Nonlinear system robust residual error multi-fault detection and reconstruction method based on sliding mode observer

Abstract

The invention discloses a nonlinear system robust residual error multi-fault detection and reconstruction method based on a sliding-mode observer, and solves the problems that an actuator fault and unknown input disturbance in a servo driving system are closely related and mutually coupled, and a fault detection algorithm is insensitive to identification of a first-degree fault, so that fault report failure or misjudgment is caused. According to the method, a general nonlinear system is transformed into two subsystems with independent fault influence conditions based on global differential homeomorphic transformation for the first time. Equivalently transforming reverse channel disturbance to forward channel disturbance by using a filter, designing a sliding mode state observer according to different actuator fault types, and respectively extracting fault information and unknown input disturbance information of a servo driving system in the two subsystems, thereby realizing decoupling of the fault and the unknown input disturbance. And the sensitivity of fault signal detection and the accuracy and robustness of fault diagnosis are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of servo drives, and in particular to a sliding mode observer-based robust residual multi-fault detection and reconstruction method for nonlinear systems. Background Art

[0002] Traditional fault detection methods rely on comparing the servo position setting with the feedback signal. However, there are various nonlinearities, modeling errors, and unknown input disturbances in the servo control system, which affect the robustness of the system fault detection algorithm and the accuracy of fault reconstruction. Summary of the Invention

[0003] In order to improve the reliability of system fault detection and reconstruction algorithms, the present invention provides a nonlinear system robust residual multiple fault detection and reconstruction method based on a sliding mode observer.

[0004] The present invention provides a nonlinear system robust residual multiple fault detection and reconstruction method based on a sliding mode observer, comprising the following steps:

[0005] Step S1: Design a sliding mode state observer for different actuator faults. Compare the actual measured value and the observed value of the system output to obtain a residual signal. Set logic rules and thresholds to determine the fault type. The nonlinear system with sensor fault is as follows:

[0006]

[0007] Step S2: Use a first-order low-pass filter to convert the sensor fault into a virtual actuator fault, and propose a basis for selecting filter parameters from the perspective of observability; wherein, the state variable z is selected as the first-order low-pass filter of the output signal:

[0008]

[0009] The original nonlinear system is transformed into:

[0010]

[0011] The above formula represents a case with actuator fault f s For a system, the substitution process equates sensor failures in the system to virtual actuator failures;

[0012] When an actuator failure occurs in the system, the observable canonical form of the system is expressed as:

[0013]

[0014] Where z = T(x) is the coordinate transformation, T(x) is the global diffeomorphism mapping; j(z) is the fault distribution matrix in the new coordinate system, d1(z), d2(z) are the unknown input disturbances of the system in the new coordinate system;

[0015] Step S3: Using global diffeomorphism transformation, the transformed nonlinear system is transformed into two subsystems again, where subsystem 1 is not directly affected by the fault and its state is partially observable; subsystem 2 is affected by the fault and its state is completely observable;

[0016] There exists a global diffeomorphism z = T(x), T(0) = 0 so that the original system can be further represented as the following two subsystems:

[0017]

[0018] Where: E(z) is the following fault distribution matrix;

[0019] For general nonlinear systems, the following sensor fault estimation algorithm is used:

[0020]

[0021] Based on Lyapunov stability theory, the Lyapunov candidate function is designed as:

[0022]

[0023] Among them, e a is the output error, e s is the fault estimation error;

[0024] By adjusting the value of the positive definite symmetric matrix ||P1||, the candidate function is guaranteed to converge asymptotically, thereby reducing the fault reconstruction error e s ; Ultimately, an enhanced sensor robust multi-fault reconstruction algorithm is implemented when both the actuator forward channel and the sensor feedback channel contain unknown input disturbances.

[0025] The beneficial effects of the present invention are:

[0026] The present invention discloses a method for robust residual multi-fault detection and reconstruction of nonlinear systems based on a sliding mode observer. The method solves the problem that actuator faults and unknown input disturbances in servo drive systems are closely related and mutually coupled, and the fault detection algorithm is insensitive to the identification of first-order faults, thus causing fault omissions or misjudgments. The method proposes for the first time a method for transforming a general nonlinear system into two independent subsystems affected by the fault based on a global differential homeomorphism transformation. A filter is used to achieve the equivalent transformation of the reverse channel disturbance to the forward channel disturbance. A sliding mode state observer is designed according to different actuator fault types. The servo drive system fault information and the unknown input disturbance information are extracted from the two subsystems respectively, thereby achieving decoupling of the fault and the unknown input disturbance. The sensitivity of fault signal detection, the accuracy and robustness of fault diagnosis are effectively improved. DETAILED DESCRIPTION

[0027] In order to improve the reliability of the system fault detection and reconstruction algorithm, the embodiment of the present invention discloses a nonlinear system robust residual multiple fault detection and reconstruction method based on a sliding mode observer. The specific implementation steps are as follows:

[0028] First, a sliding mode state observer is designed for different actuator faults. The residual signal is obtained by comparing the actual measured value of the system output with the observed value. Logical rules and thresholds are set to determine the fault type. A first-order low-pass filter is used to transform the sensor fault into a virtual actuator fault. A basis for selecting the filter parameters is proposed from the perspective of observability. Consider the following nonlinear system with sensor faults:

[0029]

[0030] Select a new state variable z as the first-order low-pass filter of the output signal:

[0031]

[0032] Then the original nonlinear system can be transformed into:

[0033]

[0034] The above formula shows that it represents a fault with actuator f s In the system, the substitution process equates the sensor failure in the system to a virtual actuator failure.

[0035] The nonlinear system is transformed into two subsystems using global diffeomorphism, one of which is not directly affected by the fault and has a partially observable state, while the other is affected by the fault but has a fully observable state. This decoupling of the fault from the unknown input disturbance is achieved. When an actuator fault occurs in the system, the observable canonical form of the system can be expressed as:

[0036]

[0037] Where z = T(x) is the coordinate transformation and T(x) is the global diffeomorphism. j (z) is the fault distribution matrix in the new coordinate system, d1(z) and d2(z) are the unknown input disturbances of the system in the new coordinate system. There exists a global differential homeomorphism z = T(x), T(0) = 0 so that the original system can be further represented as the following two subsystems:

[0038]

[0039] Where: E(z) is the following fault distribution matrix. Finally, for general nonlinear systems, the following sensor fault estimation algorithm is adopted:

[0040]

[0041] Based on Lyapunov stability theory, the Lyapunov candidate function is designed as:

[0042]

[0043] Among them, e a is the output error, e s is the fault estimation error.

[0044] By adjusting the value of the positive definite symmetric matrix ||P1||, the candidate function is guaranteed to converge asymptotically, thereby reducing the fault reconstruction error e s Finally, an enhanced sensor-robust multi-fault reconstruction algorithm is implemented that considers unknown input disturbances in both the actuator forward channel and the sensor feedback channel. This enables multi-fault detection and precise reconstruction of the servo system, laying the foundation for active fault-tolerant control algorithms.

[0045] To address the problem of actuator faults and unknown input disturbances in servo drive systems being closely related and mutually coupled, and the insensitivity of fault detection algorithms to primary fault identification, which can lead to missed faults or misdiagnoses, a method based on global diffeomorphism is proposed for the first time to transform a general nonlinear system into two independent subsystems affected by the fault. A filter is used to achieve an equivalent transformation of the reverse channel disturbance to the forward channel disturbance. A sliding mode state observer is designed based on different actuator fault types. Servo drive system fault information and unknown input disturbance information are extracted from the two subsystems, respectively, thereby achieving decoupling of the fault and unknown input disturbance. This effectively improves the sensitivity of fault signal detection and the accuracy and robustness of fault diagnosis.

[0046] The above specific embodiments do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure shall be included within the scope of protection of this disclosure.

Claims

1. A robust residual multiple fault detection and reconstruction method for nonlinear systems based on sliding mode observer, characterized in that: The following steps are involved: Step S1: Design a sliding mode state observer for different actuator faults. Compare the actual measured value and the observed value of the system output to obtain a residual signal. Set logic rules and thresholds to determine the fault type. The nonlinear system with sensor fault is as follows: Step S2: Use a first-order low-pass filter to convert the sensor fault into a virtual actuator fault, and propose a basis for selecting filter parameters from the perspective of observability; wherein, the state variable z is selected as the first-order low-pass filter of the output signal: The original nonlinear system is transformed into: The above formula represents a case with actuator fault f s For a system, the substitution process equates sensor failures in the system to virtual actuator failures; When an actuator failure occurs in the system, the observable canonical form of the system is expressed as: Where z = T(x) is the coordinate transformation, T(x) is the global diffeomorphism mapping; j (z) is the fault distribution matrix in the new coordinate system, d1(z), d2(z) are the unknown input disturbances of the system in the new coordinate system; Step S3: Using global diffeomorphism transformation, the transformed nonlinear system is transformed into two subsystems again, where subsystem 1 is not directly affected by the fault and its state is partially observable; subsystem 2 is affected by the fault and its state is completely observable; There exists a global diffeomorphism z = T(x), T(0) = 0 so that the original system can be further represented as the following two subsystems: Where: E(z) is the following fault distribution matrix; For general nonlinear systems, the following sensor fault estimation algorithm is used: Based on Lyapunov stability theory, the Lyapunov candidate function is designed as: Among them, e a is the output error, e s is the fault estimation error; By adjusting the value of the positive definite symmetric matrix ||P1||, the candidate function is guaranteed to converge asymptotically, thereby reducing the fault reconstruction error e s ; Ultimately, an enhanced sensor robust multi-fault reconstruction algorithm is implemented when both the actuator forward channel and the sensor feedback channel contain unknown input disturbances.

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