CN114559429B - Neural network control method of flexible mechanical arm based on self-adaptive iterative learning - Google Patents
Neural network control method of flexible mechanical arm based on self-adaptive iterative learning Download PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- mechanical arm
- flexible mechanical
- neural network
- control method
- error
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 71
- 238000013528 artificial neural network Methods 0.000 title claims abstract description 42
- 230000008569 process Effects 0.000 claims abstract description 9
- 238000005516 engineering process Methods 0.000 claims abstract description 7
- 230000006870 function Effects 0.000 claims description 30
- 230000005489 elastic deformation Effects 0.000 claims description 17
- 230000003044 adaptive effect Effects 0.000 claims description 9
- 238000006073 displacement reaction Methods 0.000 claims description 9
- 230000001133 acceleration Effects 0.000 claims description 8
- 238000005381 potential energy Methods 0.000 claims description 4
- 238000005452 bending Methods 0.000 claims description 3
- 230000008859 change Effects 0.000 claims description 3
- 238000013016 damping Methods 0.000 claims description 3
- 238000012938 design process Methods 0.000 abstract description 4
- 230000002401 inhibitory effect Effects 0.000 abstract description 2
- 238000004088 simulation Methods 0.000 description 34
- 238000010586 diagram Methods 0.000 description 6
- 230000000694 effects Effects 0.000 description 3
- 230000000452 restraining effect Effects 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 238000012512 characterization method Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000005265 energy consumption Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000001629 suppression Effects 0.000 description 1
Classifications
-
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Software Systems (AREA)
- Evolutionary Computation (AREA)
- Physics & Mathematics (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Medical Informatics (AREA)
- Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Fuzzy Systems (AREA)
- Mathematical Physics (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Feedback Control In General (AREA)
Abstract
The application discloses a neural network control method of a flexible mechanical arm based on self-adaptive iterative learning, which comprises the following steps: constructing a flexible mechanical arm system according to dynamic characteristics of the flexible mechanical arm; designing an initial boundary control method based on a back-stepping technology; designing a neural network item to solve the uncertainty of parameters and input saturation characteristics of the flexible mechanical arm system; designing an iteration control item to process external interference; and combining the boundary control, the neural network item and the iteration control item to obtain the boundary self-adaptive iteration neural network control method for inhibiting the flexible mechanical arm. The application can effectively restrain the vibration of the flexible mechanical arm, and considers the uncertainty of the system parameters of the flexible mechanical arm and the time-varying output limit in the design process.
Description
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. The neural network control method of the flexible mechanical arm based on the adaptive iterative learning is characterized by comprising the following steps of:
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;
the dynamic characteristics of the flexible mechanical arm comprise kinetic energy, potential energy and virtual work of non-conservative force of the flexible mechanical arm system on the flexible mechanical arm system, the kinetic energy, the potential energy and the virtual work are substituted into the Hamiltonian principle, and a dynamic model of the flexible mechanical arm system is obtained by:
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 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:
wherein m is the mass of the end load of the flexible mechanical arm, I is the hub inertia value of the flexible mechanical arm, r is the hub radius 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 a first external disturbance and a second external disturbance,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 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,>the deflection acceleration of the flexible mechanical arm at the position l;
designing virtual control quantity based on a back-stepping technology, constructing a first Lyapunov function, and obtaining an initial boundary control method;
based on the external interference of the flexible mechanical arm, constructing an iteration control item, wherein 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: adding an iteration control item and a neural network item into the initial boundary control method; updating the iteration control item according to the output of the last system; in the neural network item, according to the information of the sensor, the estimated coefficient vector is updated through a weight estimated coefficient vector update law, so that the uncertainty of the flexible mechanical arm parameter is processed.
2. The neural network control method of the flexible mechanical arm based on the adaptive iterative learning according to claim 1, wherein the process of designing the virtual control amount based on the backstepping technology is as follows:
definition of x respectively 1 (t)＝θ(t)-θ d ，x 3 (t)＝y e (l,t)，/>
Wherein thetad is the expected angle value of the flexible mechanical arm, theta (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), in particularWherein eta and gamma are the first control parameter and the second control parameter of the virtual control quantity respectively, and eta and gamma are more than 0,
definition s 1 V is 1 (t) and x 2 Error between (t), s 2 V is 2 (t) and x 4 Error between (t), in particular
3. The neural network control method of the flexible mechanical arm based on adaptive iterative learning according to claim 2, wherein the selecting the first Lyapunov function obtains the initial boundary control method as follows:
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) is 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，χ 1 (t) is a rotation angle error limiting function of the flexible mechanical arm, χ 2 (t) is a flexible mechanical arm end displacement error limiting function;
ζ 1 、ζ 2 zeta are respectively a first angle error constraint and a second angle error constraint 3 、ζ 4 The first end displacement error constraint and the second end displacement error constraint are respectively adopted; 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；
For F c (t) deriving to obtain an initial boundary control part as:
wherein Δu1 、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 the first adjustment parameter.
4. The neural network control method of the flexible mechanical arm based on adaptive iterative learning according to claim 3, wherein the neural network term specifically comprises the following steps:
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 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 Definition of H (χ) function is
χ is the variable of the function and,is the center of the receptive field and ζ is the width of the gaussian function.
5. The neural network control method of the flexible mechanical arm based on the adaptive iterative learning of claim 4, wherein the iterative control item is proposed to eliminate the influence of external disturbances 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 Is the adjustment coefficient of the second iteration term.
6. The neural network control method of the flexible mechanical arm based on adaptive iterative learning according to claim 5, wherein the obtained initial boundary control method is added into an iterative control item and a neural network item, and the process is as follows:
τ 1 adding a first iteration control term and a neural network term, tau 2 Adding a second iteration control item and a neural network item to obtain:
respectively for estimating W 1* ～W 4* ，/>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.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210174112.3A CN114559429B (en) | 2022-02-22 | 2022-02-22 | Neural network control method of flexible mechanical arm based on self-adaptive iterative learning |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210174112.3A CN114559429B (en) | 2022-02-22 | 2022-02-22 | Neural network control method of flexible mechanical arm based on self-adaptive iterative learning |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114559429A CN114559429A (en) | 2022-05-31 |
| CN114559429B true CN114559429B (en) | 2023-09-29 |
Family
ID=81716322
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210174112.3A Active CN114559429B (en) | 2022-02-22 | 2022-02-22 | Neural network control method of flexible mechanical arm based on self-adaptive iterative learning |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114559429B (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109465825A (en) * | 2018-11-09 | 2019-03-15 | 广东工业大学 | The adaptive dynamic surface control method of the RBF neural of mechanical arm flexible joint |
| CN110609471A (en) * | 2019-07-23 | 2019-12-24 | 华南理工大学 | Boundary iteration control method of marine flexible riser system based on backstepping technology |
| CN110877333A (en) * | 2019-04-12 | 2020-03-13 | 国网宁夏电力有限公司电力科学研究院 | Flexible joint mechanical arm control method |
| CN111496792A (en) * | 2020-04-27 | 2020-08-07 | 北京科技大学 | Method and system for tracking and controlling input saturation fixed time trajectory of mechanical arm |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022016152A1 (en) * | 2020-07-17 | 2022-01-20 | Path Robotics, Inc. | Real time feedback and dynamic adjustment for welding robots |
-
2022
- 2022-02-22 CN CN202210174112.3A patent/CN114559429B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109465825A (en) * | 2018-11-09 | 2019-03-15 | 广东工业大学 | The adaptive dynamic surface control method of the RBF neural of mechanical arm flexible joint |
| CN110877333A (en) * | 2019-04-12 | 2020-03-13 | 国网宁夏电力有限公司电力科学研究院 | Flexible joint mechanical arm control method |
| CN110609471A (en) * | 2019-07-23 | 2019-12-24 | 华南理工大学 | Boundary iteration control method of marine flexible riser system based on backstepping technology |
| CN111496792A (en) * | 2020-04-27 | 2020-08-07 | 北京科技大学 | Method and system for tracking and controlling input saturation fixed time trajectory of mechanical arm |
Non-Patent Citations (1)
| Title |
|---|
| 大加减速轴向移动***振动主动控制;赵志甲;《中国博士学位论文全文数据库》;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114559429A (en) | 2022-05-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108319144B (en) | Robot trajectory tracking control method and system | |
| Huang et al. | Approximation-free control for vehicle active suspensions with hydraulic actuator | |
| Liu et al. | Adaptive sliding mode control for uncertain active suspension systems with prescribed performance | |
| Cho et al. | Composite model reference adaptive control with parameter convergence under finite excitation | |
| WO2018023201A1 (en) | Adaptive terminal sliding mode control method | |
| CN107544256A (en) | Underwater robot sliding-mode control based on adaptive Backstepping | |
| CN114895564B (en) | Design method of self-adaptive neural network controller of electrically-driven flexible joint mechanical arm | |
| Ullah et al. | Neuro-adaptive fixed-time non-singular fast terminal sliding mode control design for a class of under-actuated nonlinear systems | |
| Xie et al. | Neural network‐based adaptive control of piezoelectric actuators with unknown hysteresis | |
| CN114559429B (en) | Neural network control method of flexible mechanical arm based on self-adaptive iterative learning | |
| CN117193001B (en) | Hyperbolic approach law sliding mode control method based on integral reinforcement learning | |
| CN116795126A (en) | Input saturation and output limited deformed aircraft control method | |
| CN111399379B (en) | Self-adaptive vibration control method of flexible satellite system based on output limitation | |
| CN112305917A (en) | Fixed time terminal sliding mode robust fault-tolerant control method and device for liquid-filled spacecraft | |
| CN113043266A (en) | Adaptive force tracking control method based on iterative learning | |
| CN115793447A (en) | Carrier rocket separation body attitude control method under large pneumatic uncertain condition | |
| CN112305916B (en) | Self-adaptive control method and system for mobile robot based on barrier function | |
| CN114859725A (en) | Self-adaptive event trigger control method and system for nonlinear system | |
| Cheong et al. | Joint tracking controller for multi‐link flexible robot using disturbance observer and parameter adaptation scheme | |
| Macnab | Preventing bursting in approximate-adaptive control when using local basis functions | |
| CN114415509B (en) | Servo elastic active inhibition method for remote rocket projectile | |
| Abouheaf et al. | An online model-following projection mechanism using reinforcement learning | |
| CN117359645B (en) | Self-adaptive predefined time control method for single-link mechanical arm | |
| Andrievsky et al. | Speed-gradient method in adaptive control and identification. Historical overview | |
| Ansari et al. | Quadrotor control using neuro-adaptive robust generalized dynamic inverasion |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |