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, "at least one of a, b, or c" can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or plural.

[0207] It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0208] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0209] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0210] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of the device or unit, which can be electrical, mechanical or other forms.

[0211] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0212] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0213] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0214] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for controlling preset time of a flexible link manipulator, characterized in that: The method comprises: S1. Construct a dynamic model of the flexible robotic arm; S2. Based on the singular perturbation theory, the flexible manipulator dynamics model is decomposed into a dual-time-scale model to obtain the slow-changing subsystem and the fast-changing subsystem; S3. Based on the slowly varying subsystem, a composite learning algorithm based on a neural network and a disturbance observer is used to design a preset time trajectory tracking controller through a time transformation function and a state transformation function; Among them, the S3 adopts a composite learning algorithm based on a neural network and a disturbance observer according to the slowly varying subsystem, and designs a preset time trajectory tracking controller based on a time transformation function and a state transformation function, including: S31. Using radial basis function neural network to approximate the uncertainty of dynamic model in slow-varying subsystem. S32. Define a time transformation function and a state transformation function; expand the slowly varying subsystem from a finite stable period t∈[0,T) to an infinite time domain τ∈[0,+∞); design a control scheme in the transformed new time domain τ, and perform a state transformation on the tracking error variable according to the state transformation function to obtain a transformation error; S33, defining a virtual control variable; defining a synchronization error in the time domain τ according to the virtual control variable and the conversion error; S34, constructing a velocity observer in the time domain τ and defining a velocity observation error; S35. Construct a composite disturbance observer in the time domain τ, define a composite disturbance observation error; define a neural network optimal weight estimation error; S36. Deriving the composite disturbance observation error, the velocity observation error, and the neural network optimal weight estimation error in the time domain τ; designing a trajectory tracking controller and a neural network weight update law in the time domain τ; S37, according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ, the composite disturbance observation error, the velocity observation error, the neural network optimal weight estimation error, the conversion error, and the synchronization error are made to converge to a small neighborhood near the origin in the time domain τ, and the trajectory tracking error converges asymptotically to the origin in the time domain τ; S38, obtaining a preset time trajectory tracking control scheme in the time domain t according to the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ; S39, according to the preset time trajectory tracking control scheme in the time domain t, the composite disturbance observation error, the velocity observation error, the neural network optimal weight estimation error, the conversion error, and the synchronization error are converged to a small neighborhood near the origin in the time domain t, and the trajectory tracking error converges to the origin at the preset time in the time domain t; S4. Designing a vibration suppression controller by constructing a sliding mode variable according to the fast-changing subsystem; The process of designing the vibration suppression controller in S4 is expressed by the following formulas (1) to (3): Among them, (γQ f0 ) + γQ f0 Pseudo-inverse matrix; 0<K fi ∈R nm×nm , i=1,2,3,4 is the control gain matrix; sign(·) represents the sign function; 0<γ∈R nm×2nm represents the gain matrix; Q f0 Denotes the system matrix Q f The nominal value of z1 represents the sliding mode variable; u f represents the vibration suppression controller; z2 represents the intermediate state variable of the vibration suppression controller; represents the rate of change of the intermediate state variable of the vibration suppression controller; S5. Obtaining a control input of the flexible link manipulator arm according to the preset time trajectory tracking controller and the vibration suppression controller.

2. The method for controlling the preset time of a flexible link manipulator according to claim 1, wherein: The preset time trajectory tracking control scheme in the time domain t enables the joint positions of the flexible link manipulator to track the desired trajectory within any user-preset time.

3. The method for controlling the preset time of a flexible link manipulator according to claim 1, wherein: The trajectory tracking controller in the time domain τ is expressed by the following formula (4): in, represents the trajectory tracking controller in the time domain τ; 0<K2∈R n×n is the second control gain matrix, γ is the first positive constant; σ is the second positive constant; represents the corresponding conversion error in the time domain τ; represents the corresponding synchronization error in the time domain τ; Represents a dummy control variable; 0<K1∈R n×n is the first control gain matrix; τ represents the time variable of the conversion time domain; represents the state transition coefficient; represents the corresponding position tracking error variable in the time domain τ; represents the corresponding velocity tracking error variable in the time domain τ; represents the corresponding composite disturbance observation in the time domain τ; represents the corresponding expected trajectory acceleration variable in the time domain τ; The neural network weight update law in the time domain τ is expressed by the following formula (5): in, represents the neural network weight update law in the time domain τ; represents the derivative of the inverse function of the time transformation function with respect to the time variable τ; Represents the input vector of the corresponding neural network in the time domain τ; r z >0 indicates the observation gain parameter; represents the corresponding system velocity observation error in the time domain τ; Represents the corresponding neural network basis function in the time domain τ; Represents the estimated value of the optimal weight of the neural network corresponding to the time domain τ; The disturbance observer in the time domain τ is expressed by the following formulas (6)-(9): in, represents the corresponding system velocity variable in the time domain τ; represents the corresponding system velocity variable observation value in the time domain τ; represents the corresponding composite disturbance observation value in the time domain τ; represents the nominal value of the system matrix; k p >0 indicates the first observation gain; l>0 indicates the second observation gain; represents the intermediate variable of the corresponding composite disturbance observer in the time domain τ; Represents the rate of change of the intermediate variable of the corresponding composite disturbance observer in the time domain τ.

4. The method for controlling the preset time of a flexible link manipulator according to claim 1, wherein: The process of obtaining the preset time trajectory tracking control scheme in the time domain t based on the trajectory tracking controller, the neural network weight update law, and the disturbance observer in the time domain τ is expressed by the following formulas (10) to (16): t∈[0,T),(16) Among them, u s (t) represents the preset time trajectory tracking controller in the time domain t; I represents the identity matrix of appropriate dimension; T represents the preset stable time parameter; K1 represents the first control gain matrix; K2 represents the second control gain matrix; R represents the neural network basis function; η(t) represents the input vector of the neural network; represents the synchronization error variable; x1(t) represents the position tracking error; x2(t) represents the velocity tracking error; k N (t) represents the system velocity observation error; represents the estimated value of the optimal weight of the neural network; η2(t) represents the system speed variable; represents the observed value of the system velocity variable; represents the composite perturbation observation; represents the desired trajectory acceleration variable; represents the neural network weight update law; r0(t) represents the nominal value of the system matrix; k p >0 indicates the first observation gain; l>0 indicates the second observation gain; z(t) indicates the intermediate variable of the composite disturbance observer; Represents the rate of change of the intermediate variable of the composite disturbance observer.

5. The method for controlling the preset time of a flexible link manipulator according to claim 1, wherein: According to the time transformation relationship, the takeover control scheme when t≥T is designed, which is expressed by the following formulas (17)-(23): t∈[T,+∞),(23) Where e3(t)=K5x1(t)+x2(t) represents the linear combination of position tracking error and velocity tracking error; 0<K3∈R n ×n Represents the third control gain matrix; 0<K4∈R n×n Represents the fourth control gain matrix; 0<K5∈R n×n Denotes the fifth control gain matrix.

6. A flexible link manipulator preset time control device, the flexible link manipulator preset time control device is used to implement the flexible link manipulator preset time control method according to any one of claims 1 to 5, characterized in that: The device comprises: A construction unit for constructing a dynamic model of a flexible robotic arm; The first acquisition unit is used to perform a dual-time-scale model decomposition on the flexible manipulator dynamics model based on the singular perturbation theory to obtain a slow-changing subsystem and a fast-changing subsystem; A first design unit is configured to design a preset time trajectory tracking controller based on the slowly varying subsystem by adopting a composite learning algorithm based on a neural network and a disturbance observer through a time transformation function and a state transformation function; A second design unit is configured to design a vibration suppression controller by constructing a sliding mode variable according to the fast-changing subsystem; The second acquisition unit is used to obtain the control input of the flexible link manipulator according to the preset time trajectory tracking controller and the vibration suppression controller.

7. A flexible link robot arm preset time control device, characterized in that: The flexible link mechanical arm preset time control device includes: processor; A memory having computer-readable instructions stored thereon, wherein when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program code, which can be called by a processor to execute the method according to any one of claims 1 to 5.

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