Active fault-tolerant control method of nonlinear system

Abstract

The embodiment of the invention relates to the field of dynamic systems, and discloses an active fault-tolerant control method for a nonlinear system, which comprises the following steps of: acquiring a fault estimation value through an observer, and calculating an absolute value of the fault estimation value to obtain a numerical value of a residual signal; calculating a difference value between the system state signal and the system expected signal to obtain a system tracking error, substituting a filtering error of a filter into a preset compensation calculation formula, and calculating to obtain a compensation signal; calculating a difference value between the system tracking error and the compensation signal to obtain a compensation tracking error; when the value of the residual signal is larger than or equal to the detection threshold value, it is indicated that the actuator breaks down, a calculation formula of a preset compensation control signal is obtained through design according to the Lyapunov principle, the compensation control signal is obtained through calculation, the compensation control signal can change according to a fault estimation value, and when disturbance and uncertainty exist, the compensation control signal can be accurately calculated. The fault can be flexibly and accurately estimated, the error of fault compensation error is reduced, and the control performance of active fault tolerance is improved.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of dynamic systems, and in particular to an active fault-tolerant control method for a nonlinear system. Background Art

[0002] A dynamic system is a system that changes state over time. In recent years, dynamic systems have been widely used in various fields of production and life, including chemical industry, smelting, power generation and public transportation. Dynamic systems are usually composed of a large number of components, including devices such as actuators and sensors. Due to the complex models and high device integration of these systems, people are paying more and more attention to their reliability and safety issues. Actual modern engineering systems may fail due to component damage or harsh environment. If the failure is not handled in time, it will lead to a decline in system performance and may cause the entire system to lose its normal function. Actual engineering systems are usually nonlinear dynamic systems. Therefore, the development of fault-tolerant control technology that can ensure the normal operation of the system when a nonlinear system fails is very necessary. Fault-tolerant control technology can help the system to achieve self-repair or continue to operate in the event of a failure to ensure the reliability and stability of the system. By introducing a fault-tolerant mechanism, the system can identify the fault and take corresponding measures to avoid possible interruption or damage. Therefore, the development of fault-tolerant control methods is crucial to the realization of reliable nonlinear dynamic systems.

[0003] Commonly used fault-tolerant control technologies for nonlinear systems are usually passive fault-tolerant control, which is to design a single control law using robust or adaptive ideas to deal with all possible faults. Passive fault-tolerant control methods are relatively conservative and cannot achieve the best performance of the control system in the absence of faults. Active fault-tolerant control methods use the information obtained from fault detection and diagnosis to perform fault compensation or reconstruction control. Compared with passive fault-tolerant control, active fault-tolerant control has higher reliability and can deal with more complex and unknown faults.

[0004] However, most active fault-tolerant control methods for nonlinear systems are based on the premise of accurate fault compensation. When there are disturbances and uncertainties in the system, it is difficult to accurately estimate the fault, and the fault compensation error is large, which has a negative impact on the control performance of active fault tolerance. Summary of the invention

[0005] The purpose of the present invention is to at least provide an active fault-tolerant control method for a nonlinear system, which can at least solve the technical problem that faults are difficult to estimate accurately, and at least achieve the technical effect of improving the fault-tolerant control performance.

[0006] To solve the above technical problems, at least one embodiment of the present application provides an active fault-tolerant control method for a nonlinear system, comprising:

[0007] Acquire a fault estimation value of an actuator used to control a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator;

[0008] Calculating the absolute value of the fault estimation value to obtain the value of the residual signal;

[0009] Acquiring a system state signal and a system expected signal of the nonlinear system;

[0010] Calculating the difference between the system state signal and the system expected signal to obtain a system tracking error;

[0011] Based on a preset compensation calculation formula, a compensation signal is calculated according to a filtering error of a filter, the filter is used to filter the system state signal, the filtering error is the difference between an output signal of the filter and an input signal of the filter, and the compensation signal is used to compensate the system state signal;

[0012] Calculating the difference between the system tracking error and the compensation signal to obtain a compensated tracking error;

[0013] When the value of the residual signal is greater than or equal to the detection threshold, based on the calculation formula of the preset compensation control signal, the compensation control signal is calculated according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value to obtain the compensation control signal so as to control the actuator to work according to the compensation control signal; wherein, the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

[0014] At least one embodiment of the present application further provides a fault-tolerant control device for a nonlinear system, comprising:

[0015] A fault estimation acquisition module, used for acquiring a fault estimation value of an actuator used to control a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator;

[0016] A residual signal calculation module, used to calculate the absolute value of the fault estimation value to obtain the value of the residual signal;

[0017] An expected signal acquisition module, used to acquire a system state signal and a system expected signal of the nonlinear system;

[0018] A tracking error calculation module, used for calculating the difference between the system state signal and the system expected signal to obtain a system tracking error;

[0019] A compensation signal calculation module, used for calculating a compensation signal based on a preset compensation calculation formula and a filtering error of a filter, wherein the filter is used for filtering the system state signal, the filtering error is a difference between an output signal of the filter and an input signal of the filter, and the compensation signal is used for compensating the system state signal;

[0020] A compensation tracking error module, used for calculating the difference between the system tracking error and the compensation signal to obtain a compensation tracking error;

[0021] A compensation control signal module is used to obtain a compensation control signal when the value of the residual signal is greater than or equal to a detection threshold, based on a calculation formula of a preset compensation control signal, according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value, so as to control the actuator to work according to the compensation control signal; wherein the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

[0022] At least one embodiment of the present application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned active fault-tolerant control method for nonlinear systems.

[0023] At least one embodiment of the present application further provides a computer-readable storage medium storing a computer program, wherein the computer program implements the above-mentioned active fault-tolerant control method for a nonlinear system when executed by a processor.

[0024] The active fault-tolerant control method for a nonlinear system provided by an embodiment of the present application obtains a fault estimate through an observer, and the fault estimate is used to reflect the additive fault signal of the actuator; the absolute value of the fault estimate is calculated to obtain the value of the residual signal; the system state signal and the system expected signal are obtained, the difference between the system state signal and the system expected signal is calculated to obtain the system tracking error, and the filtering error of the filter is substituted into a preset compensation calculation formula to obtain the compensation signal; the difference between the system tracking error and the compensation signal is calculated to obtain the compensated tracking error; when the value of the residual signal is greater than or equal to the detection threshold, it indicates that the actuator has a fault, and a calculation formula for a preset compensation control signal is obtained by designing the Lyapunov principle, and the system tracking error, the compensation signal, the compensated tracking error and the fault estimate are substituted into the calculation formula of the preset compensation control signal to obtain the compensated control signal, so that the compensated control signal can be changed according to the fault estimate, and when there is disturbance and uncertainty, the fault can be flexibly and accurately estimated, the error of the fault compensation error can be reduced, and the control performance of active fault tolerance can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] One or more embodiments are exemplarily described by the pictures in the corresponding drawings, and these exemplary descriptions do not constitute limitations on the embodiments.

[0026] Figure 1 is a flow chart of the active fault-tolerant control method of the nonlinear system of the present application;

[0027] Figure 2 Another flow chart of the active fault-tolerant control method for nonlinear systems of the present application;

[0028] Figure 3 A schematic diagram of signal flow of the active fault-tolerant control method for a nonlinear system described in this application;

[0029] Figure 4 A schematic diagram of a fault detection result provided in an embodiment of the present application;

[0030] Figure 5 A schematic diagram of the state and fault estimation results provided by an embodiment of the present application;

[0031] Figure 6 A schematic diagram of the output signal and tracking error results provided in an embodiment of the present application. DETAILED DESCRIPTION

[0032] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. However, it will be appreciated by those skilled in the art that in the present application, many technical details are proposed in order to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present application can also be implemented. The division of the following embodiments is for the convenience of description, and the specific implementation of the present application should not be construed as any limitation, and the various embodiments can be combined and referenced with each other under the premise of no contradiction.

[0033] In order to facilitate understanding of the embodiments of the present application, relevant content about the dynamic system is first introduced here.

[0034] A dynamic system is a system that changes state over time. In recent years, dynamic systems have been widely used in various fields of production and life, including chemical industry, smelting, power generation and public transportation. Dynamic systems are usually composed of a large number of components, including devices such as actuators and sensors. Due to the complex models and high device integration of these systems, people are paying more and more attention to their reliability and safety issues. Actual modern engineering systems may fail due to component damage or harsh environment. If the failure is not handled in time, it will lead to a decline in system performance and may cause the entire system to lose its normal function. Actual engineering systems are usually nonlinear dynamic systems. Therefore, the development of fault-tolerant control technology that can ensure the normal operation of the system when a nonlinear system fails is very necessary. Fault-tolerant control technology can help the system to achieve self-repair or continue to operate in the event of a failure to ensure the reliability and stability of the system. By introducing a fault-tolerant mechanism, the system can identify the fault and take corresponding measures to avoid possible interruption or damage. Therefore, the development of fault-tolerant control methods is crucial to the realization of reliable nonlinear dynamic systems.

[0035] At present, the commonly used fault-tolerant control technology for nonlinear systems is usually passive fault-tolerant control, that is, a single control law is designed using robust or adaptive ideas to deal with all possible faults. However, the passive fault-tolerant control method is relatively conservative and cannot achieve the best performance of the control system in the absence of faults. The active fault-tolerant control method uses the information obtained from fault detection and diagnosis to perform fault compensation or reconstruction control. Compared with passive fault-tolerant control, active fault-tolerant control has higher reliability and can deal with more complex and unknown faults. In addition, most of the current active fault-tolerant control methods for nonlinear systems are based on the premise of accurate fault compensation. When there are disturbances and uncertainties in the system, it is difficult to accurately estimate the fault, which will lead to large fault compensation errors, which in turn have an adverse effect on the performance of active fault-tolerant control.

[0036] Based on the above situation, in order to meet the needs of practical applications, for nonlinear systems, an active fault-tolerant control method with a fault error compensation mechanism is urgently needed to deal with the problem of difficult to accurately estimate faults caused by disturbances and uncertainties, and to improve the robustness and reliability of the system.

[0037] In order to solve the technical problem that fault estimation is difficult to be accurate due to the above-mentioned disturbances and uncertainties, the present invention proposes a fault-tolerant control method for a nonlinear system. The implementation details of the fault-tolerant control method for a nonlinear system of this embodiment are described in detail below. The following content is only the implementation details provided for the convenience of understanding and is not necessary for the implementation of this solution.

[0038] Embodiment 1:

[0039] The active fault-tolerant control method for nonlinear systems of this embodiment can be applied to electronic devices with communication, computing and data storage capabilities. The specific process can be as follows: Figure 1 As shown, including:

[0040] Step 110: obtaining a fault estimation value of an actuator for controlling a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator.

[0041] Specifically, the observer estimates the state signal of the nonlinear system that cannot be directly measured, such as the fault estimation value, based on the measurable output signal of the nonlinear system. Additive fault signal is the unknown input acting on the nonlinear system. When the nonlinear system is operating normally, it is zero. The appearance of unknown input will cause the system output to change independently of the known input, thus generating a fault signal.

[0042] In this embodiment, the system model of the nonlinear system contains the fault of the actuator and the unknown time-varying interference. The system model of the nonlinear system is shown in formula (1):

[0043]

[0044] In formula (1), x1(t),…,x n (t), i = 1, ..., n represents the system state signal of the nonlinear system, u0(t) is the control actuator to be designed to work; u f (t) represents the unknown actuator fault, and y(t) represents the output signal of the nonlinear system; is a nonlinear function, b is a known input gain constant; d i (t), i = 1, ..., n represents unknown time-varying interference, satisfying |d i (t)|≤D i , where D i is an unknown constant. Most nonlinear systems can be expressed by equation (1) through appropriate transformation, such as electromechanical systems, robotic arms, circuit systems, spacecraft, etc.

[0045] In this embodiment, in order to design an observer using the output signal and obtain the system state signal and fault estimate First, rewrite the system model of the nonlinear system in equation (1) into the form of equation (2), which is as follows:

[0046]

[0047] In formula (2), H(x(t))=[h1(x1(t)),…,h n(x(t))] T , d(t)=[d1(t),…,d n (t)] T , C=[1,0,…,0] 1×n Formula (2) expresses the scalar in formula (1) in vector form. Rewriting formula (1) into the form of formula (2) makes it easier to design the observer model. The observer model is shown in formula (3):

[0048]

[0049] Formula (3) is the fault indirect estimator, is a dummy variable related to failure The estimated value of Dummy variables The estimated value of The estimated value of the system state x is estimated at the same time, so as to estimate the fault of the actuator and obtain the estimated fault value of the actuator In formula (3) is the estimated value of the system state x, It is the fault of the actuator f The estimated value of .

[0050] In formula (3), L = [l1,…,l n ] T is the observer gain vector, the observer gain vector L=[l1,…,l n ] T It can be obtained by using Lyapunov stability theory, and its specific expression is obtained according to formula (1). First, construct the Lyapunov function of the estimated error system, and use formula (4) to ensure the monotonically decreasing property of the Lyapunov function, that is, the fault estimation value can be realized. The boundedness of the observer gain vector L = [l1,…,l n ] T It is obtained by the linear matrix inequality of formula (4), where formula (4) is as follows:

[0051]

[0052] Among them, L h is the Lipschitz constant of the function, Σ 1,2 =P1B-ω(A T +ωBB T )BP2, p1 and P2 are positive symmetric matrices, and ω and ε are arbitrarily given positive constants.

[0053] Step 120, calculating the absolute value of the fault estimation value to obtain the value of the residual signal.

[0054] Specifically, obtain the fault estimate Calculate the absolute value of the fault estimate The value of the residual signal r(t) is obtained, which is recorded as The value of the residual signal quantifies the extent to which the actuator has failed.

[0055] Step 130: Acquire a system state signal and a system expected signal of the nonlinear system.

[0056] Specifically, the system expected signal includes the reference signal y d and the state expectation signal α i,c . Reference signal y d The trajectory signal representing the output tracking of the nonlinear system, such as the swing angle of the robot arm as the output signal of the nonlinear system, needs to track a predetermined sinusoidal signal, which belongs to the reference signal y d α i,c is the system status signal x i Estimated value of The signal that needs to be tracked is a virtual signal in controller design.

[0057] Step 140, calculating the difference between the system state signal and the system expected signal to obtain a system tracking error.

[0058] Specifically, the output signal of the nonlinear system is determined according to the system state signal, and then the coordinate transformation is performed. For example, according to the output signal y=x1 of the nonlinear system and the reference signal y d Construct the coordinate transformation shown in formula (a):

[0059]

[0060] In formula (a), z1,…,z n is the system tracking error, α i-1 is the input signal of the first-order command filter, α i,c is the output signal of the first-order command filter, which can be (α i,c -α i-1 ) is used as the filtering error. The first-order command filter is a low-pass filter. Formula (a) is used to calculate the system tracking error value. The principle is to construct the output tracking error and the state tracking error. i,c is generated by the following first-order command filter:

[0061]

[0062] in is a preset constant, α i-1 It is the virtual control signal that needs to be designed later. The construction principle of formula (b) is a construction principle of a low-pass filter. Formula (b) can avoid directly using α in subsequent calculations. i,c The derivative of i,c The derivative of can be directly replaced by formula (b), which is used to generate from .

[0063] Step 150, based on a preset compensation calculation formula, calculate a compensation signal according to a filtering error of the filter, the filter is used to filter the system status signal, the filtering error is the difference between the output signal of the filter and the input signal of the filter, and the compensation signal is used to compensate the system status signal.

[0064] Specifically, the preset compensation calculation formula uses the compensation signal ξ to increase with time. i The upper bound of the approximation filtering error (α i,c -α i-1 ) is constructed. The filter is also a first-order command filter, which filters the system state signal, and the filtering error (α i,c -α i-1 ) is the difference between the output signal of the filter and the input signal of the filter, and the compensation signal ξ i Compensate the system state signal so that the filtered error signal has a smaller bound.

[0065] Step 160, calculating the difference between the system tracking error and the compensation signal to obtain a compensated tracking error.

[0066] Specifically, the calculation converts the system tracking error z i Subtract the compensation signal ξ i The difference is the compensation tracking error v i That is v i =z i -ξ i ,i=1,…,n. Compensation tracking error v i It can indirectly reflect the error of the output signal y of the nonlinear system because the error between the output signal y of the nonlinear system and the tracking signal is z1. If the tracking error v is guaranteed to be compensated i is relatively small, then the output tracking error z1 will also be relatively small.

[0067] Step 170, when the value of the residual signal is greater than or equal to the detection threshold, based on the calculation formula of the preset compensation control signal, the compensation control signal is calculated according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value to obtain the compensation control signal so as to control the actuator to work according to the compensation control signal; wherein, the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

[0068] Specifically, the detection threshold R is artificially set in advance. th , the detection threshold R th As a reference threshold for determining whether the actuator is faulty, the value of the residual signal r(t) is compared with the detection threshold R th Compare and determine whether a fault occurs. Specifically, the following fault detection logic is used for judgment:

[0069]

[0070] When the residual signal value r(t) is greater than or equal to the detection threshold R th When the residual signal value r(t) is less than the detection threshold R th It indicates that the actuator has no fault.

[0071] The calculation formula of the preset compensation control signal is designed for the case of actuator failure, using the system tracking error z i Calculate the feedback term of the tracking error, using the Nonlinear function Calculate the feedback term of the nonlinear function of the system, using α n,c Calculate the feedback term of the command filter output and use the compensated tracking error v i Calculate the feedback term of the disturbance estimate, using the compensation signal ξ i Calculate the feedback term of the compensation signal and use the compensation tracking error v i Calculate the feedback term to compensate for the tracking error, using the fault estimate Calculate the fault compensation term, use the Lyapunov principle to design the recursive compensation control signal u0, sum the feedback term of the system nonlinear function, the feedback term of the command filter output, the feedback term of the disturbance estimation, the feedback term of the compensation signal, the feedback term of the compensation tracking error and the fault compensation term to obtain the compensation control signal u0.

[0072] The active fault-tolerant control method of the nonlinear system of this embodiment obtains the fault estimation value through the observer The fault estimate is used to reflect the additive fault signal of the actuator; the absolute value of the fault estimate is calculated to obtain the value of the residual signal Get system status signal x iand the system expected signal y d , α i,c , calculate the system state signal x i and the system expected signal y d , α i,c The difference between the two is the system tracking error z i , substitute the filter error of the filter into the preset compensation calculation formula, and calculate the compensation signal ξ i ; Calculate the difference between the system tracking error and the compensation signal to obtain the compensated tracking error v i ; When the value of the residual signal r(t) is greater than or equal to the detection threshold R th When , it indicates that the actuator fails. The calculation formula of the preset compensation control signal is obtained by Lyapunov principle design, and the system tracking error z i , the compensation signal ξ i , the compensation tracking error v i and the fault estimate Substitute the preset compensation control signal into the calculation formula to obtain the compensation control signal u0, so that the compensation control signal can be calculated according to the fault estimation value By making changes, it can flexibly and accurately estimate the fault when there are disturbances and uncertainties, reduce the error of fault compensation error, and improve the control performance of active fault tolerance.

[0073] In one embodiment, the step of obtaining the system status signal and the system expectation signal includes:

[0074] Acquire a system state signal, an input expected signal and a state expected signal; wherein the system expected signal includes the input expected signal and the state expected signal;

[0075] Based on the relationship between the system state signal and the system output signal, calculating the system output signal according to the system state signal;

[0076] The step of calculating the difference between the system state signal and the system expected signal to obtain the system tracking error comprises:

[0077] Calculating the difference between the system output signal and the input expected signal to obtain an output tracking error;

[0078] The difference between the state expectation signal and the system state signal is calculated to obtain a state tracking error; wherein the system tracking error includes outputting the tracking error and the state tracking error.

[0079] In this embodiment, the system expected signal includes a reference signal y d and the state expectation signal α i,c , the system output signal y can be expressed by the system state signal xi To characterize, the system state signal x i There are multiple, using the subscript i to identify and distinguish, according to the system state signal x i The relationship between the system output signal y determines the system output signal, such as the system status signal x i The relationship between the system output signal y is y=x1, then the system state signal x1 can be used to represent the system output signal y. d The difference between the two is used to obtain the output tracking error z1, which is used to track the system output signal y=x1. Subtract the state expected signal α i,c The difference is taken as the state tracking error z2-z n That is, according to the output signal y=x1 of the nonlinear system and the reference signal y d Construct the coordinate transformation shown in formula (a):

[0080]

[0081] In formula (a), z1,…,z n is the system tracking error, α i-1 is the input signal of the first-order command filter, α i,c is the output signal of the first-order command filter, which can be (α i,c -α i-1 ) is used as the filtering error. The first-order command filter is a low-pass filter. Formula (a) is used to calculate the system tracking error zi. The principle is to construct the output tracking error and the state tracking error. i,c is generated by the following first-order command filter:

[0082]

[0083] in is a preset constant, α i-1 It is the virtual control signal that needs to be designed later. The construction principle of formula (b) is a construction principle of a low-pass filter. Formula (b) can avoid directly using α in subsequent calculations. i,c The derivative of i,c The derivative of can be directly replaced by formula (b), which is used to generate from .

[0084] In one embodiment, the preset compensation calculation formula is as follows:

[0085]

[0086] in, ξi represents the compensation signal corresponding to the i-th system state signal, k i , i=1,…,n represents a positive constant, α i+1,c , i=1,…,n represents the output signal of the filter corresponding to the i+1th system state signal, α i represents the input signal of the filter corresponding to the i-th system state signal, μ i ,i=1,…,n represents a positive constant,∈ i represents the positive monotonically decreasing function corresponding to the i-th system status signal, and i represents the sequence number of the system status signal. i For example, the monotonically decreasing function exp(-0.05t), the positive constant k i and μ i Determined in advance based on experience. The compensation signal ξ is calculated in this way i In order to prevent filtering error (α i,c -α i-1 ) increases excessively, the preset compensation calculation formula increases with time, making the compensation signal ξ i The upper bound of the filtering error (α i,c -α i-1 ) is close to being constructed. The filter is also a first-order command filter, which filters the system state signal, and the filtering error (α i,c -α i-1 ) is the difference between the output signal of the filter and the input signal of the filter, and the compensation signal ξ i Compensate the system status signal to make the system status signal more accurate.

[0087] In one embodiment, the calculation formula of the preset compensation control signal is obtained by back-stepping the virtual control signal using the Lyapunov principle; wherein the expression of the virtual control signal is as follows:

[0088]

[0089] in, x1 represents the first system status signal, represents the error adaptive compensation term of the i-th system state signal, α i , i=1,…,n-1 represents the i-th virtual control signal, k i , i=1,…,n-1 represents a positive constant, z i , i=1,…,n-1 represents the system tracking error of the i-th system state signal, y d represents the input expected signal, v i, i=1,…,n-1 represents the compensation tracking error of the i-th system state signal, ∈ i , i=1,…,n-1 represents the positive monotonically decreasing function corresponding to the i-th system state signal, μ i ,i=1,...,n-1 represents a positive constant, ξ i , i=1,…,n-1 represents the compensation signal of the i-th system state signal, α i,c , i=1,…,n-1 represents the state expectation signal of the i-th system state signal, c i ,i=1,...,n-1 represents a normal number, represents the estimated value of the i-th system state signal, Represents a nonlinear function about the system state signal. In this embodiment, the construction method of the calculation formula of the preset compensation control signal is the backstepping method in adaptive control. The design is performed using the Lyapunov principle, and a virtual control signal is constructed in the form of recursion, so that the actual control signal, i.e., the preset compensation control signal, is obtained in the last step of the recursion. The nonlinear system is affected by bounded unknown disturbances, and there are state estimation errors and fault estimation errors. Therefore, an adaptive compensation term is designed to compensate for the error generated in the intermediate process, i.e., an error adaptive compensation term. The error adaptive compensation term is shown as follows:

[0090]

[0091] In the formula, this formula characterizes the update law of the error adaptive compensation term, and its error includes system disturbance error and state fault estimation error. The construction principle of this formula is based on Lyapunov theory, which can ensure the boundedness of the error.

[0092] In one embodiment, the calculation formula of the preset compensation control signal is as follows:

[0093]

[0094] in, represents the online fault compensation item, u0 represents the compensation control signal, b represents a positive constant, k n represents a positive constant, z n represents the system tracking error, x1,…,x n A signal indicating the system status, represents the estimated value of the system state signal x, Indicates about The nonlinear function of n,c represents the output signal of the filter corresponding to the nth system state signal, represents the error adaptive compensation term of the nth system state signal, v n represents the compensated tracking error of the nth system state signal, ∈ n represents the positive monotonically decreasing function corresponding to the nth system state signal, ξ n represents the compensation signal of the nth system state signal, μ n represents a positive constant, v n-1 represents the compensated tracking error of the n-1th system state signal, t represents the time variable, Indicates the moment when the actuator fails. In this embodiment, it is assumed that the actuator is at time t f A failure has occurred f , and in The fault is detected at all times, that is, for In the period of time, there is a residual signal value r(t) greater than or equal to the detection threshold R th ,r(t)>R th .

[0095] The indicator function is denoted as I d (t), that is

[0096]

[0097] The online fault compensation term is defined as Design an actual active fault-tolerant control law with fault compensation, that is, the calculation formula of the preset compensation control signal. This term is constructed because the actuator has additive faults. The design of this online fault compensation term can compensate for the impact of the actuator fault. However, due to the fault estimation value It is not completely accurate, and there is a fault estimation error. Therefore, the fault estimation error is taken as part of the intermediate error and used The adaptive compensation term generated To compensate, that is, through Make compensation.

[0098] In one embodiment, the method further comprises:

[0099] When the value of the residual signal is less than the detection threshold, based on the calculation formula of the preset fault-free control signal, the fault-free control signal is calculated according to the system tracking error, the compensation signal and the compensated tracking error, so as to control the actuator to work according to the fault-free control signal; wherein, the calculation formula of the preset fault-free control signal is designed using the Lyapunov principle.

[0100] In this embodiment, when the value r(t) of the residual signal is less than the detection threshold R thWhen , it indicates that the actuator has no fault and there is no need to set the online fault compensation item Λ f (t), design the actual active fault-tolerant control law with fault compensation, that is, the calculation formula of the preset compensation control signal. This term is constructed because the actuator has additive faults. The design of this online fault compensation term can compensate for the impact of the actuator fault. Using the system tracking error z i Calculate the feedback term of the tracking error, using the Nonlinear function Calculate the feedback term of the nonlinear function of the system, using α n,c Calculate the feedback term of the command filter output and use the compensated tracking error v i Calculate the feedback term of the disturbance estimate, using the compensation signal ξ i Calculate the feedback term of the compensation signal and use the compensation tracking error v i Calculate the feedback term for compensating the tracking error, use the Lyapunov principle to design the recursive compensation control signal u0, sum the feedback term of the system nonlinear function, the feedback term of the command filter output, the feedback term of the disturbance estimation, the feedback term of the compensation signal and the feedback term for compensating the tracking error to obtain the fault-free control signal u0.

[0101] In one embodiment, the calculation formula of the preset fault-free control signal is as follows:

[0102]

[0103] in, u0 represents the fault-free control signal, b represents a positive constant, k n represents a positive constant, z n represents the system tracking error, x1,…,x n A signal indicating the system status, represents the estimated value of x, Indicates about The nonlinear function of n,c represents the output signal of the filter corresponding to the nth system state signal, represents the error adaptive compensation term of the nth system state signal, v n represents the compensated tracking error of the nth system state signal, ∈ n represents the positive monotonically decreasing function corresponding to the nth system state signal, ξ n represents the compensation signal of the nth system state signal, μ n represents a positive constant, v n-1represents the compensated tracking error of the n-1th system state signal. In this embodiment, each item on the right side of the calculation formula of the preset fault-free control signal is respectively the feedback item of the tracking error, the feedback item of the system nonlinear function, the feedback item of the command filter output, the feedback item of the disturbance estimation, the feedback item of the compensation signal, and the feedback item of the compensated tracking error. The purpose of the calculation formula of the preset fault-free control signal is to ensure the Lyapunov stability of the system error dynamics equation.

[0104] Embodiment 2:

[0105] The active fault-tolerant control method for nonlinear systems of this embodiment can be applied to electronic devices with communication, computing and data storage capabilities. The specific process can be as follows: Figure 2 As shown, including:

[0106] Step 1: Use the following formula to represent the system model of the nonlinear system with actuator faults and unknown disturbances, and obtain the output signal of the target nonlinear system model.

[0107]

[0108] In this system, x1(t),…,x n (t) represents the state of the system, And x(t) is defined as u0(t) is the input signal of the system to be designed; u f (t) represents unknown actuator fault; y(t) represents the system output; is a nonlinear function; b is a known input gain constant; d i (t), i = 1, ..., n represents unknown time-varying interference, satisfying |d i (t)|≤D i , where D i is an unknown constant. Most nonlinear systems can be expressed by equation (1) through appropriate transformation, such as electromechanical systems, robotic arms, circuit systems, spacecraft, etc.

[0109] Step 2: Design an observer using the output signal to estimate the state and fault simultaneously.

[0110] Rewrite the system equation (1) as follows:

[0111]

[0112] where H(x(t))=[h1(x1(t)),…,h n (x(t))] T , d(t)=[d1(t),…,d n (t)] T ,as well as C=[1,0,…,0] 1×n Formula (2) expresses the scalar in formula (1) in vector form, rewriting formula (1) into the form of formula (2), which is convenient for the design of the observer formula (3).

[0113] Design state and fault observers as:

[0114]

[0115] in, A dummy variable related to failure The estimate of Formula (3) is the indirect fault estimator. and status Simultaneous estimation is performed to achieve fault estimation.

[0116] in and They are x and u respectively f The estimated value of L = [l1,…,l n ] T is the observer gain vector, which is obtained by using the Lyapunov stability theory, but the specific expression is obtained based on system (1). First, the Lyapunov function of the estimation error system is constructed. Equation (4) can ensure the monotonically decreasing property of the Lyapunov function, that is, the boundedness of the estimation error can be achieved. The observer gain vector L = [l1,…,l n ] T It is found through the following linear matrix inequality:

[0117]

[0118] Among them, in formula (4) Σ 1,2 =P1B-ω(A T +ωBB T )BP2, L h is the Lipschitz constant of function H, P1 and P2 are positive symmetric matrices; ω and ε are arbitrarily given positive constants.

[0119] Step 3: Use the fault estimation value to generate a residual signal to determine whether a fault has occurred.

[0120] According to the fault estimation value, the residual signal for fault detection is designed, which is recorded as It is used as an indicator to detect the occurrence of a fault. Given a detection threshold R th , use the following fault detection logic to determine whether a fault occurs:

[0121]

[0122] Step 4: Design an Active Fault-Tolerant Controller

[0123] First, according to the system output y=x1 and the reference signal y d Construct the following coordinate transformation, with reference signal y d The trajectory signal that represents the system output tracking, for example, the swing angle of the robot arm (i.e., the system output) needs to track a given sinusoidal signal (reference signal). i,c is the state x i The estimated value of is a signal that needs to be tracked and is a virtual signal in controller design. i-1 and α i,c are the input and output of the first-order command filter (i.e., a low-pass filter), so (α i,c -α i-1 ) as the filtering error.

[0124] z1 = x1-y d , (a)

[0125]

[0126] Formula (a) is used to calculate the tracking error. The principle is to construct the output tracking error and the state tracking error. i,c is generated by the following first-order command filter:

[0127]

[0128] in is a given constant, α i-1 is the virtual control signal that needs to be designed next. The construction principle of formula (b) is a low-pass filter, which avoids directly using α in subsequent calculations. i,c The derivative of i,c The derivative of can be directly replaced by formula (b), which is used to generate from .

[0129] definition In order to prevent filtering error (α i,c -α i-1 ) becomes very large, we introduce a compensation signal ξ i , is given by:

[0130]

[0131] where k i and μ i is a positive constant, ξ i (0) = 0. Define the compensation tracking error as v i =zi -ξ i ,i=1,…,n. The compensation tracking error vi can indirectly reflect the error of the output signal y because the output signal error is z1. Compensation signal ξ i The construction principle is to increase the compensation signal ξ as time increases. i The upper bound of the filtering error (α i,c -α i-1 ). If the compensation error can be kept small, that is, by ensuring the compensation tracking error v i is relatively small, then the filtering error is also relatively small. ∈ i is a given positive monotonically decreasing function, such as exp(-0.05t).

[0132] Design virtual control signals:

[0133]

[0134] The construction method of formula (5) is the backstepping method in adaptive control. The principle is to use the Lyapunov principle to design. The virtual control signal is constructed in the form of recursion, so that the actual control signal is obtained in the last step of the recursion.

[0135] The system is affected by bounded unknown disturbances, and there are state estimation errors and fault estimation errors. Therefore, an adaptive compensation term is designed to compensate for the errors generated in the intermediate process:

[0136]

[0137] Formula 6 is the update law of the adaptive compensation term of the error (including system disturbance, state fault estimation error, etc.). The construction principle is based on the Lyapunov theory, which can ensure the boundedness of the error.

[0138] Design the actual control law under fault-free conditions:

[0139]

[0140] Each term on the right side of formula (7) is: feedback term of tracking error, feedback term of system nonlinear function, feedback term of command filter output, feedback term of disturbance estimation, feedback term of compensation signal, feedback term of compensation tracking error. They are all related to the variables obtained in the previous design, and the purpose is to ensure the Lyapunov stability of the system error dynamics equation.

[0141] Assume that at time t f A failure has occurred f , and in The fault is detected at all times, that is, for r(t)>R th . Let the indicator function be Id (t), that is

[0142]

[0143] The online fault compensation term is defined as Design a practical active fault-tolerant control law with fault compensation as

[0144]

[0145] Formula (8) is constructed because the system has additive actuator faults, and the fault compensation term is designed to compensate for the impact of the actuator fault. However, since the fault estimation is not completely accurate, there is a fault estimation error. Therefore, we regard the fault estimation error as part of the intermediate error and use the adaptive compensation term \hat{W}_n generated by formula (6) to compensate, which is the fourth to last term on the right side of formula (8).

[0146] The specific process of active fault-tolerant control law design method is as follows: Figure 3 shown.

[0147] Step 5: Generate the final control signal u0 and transmit it to the actuator to perform the corresponding action.

[0148] As an example, a robotic arm system is selected as a specific simulation embodiment. It is assumed that a fault occurs at 15 seconds in the simulation, and a given fault detection threshold is 0.01. Figure 4 is the fault detection result, Figure 5 are the status and fault estimation results, Figure 6 is the output signal and tracking error curve. It can be seen that the fault can be detected in time after the fault occurs, and the state and fault estimation errors are bounded, and the output tracking of the nonlinear system can be achieved in the case of a fault and a small tracking error can be guaranteed.

[0149] The active fault-tolerant control method for a nonlinear system of the present embodiment includes: obtaining an output signal of a target nonlinear system model; using the output signal to design an observer to simultaneously estimate a state and a fault; using a fault estimation value to generate a residual signal, once the residual signal exceeds a given threshold, it is determined that a fault occurs, otherwise it is determined that the fault does not occur; using a reference signal, a system output signal and a state estimation value to design a controller under fault-free conditions; when a fault is detected, using the fault estimation value to obtain a fault compensation item, and performing fault compensation in the controller; designing an adaptive compensation item to compensate for errors generated in the intermediate process, so as to achieve accurate fault tolerance of the fault.

[0150] Embodiment three:

[0151] Step 1: The system model of the nonlinear system with actuator faults and unknown disturbances is expressed as follows:

[0152]

[0153] In this system, x1(t),…,x n (t) represents the state of the system, x(t) is defined as u0(t) is the input signal of the system to be designed; u f (t) represents unknown actuator fault; y(t) represents the system output; is a nonlinear function; b is a known input gain constant; d i (t), i = 1, ..., n represents unknown time-varying interference, satisfying |d i (t)|≤D i , where D i is an unknown constant.

[0154] Step 2: Design the output observer

[0155] Rewrite system (1) as follows:

[0156]

[0157] where H(x(t))=[h1(x1(t)),…,h n (x(t))] T ,d(t)=[d1(t),…,d n (t)] T ,as well as C=[1,0,…,0] 1×n .

[0158] Design state and fault observers as

[0159]

[0160] in and They are x and u respectively f The estimated value of L = [l1,…,l n ] T is the observer gain vector, which is obtained by the following linear matrix inequality:

[0161]

[0162] Among them, in formula (4) Σ 1,2 =P1B-ω(A T +ωBB T )BP2, L his the Lipschitz constant of function H, P1 and P2 are positive symmetric matrices; ω and ε are arbitrarily given positive constants.

[0163] According to the fault estimation value, the residual signal for fault detection is designed, which is recorded as It is used as an indicator to detect the occurrence of a fault. Given a detection threshold R th , the following fault detection logic is used:

[0164]

[0165] Step 3: Design an Active Fault-Tolerant Controller

[0166] First, according to the system output y=x1 and the reference signal y d Construct the following coordinate transformation:

[0167] z1=x1-y d ,

[0168]

[0169] where α i,c is generated by the following first-order command filter:

[0170]

[0171] in is a given constant, α i-1 It is the virtual control signal that needs to be designed next.

[0172] definition In order to prevent filtering error (α i,c -α i-1 ) becomes very large, and the compensation signal ξ is introduced i , is given by:

[0173]

[0174] where k i and μ i is a positive constant, ξ i (0) = 0. Define the compensation tracking error as v i =z i -ξ i ,i=1,…,n.

[0175] Design virtual control signals:

[0176]

[0177] Design error adaptive compensation term:

[0178]

[0179] Design the actual control law under fault-free conditions:

[0180]

[0181] Assume that at time t f A failure has occurred f , and in The fault is detected at all times, that is, for r(t)>R th . Let the indicator function be I d (t), that is

[0182]

[0183] The online fault compensation term is defined as Design a practical active fault-tolerant control law with fault compensation as

[0184]

[0185] Beneficial effects: The present invention provides an active fault-tolerant control method for a nonlinear system, an observer is designed for fault detection, state and fault estimation, and the designed controller has an estimation error adaptive compensation mechanism. The problem of handling uncertainty estimation errors is transformed into a new interference elimination problem, and a disturbance adaptive compensation term is designed, so that the system has stronger robustness and can compensate for the fault more quickly after an actuator fault occurs.

[0186] Embodiment 4:

[0187] Another embodiment of the present application relates to an active fault-tolerant control device for a nonlinear system. The implementation details of the fault-tolerant control device for a nonlinear system of this embodiment are described in detail below. The following content is only the implementation details provided for easy understanding and is not necessary for the implementation of this solution. The active fault-tolerant control device for a nonlinear system of this embodiment includes a fault estimation acquisition module, a residual signal calculation module, an expected signal acquisition module, a tracking error calculation module, a compensation signal calculation module, a compensation tracking error module and a compensation control signal module.

[0188] A fault estimation acquisition module, used for acquiring a fault estimation value of an actuator used to control a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator;

[0189] A residual signal calculation module, used to calculate the absolute value of the fault estimation value to obtain the value of the residual signal;

[0190] An expected signal acquisition module, used to acquire a system state signal and a system expected signal of the nonlinear system;

[0191] A tracking error calculation module, used for calculating the difference between the system state signal and the system expected signal to obtain a system tracking error;

[0192] A compensation signal calculation module, used for calculating a compensation signal based on a preset compensation calculation formula and a filtering error of a filter, wherein the filter is used for filtering the system state signal, the filtering error is a difference between an output signal of the filter and an input signal of the filter, and the compensation signal is used for compensating the system state signal;

[0193] A compensation tracking error module, used for calculating the difference between the system tracking error and the compensation signal to obtain a compensation tracking error;

[0194] A compensation control signal module is used to obtain a compensation control signal when the value of the residual signal is greater than or equal to a detection threshold, based on a calculation formula of a preset compensation control signal, according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value, so as to control the actuator to work according to the compensation control signal; wherein the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

[0195] It is worth mentioning that all modules involved in this embodiment are logic modules. In practical applications, a logic unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, in order to highlight the innovative part of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed by this application, but this does not mean that there are no other units in this embodiment.

[0196] Embodiment five:

[0197] Another embodiment of the present application relates to an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the active fault-tolerant control method for nonlinear systems in the above-mentioned embodiments.

[0198] Among them, the memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripherals, voltage regulators, and power management circuits, which are well known in the art and are therefore not further described herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on a wireless medium via an antenna, and further, the antenna also receives data and transmits the data to the processor.

[0199] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0200] Embodiment six:

[0201] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program, which implements the above method embodiment when executed by a processor.

[0202] That is, those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as: ROM), random access memory (Random Access Memory, referred to as: RAM), disk or optical disk and other media that can store program codes.

[0203] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. An active fault-tolerant control method for a nonlinear system, characterized in that: include: 。 Acquiring a fault estimation value of an actuator for controlling a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator; Calculating the absolute value of the fault estimation value to obtain the value of the residual signal; Acquiring a system state signal and a system expected signal of the nonlinear system; Calculating the difference between the system state signal and the system expected signal to obtain a system tracking error; Based on a preset compensation calculation formula, a compensation signal is calculated according to a filtering error of a filter, the filter is used to filter the system state signal, the filtering error is the difference between an output signal of the filter and an input signal of the filter, and the compensation signal is used to compensate the system state signal; Calculating the difference between the system tracking error and the compensation signal to obtain a compensated tracking error; When the value of the residual signal is greater than or equal to the detection threshold, based on the calculation formula of the preset compensation control signal, the compensation control signal is calculated according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value to obtain the compensation control signal so as to control the actuator to work according to the compensation control signal; wherein, the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

2. The active fault-tolerant control method according to claim 1, characterized in that: The step of obtaining the system status signal and the system expectation signal comprises: Acquire a system state signal, an input expected signal and a state expected signal; wherein the system expected signal includes the input expected signal and the state expected signal; Based on the relationship between the system state signal and the system output signal, calculating the system output signal according to the system state signal; The step of calculating the difference between the system state signal and the system expected signal to obtain the system tracking error comprises: Calculating the difference between the system output signal and the input expected signal to obtain an output tracking error; The difference between the state expectation signal and the system state signal is calculated to obtain a state tracking error; wherein the system tracking error includes outputting the tracking error and the state tracking error.

3. The active fault-tolerant control method according to claim 1, characterized in that: The preset compensation calculation formula is as follows: in, ξ i represents the compensation signal corresponding to the i-th system state signal, k i , i=1,…,n represents a positive constant, α i+1,c , i=1,…,n represents the output signal of the filter corresponding to the i+1th system state signal, α i represents the input signal of the filter corresponding to the i-th system state signal, μ i ,i=1,…,n represents a positive constant,∈ i represents a positive monotonically decreasing function corresponding to the i-th system status signal, and i represents the sequence number of the system status signal.

4. The active fault-tolerant control method according to claim 1, characterized in that: The calculation formula of the preset compensation control signal is obtained by back-stepping the virtual control signal using the Lyapunov principle; wherein the expression of the virtual control signal is as follows: in, i=1,…,n-1, i=1,…,n-1, i=1,…,n-1, x1 represents the first system status signal, represents the error adaptive compensation term of the i-th system state signal, α i , i=1,…,n-1 represents the i-th virtual control signal, k i , i=1,…,n-1 represents a positive constant, z i , i=1,…,n-1 represents the system tracking error of the i-th system state signal, y d represents the input expected signal, v i , i=1,…,n-1 represents the compensation tracking error of the i-th system state signal, ∈ i , i=1,…,n-1 represents the positive monotonically decreasing function corresponding to the i-th system state signal, μ i ,i=1,...,n-1 represents a positive constant, ξ i , i=1,…,n-1 represents the compensation signal of the i-th system state signal, α i,c , i=1,…,n-1 represents the state expectation signal of the i-th system state signal, c i ,i=1,...,n-1 represents a positive constant, i=2,…,n-1 represents the estimated value of the i-th system state signal, i=1, ..., n-1 represents a nonlinear function of the system state signal.

5. The active fault-tolerant control method according to claim 1, characterized in that: The calculation formula of the preset compensation control signal is as follows: in, represents the online fault compensation item, u0 represents the compensation control signal, b represents a positive constant, k n represents a positive constant, z n represents the tracking error of the system, x=x n =[x1,…,x n ] T ,x1,…,x n A signal indicating the system status, represents the estimated value of the system state signal x, Indicates about The nonlinear function of n,c represents the output signal of the filter corresponding to the nth system state signal, represents the error adaptive compensation term of the nth system state signal, v n represents the compensated tracking error of the nth system state signal, ∈ n represents the positive monotonically decreasing function corresponding to the nth system state signal, ξ n represents the compensation signal of the nth system state signal, μ n represents a positive constant, v n-1 represents the compensated tracking error of the n-1th system state signal, t represents the time variable, Indicates the moment when the actuator fails. represents the fault estimation value.

6. The active fault-tolerant control method according to claim 1, characterized in that: The method further comprises: When the value of the residual signal is less than the detection threshold, based on the calculation formula of the preset fault-free control signal, the fault-free control signal is calculated according to the system tracking error, the compensation signal and the compensated tracking error, so as to control the actuator to work according to the fault-free control signal; wherein, the calculation formula of the preset fault-free control signal is designed using the Lyapunov principle.

7. The active fault-tolerant control method according to claim 6, characterized in that: The calculation formula of the preset fault-free control signal is as follows: in, u0 represents the fault-free control signal, b represents a positive constant, k n represents a positive constant, z n represents the system tracking error, x1,…,x n A signal indicating the system status, represents the estimated value of x, Indicates about The nonlinear function of n,c represents the output signal of the filter corresponding to the nth system state signal, represents the error adaptive compensation term of the nth system state signal, v n represents the compensated tracking error of the nth system state signal, ∈ n represents the positive monotonically decreasing function corresponding to the nth system state signal, ξ n represents the compensation signal of the nth system state signal, μ n represents a positive constant, v n-1 Represents the compensated tracking error of the n-1th system status signal.

8. An active fault-tolerant control device for a nonlinear system, characterized in that: include: A fault estimation acquisition module, used for acquiring a fault estimation value of an actuator used to control a nonlinear system through an observer, wherein the fault estimation value is used to reflect an additive fault signal of the actuator; A residual signal calculation module, used to calculate the absolute value of the fault estimation value to obtain the value of the residual signal; An expected signal acquisition module, used to acquire a system state signal and a system expected signal of the nonlinear system; A tracking error calculation module, used for calculating the difference between the system state signal and the system expected signal to obtain a system tracking error; A compensation signal calculation module, used for calculating a compensation signal based on a preset compensation calculation formula and a filtering error of a filter, wherein the filter is used for filtering the system state signal, the filtering error is a difference between an output signal of the filter and an input signal of the filter, and the compensation signal is used for compensating the system state signal; A compensation tracking error module, used for calculating the difference between the system tracking error and the compensation signal to obtain a compensation tracking error; A compensation control signal module is used to obtain a compensation control signal when the value of the residual signal is greater than or equal to a detection threshold, based on a calculation formula of a preset compensation control signal, according to the system tracking error, the compensation signal, the compensated tracking error and the fault estimation value, so as to control the actuator to work according to the compensation control signal; wherein the calculation formula of the preset compensation control signal is designed using the Lyapunov principle.

9. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the active fault-tolerant control method for a nonlinear system as claimed in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the active fault-tolerant control method for a nonlinear system according to any one of claims 1 to 7 is implemented.

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