CN110879589A - Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy - Google Patents

Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy Download PDF

Info

Publication number
CN110879589A
CN110879589A CN201911276265.3A CN201911276265A CN110879589A CN 110879589 A CN110879589 A CN 110879589A CN 201911276265 A CN201911276265 A CN 201911276265A CN 110879589 A CN110879589 A CN 110879589A
Authority
CN
China
Prior art keywords
fault
strategy
backstepping
mechanical arm
controller
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.)
Pending
Application number
CN201911276265.3A
Other languages
Chinese (zh)
Inventor
张宪福
朱菲
常艳洁
陈现栋
李含丰
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong University
Original Assignee
Shandong University
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Shandong University filed Critical Shandong University
Priority to CN201911276265.3A priority Critical patent/CN110879589A/en
Publication of CN110879589A publication Critical patent/CN110879589A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0224—Process history based detection method, e.g. whereby history implies the availability of large amounts of data
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a mechanical arm fault-tolerant control method and system based on a backstepping strategy and a sliding mode strategy, which comprises the following steps: establishing a fault dynamic model of the mechanical arm system; constructing a virtual controller by utilizing a backstepping design method based on the model; then, a first-order synovial differentiator is used for effectively estimating the derivative of the virtual controller; processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation; and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function. According to the method, the first-order synovial differentiator is applied to the backstepping design, the problem of 'explosion complexity' of derivation of a virtual controller is effectively avoided, and the aim of controlling the rotation angle of the mechanical arm to be bounded to track a target signal is fulfilled under the condition that the mechanical arm controller breaks down.

Description

Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy
Technical Field
The invention belongs to the technical field of control, and particularly relates to a mechanical arm fault-tolerant control method based on a backstepping strategy and a sliding mode strategy.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The inventor finds that the research of the mechanical arm control system is also focused widely along with the development of the robot. The controller failure is a common problem in engineering application, and if the controller of the mechanical arm fails, the controller cannot be timely and effectively processed, and the consequences can be imagined.
In recent years, in order to ensure the reliability and safety of engineering, the research on fault-tolerant control of mechanical arms has become a subject which is concerned and has a challenge. On the one hand, structural design techniques represented by the backstepping design were proposed in the 80's of the 20 th century, and since the introduction of the backstepping design into the robot arm system by researchers, it became an indispensable fundamental method for studying the problems associated with the robot arm system.
On the other hand, in recent years, the sliding mode protocol is gradually paid attention to by the students with the advantages of high response speed, simple physical implementation and the like, and a series of research results are generated; the first-order synovial differentiator developed from sliding mode control is an important approach to solve the difficulty of 'complexity explosion' in derivation of a virtual controller in a typical backstepping design method, but the method is not applied to research on solving the problem of failure of a controller of a mechanical arm.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a mechanical arm fault-tolerant control method based on a backstepping strategy and a sliding mode strategy, and the mechanical arm fault-tolerant control strategy is designed by means of a self-adaptive method and hyperbolic function characteristics.
In order to achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
a mechanical arm fault-tolerant control method based on a backstepping strategy and a sliding mode strategy comprises the following steps:
establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
In the further technical scheme, the fault dynamic model of the mechanical arm system is as follows:
Figure BDA0002315647390000021
wherein: j represents the moment of inertia of the engine, M is the mass of the rigid link, q is the angle of the rigid link, B is the damping coefficient, l is the length of the axial center, g is the gravitational acceleration; wherein:
Figure BDA0002315647390000022
u (t) is the actual control input, k is more than 0 and less than or equal to kj≤1、
Figure BDA0002315647390000029
V (t) is the design controller for the fault parameters.
Figure BDA0002315647390000023
And
Figure BDA0002315647390000024
respectively represent a fault start time and an end time, and
Figure BDA0002315647390000025
and
Figure BDA0002315647390000026
m is the total number of failures, s is start, and e is end.
The system is further represented as the following mathematical model:
Figure BDA0002315647390000027
wherein: x is the number of1＝q、
Figure BDA0002315647390000028
Representing an unknown parameter.
In actual engineering, the design target of the mechanical arm is as follows: the controller (u) is designed so that the system rotation angle (q) can reach the desired rotation angle (r) under the control. In practical application, unpredictable failure conditions often occur to the force generated by the controller, so how to utilize the relevant information of the system to realize the design target under the failure condition of the design controller needs to be considered, and further the fault-tolerant control in the scheme is provided. The related information of the mechanical arm system is quantized during modeling, so that in the design scheme, the compensator (v) can design effective control on the output quantity (namely the rotation angle q) of the mechanical arm by directly using the related quantity of the system quantized information (the rotational inertia of an engine, the mass of a rigid connecting rod, a damping coefficient and the length of an axial center), and finally the difference between the actual effect and the expected control target (r) is controlled within a certain range.
In the further technical scheme, a virtual controller is constructed by applying a reverse design method;
introducing coordinate transformation:
y1＝x1-r(t)，y2＝x2-l(t)
selecting a Lyapunov preparation function:
Figure BDA0002315647390000031
the virtual controller is constructed as follows:
Figure BDA0002315647390000032
wherein: r (t) is a tracking signal, l (t) is a virtual controller, c1To design forAnd (4) parameters.
In a further technical scheme, a first-order synovial differentiator is used for effectively estimating the derivative of the virtual controller: the first-order synovial differentiator is formed as:
Figure BDA0002315647390000033
h0、h1two states of a differentiator system, C0、C1Two design parameters for the system.
The further technical scheme is that adaptive control is applied to process parameters:
the adaptive update rate of the unknown parameters inherent to the system is designed as follows:
Figure BDA0002315647390000034
wherein:
Figure BDA0002315647390000035
is theta ═ theta1，θ2)TГ, Λ is a two-dimensional design matrix.
In a further technical scheme, the self-adaptive update rate of the fault parameter related quantity of the system controller is as follows:
first, the associated symbol definition is given:
Figure BDA0002315647390000036
the adaptive update rate of the two is designed as follows:
Figure BDA0002315647390000041
Figure BDA0002315647390000042
wherein:
Figure BDA0002315647390000043
Figure BDA0002315647390000044
are respectively as
Figure BDA0002315647390000045
Estimation of p, γ1、γ2、c2、σ1、σ2To adjust the parameters.
The further technical scheme is that a Lyapunov function is constructed:
Figure BDA0002315647390000046
wherein:
Figure BDA0002315647390000047
Figure BDA0002315647390000048
respectively utilizing the results of adaptive estimation and synovial estimation for corresponding estimation errors, and designing a controller with a hyperbolic function:
Figure BDA0002315647390000049
according to the setting of the self-adaptive update rate of the unknown parameters of the system and the estimation setting of the virtual controller through a first-order synovial differentiator, the derivative of the Lyapunov preparation function obtained by derivation can meet the following conditions:
Figure BDA00023156473900000410
wherein: k. Δ is a substitute sign for the relevant parameter.
The invention discloses a design strategy of a mechanical arm fault-tolerant controller based on a backstepping strategy and a slip film strategy, and the controller relates to the acquisition by utilizing the mechanical arm fault-tolerant control method based on the backstepping strategy and the slip film strategy.
The above one or more technical solutions have the following beneficial effects:
(1) the method and the device reduce the requirement of the mechanical arm for tracking the target by the rotation angle, only need the first derivative of the tracking target function to exist and be bounded, and do not need to obtain the display form of the tracking target function.
(2) The lambda matrix in the design of the method replaces parameters in the traditional scheme, so that the self-adaptive effect of unknown parameters is enhanced, and the phenomenon that the estimation effect of the used parameters is poor in the past is improved.
(3) The method applies the first-order synovial differentiator to the backstepping design, and effectively avoids the problem of 'explosion complexity' of derivation of the virtual controller.
(4) The method combining the first-order synovial differentiator and the backstepping design is applied to the fault-tolerant control of the mechanical arm system for the first time, the controller fault is effectively compensated, the stability of the control of the rotation angle in the mechanical arm system is ensured, and the control safety of the mechanical arm system is improved.
(5) According to the method, the hyperbolic function tanh (x) is applied to the fault-tolerant control of the mechanical arm system for the first time, and the accuracy of the tracking error is effectively improved.
(6) When the present disclosure constructs a model, the system parameters are combined
Figure BDA0002315647390000051
The unknown condition effectively increases the universality of the research objects.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a schematic block diagram of a robotic arm system embodying the present disclosure;
FIG. 2 is an error plot of a robot arm rotation angle q tracking target signal r according to an embodiment of the present disclosure;
FIG. 3 is a graph of the estimated error of a first order synovial differentiator in accordance with an embodiment of the present disclosure;
4(a) -4 (d) are graphs of adaptive estimation of unknown parameters and related quantities of fault parameters according to embodiments of the present disclosure;
fig. 5 is a flow chart of an embodiment of the disclosure.
Detailed Description
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
The general idea provided by the invention is as follows:
referring to fig. 5, the mechanical arm fault-tolerant control strategy is designed based on a backstepping design method and a first-order synovial differentiator method, and by means of an adaptive method and hyperbolic function characteristics. Firstly, establishing a mathematical model of a mechanical arm system according to an internal operation mechanism of the mechanical arm system; secondly, constructing a virtual controller according to a backstepping design method; the effective estimation of the derivative of the virtual controller is carried out by means of a first-order synovial differentiator; carrying out proper estimation processing on unknown parameters existing in the system, including the inherent unknown parameters and fault parameters of the system by using self-adaptive estimation; and returning to the backstepping design method again, designing a final controller by means of the results of self-adaptive estimation and sliding mode estimation and a hyperbolic function, and effectively achieving the aim of fault-tolerant control of the mechanical arm system. The method not only effectively avoids the generation of the problem of complex explosiveness and weakens the requirement of tracking signals, but also enhances the range of research targets and improves the self-adaptive efficiency.
Example one
Referring to fig. 1, the embodiment discloses a fault-tolerant control method for a mechanical arm based on a backstepping strategy and a sliding mode strategy, and first, a fault dynamic model of the mechanical arm system is established according to an internal operation mechanism of the mechanical arm system:
Figure BDA0002315647390000061
wherein: j denotes the rotational inertia of the engine, M is the mass of the rigid link, q is the angle of the rigid link, B is the damping coefficient, l is the length of the axial center, and g is the gravitational acceleration. Wherein:
Figure BDA0002315647390000062
here: k is more than 0 and less than or equal to kj≤1、
Figure BDA0002315647390000063
V (t) for the fault parameters, a design controller,
Figure BDA0002315647390000064
and
Figure BDA0002315647390000065
respectively represent a fault start time and an end time, and
Figure BDA0002315647390000066
and
Figure BDA0002315647390000067
in practical engineering, some faults often occur in the design input force v (t) of the mechanical arm system, so that the design input force is inconsistent with the actual input force u (t), and a certain relation exists between v (t) and u (t) is fully considered, so that the design input force is modeled as
Figure BDA0002315647390000071
kjIs a constant coefficient of the designed controller, with size limitations: greater than zero and less than or equal to 1, and is called an unknown fault parameter because it is unknown, and each j can represent kjFor constants of different sizes, m has the same effect as n in other design schemes;
Figure BDA0002315647390000072
is also an unknown constant fault parameter, but its size is not limited, representing a fault quantity independent of v (t), but in general
Figure BDA0002315647390000073
The value of (a) is not too large;
when k isj＝1，
Figure BDA0002315647390000074
Then it is that the controller has not failed.
j ═ 1, 2.. m: indicating that the two fault parameters in each time period may be different in size, for a total of m fault time periods.
Figure BDA0002315647390000075
And
Figure BDA0002315647390000076
the fault parameter is represented as a plurality of continuous constant compositions which become fault at any time.
The system is further represented as a mathematical model that can use a back-stepping design method:
Figure BDA0002315647390000077
wherein: x is the number of1＝q，
Figure BDA0002315647390000078
Representing an unknown parameter; and according to the actual situation x1Is the output signal of the system.
In actual engineering, a signal that can be directly measured or obtained is referred to as an output signal. In the system of the invention, the signal which can be directly obtained is the angle q of the mechanical arm, and the x is the time of modeling1Q, then x1Is the output signal of the robot arm system.
In practice, some information in the arm system (mass of the rigid link, damping coefficient, length of the axial centre) may not be available, so these possibly unknown quantities are taken into full account in the engineering design for modelling
Figure BDA0002315647390000079
To represent unknown parameters and to estimate them in an adaptive manner in the following design step.
Constructing a virtual controller by applying a backstepping design method:
from the backstepping design method, coordinate transformation should be introduced first:
y1＝x1-r(t)，y2＝x2-l(t)
constructing a suitable Lyapunov preparation function, where:
Figure BDA0002315647390000081
in order to make the final lyapunov preparation function satisfy a certain condition, the virtual controller is constructed as follows:
Figure BDA0002315647390000082
wherein: r (t) is a target signal, l (t) is a virtual controller, c1Is a design parameter greater than 1. The tracking signal can also be designed according to the actual tracking target, for example, if the tracking signal is set to 0, the output effect of the system is near 0, and the simulation of the schemeThe tracking error of the real example is shown in figure 2.
Efficient estimation of the derivative of a virtual controller constructed by the backstepping design method by means of a first order synovial differentiator, as described with reference to FIG. 3
The first-order synovial differentiator is formed as:
Figure BDA0002315647390000083
here: sign is a sign function; c0、C1Setting two design parameters related to the virtual controller, wherein the specific size needs debugging; h is0、h1Two states of a first-order synovial differentiator system. It can be seen from the knowledge of the first-order synovial differentiator that the parameter C can be adjusted0、C1And two system states h in a first-order synovial differentiator0、h1Initial value h of0(0)、h1(0) The derivative of the virtual controller l (t) can be used as η0And (4) effective estimation.
Referring to fig. 4(a) -4 (d), adaptive control is used to properly process the fault parameters or unknown parameters of the system, and the estimation process is performed to the unknown quantities to be estimated by adjusting the adaptive rate and parameters in a synovial differentiator:
the adaptive update rate of the unknown parameters inherent to the system is designed as follows:
Figure BDA0002315647390000084
wherein:
Figure BDA0002315647390000085
is theta ═ theta1，θ2)TГ, Λ is a two-dimensional design matrix, for convenience of operation, the two design matrices are preferably diagonal matrices, and the size of the Λ matrix elements is related to system parameters, requiring specific debugging.
The design idea of the self-adaptive update rate of the fault parameter related quantity of the system controller is as follows: effective adaptation to the fault parameters is facilitated, where the relevant symbolic definitions are first given:
β＝inf1≤j≤m{kj}，
Figure BDA0002315647390000091
the purpose of the definition of the correlation symbols here is to take into account the fault parameter kjIs present such that the control force v (t) is minimal (i.e. inf)1≤j≤m{kjThe contribution of) and
Figure BDA0002315647390000092
the occurrence of the maximum deviation (i.e. the maximum deviation) which results in the control force v (t)
Figure BDA0002315647390000093
The effect brought about) can be achieved. The control objective can be reached when the fault is the most serious, and the control objective can be reached under the condition that the fault occurs generally.
Since the actual values of both quantities are unknown, an adaptive estimation is required here, and the adaptive update rates of both are designed as:
Figure BDA0002315647390000094
Figure BDA0002315647390000095
wherein:
Figure BDA0002315647390000096
Figure BDA0002315647390000097
are respectively as
Figure BDA0002315647390000098
Estimation of p, γ1、γ2、c2、σ1、σ2For adjusting the parameters, here c2It only needs to be greater than 1, but σ1、σ2The value of (c) needs to be specifically adjusted according to the setting of the system-inherent parameter.
Returning to the reverse step design method again, according to the corresponding control theory research foundation, the Lyapunov function is constructed:
Figure BDA0002315647390000099
wherein:
Figure BDA00023156473900000910
Figure BDA00023156473900000911
respectively the corresponding estimation error. By means of the results of the adaptive estimation, the synovial estimation in the above embodiments, and by means of hyperbolic functions
Figure BDA00023156473900000912
(e is any positive number) the nature of the final controller is designed:
Figure BDA0002315647390000101
when modeling the system, firstly, the internal relevant information (the mass of the rigid connecting rod, the damping coefficient and the length of the axial center) of the system is quantized, so in the actual engineering, when designing the control force for the mechanical arm system, the information is quantized firstly, and then the design of v (t) in the scheme is used for realizing the fault-tolerant control.
According to the scheme, the unknown parameters of the system are adaptively updated at a rate, the virtual controller is estimated by a first-order synovial differentiator, and the derivative of the Lyapunov preparatory function obtained by derivation is satisfied as follows:
Figure BDA0002315647390000102
wherein: k. and delta is a parameter and can be obtained according to related theoretical research knowledge in the control field, so that the aim of fault-tolerant control of the mechanical arm system is fulfilled.
It follows that applying a designed control force v to the system enables the output signal x of the robotic arm system to be output in the event of a failure1Bounded tracking of a target signal r.
According to the specific form of the designed controller v, in practical engineering application, the engineering parameters that need to be adjusted are mainly: lambda, sigma1、σ2、C0、C1. Although the parameter values are out of range, if these debug parameters are set incorrectly, the system outputs signal x1(i.e., the arm rotation angle q) is not effectively controlled, and therefore, can be based on the system output signal x1The actual tracking effect of the target signal r is used to know whether the debugging parameters are close to the corresponding actual values.
Here, in the simulation, it is not provided: the tracking target is r (t) sin (t), and the initial values are x1(0)＝0.5、x2(0)＝0、
Figure BDA0002315647390000103
Figure BDA0002315647390000104
h0(0)＝-20、h1(0)＝-2。
The parameters are respectively: b-0.5, J-M-0.25, l-1, g-10, kj＝0.5、
Figure BDA0002315647390000105
Figure BDA0002315647390000106
(i.e., β -2, p-10, θ)1＝-2、θ2＝-10)，c1＝20、c2＝20、E＝5、Г＝diag{1，1}、Λ＝diag{0.4，0.013}、γ1＝1、γ2＝1、σ1＝0.012、σ2＝0.07、C0＝8、C1＝10。
The simulation result is the output signal x of the mechanical arm system1(i.e., the arm rotation angle q) and the target signal r.
In another embodiment, the invention discloses a mechanical arm fault-tolerant system based on a backstepping method and a slip film method, which comprises a controller, wherein the controller is involved in obtaining by using the mechanical arm fault-tolerant control method based on the backstepping strategy and the slip film strategy.
Example two
The present embodiment aims to provide a computing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the following steps, including:
establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
EXAMPLE III
An object of the present embodiment is to provide a computer-readable storage medium.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, performs the steps of:
establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
The steps involved in the apparatus of the above embodiment correspond to the first embodiment of the method, and the detailed description thereof can be found in the relevant description of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media containing one or more sets of instructions; it should also be understood to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any of the methods of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. A mechanical arm fault-tolerant control method based on a backstepping strategy and a sliding mode strategy is characterized by comprising the following steps: establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
2. The method for controlling the fault tolerance of the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in claim 1, wherein the fault dynamic model of the mechanical arm system is as follows:
Figure FDA0002315647380000011
wherein: j represents the moment of inertia of the engine, M is the mass of the rigid link, q is the angle of the rigid link, B is the damping coefficient, l is the length of the axial center, g is the gravitational acceleration;
wherein:
Figure FDA0002315647380000012
u (t) is the actual control input, 0 < k-≤kj≤1、
Figure FDA0002315647380000013
V (t) for the fault parameters, a design controller,
Figure FDA0002315647380000014
and
Figure FDA0002315647380000015
respectively represent a fault start time and an end time, and
Figure FDA0002315647380000016
and
Figure FDA0002315647380000017
the system is further represented as the following mathematical model:
Figure FDA0002315647380000018
wherein: x is the number of1＝q、
Figure FDA0002315647380000019
Figure FDA00023156473800000110
Representing an unknown parameter.
3. The fault-tolerant control method for the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in claim 2, wherein a virtual controller is constructed by applying a backstepping design method:
introducing coordinate transformation:
y1＝x1-r(t)，y2＝x2-l(t)
selecting a Lyapunov preparation function:
Figure FDA0002315647380000021
the virtual controller is constructed as follows:
Figure FDA0002315647380000022
wherein: r (t) is a tracking signal, l (t) is a virtual controller, c1Are design parameters.
4. A method for fault-tolerant control of mechanical arms based on a backstepping strategy and a slip film strategy according to claim 1 or 3, characterized in that a first-order slip film differentiator is used to effectively estimate the derivative of the virtual controller: the first-order synovial differentiator is formed as:
Figure FDA0002315647380000023
5. the method for controlling the fault tolerance of the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in claim 3, wherein the parameters are processed by using adaptive control:
the adaptive update rate of the unknown parameters inherent to the system is designed as follows:
Figure FDA0002315647380000024
wherein:
Figure FDA0002315647380000025
is theta ═ theta1，θ2)TГ, Λ is a two-dimensional design matrix.
6. The method for controlling the fault tolerance of the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in claim 3, wherein the adaptive update rate of the fault parameter related quantity of the system controller is as follows:
first, the associated symbol definition is given:
β＝inf1≤j≤m{kj}，
Figure FDA0002315647380000026
the adaptive update rate of the two is designed as follows:
Figure FDA0002315647380000031
Figure FDA0002315647380000032
wherein:
Figure FDA0002315647380000033
Figure FDA0002315647380000034
are respectively as
Figure FDA0002315647380000035
Estimation of p, γ1、γ2、c2、σ1、σ2To adjust the parameters.
7. The method for controlling the fault tolerance of the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in claim 3, wherein a Lyapunov function is constructed:
Figure FDA0002315647380000036
wherein:
Figure FDA0002315647380000037
Figure FDA0002315647380000038
respectively utilizing the results of adaptive estimation and synovial estimation for corresponding estimation errors, and designing a controller with a hyperbolic function:
Figure FDA0002315647380000039
according to the setting of the self-adaptive update rate of the unknown parameters of the system and the estimation setting of the virtual controller through a first-order synovial differentiator, the derivative of the Lyapunov preparation function obtained by derivation can meet the following conditions:
Figure FDA00023156473800000310
wherein: k. Δ is a substitute sign for the relevant parameter.
8. A fault-tolerant control system for a mechanical arm based on a backstepping strategy and a slip film strategy, which comprises a controller, and is characterized in that the controller is obtained by using the fault-tolerant control method for the mechanical arm based on the backstepping strategy and the slip film strategy as claimed in any one of claims 1 to 7.
9. A computing device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to perform steps comprising:
establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
10. A computer-readable storage medium, having a computer program stored thereon, the program, when executed by a processor, performing the steps of:
establishing a fault dynamic model of the mechanical arm system;
constructing a virtual controller by utilizing a backstepping design method based on the model;
effectively estimating the derivative of the virtual controller by using a first-order synovial differentiator;
processing unknown parameters and fault parameters existing in the system model by using self-adaptive estimation;
and designing the final controller by a backstepping design method by means of the results of self-adaptive estimation and sliding film estimation and a hyperbolic function.
CN201911276265.3A 2019-12-12 2019-12-12 Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy Pending CN110879589A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911276265.3A CN110879589A (en) 2019-12-12 2019-12-12 Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911276265.3A CN110879589A (en) 2019-12-12 2019-12-12 Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy

Publications (1)

Publication Number Publication Date
CN110879589A true CN110879589A (en) 2020-03-13

Family

ID=69731666

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911276265.3A Pending CN110879589A (en) 2019-12-12 2019-12-12 Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy

Country Status (1)

Country Link
CN (1) CN110879589A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113296401A (en) * 2021-05-17 2021-08-24 哈尔滨工业大学 Direct obstacle avoidance tracking control method based on switching strategy and storage medium

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6208914B1 (en) * 1996-11-21 2001-03-27 Barron Associates, Inc. System for improved receding-horizon adaptive and reconfigurable control
CN104485866A (en) * 2014-12-15 2015-04-01 南京理工大学 Motor indirect adaptive robust output feedback control method based on high-order slip-form differentiator
CN104950677A (en) * 2015-06-17 2015-09-30 浙江工业大学 Mechanical arm system saturation compensation control method based on back-stepping sliding mode control
CN108549235A (en) * 2018-05-14 2018-09-18 西北工业大学 A kind of motor driving single connecting rod manipulator it is limited when neural network control method
CN110170992A (en) * 2019-04-02 2019-08-27 长春工业大学 A kind of modular mechanical arm multiple faults fault tolerant control method based on Dynamic Programming

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6208914B1 (en) * 1996-11-21 2001-03-27 Barron Associates, Inc. System for improved receding-horizon adaptive and reconfigurable control
CN104485866A (en) * 2014-12-15 2015-04-01 南京理工大学 Motor indirect adaptive robust output feedback control method based on high-order slip-form differentiator
CN104950677A (en) * 2015-06-17 2015-09-30 浙江工业大学 Mechanical arm system saturation compensation control method based on back-stepping sliding mode control
CN108549235A (en) * 2018-05-14 2018-09-18 西北工业大学 A kind of motor driving single connecting rod manipulator it is limited when neural network control method
CN110170992A (en) * 2019-04-02 2019-08-27 长春工业大学 A kind of modular mechanical arm multiple faults fault tolerant control method based on Dynamic Programming

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
邹思凡 等: ""改进非线性干扰观测器的机械臂自适应反演滑模控制"", 《计算机应用》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113296401A (en) * 2021-05-17 2021-08-24 哈尔滨工业大学 Direct obstacle avoidance tracking control method based on switching strategy and storage medium
CN113296401B (en) * 2021-05-17 2022-04-19 哈尔滨工业大学 Direct obstacle avoidance tracking control method based on switching strategy and storage medium

Similar Documents

Publication Publication Date Title
CN110170992B (en) Multi-fault-tolerant control method for modular mechanical arm based on dynamic programming
CN112621759B (en) Teleoperation system fractional order sliding mode synchronous control method based on event trigger mechanism
CN108058188B (en) Control method of robot health monitoring and fault diagnosis system
CN112338912B (en) Finite time stability control method and system for flexible single-chain mechanical arm
CN112904728A (en) Mechanical arm sliding mode control trajectory tracking method based on improved approach law
CN106527152A (en) Design method and system of closed-loop fractional-order PD&lt;alpha&gt; type iterative learning robot controller
CN109986562B (en) Planar mechanical arm system and distributed fault-tolerant control method thereof
CN107621783B (en) Self-adaptive robust control method for transmitting platform based on friction compensation
CN106078741A (en) Based on a determination that the limited performance flexible mechanical arm control method of theory of learning
CN110580373B (en) Preprocessing collaborative simulation method and device
CN107831774B (en) Passive fault-tolerant control method of rigid body satellite attitude system based on self-adaptive PI control
CN112528434A (en) Information identification method and device, electronic equipment and storage medium
CN115502986A (en) Multi-joint mechanical arm event drive control method based on state observer
CN110879589A (en) Mechanical arm fault-tolerant control method and system based on backstepping strategy and sliding mode strategy
CN115319800A (en) Design method of preset time controller of double-joint mechanical arm
CN113219825B (en) Single-leg track tracking control method and system for four-leg robot
CN108406766B (en) Synchronous control method for multi-mechanical arm system based on composite integral sliding mode
CN115236990A (en) Generalized estimator, generalized interference rejection controller and design method
CN114924485A (en) Over-driven underwater robot dynamic positioning self-adaptive fault-tolerant control architecture and method
CN110928239B (en) Control method and system for feeding system of numerical control machine tool with time delay
CN118381406B (en) Vector decoupling control method for permanent magnet synchronous motor and related equipment
CN103713654B (en) The rolling window non-causal inverse control method that flexible arm terminal end path is followed the tracks of
CN114815785B (en) Nonlinear system actuator robust fault estimation method based on finite time observer
CN114624994B (en) Novel active disturbance rejection control method and system of high-order flexible linear system
CN118493408B (en) Control method, device and system for mechanical arm based on self-adaptive controller and storage medium

Legal Events

Date Code Title Description
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20200313

RJ01 Rejection of invention patent application after publication