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CN114559429B - Neural network control method for flexible manipulator based on adaptive iterative learning - Google Patents

Neural network control method for flexible manipulator based on adaptive iterative learning Download PDF

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CN114559429B
CN114559429B CN202210174112.3A CN202210174112A CN114559429B CN 114559429 B CN114559429 B CN 114559429B CN 202210174112 A CN202210174112 A CN 202210174112A CN 114559429 B CN114559429 B CN 114559429B
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robotic arm
flexible robotic
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CN114559429A (en
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刘屿
邬晓奇
李林
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South China University of Technology SCUT
Guangzhou Institute of Modern Industrial Technology
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Guangzhou Institute of Modern Industrial Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

本发明公开了一种基于自适应迭代学习的柔性机械臂的神经网络控制方法，该方法过程如下：根据柔性机械臂的动力学特征构建柔性机械臂系统；基于反步技术设计初始边界控制方法；设计神经网络项解决柔性机械臂系统参数不确定性和输入饱和特征；设计迭代控制项处理外在干扰；结合边界控制、神经网络项和迭代控制项，得到抑制柔性机械臂的边界自适应迭代神经网络控制方法。本发明能够有效抑制柔性机械臂的振动，并且在设计过程中考虑到了柔性机械臂系统参数不确定性和时变输出限制。

The invention discloses a neural network control method for a flexible manipulator based on adaptive iterative learning. The method process is as follows: construct a flexible manipulator system according to the dynamic characteristics of the flexible manipulator; design an initial boundary control method based on back-stepping technology; Design the neural network term to solve the parameter uncertainty and input saturation characteristics of the flexible manipulator system; design the iterative control term to deal with external interference; combine the boundary control, neural network term and iterative control term to obtain the boundary adaptive iterative neural network that suppresses the flexible manipulator. Network control methods. The invention can effectively suppress the vibration of the flexible manipulator, and takes into account the uncertainty of the parameters of the flexible manipulator system and the time-varying output limitations during the design process.

Description

Neural network control method of flexible mechanical arm based on self-adaptive iterative learning
Technical Field
The application relates to the technical field of vibration control, in particular to a neural network control method of a flexible mechanical arm based on self-adaptive iterative learning.
Background
By virtue of the excellent characteristics of light weight, high efficiency, low energy consumption and the like, flexible materials are widely used for manufacturing mechanical arms, marine risers, spacecraft and other devices. Compared with the traditional mechanical arm, the flexible mechanical arm has better ductility, flexibility and stronger toughness, and is convenient for being widely applied in modern technology. Under the effect of external disturbance, the flexible mechanical arm can continuously generate elastic deformation, high-frequency vibration is easy to cause, and the movement deviation of the tail end is too large, so that the stability and the accuracy of the system are directly influenced. Therefore, how to effectively inhibit the elastic deformation and vibration of the flexible mechanical arm is a problem to be solved.
Under the existing research, the boundary control method is a control method for effectively inhibiting the vibration of the flexible mechanical arm; however, in the design process, the input saturation characteristic and the parameter uncertainty characteristic of the flexible mechanical arm system are rarely considered, and in addition, the control output limit of the flexible mechanical arm system is always time-varying; these characteristics are ubiquitous in practice, and neglecting these characteristics, flexible mechanical arms are prone to instability.
Disclosure of Invention
The application aims to solve the defects in the prior art and provides a neural network control method of a flexible mechanical arm based on self-adaptive iterative learning.
The aim of the application can be achieved by adopting the following technical scheme:
a neural network control method of a flexible mechanical arm based on self-adaptive iterative learning comprises the following steps:
according to the dynamic characteristics of the flexible mechanical arm, constructing a dynamic model of the flexible mechanical arm system by utilizing the Hamiltonian principle;
designing virtual control quantity based on a back-stepping technology, and constructing a first Lyapunov function to obtain an initial boundary control method;
based on the flexible mechanical arm being interfered by the outside, an iteration control item is constructed, and the iteration control item is given in an implicit mode.
Based on the input saturation characteristic and parameter uncertainty of the flexible mechanical arm system, a neural network item is provided for solving the influence caused by the input saturation and parameter uncertainty;
combining the initial boundary control method with the iteration control item and the neural network item, comprising: and adding an iteration control item and a neural network item into the initial boundary control method.
Further, the dynamic characteristics of the flexible mechanical arm include kinetic energy, potential energy and virtual work of the flexible mechanical arm system, which are made by non-conservative force on the flexible mechanical arm system, and the kinetic energy, potential energy and virtual work are substituted into the Hamiltonian principle, so that a dynamic model of the flexible mechanical arm system is obtained as follows:
wherein l is the length of the flexible mechanical arm, ρ is the density of the flexible mechanical arm, s is the length variable, c is the damping coefficient of the flexible mechanical arm, EI is the bending stiffness of the flexible mechanical arm, T is the tension of the flexible mechanical arm, and>representing the first derivative of the deflection value y (s, t) of the flexible manipulator with respect to time t,,,>representing the second derivative of y (s, t) with respect to time t, w "(s, t) and w" (s, t) representing the second and fourth derivatives, respectively, of the elastic deformation value w (s, t) of the flexible mechanical arm with respect to s;
the boundary conditions are:
m is the mass of the end load of the flexible mechanical arm system, I is the inertia value of the hub of the flexible mechanical arm, r is the radius of the hub of the flexible mechanical arm, u1 (t) and u2 (t) are respectively a first control input and a second control input, d1 (t) and d2 (t) are respectively external disturbance of the first mechanical arm system and the second mechanical arm system,the angular acceleration of the rotation angle of the flexible mechanical arm is that w (0, t) is the elastic deformation value of the flexible mechanical arm at the length of 0, w (l, t) is the elastic deformation value of the flexible mechanical arm at the length of l, w ' (0, t) is the first-order deflection of w (0, t) to s, w "(0, t) is the second order bias of w (0, t) to s, w '" (0, t) is the third order bias of w (0, t) to s, w ' (l, t) is w (l, t) first order bias for t, w ' (l, t) is the second order bias for w (l, t) to t, w ' (l, t) is the third order bias for w (l, t) to t,>is the deflection acceleration of the flexible mechanical arm at l.
According to the Hamiltonian principle, a dynamic model of the flexible mechanical arm can be obtained, the dynamic model of the flexible mechanical arm is a high-order dynamic model, and the dynamic model solves the problem of high-dimensional coupling association of the flexible mechanical arm; the dynamic model comprises boundary conditions, provides a foundation for the design of a boundary control method, and simplifies the design process of the boundary control method.
Further, define x respectively 1 (t)＝θ(t)-θ d ，x 3 (t)＝y e (l,t)，
θd is the expected angle value of the flexible mechanical arm, θ (t) is the rotation angle of the flexible mechanical arm, and x 1 (t) is a first state quantity,is the rotation angular velocity, x of the flexible mechanical arm 2 (t) is a second state quantity, y e (l, t) is the deflection error of the flexible mechanical arm at l, x 3 (t) is a third state quantity, +.>For the deflection speed of the flexible arm at l, x 4 (t) is a fourth state quantity;
definition v 1 (t) is x 2 Virtual control amount of (t), v 2 (t) is x 4 The virtual control amount of (t),wherein eta and gamma are respectively a first control parameter and a second control parameter of the virtual control quantity, eta and gamma are more than 0,
definition s1 (t) is v 1 (t) and x 2 Error between (t), s2 (t) is v 2 (t) and x 4 Error between (t)The difference in the number of the two,
will x 2 (t)、x 4 (t) each is regarded as an independent subsystem, a virtual control quantity is proposed, each state quantity is controlled through the virtual control quantity, the virtual control quantity can eliminate nonlinear terms of the first Lyapunov function derivative in the next step, and the virtual control quantity is constructed so that the control method design process can be simplified.
Further, a first Lyapunov function is selected, and the initial boundary control method is obtained through the following steps:
the first Lyapunov function is:
F c (t)＝F 1 (t)+F 2 (t)+F b (t)+F d (t)
wherein ,
where w' (s, t) represents the first derivative of w (s, t) with s, y e (s, t) is the deflection error of the flexible mechanical arm, F 1 (t) is an energy term, F 2 (t) represents an energy cross term, F b (t) is an energy addition term, F d (t) is a function term to satisfy an output limit; k > 0 is the energy addition term F b Forward control parameters in (t) to ensure F b (t) > 0. X1 (t) is a rotation angle error limiting function of the flexible mechanical armχ2 (t) is a flexible manipulator end displacement error limiting function;
ζ 1 、ζ 2 respectively a first angle error constraint, a second angle error constraint and ζ 3 、ζ 4 Respectively restraining the displacement errors of the first end and the displacement errors of the second end; j (x) 1 (t)) and J (x) 3 (t)) are step functions, when x 1 (t)＞0，J(x 1 (t))＝1；x 1 (t)≤0，J(x 1 (t))=0, when x 3 (t)＞0，J(x 3 (t))＝1；x 3 (t)≤0，J(x 3 (t))＝0；
Deriving Fc (t), according to Lyapunov stability principle, in order to guarantee negative qualitative of the derivative of the first Lyapunov function, the initial boundary control part is designed to:
wherein Δu1 ，Δu 2 Respectively a first input error, a second input error, tau 1 For the first initial boundary control method, τ 2 For the second initial boundary control method,is d 1 Upper limit value of (t),>is d 2 (t)Upper limit value, k 1 Is a first adjustment parameter;
in the initial boundary control method, τ 1 Acting on the left hub of the flexible mechanical arm, and tau 2 The boundary control method acts on the right boundary of the flexible mechanical arm, the state information of the flexible mechanical arm is obtained in real time through a sensor or an actuator, and the problems of large rotation angle and vibration of the flexible mechanical arm are solved.
Further, in order to solve the uncertainty of system parameters and input errors in the initial boundary control method, a neural network term is proposed, which specifically includes:
W 1* for the first ideal weight coefficient vector, W 2* For the second ideal weight coefficient vector, W 3* For the third ideal weight coefficient vector, W 4* For the fourth ideal weight coefficient vector, ε 1 is the first approximation error, ε 2 Is the second approximation error, ε 3 Is the third approximation error, ε 4 Is the fourth approximation error, X 1 Is the first state vector, X 2 Is the second state vector, X 3 Is the third state vector, X 4 Is the fourth state vector, X 1 ＝[x 1 (t) s 1 x 2 (t)] T ，X 2 ＝[x 1 (t) x 2 (t) Δu 1 ] T ，X 3 ＝[x 3 (t) s 2 x 4 (t)] T ，X 4 ＝[x 3 (t) x 4 (t) Δu 1 ] T For H (χ) function, it is defined as
χ is a function variable that is used to determine the function,is the center of the receptive field and ζ is the width of the gaussian function;
to estimate the ideal weight coefficients, defineFor the weight estimation coefficient vector, the update law of each weight estimation coefficient vector is respectively as follows
c 1 ～c 4 The first adjusting coefficient, the second adjusting coefficient, the third adjusting coefficient and the fourth adjusting coefficient of the weight coefficient vector update law are respectively,for the first estimated weight coefficient vector, +.>For the second estimated weight coefficient vector, +.>For the third estimated weight coefficient vector, +.>And estimating a weight coefficient vector for the fourth.
Neural network control solves the problem of I h Parameter uncertainty such as m and input error Deltau 1 、Δu 2 . In the weight estimation coefficient vector update law, X is used for 1 ～X 4 and s1 、s 2 Updating each ideal weight estimation coefficient vector, and continuously approximating each ideal weight coefficient vector to thereby approximate I h Parameters such as m, etc.
Further, the design iteration term eliminates the influence of external interference d1 (t) and d2 (t) of the flexible mechanical arm system on the flexible mechanical arm system, and the process is as follows:
eliminating external interference d 1 The first iteration control term of (t) is delta 1 (t) cancellation of external interference d 2 The second iteration control term of (t) is delta 2 (t)；Δ 1 (t) and delta 2 (t) all exist in an implicit form, and the iterative update law is as follows:
first interference error, second interference error, & lt/L & gt>Respectively->Regarding the rate of change of time, +.>Delta respectively 1 (t)、Δ 2 Iterative update law, alpha, of (t) 1 For the adjustment coefficient of the first iteration term, alpha 2 An adjustment coefficient for the second iteration term;
in this technical feature, Δm (t), m=1, 2 are used for compensation cancellation in the boundary control methodIs a term of iteration of (a); in each control input law update, based on sensor information, the iteration item is accurately calculated to better track external interference by updating the iteration item through the iteration update law, so that the external interference of the flexible mechanical arm is processed.
Further, the obtained initial boundary control method is added into an iteration control item and a neural network item to obtain the neural network control method of the flexible mechanical arm based on the self-adaptive iteration technology, and the method specifically comprises the following steps:
in this technical feature, an iteration term and a neural network term are introduced, as compared with the initial boundary control method. In the initial boundary control method, there is I h And introducing a neural network item to continuously measure the state of the system and adjust the parameters so that the flexible mechanical arm can operate in an optimal state, and simultaneously, the iteration item can compensate interference errors and solve the problems of large vibration and the like.
Compared with the prior art, the application has the following advantages and effects:
compared with the traditional control method, the neural network control method of the flexible mechanical arm based on the adaptive iteration technology is easy to realize, high in control precision, strong in adaptability and small in number of required sensors or actuators. The neural network control method comprises iteration items, can utilize the prior related information to generate expected output, improves control quality, has obvious interference suppression effect along with the increase of iteration times, and reduces the vibration of the flexible mechanical arm. In the actual working process of the flexible mechanical arm, input limitation exists, accurate parameters of the flexible mechanical arm system are difficult to acquire, and after a neural network item is introduced, the parameters are obtained through X 1 ～X 4 and s1 ,s 2 The ideal weight estimation coefficient is updated, and the accurate value of the system parameter of the flexible mechanical arm is continuously approximated, so that the system parameter is continuously adjusted to achieve the purpose of adapting to the uncertainty of the flexible mechanical arm and solve the problem of input limitation.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a schematic flow diagram of a neural network control method of a flexible mechanical arm based on adaptive iterative learning disclosed by the application;
FIG. 2 is a schematic illustration of the structure of the disclosed flexible robotic arm system;
FIG. 3 is a schematic diagram of simulation results of elastic deformation w (s, t) of the flexible mechanical arm of simulation 1 in the embodiment;
FIG. 4 is a schematic diagram of simulation results of the elastic deformation w (s, t) of the flexible mechanical arm of simulation 2 in the embodiment;
FIG. 5 is a schematic diagram of simulation results of the elastic deformation w (s, t) of the flexible mechanical arm of simulation 3 in the embodiment;
FIG. 6 is a schematic diagram of simulation results of the flexible mechanical arm elastic deformation w (s, t) of simulation 4 in the embodiment;
FIG. 7 shows the maximum value of the elastic deformation w (l, t) of the end of the flexible mechanical arm and the number of iterations k in the embodiment of the present application max Is a schematic diagram of the relationship of (a).
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Example 1
Fig. 1 is a flowchart of a neural network control method of a flexible mechanical arm based on adaptive iterative learning, which is disclosed in the embodiment, and includes the following steps:
s1, according to the dynamic characteristics of the flexible mechanical arm, a dynamic model of the flexible mechanical arm is provided.
FIG. 2 is a schematic view of a flexible mechanical arm, with a hub of the flexible mechanical arm on the left side and a fixed load of mass m on the right side, with a hub radius r, u 1 (t) is the control input at the hub, d 1 (t) is a first external disturbance, u 2 (t) is the control input at the right boundary, d 2 (t) is second external interference, θ (t) is a rotation angle, y (s, t) is an offset value of the flexible mechanical arm, w (s, t) is an elastic deformation value of the flexible mechanical arm, and basic properties of the flexible mechanical arm are as follows: the length is l, the density is ρ, the length variable is s, the damping coefficient is c, the bending stiffness is EI, the tension is T, and the hub inertia value is I.
The kinetic equation of the flexible mechanical arm is:
representing the yaw rate of the flexible mechanical arm, +.>The deflection acceleration of the flexible mechanical arm, w '(s, t) and w' (s, t) respectively represent the second derivative and the fourth derivative of the elastic deformation value w (s, t) of the flexible mechanical arm to s;
the boundary conditions are:
the angular acceleration of the flexible mechanical arm is that w (0, t) is the elastic deformation value of the flexible mechanical arm at the position with the length of 0, w (l, t) is the elastic deformation value of the flexible mechanical arm at the position with the length of l, w ' (0, t) is the first-order deflection of w (0, t) to s, w "(0, t) is the second order bias of w (0, t) to s, w '" (0, t) is the third order bias of w (0, t) to s, w ' (l, t) is w (l, t) first order bias for t, w ' (l, t) is the second order bias for w (l, t) to t, w ' (l, t) is the third order bias for w (l, t) to t,>is the deflection acceleration of the flexible mechanical arm at l.
S2, constructing virtual control based on a dynamic model of the flexible mechanical arm system.
Definition x 1 (t)＝θ(t)-θ d ，x 3 (t)＝y e (l,t)，
θ d Is the expected angle value of the flexible mechanical arm, x 1 (t) is a first state quantity,for angular velocity of rotation, x 2 (t) is a second state quantity, y e (l, t) is the deflection error of the flexible mechanical arm at l, x 3 (t) is a third state quantity, +.>For the deflection speed of the flexible arm at l, x 4 (t) is a fourth state quantity
x 2 The virtual control amount of (t) isx 4 (t) virtual control amount is +.>η, γ are the first control parameter and the second control parameter of the virtual control respectively, η, γ > 0,
v 1 (t) and x 2 The error between (t) isv 2 (t) and x 4 The error between (t) is
S3, selecting a first Lyapunov function, and obtaining an initial boundary control method according to the Lyapunov stability theory.
F c (t)＝F 1 (t)+F 2 (t)+F b (t)+F d (t)
w' (s, t) represents the first derivative of w (s, t) with s, y e (s, t) is the deflection error of the flexible mechanical arm, F 1 (t) is an energy term, F 2 (t) represents an energy cross term, F b (t) is an energy addition term, F d (t) is a function term to satisfy an output limit; k > 0 is the energy addition term F b Forward control parameters in (t) to ensure F b (t) > 0, wherein： ζ 1 、ζ 2 Respectively a first angle error constraint, a second angle error constraint and ζ 3 、ζ 4 Respectively restraining the displacement errors of the first end and the displacement errors of the second end; j (x) 1 (t)) and J (x) 3 (t)) are step functions, when x 1 (t)＞0，J(x 1 (t))＝1；x 1 (t)≤0，J(x 1 (t))=0, when x 3 (t)＞0，J(x 3 (t))＝1；x 3 (t)≤0，J(x 3 (t))＝0；
Taking the derivative of Fc (t), according to the lyapunov principle, the initial boundary control part is designed to:
Δu 1 、Δu 2 respectively a first input error, a second input error, τ 1 For the first initial boundary control method, τ 2 For the second initial boundary control method,is d 1 Upper limit value of (t),>is d 2 Upper limit value of (t), k 1 Is a first adjustment parameter;
s4, providing a neural network item to solve m and I h Parameter uncertainty and Deltau 1 ,Δu 2 Input error problem:
W 1* for the first ideal weight coefficient vector, W 2* For the second ideal weight coefficient vector, W 3* For the third ideal weight coefficient vector, W 4* Epsilon as the fourth ideal weight coefficient vector 1 Is a first approximation error, ε 2 Is the second approximation error, ε 3 Is the third approximation error, ε 4 Is the fourth approximation error, X 1 X is the first state vector 2 X is the second state vector 3 X is the third state vector 4 X is the fourth state vector 1 ＝[x 1 (t) s 1 x 2 (t)] T ，X 2 ＝[x 1 (t) x 2 (t) Δu 1 ] T ，X 3 ＝[x 3 (t) s 2 x 4 (t)] T ，X 4 ＝[x 3 (t) x 4 (t) Δu 1 ] T The H (χ) function is defined in the specification.
Definition of the definitionFor the weight estimation coefficient vector, the update law of each weight estimation coefficient vector is respectively as follows
c 1 ～c 4 The weight coefficient vector update law is respectively a first adjustment coefficient, a second adjustment coefficient, a third adjustment coefficient and a fourth adjustment coefficient，For the first estimated weight coefficient vector, +.>For the second estimated weight coefficient vector, +.>For the third estimated weight coefficient vector, +.>And estimating a weight coefficient vector for the fourth.
S5, providing an iteration control item to process the external interference d 1(t) and d2 (t)。
The first iteration control term is delta 1 (t) handling external interference d 1 (t) the second iteration control term is delta 2 (t) handling external interference d 2 (t) the iteration control method is as follows:
first interference error, second interference error, respectively +.>Respectively->Regarding the rate of change of time, +.>Delta respectively 1 (t)、Δ 2 Iterative update law, alpha, of (t) 1 For the adjustment coefficient of the first iteration term, alpha 2 Is the adjustment coefficient of the second iteration term.
And S6, adding a neural network item and an iteration control item on the basis of the initial boundary control method given in the step S3, and obtaining the neural network control method based on self-adaptive iteration learning.
S7, constructing a Lyapunov function of the closed-loop flexible mechanical arm system based on the flexible mechanical arm system and the proposed control method;
the Lyapunov function of the closed loop flexible robotic arm system is:
F(t)＝F f (t)+F h (t),
wherein Respectively corresponding weight coefficient vector errors alpha 1 、α 2 Respectively F h (t) a first tuning parameter, a second tuning parameter.
S8, based on the Lyapunov stability principle, verifying the stability of the mechanical arm system under the action of the self-adaptive iterative neural network control method.
In this embodiment, the positive nature of the function F (t) is verified. According to the scaling principle of inequality, there is a scaling principle for F2 (t) wherein z1 ＞0。
When meeting the requirementsWhen F1 (t) +F2 (t) is positive.
Definition of the definitionThen we have 0 < lambda 1 F 1 (t)≤F 1 (t)+F 2 (t)≤λ 2 F 1 (t)。
Definition of the definitionThen there are: 0 < lambda 1 [F 1 (t)+f(t)]≤F(t)≤λ 2 [F 1 (t)+f(t)]Positive characterization of F (t) is therefore demonstrated.
Validating the first derivative of F (t)The negative qualitative method of (2) is as follows:
fh (t) is obtained by deriving time and combining iteration termsThe method can obtain:
ff (t) is derived over time, in combination with u 1(t) and u2 (t) obtainable:
wherein μc1 ＝max{μ 1 ,μ 2 }，μ c2 ＝max{μ 3 ,μ 4 }。
By combining the formula (1) and the formula (2), is obtained by scaling and simplifyingThe method comprises the following steps:
wherein μ m ＝max{μ c1 ,μ c2 }，σ 1 ＝ηEI-16βl 4 ，σ 2 ＝γc-ηρ，σ 3 ＝k 1 -1，σ 4 ＝k 2 -1，σ 5 ＝k p η-2βlr 2 -8βl 3 ，σ 6 ＝η-γμ m 。
In the above, some parameters need to satisfy σ i This condition is > 0 (i=1, 2,..6).
For formula (3), further:
wherein phi satisfies
φ 2 ＝min{c 1 δ 1 ,c 2 δ 2 ,c 3 δ 3 ,c 4 δ 4 }，φ 3 ＝min{α 1 ,α 2 ,1-α 1 ,1-α 2 }. The above proves thatThe system is asymptotically stable under the control method of the design.
Example 2
Digital simulation is carried out on the flexible mechanical arm system by Matlab simulation software to obtain a simulation result to verify a designed control method u 1 ,u 2 Is effective in the following. In the simulation, the angle error constraint is selected as ζ 1 ＝0.25e -0.1t +0.01，ζ 2 ＝0.1e -0.2t +0.01; selecting the displacement error constraint of the tail end of the mechanical arm as zeta 3 ＝2.5e -0.1t +0.05，ζ 4 ＝e -0.2t +0.05。
Table 1 shows the parameters of the flexible mechanical arm system, and Table 2 shows the control method u 1 ,u 2 The parameters selected in the different simulation cases.
TABLE 1 Flexible mechanical arm System parameters
TABLE 2 selected parameters for different simulation scenarios
k k 1 η γ α 1 α 2 k max
Simulation 1 200 200 0 0 0.9 0.9 3
Emulation 2 200 200 1 4.5 0.9 0.9 3
Simulation 3 200 200 1 4.5 0.9 0.9 5
Simulation 4 200 200 1 4.5 0.9 0.9 10
In Table 2, k max Representative is the number of iterations.
FIGS. 3 to 7 show simulation results, FIG. 3 shows simulation results of simulation 1, FIG. 4 shows simulation results of simulation 2, FIG. 5 shows simulation results of simulation 3, FIG. 6 shows simulation results of simulation 4, FIG. 7 shows the simulation results when k is max And taking simulation results with different numbers, namely different iteration times. It can be clearly seen that in simulation 1, that is, when the flexible mechanical arm system has no neural network item in the control method, it can be seen from fig. 3 that the flexible mechanical arm system is unstable in operation, the system has large vibration, and cannot operate stably, that is, the problem of uncertainty of system parameters is not solved, so that vibration occurs. Fig. 4 shows a simulation value when the iteration number is 3, and after the controller designed by the patent is applied, the vibration condition of the flexible mechanical arm is greatly improved, and the mechanical arm can work stably. FIG. 5 shows a simulation value for an iteration number of 5, which further improves vibration compared to an iteration number of 3; fig. 6 shows that the simulation value is smaller when the number of iterations is 10, and the control effect is further improved compared with the simulation 2 and the simulation 3. From fig. 7, it can be seen that the vibration value of the flexible mechanical arm is smaller as the number of iterations is gradually increased.
From simulation results, the control method designed by the patent can effectively inhibit disturbance of the flexible mechanical arm and can effectively process external disturbance of the flexible mechanical arm. In the iteration term, the iteration term can store the previous control experience and be used again in the next control process, so that the external interference is continuously and accurately approximated; as the number of iterations increases, the iteration term can better handle errors, making the vibration value smaller.
The above examples are preferred embodiments of the present application, but the embodiments of the present application are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present application should be made in the equivalent manner, and the embodiments are included in the protection scope of the present application.

Claims (6)

1.一种基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，所述神经网络控制方法包括以下步骤：1. A neural network control method for a flexible robotic arm based on adaptive iterative learning, characterized in that the neural network control method includes the following steps: 根据柔性机械臂的动力学特征，利用哈密顿原理构建柔性机械臂系统的动力学模型；Based on the dynamic characteristics of the flexible robotic arm, a dynamic model of the flexible robotic arm system is constructed using Hamilton's principle; 所述柔性机械臂的动力学特征包括柔性机械臂系统的动能、势能以及非保守力对柔性机械臂系统所做的虚功，将动能、势能、虚功代入哈密顿原理，得到柔性机械臂系统的动力学模型为：The dynamic characteristics of the flexible robotic arm include the kinetic energy, potential energy, and virtual work done by non-conservative forces on the flexible robotic arm system. Substituting the kinetic energy, potential energy, and virtual work into Hamilton's principle, the dynamic model of the flexible robotic arm system is obtained as follows: 其中l为柔性机械臂长度，ρ为柔性机械臂密度，s为长度变量，c为柔性机械臂阻尼系数，EI为柔性机械臂弯曲刚度，T为柔性机械臂张力，表示柔性机械臂的偏转速度，柔性机械臂的偏转加速度，w″(s,t)和w””(s,t)分别表示柔性机械臂的弹性形变值w(s,t)对s的二次导数和四次导数；in l represents the length of the flexible robotic arm, ρ represents the density of the flexible robotic arm, s represents the length variable, c represents the damping coefficient of the flexible robotic arm, EI represents the bending stiffness of the flexible robotic arm, and T represents the tension of the flexible robotic arm. This indicates the deflection speed of the flexible robotic arm. The deflection acceleration of the flexible robotic arm, w″(s,t) and w””(s,t) represent the second and fourth derivatives of the elastic deformation value w(s,t) of the flexible robotic arm with respect to s, respectively. 边界条件为：The boundary conditions are: 其中，m为柔性机械臂末端负载的质量，I为柔性机械臂轮毂惯性值，r为柔性机械臂轮毂半径，u1(t)、u2(t)分别为第一、第二控制输入，d1(t)、d2(t)分别为第一、第二外部扰动，为柔性机械臂旋转角度的角加速度，w(0,t)为柔性机械臂在长度为0处的弹性形变值，w(l,t)为柔性机械臂在长度为l的弹性形变值，w′(0,t)为w(0,t)对s的一阶偏导，w″(0,t)为w(0,t)对s的二阶偏导，w″′(0,t)为w(0,t)对s的三阶偏导，w′(l,t)为w(l,t)对t的一阶偏导，w″(l,t)为w(l,t)对t的二阶偏导，w″′(l,t)为w(l,t)对t的三阶偏导，为柔性机械臂在l处的偏转加速度；Where m is the mass of the end effector load of the flexible robotic arm, I is the hub inertia of the flexible robotic arm, r is the hub radius of the flexible robotic arm, u1(t) and u2(t) are the first and second control inputs, respectively, and d1(t) and d2(t) are the first and second external disturbances, respectively. Let be the angular acceleration of the flexible robotic arm's rotation angle, w(0,t) be the elastic deformation of the flexible robotic arm at length 0, w(l,t) be the elastic deformation of the flexible robotic arm at length l, w′(0,t) be the first partial derivative of w(0,t) with respect to s, w″(0,t) be the second partial derivative of w(0,t) with respect to s, w″′(0,t) be the third partial derivative of w(0,t) with respect to s, w′(l,t) be the first partial derivative of w(l,t) with respect to t, w″(l,t) be the second partial derivative of w(l,t) with respect to t, and w″′(l,t) be the third partial derivative of w(l,t) with respect to t. Let l be the deflection acceleration of the flexible robotic arm at point l; 基于反步技术设计虚拟控制量，构建第一Lyapunov函数，并得到初始边界控制方法；Virtual control variables are designed based on backstepping techniques, the first Lyapunov function is constructed, and the initial boundary control method is obtained. 基于柔性机械臂受到外部干扰，构建迭代控制项，迭代控制项以隐式形式给出；Based on the external disturbances experienced by the flexible robotic arm, an iterative control term is constructed, which is given implicitly. 基于柔性机械臂系统的输入饱和特性和参数不确定性，提出神经网络项用于解决输入饱和与参数不确定性带来的影响；Based on the input saturation characteristics and parameter uncertainty of flexible robotic arm systems, a neural network term is proposed to address the impact of input saturation and parameter uncertainty. 将所述的初始边界控制方法和迭代控制项、神经网络项相结合，包括：往初始边界控制方法加入迭代控制项和神经网络项；迭代控制项根据上一次系统的输出进行更新；神经网络项中，根据传感器的信息，通过权重估计系数向量更新律更新估计系数向量，从而处理柔性机械臂参数不确定性。The initial boundary control method is combined with iterative control terms and neural network terms, including: adding iterative control terms and neural network terms to the initial boundary control method; updating the iterative control terms based on the previous system output; and updating the estimated coefficient vector based on sensor information using a weighted estimated coefficient vector update law to handle the uncertainty of the flexible robotic arm parameters. 2.根据权利要求1所述的基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，所述基于反步技术设计虚拟控制量的过程如下：2. The neural network control method for a flexible robotic arm based on adaptive iterative learning according to claim 1, characterized in that the process of designing the virtual control quantity based on backstepping technology is as follows: 分别定义x1(t)＝θ(t)-θd，x3(t)＝ye(l,t)， Define x <sub>1</sub> (t) = θ(t) - θ<sub>d</sub> respectively. x³ (t) = ye (l,t), 其中θd为柔性机械臂期望角度值，θ(t)为柔性机械臂旋转角度，x1(t)为第一状态量，为柔性机械臂旋转角速度，x2(t)为第二状态量，ye(l,t)为柔性机械臂在l处的偏转误差，x3(t)为第三状态量，为柔性机械臂在l处的偏转速度，x4(t)为第四状态量；Where θd is the desired angle value of the flexible robotic arm, θ(t) is the rotation angle of the flexible robotic arm, and x1 (t) is the first state variable. Let x <sub>2 </sub> be the rotational angular velocity of the flexible robotic arm, x<sub>2</sub>(t) be the second state variable, y <sub>e</sub> (l,t) be the deflection error of the flexible robotic arm at point l, and x <sub>3</sub> (t) be the third state variable. Let x be the deflection velocity of the flexible robotic arm at point l, and let x4 (t) be the fourth state variable. 定义v1(t)为x2(t)的虚拟控制量，v2(t)为x4(t)的虚拟控制量，具体为其中，η,γ分别为虚拟控制量的第一控制参数、第二控制参数，且η,γ＞0,Define v1 (t) as the virtual control variable of x2 (t) and v2 (t) as the virtual control variable of x4 (t), specifically as follows: Where η and γ are the first and second control parameters of the virtual control quantity, respectively, and η,γ > 0. 定义s1为v1(t)与x2(t)之间的误差，s2为v2(t)与x4(t)之间的误差，具体为Let s1 be the error between v1 (t) and x2 (t), and s2 be the error between v2 (t) and x4 (t). Specifically... 3.根据权利要求2所述的基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，所述选取第一Lyapunov函数，得到初始边界控制方法的过程如下：3. The neural network control method for a flexible robotic arm based on adaptive iterative learning according to claim 2, characterized in that the process of selecting the first Lyapunov function to obtain the initial boundary control method is as follows: 第一Lyapunov函数为：The first Lyapunov function is: Fc(t)＝F1(t)+F2(t)+Fb(t)+Fd(t)F c (t)=F 1 (t)+F 2 (t)+F b (t)+F d (t) 其中，in, 式中w′(s,t)表示w(s,t)对s的一阶导数，ye(s,t)为柔性机械臂的偏转误差，F1(t)为能量项，F2(t)为能量交叉项，Fb(t)为能量附加项，Fd(t)是用来满足输出限制的函数项；k＞0是能量附加项Fb(t)中的正向控制参数，用来保证Fb(t)＞0，χ1(t)为柔性机械臂旋转角度误差限制函数，χ2(t)为柔性机械臂末端位移误差限制函数；In the formula, w′(s,t) represents the first derivative of w(s,t) with respect to s, ye (s,t) is the deflection error of the flexible robotic arm, F1 (t) is the energy term, F2 (t) is the energy cross term, Fb (t) is the energy addition term, Fd (t) is the function term used to satisfy the output limit; k＞0 is the positive control parameter in the energy addition term Fb (t), used to ensure that Fb (t)＞0, χ1 (t) is the rotation angle error limit function of the flexible robotic arm, and χ2 (t) is the end displacement error limit function of the flexible robotic arm. ζ1、ζ2分别为第一角度误差约束、第二角度误差约束，ζ3、ζ4分别为第一末端位移误差约束、第二末端位移误差约束；J(x1(t))与J(x3(t))都是阶跃函数，当x1(t)＞0，J(x1(t))＝1；x1(t)≤0，J(x1(t))＝0，当x3(t)＞0，J(x3(t))＝1；x3(t)≤0，J(x3(t))＝0； ζ1 and ζ2 are the first and second angle error constraints, respectively; ζ3 and ζ4 are the first and second end displacement error constraints, respectively; J( x1 (t)) and J( x3 (t)) are both step functions. When x1 (t) > 0, J( x1 (t)) = 1; when x1 (t) ≤ 0, J( x1 (t)) = 0. When x3 (t) > 0, J( x3 (t)) = 1; when x3 (t) ≤ 0, J( x3 (t)) = 0. 对Fc(t)求导，得到初始边界控制部分为：Taking the derivative of Fc (t), we obtain the initial boundary control part as follows: 其中Δu1、Δu2分别为第一输入误差、第二输入误差，τ1为第一初始边界控制方法，τ2为第二初始边界控制方法，是d1(t)的上限值，是d2(t)的上限值，k1是第一调节参数。Where Δu1 and Δu2 are the first and second input errors, respectively, τ1 is the first initial boundary control method, and τ2 is the second initial boundary control method. It is the upper limit of d1 (t). d2 (t) is the upper limit of d2(t), and k1 is the first adjustment parameter. 4.根据权利要求3所述的基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，所述神经网络项具体如下：4. The neural network control method for a flexible robotic arm based on adaptive iterative learning according to claim 3, wherein the neural network term is specifically as follows: W1*为第一理想权重系数向量，W2*为第二理想权重系数向量，W3*为第三理想权重系数向量，W4*为第四理想权重系数向量，ε1是第一近似值误差，ε2是第二近似值误差，ε3是第三近似值误差，ε4是第四近似值误差，X1为的第一状态向量，X2为的第二状态向量，X3为的第三状态向量，X4为的第四状态向量，X1＝[x1(t) s1 x2(t)]T，X2＝[x1(t) x2(t) Δu1]T，X3＝[x3(t)s2 x4(t)]T，X4＝[x3(t) x4(t) Δu1]T，对于H(χ)函数的定义为 W1* is the first ideal weight coefficient vector, W2 * is the second ideal weight coefficient vector, W3 * is the third ideal weight coefficient vector, and W4 * is the fourth ideal weight coefficient vector. ε1 is the first approximation error, ε2 is the second approximation error, ε3 is the third approximation error, and ε4 is the fourth approximation error. X1 is the first state vector, X2 is the second state vector, X3 is the third state vector, and X4 is the fourth state vector. X1 = [ x1 (t) s1x2 (t)] T , X2 = [ x1 (t) x2 (t) Δu1 ] T , X3 = [ x3 (t) s2x4 (t)] T , X4 = [ x3 (t) x4 (t) Δu1 ] T . The definition of the H(χ) function is ... χ是函数变量，是感受野的中心，ξ是高斯函数的宽度。χ is a function variable. ξ is the center of the receptive field, and ξ is the width of the Gaussian function. 5.根据权利要求4所述的基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，提出迭代控制项消除柔性机械臂系统外干扰d1(t)和d2(t)对柔性机械臂系统的影响，过程如下：5. The neural network control method for a flexible robotic arm based on adaptive iterative learning according to claim 4, characterized in that iterative control terms are proposed to eliminate the influence of external disturbances d1(t) and d2(t) on the flexible robotic arm system, the process of which is as follows: 消除外干扰d1(t)的第一迭代控制项为Δ1(t)，消除外干扰d2(t)的第二迭代控制项为Δ2(t)；Δ1(t)与Δ2(t)都为隐式形式存在，迭代更新律为：The first iteration control term for eliminating external disturbance d1 (t) is Δ1 (t), and the second iteration control term for eliminating external disturbance d2 (t) is Δ2 (t); both Δ1 (t) and Δ2 (t) exist implicitly, and the iteration update law is: 分别为第一干扰误差，第二干扰误差，分别为关于时间的变化率，分别为Δ1(t)、Δ2(t)的迭代更新律，α1为第一迭代项的调节系数，α2为第二迭代项的调节系数。 These are the first interference error and the second interference error, respectively. They are respectively Regarding the rate of change over time, Let α1 be the iterative update law for Δ1 (t) and Δ2 (t), respectively, where α1 is the adjustment coefficient of the first iteration term and α2 is the adjustment coefficient of the second iteration term. 6.根据权利要求5所述的基于自适应迭代学习的柔性机械臂的神经网络控制方法，其特征在于，将得到的初始边界控制方法加入迭代控制项和神经网络项，过程如下：6. The neural network control method for a flexible robotic arm based on adaptive iterative learning according to claim 5, characterized in that the obtained initial boundary control method is added to the iterative control term and the neural network term, as follows: τ1加入第一迭代控制项和神经网络项，τ2加入第二迭代控制项和神经网络项，得到：Adding the first iteration control term and the neural network term to τ1 , and adding the second iteration control term and the neural network term to τ2 , we get: 分别用来估计W1*～W4*，为第一估计权重系数向量，为第二估计权重系数向量，为第三估计权重系数向量，为第四估计权重系数向量。 They were used to estimate W1 * to W4 * respectively. This is the first estimated weight coefficient vector. This is the second estimated weight coefficient vector. This is the third estimated weight coefficient vector. This is the fourth estimated weight coefficient vector.
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