A Fault Diagnosis Method for Robotic Arm Actuators Based on Adaptive Finite-Time Observer

Abstract

The present invention relates to a method for fault diagnosis of a manipulator actuator based on an adaptive finite-time observer, the steps of which are: establishing a rigid manipulator dynamics model; converting the rigid manipulator dynamics model into a state space model; performing an extended transformation on the state space model to obtain an extended system; designing an adaptive finite-time observer according to the extended system; designing a fault diagnosis strategy based on the residual information generated by the adaptive finite-time observer; and completing the manipulator actuator fault diagnosis task according to the fault diagnosis strategy. The present invention makes the manipulator actuator error system bounded and stable within a finite time, outputs the manipulator actuator state estimation value, and ensures that the fault estimation error is robust to external disturbances and system uncertainties within a finite time. It has high sensitivity to manipulator actuator faults and strong resistance to unknown disturbances. The scheme is simple and avoids the limitations of traditional adaptive methods, and has feasibility and universality.

Description

Technical Field

[0001] The invention belongs to the field of fault diagnosis, and in particular relates to a method for diagnosing a mechanical arm actuator fault based on an adaptive finite time observer. Background Art

[0002] Robotic arms have the advantages of high precision, high speed, and high efficiency, so they are increasingly used in various fields, such as aerospace, marine engineering, and industrial engineering. However, due to the high nonlinearity, strong coupling, and time-varying nature of the robotic arm system, its structure is very complex, and it needs to work for a long time in various unknown environments. It will be affected by various uncertain factors, and it is inevitable that various problems will arise in the process of performing tasks. Therefore, fault diagnosis technology is a key technology to improve system safety, reliability, and reduce accident risks, and it is also very important for the widespread application of robotic arms in production and life.

[0003] Designing a suitable fault diagnosis method for uncertain nonlinear systems such as robotic arms, which are difficult to establish accurate mathematical models and have complex system structures, has become the focus of many researchers. Among the existing methods, the feedback linearization observer is stable but lacks robustness; the sliding mode observer has good robustness and stability but is prone to jitter under uncertain conditions; the fuzzy logic observer can work in uncertain environments but needs to be further optimized in terms of reliability; the traditional adaptive observer has partially solved the above problems, but it cannot further solve the behavior of the system within a specific time and the minor faults that occur in the system within a short period of time. Summary of the invention

[0004] The present invention provides a method for fault diagnosis of a robotic arm actuator based on an adaptive finite-time observer, which aims to solve the problems of existing diagnostic methods, such as lack of robustness, generation of jitter phenomenon, suppression of external disturbances and uncertainties, and the behavior of the system within a specific time and minor faults occurring in the system within a short time.

[0005] To achieve the purpose of the present invention, the technical solution is as follows:

[0006] A method for fault diagnosis of a robotic arm actuator based on an adaptive finite-time observer is described in detail in the following steps:

[0007] Step 1: Establish a rigid body robotic arm dynamics model;

[0008] Step 2: Convert the rigid body manipulator dynamics model into a state space model;

[0009] Step 3: Extend and transform the state space model to obtain an extended system;

[0010] Step 4: Design an adaptive finite-time observer based on the extended system;

[0011] Step 5: Design the fault diagnosis strategy based on the residual information generated by the adaptive finite-time observer;

[0012] Step 6: Complete the robot arm actuator fault diagnosis task according to the fault diagnosis strategy.

[0013] Furthermore, the dynamic model of the rigid body manipulator in step 1 is:

[0014]

[0015] Among them, θ, are the angle, angular velocity, and angular acceleration of the rigid robot arm link respectively; M(θ) is the inertia matrix of the robot arm; is the Coriolis force and centrifugal force; G(θ) is the gravity term; τ is the joint torque, d is the external disturbance and uncertainty; f a (t) is the fault term; t represents time; β(tT) is a diagonal matrix that describes the time characteristics of the fault; T is the time when the unknown fault occurs; ψ a (t) refers to the nonlinear hazard function; β(tT)ψ a (t) is the unknown actuator fault vector, which represents the dynamic changes of the system when the actuator fault occurs.

[0016] Furthermore, the state space model is:

[0017]

[0018] Among them, x(t) is the state vector; is the derivative of x(t); τ(t) is the input vector; y(t) is the output vector; β(tT)ψ a (x,τ) represents the actuator failure of the robot system; f(x,τ) represents the nonlinear term that satisfies the Lipschitz condition; φ(t,x,τ) represents the system uncertainty; d1(t) represents the external disturbance; A, B, C, D are known matrices of appropriate dimension.

[0019] Furthermore, in the state-space model, since the state-space system is observable, (A, C) is observable and the nonlinear term f(x, τ) and the fault function ψ a (x,τ) satisfies the Lipschitz condition:

[0020]

[0021]

[0022] Among them, λ1>0,λ2>0, are known Lipschitz constants; x is the state of the robot system, is the estimated state of x. Further, the extended transformation of the state space model in step 3 is:

[0023]

[0024] Among them, z(t) is the expanded state variable, is the derivative of z(t), τ(t) is the control input, ψ a (x,τ) is the fault function, φ(t,x,τ) is the uncertainty, is the expanded matrix, It also corresponds to the expanded matrix. It is expressed as follows:

[0025] is the derivative of the external disturbance d1; I n ,I q are all identity matrices of suitable dimension.

[0026] Furthermore, the state variable z(t) must satisfy

[0027] The control input τ(t) must satisfy

[0028] The uncertainty φ(t,x,τ) must satisfy

[0029] The derivative of the hazard function is Need to meet

[0030] Among them, z a ,τ a ,w,ψ are given positive scalars, and t∈[0,T] is a finite time window.

[0031] Furthermore, the adaptive finite-time observer in step 4 is:

[0032]

[0033] in, Represent the state estimation vector, output estimation vector and estimated value of unknown parameter α of the observer respectively; for The derivative of is the estimated value of x; K represents the gain matrix of the observer.

[0034] Furthermore, the adaptive finite-time observer needs to satisfy the following conditions:

[0035] The unknown parameter α of the introduced fault vector is bounded, such that:

[0036] ||α||≤λ3;

[0037] Among them, λ3 is a constant greater than 0;

[0038] There exists a gain matrix K and a symmetric positive definite matrix P such that the following matrix inequality holds:

[0039] (A-KC) T P+P(A-KC)+λ 2 PP+I<0

[0040] Among them, (A-KC) T is the transposed matrix of (A-KC); λ=λ1+λ2λ3 are constants; I is the unit matrix;

[0041] There exists a vector function g(x,τ) such that the symmetric positive definite matrix P in the above formula satisfies the following relationship:

[0042] Pf(x,τ)=C T g(x,τ)

[0043] Among them, C T is the transposed matrix of C.

[0044] Furthermore, the adaptive law of the unknown parameter α is:

[0045]

[0046] in, are the estimated values ​​of x, z, and α respectively. For estimated value The derivative of for The transposed matrix of ; δ>0 is a constant.

[0047] Furthermore, the fault diagnosis strategy of the robot arm actuator in step 5 is:

[0048]

[0049] Among them, e out is the residual evaluation function; th is the fault judgment threshold set for the observer; e out , th are represented as follows:

[0050]

[0051] Among them, |||| is the modulus of the vector; is the output observation error, r Tis the transpose of r; t is time, and T1 is the evaluation moment of the finite time window.

[0052]

[0053] Among them, Δψ(t) is the disturbance term of the robot system (the sum of external disturbance and uncertainty) and its norm is bounded; e out (t) is the output residual when there is interference in the system; the l2 norm mathematically represents the Euclidean distance of a large vector; sup is its supremum in the mathematical sense.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] (1) Compared with the existing robot arm actuator fault diagnosis method, the present invention can accurately estimate fault information and has the ability to suppress external disturbances and system uncertainties;

[0056] (2) For faults within a specific time range and minor faults that occur in the system within a short period of time, the present invention can improve the fault diagnosis efficiency of the system and accurately diagnose system faults;

[0057] (3) The designed finite-time observer has a non-singular structure, which is easy to calculate and implement, and can achieve rapid diagnosis;

[0058] (4) Compared with the traditional robot arm actuator fault diagnosis method, the present invention improves the robustness, stability and reliability of fault diagnosis and ensures the safety of the robot arm actuator system;

[0059] (5) The present invention has clear ideas, simple structure and is easy to implement in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a flow chart of the method of the present invention;

[0061] Figure 2 It is a comparison between the diagnosis results of the early minor fault signals of the robot arm actuator and the traditional adaptive method;

[0062] Figure 3 It is a comparison between the diagnosis results of the time-varying fault signal of the robot arm actuator and the traditional adaptive method;

[0063] Figure 4 It is the comparison between the diagnosis results of the periodic fault signal of the robot arm actuator and the traditional adaptive method. DETAILED DESCRIPTION

[0064] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings. The specific implementation of the present invention adopts a double-link robotic arm system. However, the method of the present invention is still universally applicable to other robotic arm systems.

[0065] The present invention proposes an adaptive finite time observer within a specific time range, which has a non-singular structure, is simple to calculate and implement, and accurately completes the estimation of fault information; when the actuator failure occurs in the manipulator system, the proposed adaptive algorithm can realize fast state and fault estimation; at the same time, on the basis of the above, by ∞ The introduction of the theory effectively suppresses the influence of external disturbance on fault diagnosis. The invention solves the problems of frequent fault changes, difficulty in detecting minor faults and slow fault diagnosis, and effectively ensures the safety of the robot arm actuator system.

[0066] like Figure 1 As shown in FIG. 1 , a method for fault diagnosis of a robot arm actuator based on an adaptive finite time observer is described, and the specific implementation steps are as follows:

[0067] Step 1: Establish a rigid body robotic arm dynamics model;

[0068] The dynamic model of the rigid body manipulator is:

[0069]

[0070] Among them, θ, are the angle, angular velocity, and angular acceleration of the rigid robot arm link respectively; M(θ) is the inertia matrix of the robot arm; is the Coriolis force and centrifugal force; G(θ) is the gravity term; τ is the joint torque, d is the external disturbance and uncertainty; f a (t) is the fault term, and t represents time.

[0071] β(tT) is a diagonal matrix, that is, β(tT) = diag(β1(tT),β2(tT),...,β n (tT)), describes the time characteristics of the fault (reflects the development speed of the fault); T is the time when the unknown fault occurs; ψ a (t) refers to the nonlinear fault function; hence β(tT)ψ a (t) is the unknown actuator fault vector, which represents the dynamic changes of the system when the actuator fault occurs.

[0072] Step 2: Convert the rigid body manipulator dynamics model into a state space model;

[0073] Considering that the system specifically studied in the present invention is a two-link robotic arm, the robotic arm system can be described as:

[0074]

[0075] Among them, θ i ,w iare the angle and angular velocity of the robot arm link i; f i is a variable θ, Related nonlinear functions; β(t-T0) and β(t-T1) are the fault occurrence functions at time T0 and T1 respectively; ψ ai is the fault function. (i=1,2)

[0076] When the state variable is defined as: x(t) = [x1, x2] T , and x1=[θ1,θ2] T ,x2=[w1,w2] T Obviously, formula (2) can be further expressed as a state space model in the following form:

[0077]

[0078] Among them, x(t) is the state vector; is the derivative of x(t); τ(t) is the input vector; y(t) is the output vector; β(tT)ψ a (x,τ) represents the system actuator failure; f(x,τ) represents the nonlinear term that satisfies the Lipschitz condition; φ(t,x,τ) represents the system uncertainty; d1(t) represents the external disturbance; A, B, C, D are known matrices of appropriate dimension.

[0079] Note: 1 The state space system is observable, so (A, C) is also observable;

[0080] 2 Nonlinear term f(x,τ), fault function ψ a (x,τ) satisfies the Lipschitz condition, and there exists λ1>0,λ2>0:

[0081]

[0082]

[0083] Step 3: Extended transformation of the state space model;

[0084] Taking the external disturbance d1(t) as the auxiliary state, we can get from formula (3):

[0085]

[0086] in, is the derivative of the external disturbance d1; I n ,I q are all identity matrices of suitable dimension.

[0087] The state variable z(t), control input τ(t), uncertainty φ(t,x,τ) and the derivative of the fault function in equation (6) are satisfy: z a ,τ a ,w,ψ are given positive scalars, and t∈[0,T] is a finite time window.

[0088] Step 4: Design an adaptive finite-time observer based on the extended system:

[0089] 1) Make the error system of the robot arm actuator bounded and stable within a finite time;

[0090] 2) Output the estimated value of the robot arm actuator state and ensure that the fault estimation error is robust to external disturbances and system uncertainties within a finite time.

[0091] Note: The unknown parameter α of the fault vector introduced by 1 is bounded, such that:

[0092] ||α||≤λ3 (7)

[0093] Wherein, λ3 is a constant greater than 0.

[0094] 2There exists a gain matrix K and a symmetric positive definite matrix P such that the following matrix inequality holds:

[0095] (A-KC) T P+P(A-KC)+λ 2 PP+I<0 (8)

[0096] Among them, (A-KC) T is the transposed matrix of (A-KC); λ=λ1+λ2λ3 are constants; I is the unit matrix.

[0097] 3 There exists a vector function g(x,τ) such that P in (8) satisfies the following relationship:

[0098] Pf(x,τ)=C T g(x,τ) (9)

[0099] Among them, C T is the transposed matrix of C.

[0100] Then the fault diagnosis observer can be designed as:

[0101]

[0102] in, Represent the state estimation vector, output estimation vector and estimated value of unknown parameter α of the observer respectively; for The derivative of is the estimated value of x; K represents the gain matrix of the observer.

[0103] In the above case, in order to ensure the asymptotic stability of the designed observer, the adaptive law of α is:

[0104]

[0105] in, are the estimated values ​​of x, z, and α respectively. For estimated value The derivative of for The transposed matrix of ; δ>0 is a constant.

[0106] Step 5: Design the fault diagnosis strategy based on the residual information generated by the adaptive finite-time observer;

[0107] A fault diagnosis strategy is designed to improve the accuracy of fault diagnosis. The specific logical relationship is as follows:

[0108]

[0109] Among them, e out is the residual evaluation function; th is the fault judgment threshold set for the observer; e out , th are represented as follows:

[0110]

[0111] Among them, || || is the modulus of the vector; is the output observation error, r T is the transpose of r; t is time, and T1 is the evaluation moment of the finite time window.

[0112]

[0113] Among them, Δψ(t) is the disturbance term of the robot system (the sum of external disturbance and uncertainty) and its norm is bounded; e out (t) is the residual information output by the adaptive finite-time observer when there is interference in the system; the l2 norm mathematically represents the Euclidean distance of a large vector; sup is its supremum in the mathematical sense.

[0114] The fault residual value e calculated by real-time observation out Compared with the fault judgment threshold th, if there is a certain time or a certain period of time, there is ||e out ||>th is established, then it is determined that the robot arm actuator system fails at this time.

[0115] Step 6: Complete the robot arm actuator fault diagnosis task according to the fault diagnosis strategy.

[0116] Example 1

[0117] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation cases of the method of the present invention are as follows:

[0118] The rigid body manipulator dynamics model in the form of equation (1) is transformed into a state space model in the form of equation (3), and then the state equation and output equation in the form of equation (6) are obtained by expanding and transforming it. Define the state variables x1 = θ1, x2 = θ2, then the two-link manipulator can be described as:

[0119]

[0120] When the parameters of a typical two-link robot arm system are m1=1kg, m2=1.5kg, l1=1.0m, l2=0.8m, g=10N / kg. (m is the mass of the robot arm link; l is the length of the robot arm link), then:

[0121]

[0122]

[0123] Expected trajectory Initial conditions According to the method of the present invention, an adaptive finite-time observer is constructed as shown in formula (10), and δ=10 is selected. Solved by LMI toolbox:

[0124] The judgment threshold th in the fault diagnosis logic is preset, and then the adaptive finite time observer designed according to the present invention is used to diagnose the fault of the robot arm actuator. When the system faults are early minor faults within a limited time range, f a1 (t), time-varying fault f a2 (t) and periodic fault f a3 (t) time:

[0125]

[0126]

[0127]

[0128] Figure 2 , Figure 3 and Figure 4The following are the diagnosis results of three different types of faults of the robot arm (early minor faults, time-varying faults, and periodic faults), and compared with the traditional adaptive fault diagnosis method. From the analysis of the figure, it can be seen that when different types of faults occur in the robot arm actuator system within 6-11 seconds, this method can quickly detect the fault and accurately estimate the fault information; in the initial state, this method can effectively weaken the chattering phenomenon; from the local magnification of the figure, it can be seen that this method has a higher diagnostic accuracy and better results.

[0129] It can be seen that the fault diagnosis method designed by the present invention has more obvious advantages than the traditional adaptive fault diagnosis method: due to the influence of initial value deviation, external disturbance and system uncertainty, Figure 2-4 It is known that the comparison method has a large vibration in the initial stage, while the method designed by the present invention has a certain vibration suppression ability; the method of the present invention has a certain adaptability to different types of faults; the method of the present invention can accurately detect faults within a limited time range, accurately estimate fault information, improve fault diagnosis efficiency, and pave the way for subsequent fault-tolerant control research; the method of the present invention diagnoses faults within a limited time and provides a new solution to the problem of mechanical arm actuator system failure. In short, the invention has a clear idea, a simple structure, and is easy to implement in engineering, which ensures the safety and reliability of the mechanical arm actuator system.

[0130] The above examples are merely examples for clearly illustrating the present invention, rather than limitations on the implementation modes of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of the above description to facilitate the understanding and implementation of the invention.

Claims

1. A method for fault diagnosis of a robot arm actuator based on an adaptive finite time observer, characterized in that: The specific implementation steps are as follows: Step 1: Establish a rigid body robotic arm dynamics model; Step 2: Convert the rigid body manipulator dynamics model into a state space model; Step 3: Extend and transform the state space model to obtain an extended system; Step 4: Design an adaptive finite-time observer based on the extended system; Step 5: Design the fault diagnosis strategy based on the residual information generated by the adaptive finite-time observer; Step 6: Complete the robot arm actuator fault diagnosis task according to the fault diagnosis strategy; The adaptive finite time observer in step 4 is: in, Represent the state estimation vector, output estimation vector and estimated value of unknown parameter α of the observer respectively; for The derivative of is the estimated value of x, x is the state of the robot system; K represents the gain matrix of the observer; t represents time, t∈[0,T] is a finite time window; A, B, C are known matrices of suitable dimension; τ is the joint torque; f(x,τ) represents a nonlinear term that satisfies the Lipschitz condition; β(tT)ψa(x,τ) represents the actuator failure of the robot system; φ(t,x,τ) represents the system uncertainty; is the expanded matrix, It also corresponds to the expanded matrix, which is expressed as follows: is the derivative of the external disturbance d1; In, Iq are both unit matrices of appropriate dimension; The adaptive finite-time observer must meet the following conditions: The unknown parameter α of the introduced fault vector is bounded, such that: ||α||≤λ3; Among them, λ3 is a constant greater than 0; There exists a gain matrix K and a symmetric positive definite matrix P such that the following matrix inequality holds: (A-KC) T P+P(A-KC)+λ 2 PP+I<0 Among them, (A-KC) T is the transposed matrix of (A-KC); λ=λ1+λ2λ3 is a constant; I is the identity matrix; there exists a vector function g(x,τ) such that the symmetric positive definite matrix P in the above formula satisfies the following relationship: Pf(x,τ)=C T g(x,τ) Among them, C T is the transposed matrix of C; The adaptive law of the unknown parameter α is: in, are the estimated values ​​of x, z, and α respectively. For estimated value The derivative of for The transposed matrix of ; δ>0 is a constant; The fault diagnosis strategy of the robot actuator in step 5 is: Among them, e out is the residual evaluation function; th is the fault judgment threshold set for the observer; e out , th are represented as follows: Among them, || || is the modulus of the vector; is the output observation error, r T is the transpose of r; t is time, T1 is the evaluation moment of the finite time window; Among them, Δψ(t) is the disturbance term of the robot system and its norm is bounded; e out (t) is the output residual when there is interference in the system; the l2 norm mathematically represents the Euclidean distance of a large vector; sup is its supremum in the mathematical sense.

2. The method for fault diagnosis of a mechanical arm actuator based on an adaptive finite time observer according to claim 1, characterized in that: The dynamic model of the rigid body manipulator in step 1 is: Among them, θ, are the angle, angular velocity, and angular acceleration of the rigid robot arm link respectively; M(θ) is the inertia matrix of the robot arm; is the Coriolis force and centrifugal force; G(θ) is the gravity term; τ is the joint torque, d is the external disturbance and uncertainty; f a (t) is the fault term; t represents time; β(tT) is a diagonal matrix that describes the time characteristics of the fault; T is the time when the unknown fault occurs; ψ a (t) refers to the nonlinear hazard function; β(tT)ψ a (t) is the unknown actuator fault vector, which represents the dynamic changes of the system when the actuator fault occurs.

3. The method for fault diagnosis of a mechanical arm actuator based on an adaptive finite time observer according to claim 1, characterized in that: The state space model is: Among them, x(t) is the state vector; is the derivative of x(t); τ(t) is the input vector; y(t) is the output vector; β(tT)ψ a (x,τ) represents the actuator failure of the robot system; f(x,τ) represents the nonlinear term that satisfies the Lipschitz condition; φ(t,x,τ) represents the system uncertainty; d1(t) represents the external disturbance; A, B, C, D are known matrices of appropriate dimension.

4. The method for fault diagnosis of a mechanical arm actuator based on an adaptive finite time observer according to claim 3 is characterized in that: In the state-space model, since the state-space system is observable, (A, C) is observable and the nonlinear term f(x, τ) and the fault function ψ a (x,τ) satisfies the Lipschitz condition: Among them, λ1>0,λ2>0, are known Lipschitz constants; x is the state of the robot system, is the estimated state of x.

5. The method for fault diagnosis of a robot arm actuator based on an adaptive finite time observer according to claim 1, characterized in that: The extended transformation of the state space model in step 3 is: Among them, z(t) is the expanded state variable, is the derivative of z(t), τ(t) is the control input, ψ a (x,τ) is the fault function, φ(t,x,τ) is the uncertainty, is the expanded matrix, It also corresponds to the expanded matrix, which is expressed as follows: is the derivative of the external disturbance d1; I n ,I q are all identity matrices of suitable dimension.

6. The method for fault diagnosis of a robot arm actuator based on an adaptive finite time observer according to claim 5, characterized in that: The state variable z(t) must satisfy The control input τ(t) must satisfy The uncertainty φ(t,x,τ) must satisfy The derivative of the hazard function is Need to meet Among them, z a ,τ a ,w,ψ are given positive scalars, and t∈[0,T] is a finite time window.

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