A sensor fault estimation method suitable for a nonlinear generalized uncertain manipulator system

Abstract

The application is suitable for a sensor fault estimation method for a nonlinear generalized uncertain robot arm system, and the steps are as follows: a rigid robot arm dynamics model is established; the rigid robot arm dynamics model is converted into a state space model; the state space model is extended and transformed to obtain an augmented system; an augmented state observer is designed according to the augmented system; a fault estimation strategy is designed from residual information generated by the augmented state observer, and a Lipschitz condition is used to process nonlinear terms in the system; and the robot arm sensor fault estimation task is completed according to the presence or absence of interference. The application makes the robot arm sensor error system bounded and stable in a limited time, considers interference terms in the system, and gives a suitable estimation error system asymptotic stability method in two cases, so that the sensor fault in the robot arm system can be asymptotically estimated. Therefore, the application has certain reliability and practicality.

Description

Technical Field

[0001] This invention belongs to the field of fault estimation and relates to a sensor fault estimation method applicable to nonlinear generalized uncertain robotic arm systems. Background Technology

[0002] Robotic arms possess advantages such as high precision, high speed, and high efficiency, leading to their increasing application in various fields, including aerospace, marine engineering, and industrial engineering. However, the highly nonlinear, strongly coupled, and time-varying nature of robotic arm systems results in complex structures. Furthermore, their prolonged operation in various unknown environments exposes them to uncertainties, inevitably leading to problems during task execution. Therefore, sensor fault estimation technology for robotic arm systems is crucial for improving system safety, reliability, and reducing accident risks, and is vital for the widespread application of robotic arms in production and daily life. Designing a suitable sensor fault estimation method for uncertain nonlinear systems like robotic arms, which are difficult to model precisely and have complex structures, has become a focus for many researchers. Existing methods include feedback linearized observers, which offer stability but lack robustness; sliding mode observers, while possessing good robustness and stability, are prone to chattering under uncertain conditions; fuzzy logic observers, while capable of operating in uncertain environments, require further reliability optimization; and traditional adaptive observers, while partially addressing these issues, cannot further estimate system behavior within specific timeframes or minor faults occurring within short periods. Summary of the Invention

[0003] This invention provides a sensor fault estimation method applicable to nonlinear generalized uncertain robotic arm systems. Its purpose is to solve the problems of existing estimation methods, such as insufficient robustness, chattering phenomenon, suppression of external disturbances and uncertainties, and limitations in addressing the behavior of the system within a specific time period and minor faults occurring in the system within a short period of time.

[0004] To achieve the objective of this invention, the technical solution is as follows:

[0005] A sensor fault estimation method applicable to nonlinear generalized uncertain robotic arm systems is proposed, and its specific implementation steps are as follows:

[0006] Step (1): Establish the dynamic model of the rigid body manipulator;

[0007] Step (2): Convert the dynamic model of the rigid body manipulator into a state-space model;

[0008] Step (3): Extend the state-space model to obtain the augmented system;

[0009] Step (4): Design an augmented state observer based on the augmented system;

[0010] Step (5): Design a fault estimation strategy using the residual information generated by the augmented state observer;

[0011] Step (6): Design reasonable fault estimation strategies based on whether there is a disturbance;

[0012] Step (7): Fault estimation.

[0013] Furthermore, the dynamic model of the rigid body manipulator described in step (1) is as follows:

[0014] ,

[0015] in, , , These are the angle, angular velocity, and angular acceleration of the rigid body robotic arm link, respectively. It is the inertia matrix of the robotic arm; These are Coriolis force and centrifugal force; It is a gravity term; It is joint torque. It is external disturbance and uncertainty; It is a fault item; Indicates time; It is a diagonal matrix that describes the temporal characteristics of the fault. The time when the unknown fault occurred; This refers to a nonlinear fault function; The unknown sensor fault vector represents the dynamic changes of the system when a sensor fault occurs.

[0016] Furthermore, the state-space model described in step (2) is as follows:

[0017] ,

[0018] in, Let this be the system's state vector; yes The derivative; This is a nonlinear vector of the system that varies with time. To control the input vector; To measure the output vector, This is system interference; The problem is a sensor malfunction. It is a generalized matrix, that is ; H is a known matrix of appropriate dimension; , To represent the uncertainty of the model, it can be expressed as:

[0019] ,

[0020] in Given a matrix of appropriate dimension, The matrix is ​​an unknown time-varying matrix and satisfies .

[0021] To address the uncertainty in the input, a feedback control law is used, making... Transform the system into:

[0022] ,

[0023] This generalized system is observable, that is, it has Nonlinear terms in generalized systems Satisfying the Lipschitz condition: .

[0024] in Represents the Euclidean norm. is the Lipsitz constant.

[0025] By incorporating sensor faults as part of the augmented state in the augmented state observer, the state and sensor faults in the original system are estimated by constructing the augmented state observer.

[0026] Furthermore, the augmentation system described in step (3) is: [The rest of the text is missing, so the translation ends here.] ,

[0027] ,

[0028] in:

[0029] , , , , ,

[0030] , .

[0031] Since this system is observable, then... The ranks are full.

[0032] remember,

[0033] ,

[0034] Then there is .

[0035] Therefore, the augmented system can be transformed into:

[0036] .

[0037] By designing an augmented state observer, robust estimation of sensor faults in the original generalized system can be achieved.

[0038] Furthermore, the augmented state observer mentioned in step (4) is:

[0039] ,

[0040] make ,

[0041] Furthermore, the residual information generated by the augmented state observer in step (5) is as follows:

[0042] = ,

[0043] in, .

[0044] Therefore, the error dynamic equation of the observer can be proven to be robustly asymptotically stable using the Lyapunov function, and the gain matrix of the augmented state observer can be obtained, thereby achieving robust estimation of the original system state and sensor faults.

[0045] Furthermore, in step (6), reasonable fault estimation strategies are designed based on whether or not there is a disturbance:

[0046] When the system is free from interference:

[0047] Get Lyapunov function Then we have:

[0048]

[0049] ,

[0050] make ,but:

[0051] ,

[0052] Furthermore, due to And since the system satisfies the Lipschitz condition, we can obtain:

[0053] ,

[0054] ,

[0055] ,

[0056] Right now:

[0057] ,

[0058] Therefore, this method can be used to handle the nonlinear part of the system, where, .

[0059] Then, based on the constraints of the uncertain matrix ,have Therefore, the original expression satisfies:

[0060] ,

[0061] make We can conclude that:

[0062] ,

[0063] ,

[0064] According to Schur's complement lemma, the linear matrix inequality can be obtained as follows:

[0065] ,

[0066] Then when When the error dynamic equation is stable, the error dynamic equation is stable, where It is a positive definite matrix. Here is the gain matrix. , .

[0067] When interference exists in the system:

[0068] make ,in For Lyapunov functions, it is obvious that when At that time, there is ,Right now:

[0069] ,

[0070] ,

[0071] again,

[0072] ,

[0073] Therefore,

[0074] ,

[0075] parameter It can be used as a term to suppress interference. Sensor malfunction The performance indicators affected, when When it becomes smaller, it means

[0076] The impact of disturbances on faults is reduced, thereby enabling the augmented state observer to make robust estimations of sensors.

[0077] because:

[0078]

[0079] ,

[0080] It can be known that:

[0081] ,

[0082] According to the above formula, we can obtain:

[0083] ,

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] =

[0090]

[0091] .

[0092] make , , ,

[0093] so:

[0094] ,

[0095] From the above, it can be seen that when At that time, the error dynamic equation is asymptotically stable, while ensuring This reduces the impact of external interference on fault estimation and enables the estimation of sensor faults in the system. According to Schur's complement lemma, when... When the time condition is met, the dynamic equation of the augmented state observer error is robustly asymptotically stable.

[0096] Due to augmentation state ,and Therefore, augmented states can be observed by designing observers. Estimation is performed to obtain the estimated value. Finally passed Obtain robust estimation of the sensor Based on whether the system has faults or not, the gain matrix of the augmented state observer can be calculated using the linear matrix inequality. The constructed observer can then be used to estimate sensor faults in the original system. Considering a nonlinear system and an augmented state observer, if a symmetric positive definite matrix exists... and gain matrix This makes the linear matrix inequality hold, so we can... Sensor malfunctions in the system Perform robust estimation.

[0097] Further, step (7) involves fault estimation.

[0098] Compared with existing inventions, the present invention has the following advantages:

[0099] (1) Compared with the existing fault estimation methods of dual-link robotic arms, the present invention can accurately estimate fault information, effectively process the generalized and nonlinear terms that appear in the system, and has a good suppression effect on system interference.

[0100] (2) Compared with the traditional fault estimation method of double-link robotic arm, the present invention improves the robustness, stability and reliability of fault estimation, and ensures the safety of the double-link robotic arm system.

[0101] (3) The present invention has a clear concept and is easy to implement. Attached Figure Description

[0102] Figure 1 This is a flowchart of the steps described in this invention;

[0103] Figure 2 This is a schematic diagram of the dual-link robotic arm structure described in this invention; Detailed Implementation

[0104] A sensor fault estimation method for nonlinear generalized uncertain robotic arm systems includes the following steps:

[0105] Step (1): Establish the dynamic model of the rigid body manipulator;

[0106] Step (2): Convert the dynamic model of the rigid body manipulator into a state-space model;

[0107] Step (3): Extend the state-space model to obtain the augmented system;

[0108] Step (4): Design an augmented state observer based on the augmented system;

[0109] Step (5): Design a fault estimation strategy using the residual information generated by the augmented state observer;

[0110] Step (6): Design reasonable fault estimation strategies based on whether there is a disturbance;

[0111] Step (7): Fault estimation.

[0112] This invention constructs a dynamic model of a rigid manipulator and proposes a sensor fault estimation method applicable to nonlinear generalized uncertain manipulator systems. This invention solves the problems of fault estimation and suppression of external interference in nonlinear generalized systems, while also addressing the uncertainty problem in the system.

[0113] Furthermore, the dynamic model of the rigid body manipulator described in step (1) is as follows:

[0114] ,

[0115] in, , , These are the angle, angular velocity, and angular acceleration of the rigid body robotic arm link, respectively. It is the inertia matrix of the robotic arm; These are Coriolis force and centrifugal force; It is a gravity term; It is joint torque. It is external disturbance and uncertainty; It is a fault item; Indicates time; It is a diagonal matrix that describes the temporal characteristics of the fault. The time when the unknown fault occurred; This refers to a nonlinear fault function; The unknown sensor fault vector represents the dynamic changes of the system when a sensor fault occurs.

[0116] Considering that the system specifically studied in this invention is a dual-link robotic arm, the robotic arm system can be described as follows:

[0117] ,

[0118] in These are the robotic arm links Angle and angular velocity; It is a variable The relevant nonlinear functions. Therefore, the dynamic model can be transformed into a state-space model:

[0119] ,

[0120] ,

[0121] In the formula For system output, It is the inertia matrix of the robotic arm; These are Coriolis force and centrifugal force; It is a gravity term; It is joint torque. These are sensor fault items generated when the system outputs data. Definition If we consider the system state, then the model can be transformed into:

[0122] ,

[0123] in, , These are the inertia matrices of the robotic arm for the two links.

[0124] Furthermore, the state-space model described in step (2) is as follows:

[0125] ,

[0126] in, Let this be the system's state vector; yes The derivative; This is a nonlinear vector of the system that varies with time. To control the input vector; To measure the output vector, This is system interference; The problem is a sensor malfunction. It is a generalized matrix, that is ; and Given a known matrix of appropriate dimensions; , To represent the uncertainty of the model, it can be expressed as:

[0127] ,

[0128] and for any scalar All satisfy:

[0129] ,

[0130] in Given a matrix of appropriate dimension, The matrix is ​​an unknown time-varying matrix and satisfies .

[0131] To address the uncertainty in the input, a feedback control law is used, making... Transform the system into:

[0132] ,

[0133] This generalized system is observable, that is, it has The nonlinear terms in this generalized system Satisfying the Lipschiz condition: .

[0134] in Represents the Euclidean norm. is the Lipsitz constant.

[0135] By incorporating sensor faults as part of the augmented state in the augmented state observer, the state and sensor faults in the original system are estimated by constructing the augmented state observer.

[0136] Furthermore, the augmentation system described in step (3) is: [The rest of the text is missing, so the translation ends here.] ,

[0137] ,

[0138] in:

[0139] , , , , ,

[0140] , .

[0141] Since this system is observable, then... The ranks are full.

[0142] remember,

[0143] ,

[0144] Then there is .

[0145] Therefore, the augmented system can be transformed into:

[0146] .

[0147] By designing an augmented state observer, robust estimation of sensor faults in the original generalized system can be achieved.

[0148] Furthermore, the augmented state observer mentioned in step (4) is:

[0149] ,

[0150] make ,

[0151] Furthermore, the residual information generated by the augmented state observer in step (5) is as follows:

[0152] ,

[0153] in, .

[0154] Therefore, the error dynamic equation of the observer can be proven to be robustly asymptotically stable using the Lyapunov function, and the gain matrix of the augmented state observer can be obtained, thereby achieving robust estimation of the original system state and sensor faults.

[0155] Furthermore, in step (6), reasonable fault estimation strategies are designed based on whether or not there is a disturbance:

[0156] When the system is free from interference:

[0157] Get Lyapunov function Then we have:

[0158]

[0159] ,

[0160] make ,but:

[0161] ,

[0162] Furthermore, due to And since the system satisfies the Lipschiz condition, we can obtain:

[0163] ,

[0164] ,

[0165] ,

[0166] Right now:

[0167] ,

[0168] Therefore, this method can be used to handle the nonlinear part of the system, where, .

[0169] Then, based on the constraints of the uncertain matrix ,have Therefore, the original expression satisfies:

[0170] ,

[0171] Therefore, according to the Lipschiz condition, let We can conclude that:

[0172] ,

[0173] ,

[0174] According to Schur's complement lemma, the linear matrix inequality can be obtained as follows:

[0175] ,

[0176] Then when When the error dynamic equation is stable, the error dynamic equation is stable, where It is a positive definite matrix. Here is the gain matrix. , .

[0177] When interference exists in the system:

[0178] make ,in For Lyapunov functions, it is obvious that when At that time, there is ,Right now:

[0179] ,

[0180] ,

[0181] again,

[0182] ,

[0183] Therefore,

[0184] ,

[0185] parameter It can be used as a term to suppress interference. Sensor malfunction The performance indicators affected, when When it becomes smaller, it means

[0186] The impact of disturbances on faults is reduced, thereby enabling the augmented state observer to make robust estimations of sensors.

[0187] because:

[0188]

[0189] ,

[0190] It can be known that:

[0191] ,

[0192] According to the above formula, we can obtain:

[0193] ,

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201] .

[0202] make , , ,

[0203] so:

[0204] ,

[0205] From the above, it can be seen that when At that time, the error dynamic equation is asymptotically stable, while ensuring This reduces the impact of external interference on fault estimation and enables the estimation of sensor faults in the system. According to Schur's complement lemma, when... When the time condition is met, the dynamic equation of the augmented state observer error is robustly asymptotically stable.

[0206] Due to augmentation state ,and Therefore, augmented states can be observed by designing observers. Estimation is performed to obtain the estimated value. Finally passed Obtain robust estimation of the sensor Based on whether the system has faults or not, the gain matrix of the augmented state observer can be calculated using the linear matrix inequality. The constructed observer can then be used to estimate sensor faults in the original system. Considering a nonlinear system and an augmented state observer, if a symmetric positive definite matrix exists... and gain matrix This makes the linear matrix inequality hold, so we can... Sensor malfunctions in the system Perform robust estimation.

[0207] Further, step (7) involves fault estimation.

[0208] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sensor fault estimation method applicable to nonlinear generalized uncertain robotic arm systems, characterized in that: Includes the following steps: Step (1): Establish the dynamic model of the rigid body manipulator; Step (2): Convert the dynamic model of the rigid body manipulator into a state-space model; The state-space model in step (2) is as follows: ， in, Let this be the system's state vector; yes The derivative; This is a nonlinear vector of the system that varies with time. To control the input vector; To measure the output vector, This is system interference; The problem is a sensor malfunction. It is a generalized matrix, that is ; H is a known matrix of appropriate dimension; , The appropriate dimension matrix to represent the uncertainty of the model; Step (3): Perform an augmented transformation on the state-space model to obtain the augmented system; Step (4): Design an augmented state observer based on the augmented system; Step (5): Design a fault estimation strategy using the residual information generated by the augmented state observer; Step (6): Design suitable fault estimation strategies based on whether there is a disturbance or not; and use the Lipschitz condition to handle the nonlinear terms in the system; Step (7): Fault estimation.

2. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 1, characterized in that: The dynamic model of the rigid body manipulator in step (1) is as follows: ， in, , , These are the angle, angular velocity, and angular acceleration of the rigid body robotic arm link, respectively. It is the inertia matrix of the robotic arm; These are Coriolis force and centrifugal force; It is a gravity term; It is joint torque. It is external disturbance and uncertainty; It is a fault item; Indicates time; It is a diagonal matrix that describes the temporal characteristics of the fault. The time when the unknown fault occurred; This refers to a nonlinear fault function; The unknown sensor fault vector represents the dynamic changes of the system when a sensor fault occurs.

3. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 2, characterized in that: The uncertainty of the state-space model is represented as: ， and satisfy , in, Given a matrix of appropriate dimension, The matrix is ​​an unknown time-varying matrix and satisfies .

4. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 3, characterized in that: The augmentation system in step (3) is: [The rest of the text is missing.] ， in: , ， ， ， ， ， ； in, Represents a constant; For augmented state vectors; For augmented singular matrices; To augment the system matrix; To augment the output matrix; This is the perturbation input matrix for augmenting the system.

5. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 4, characterized in that: The augmented state observer in step (4) is: ； in, Here is the gain matrix. express The estimated state; It is a constant matrix without differential terms.

6. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 5, characterized in that: The residual information generated by the augmented state observer in step (5) is as follows: ， in, .

7. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 6, characterized in that: Nonlinear terms in generalized systems Satisfying the Lipschitz condition: ； in Represents the Euclidean norm. is the Lipsitz constant.

8. The sensor fault estimation method for a nonlinear generalized uncertain robotic arm system according to claim 7, characterized in that: In step (6), fault estimation strategies are designed according to whether there is a disturbance or not, including: When the system is free from disturbances, the linear matrix inequalities can be obtained: ， Then when When the error dynamic equation is stable, then, It is a positive definite matrix. Here is the gain matrix. , , Let Lipsitz constant be _____. ; When interference exists in the system, we can obtain: ， in, To suppress interference terms Sensor malfunction The affected performance metrics, when As time goes on, the error dynamic equation gradually stabilizes.

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