A solution method for multiple small fault estimator design of nonlinear systems

Abstract

The present application relates to a kind of solving method for the design of nonlinear system multiple small fault estimator, first establish the discrete-time system model containing actuator and sensor multiple fault and nonlinear term, then introduce nonsingular transformation and decompose the original system into two subsystems: subsystem 1 only contains external disturbance, subsystem 2 contains both actuator fault and sensor fault. Based on two subsystems, two iterative learning estimators 1 and 2 are designed, and an integrated solution method for designing two estimator parameters is applied using optimization algorithms. Finally, a multiple small fault estimation strategy for nonlinear systems is presented, and accurate estimation is achieved when multiple faults occur concurrently. The present application can accurately estimate the actuator and sensor faults of nonlinear discrete-time systems, while simultaneously counteracting the influence of external disturbances on fault estimation results, effectively estimating small faults in the system, and improving the system's fault handling capability and fault tolerance performance. The solving method of the present application is simple and easy to implement in practical engineering systems.

Description

Technical Field

[0001] This invention relates to the field of multiple faults and minor faults estimation for nonlinear discrete-time systems, and more specifically to a solution method that can be used for designing multiple minor fault estimators for nonlinear systems. Background Technology

[0002] Fault estimation is a widely studied topic in the field of fault diagnosis. With the continuous development of science and technology and society, the complexity of modern control systems is also increasing. Therefore, it is necessary to conduct in-depth research on the fault diagnosis problem of complex nonlinear systems to improve the safety and reliability of control systems. Meanwhile, fault estimation technology is an advanced fault diagnosis method that can simultaneously provide information on the time, location, and magnitude of a fault. The estimation results can be used for further processing of system faults and fault-tolerant control, thus possessing significant research value and application prospects.

[0003] Currently, most control systems are discrete-time systems. Traditional fault estimation methods based on continuous systems cannot be directly applied to discrete-time systems. Therefore, this invention focuses on the development and design of estimators for discrete-time systems. Furthermore, the estimator solution method designed in this invention can integrate the solution of two estimators, greatly simplifying the estimator design process and improving its convenience. In addition, currently common estimator design strategies are generally disturbance suppression strategies, that is, using optimization to suppress the influence of external disturbances on the fault estimation results as much as possible, such as adaptive estimators, proportional-integral estimators, and H-type estimators. ∞ Estimators, etc. While these estimators can effectively estimate system faults, they cannot effectively handle the problem of estimating minor faults. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a solution method for designing estimators for multiple minor faults in nonlinear systems. This method, based on the aforementioned estimators, applies an interference cancellation strategy to the estimator design. Specifically, after estimating external interferences to the system, these interferences are incorporated into other system estimation results for cancellation, effectively completing the task of estimating minor faults in the system. This invention also applies the idea of ​​augmented estimation to treat sensor faults as augmented state vectors of the system, thereby completing the estimation work when multiple faults occur concurrently in the system.

[0005] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0006] A solution method for designing multiple small fault estimators for nonlinear systems includes the following steps:

[0007] A discrete-time system model containing multiple faults of actuators and sensors, as well as nonlinear terms, is established. A non-singular transformation is introduced to decompose the original system into two subsystems. Subsystem 1 contains only external disturbances, while subsystem 2 contains actuator faults and sensor faults.

[0008] Based on two subsystems, two iterative learning estimators, 1 and 2, and their estimation errors are designed respectively; an integrated solution method for the parameters of the two estimators is designed using optimization algorithms.

[0009] A strategy for estimating multiple minor faults in a nonlinear system is presented, and accurate estimation is achieved when multiple faults occur concurrently.

[0010] The mathematical model of the nonlinear discrete-time system is as follows:

[0011]

[0012] Where x(k) is the system state; x(k+1) is the state at the next moment after x(k); y(k) is the system output; d(k) is the external disturbance; and u(k) is the system control input. For nonlinear terms; f a (k) indicates a system actuator failure; f s (k) indicates a system sensor failure; A p B is the state gain matrix; p To control the input gain matrix; C p F is the output gain matrix; ap For actuator fault matrix; F sp D is the sensor fault matrix; p M is the external interference gain matrix; p Let be the gain matrix of the nonlinear term, and k be the discrete-time variable.

[0013] By introducing a non-singular transformation, the original system is decomposed into two subsystems. The mathematical models of subsystem 1 and subsystem 2 are as follows:

[0014]

[0015]

[0016] in, Matrix T is the non-singular transformation matrix of the state vector, and matrix S is the non-singular transformation matrix of the output vector; A 11 Let matrix A p Block matrix 1, A 12 Let matrix A p The block matrix 2, A 21 Let matrix A p Block matrix 3, A22 Let matrix A p The block matrix 4; B1 is matrix B p The block matrix B1 and B2 are matrix B p The block matrix 2; M1 is matrix M p The block matrix 1; M2 is matrix M p The block matrix 2; D1 is matrix D p The block matrix 1; D2 is matrix D p The block matrix 2; F a2 Let matrix F ap The block matrix 2; F s2 Let matrix F sp Block matrix 2; C 11 For matrix C p Block matrix 1, C 22 For matrix C p The block matrix 4; T -1 Let z1 be the inverse matrix of matrix T; z2 be the state vector of subsystem 1; z3 be the state vector of subsystem 2; and z4 be the inverse matrix of matrix T. w1 is the output vector of subsystem 1, and w2 is the output vector of subsystem 2, where... d(k) represents external disturbance; u(k) represents system control input; For nonlinear terms; f a (k) indicates a system actuator failure; f s (k) represents the system sensor fault; k is a discrete-time variable.

[0017] By defining augmented states and f(k)=F a2 f a (k)+D2d(k), the two subsystems can be transformed into:

[0018]

[0019]

[0020] Where z1(k+1) is the state of z1(k) at the next time step; for The state at the next time step; w1 is the output vector of subsystem 1, w2 is the output vector of subsystem 2; matrix E is E = [I 0], I is the identity matrix; matrix for matrix for matrix for d(k) represents external disturbance; u(k) represents system control input; For nonlinear terms; fa (k) indicates a system actuator failure; f s (k) represents the system sensor fault; k is a discrete-time variable.

[0021] The unknown input iterative learning estimators 1 and 2 designed for the two subsystems can be described as follows:

[0022]

[0023]

[0024] Where ξ1(k) is the state value of the unknown input iterative learning estimator 1, and ξ1(k+1) is the state of ξ1(k) at the next time step; This is an estimate of z1(k); This is an estimate of w1(k); This is an estimate of d(k). for The state at the next time step; matrices N1, U1, L1, V1 and F are the gain matrix parameters of estimator 1; ξ2(k) is the state value of estimator 2 when iteratively learning unknown input, and ξ2(k+1) is the state of ξ2(k) at the next time step; for The estimated value; This is an estimate of w2(k); Let f(k) be an estimate. for The state at the next time step; matrices N2, U2, L2, V2, and G are the gain matrix parameters of estimator 2; Representing matrix C 11 The pseudo-inverse matrix operation, i.e. in Representing matrix C 11 The transpose of , where k is a discrete-time variable.

[0025] The estimation errors of the two estimators are expressed as follows:

[0026]

[0027]

[0028] in, Let e1(k+1) be the estimation error of estimator 1, and let e1(k+1) be the state of e1(k) at the next time step. e represents the estimation error of estimator 2, and e2(k+1) represents the state at the next time step after e2(k); e f (k) represents the estimation error of variable f, i.e. The estimation error for the estimated nonlinear term, i.e. Matrices N1 and U1 are the gain matrix parameters of estimator 1; matrices N2 and U2 are the gain matrix parameters of estimator 2, and k is a discrete-time variable.

[0029] To solve for the estimator parameters, new error estimation state vectors are introduced respectively. and The error estimation dynamics of the two estimators then become:

[0030]

[0031]

[0032] in, Let e1(k+1) be the estimation error of estimator 1, and let e1(k+1) be the state of e1(k) at the next time step. e2(k+1) represents the estimation error of estimator 2, and e2(k+1) represents the state of e2(k) at the next time step. for The state at the next moment; for The state at the next moment; Δd(k) is defined as Δd(k) = d(k+1) - d(k); Δf(k) is defined as Δf(k) = f(k+1) - f(k); The estimation error for the estimated nonlinear term, i.e. I is the identity matrix, and k is the discrete-time variable.

[0033] The method for integrating the two estimator parameters using the application optimization algorithm is as follows: The following steps are performed to solve the parameters of estimators 1 and 2, resulting in dynamic convergence of the two error estimates:

[0034] a. For the two subsystems, design iterative learning estimators 1 and 2 for unknown inputs;

[0035] b. If there exist symmetric positive definite matrices P1 and P2, and optimal parameters γ, such that the ensemble optimization problem described by the linear matrix inequality has a solution, i.e., satisfies:

[0036] minγ

[0037]

[0038] Then the error estimation converges dynamically;

[0039] Where: * denotes the symmetric term of a symmetric matrix, the symbol T denotes the transpose operation of a matrix, and I is the identity matrix;

[0040] This completes the design of the two estimators.

[0041] The nonlinear system multiple minor fault estimation strategy is as follows: The obtained estimator parameters are used to estimate the external disturbance d and the newly defined state vector f in both subsystems, thus completing the simultaneous estimation task of minor faults in the system actuators and sensors; the estimation results of the actuator and sensor faults by the two estimators are as follows:

[0042]

[0043]

[0044] in, For actuator failure f a The estimated value of (k); Let matrix F a2 The pseudo-inverse matrix, i.e. For actuator failure f s The estimated value of (k); I is the identity matrix, and k is the discrete-time variable.

[0045] The present invention has the following beneficial effects and advantages:

[0046] 1. This invention applies an estimator design method based on a mathematical model of a nonlinear discrete-time system to design a solution method for designing an estimator for multiple minor faults in a nonlinear system, enabling effective and accurate estimation of concurrent minor faults in the system after multiple faults occur.

[0047] 2. The outstanding advantages of this invention compared with existing technologies are as follows: First, it extends the design of nonlinear system fault estimators to discrete-time systems, and the results can be directly applied to time-based engineering systems, greatly expanding its application scope and value. Second, based on the augmentation concept, the estimator can simultaneously complete the estimation task when system actuators and sensors fail concurrently. In addition, the integration design of the two estimators based on optimization methods can improve the design efficiency and convenience of the estimator. Third, by adopting an interference cancellation strategy in the design of the estimator, it can effectively complete the robust estimation task of minor faults, greatly improving the accuracy of fault estimation results and laying a solid foundation for subsequent fault handling and fault-tolerant control. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method of the present invention;

[0049] Figure 2 Fault estimation results for actuators (servo motors) of flexible joint robot arms;

[0050] Figure 3 Fault estimation results for sensors (encoders) in a flexible joint robot arm. Detailed Implementation

[0051] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0052] like Figure 1 The diagram shown is a flowchart of the method of this invention. This invention proposes a solution method that can be used for the design of multiple small fault estimators for nonlinear systems, including the following steps:

[0053] Step 1: Give the mathematical model of the nonlinear discrete-time system, considering the concurrent failure of the system actuator and sensor, as well as the nonlinear terms and external disturbances.

[0054] The mathematical model of the nonlinear discrete-time system is as follows:

[0055]

[0056] Where x(k) is the system state; x(k+1) is the state at the next moment after x(k); y(k) is the system output; d(k) is the external disturbance; and u(k) is the system control input. For nonlinear terms; f a (k) indicates a system actuator failure; f s (k) indicates a system sensor failure; A p B is the state gain matrix; p To control the input gain matrix; C p F is the output gain matrix; ap For actuator fault matrix; F sp D is the sensor fault matrix; p M is the external interference gain matrix; p Let be the gain matrix of the nonlinear term, and k be the discrete-time variable.

[0057] Step 2: Introduce a non-singular transformation to decompose the original system into two subsystems, the models of which are as follows:

[0058]

[0059]

[0060] in, Matrix T is the non-singular transformation matrix of the state vector, and matrix S is the non-singular transformation matrix of the output vector; A 11 Let matrix A p Block matrix 1, A12 Let matrix A p The block matrix 2, A 21 Let matrix A p Block matrix 3, A 22 Let matrix A p The block matrix 4; B1 is matrix B p The block matrix B1 and B2 are matrix B p The block matrix 2; M1 is matrix M p The block matrix 1; M2 is matrix M p The block matrix 2; D1 is matrix D p The block matrix 1; D2 is matrix D p The block matrix 2; F a2 Let matrix F ap The block matrix 2; F s2 Let matrix F sp Block matrix 2; C 11 For matrix C p Block matrix 1, C 22 For matrix C p The block matrix 4; T -1 Let z1 be the inverse matrix of matrix T; z2 be the state vector of subsystem 1; z3 be the state vector of subsystem 2; and z4 be the inverse matrix of matrix T. w1 is the output vector of subsystem 1, and w2 is the output vector of subsystem 2, where... d(k) represents external disturbance; u(k) represents system control input; For nonlinear terms; f a (k) indicates a system actuator failure; f s (k) represents the system sensor fault; k is a discrete-time variable.

[0061] Step 3: Define augmenting states and f(k)=F a2 f a (k)+D2d(k), the two subsystems can be transformed into:

[0062]

[0063]

[0064] Where z1(k+1) is the state of z1(k) at the next time step; for The state at the next time step; w1 is the output vector of subsystem 1, w2 is the output vector of subsystem 2; matrix E is E = [I 0], I is the identity matrix; matrix for matrix for matrix for d(k) represents external disturbance; u(k) represents system control input; For nonlinear terms; f a (k) indicates a system actuator failure; f s (k) represents the system sensor fault; k is a discrete-time variable.

[0065] Step 4: The unknown input iterative learning estimators 1 and 2 designed for the two subsystems can be described as follows:

[0066]

[0067]

[0068] Among them, the unknown input iterative learning estimator 1 is designed based on subsystem 1 and is used to estimate external disturbances; the unknown input iterative learning estimator 2 is designed based on subsystem 2 and is used to estimate actuator and sensor faults; ξ1(k) is the state value of the unknown input iterative learning estimator 1, and ξ1(k+1) is the state of ξ1(k) at the next time step. This is an estimate of z1(k); This is an estimate of w1(k); This is an estimate of d(k). for The state at the next time step; matrices N1, U1, L1, V1 and F are the gain matrix parameters of estimator 1; ξ2(k) is the state value of estimator 2 when iteratively learning unknown input, and ξ2(k+1) is the state of ξ2(k) at the next time step; for The estimated value; This is an estimate of w2(k); Let f(k) be an estimate. for The state at the next time step; matrices N2, U2, L2, V2, and G are the gain matrix parameters of estimator 2; Representing matrix C 11 The pseudo-inverse matrix operation, i.e. in Representing matrix C 11 The transpose of , where k is a discrete-time variable.

[0069] Step 5: The estimation error of the two estimators can be expressed as:

[0070]

[0071]

[0072] in, Let e1(k+1) be the estimation error of estimator 1, and let e1(k+1) be the state of e1(k) at the next time step. e represents the estimation error of estimator 2, and e2(k+1) represents the state at the next time step after e2(k); e f (k) represents the estimation error of variable f, i.e. The estimation error for the estimated nonlinear term, i.e. Matrices N1 and U1 are the gain matrix parameters of estimator 1; matrices N2 and U2 are the gain matrix parameters of estimator 2, and k is a discrete-time variable.

[0073] Step 6: To facilitate the solution of the observer parameters, new error estimation state vectors are introduced respectively. and Then the error estimation dynamic described in step 5 becomes

[0074]

[0075]

[0076] in, Let e1(k+1) be the estimation error of estimator 1, and let e1(k+1) be the state of e1(k) at the next time step. e2(k+1) represents the estimation error of estimator 2, and e2(k+1) represents the state of e2(k) at the next time step. for The state at the next moment; for The state at the next moment; Δd(k) is defined as Δd(k) = d(k+1) - d(k); Δf(k) is defined as Δf(k) = f(k+1) - f(k); The estimation error for the estimated nonlinear term, i.e. I is the identity matrix, and k is the discrete-time variable.

[0077] Step 7: Apply optimization algorithms to design an ensemble solution method for the parameters of the two estimators, while ensuring that the error estimation dynamics described in Step 6 are asymptotically stable. The solution steps for the parameters of estimators 1 and 2 are as follows: For the two subsystems obtained in Step 3, design the unknown input iterative learning estimators 1 and 2 described in Step 4. If there exist symmetric positive definite matrices P1 and P2, and optimal parameters γ, such that the ensemble optimization problem described by the following linear matrix inequality has a solution, i.e., satisfying:

[0078] minγ

[0079]

[0080] The error estimation dynamics described in step 6 are asymptotically stable, where: * represents the symmetric term of the symmetric matrix, the symbol T represents the transpose operation of the matrix; I is the identity matrix. This completes the design of the two estimators.

[0081] Step 8: Apply the obtained estimator parameters to estimate the external disturbance d and the newly defined state vector f in the two subsystems. Finally, complete the simultaneous estimation task of minor faults in the system actuators and sensors. The estimation results of the actuator and sensor faults by the two estimators are as follows:

[0082]

[0083]

[0084] in, For actuator failure f a The estimated value of (k); Let matrix F a2 The pseudo-inverse matrix, i.e. For actuator failure f s The estimated value of (k); I is the identity matrix, and k is the discrete-time variable.

[0085] Example:

[0086] Here, we take a flexible articulated robotic arm with a sampling period of 0.01 s as an example to illustrate the effectiveness of the proposed solution method for designing multiple small fault estimators for nonlinear systems. The model parameters of this nonlinear discrete-time system are:

[0087]

[0088]

[0089] The non-singular transformation matrices T and S are respectively:

[0090]

[0091] but

[0092] A 21 = [0.486 - 0.486 - 0.486],

[0093] A 22 =0.9875, B2 = 0.216, F a2 =0.216, E2=21.6, D2 = 0,

[0094] M2 = 0, C 22 =1,F s2 =1.

[0095] Therefore, the gain matrices N1, U1, L1, V1 and F parameters of estimator 1 are obtained as follows:

[0096]

[0097] F = [-0.42021.2604].

[0098] The obtained gain matrices N2, U2, L2, V2 and G parameters of estimator 2 are as follows:

[0099] G = 0.180

[0100] Example Analysis:

[0101] As can be seen from the above results, the solution method proposed in this invention can quickly solve for the gain matrix parameters of the two estimators, realize the integrated solution of the estimator parameters, greatly improve the convenience and usability of the algorithm, and the obtained relevant parameters can be directly applied to practical engineering systems. It has broad application prospects and value for improving the reliability and safety of modern nonlinear control systems.

[0102] also, Figure 2 The results of fault estimation for the actuator (servo motor) of the flexible joint robot arm; Figure 3 For the sensor (encoder) fault estimation results of the flexible joint robot arm, from Figure 2-3 The simulation results show that this method effectively estimates the faults of the system actuator (servo motor) and sensor (encoder) by collecting the position and velocity information of the output end of the flexible joint robot arm and the position and velocity information of the motor end, achieving the expected results.

[0103] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A solution method for designing multiple small fault estimators for nonlinear systems, characterized in that, Includes the following steps: S1. Establish a discrete-time system model containing multiple faults of actuators and sensors as well as nonlinear terms. Introduce a non-singular transformation to decompose the original system into two subsystems. Subsystem 1 contains only external disturbances, while subsystem 2 contains actuator faults and sensor faults. The discrete-time system model for the nonlinear term is as follows: ； in, This refers to the system status; for The state at the next moment; For system output; External interference; For system control input; It is a nonlinear term; The problem is a system actuator malfunction. The problem is a sensor malfunction in the system. A p This is the state gain matrix; B p To control the input gain matrix; C p This is the output gain matrix; F ap For actuator fault matrix; F sp For sensor fault matrix; D p External interference gain matrix; M p The gain matrix is ​​a nonlinear term. k For discrete-time variables; After introducing a non-singular transformation to decompose the original system into two subsystems, the mathematical models of subsystem 1 and subsystem 2 are as follows: ； ； in, , ;matrix T Let be the non-singular transformation matrix of the state vector, and let be the matrix. S The non-singular transformation matrix of the output vector; A 11 For matrix A p Block matrix 1, A 12 For matrix A p Block matrix 2, A 21 For matrix A p Block matrix 3, A 22 For matrix A p Block matrix 4; B 1 is a matrix B p Block matrix 1, B 2 is a matrix B p Block matrix 2; M 1 is a matrix M p Block matrix 1; M 2 is a matrix M p Block matrix 2; D 1 is a matrix D p Block matrix 1; D 2 is a matrix D p Block matrix 2; F a2 For matrix F ap Block matrix 2; F s2 Let matrix F sp Block matrix 2; C 11 For matrix C p Block matrix 1, C 22 For matrix C p Block matrix 4; T -1 For matrix T The inverse matrix; Let be the state vector of subsystem 1. Let be the state vector of subsystem 2, where ; This is the output vector of subsystem 1. Let be the output vector of subsystem 2, where ; External interference; For system control input; It is a nonlinear term; The problem is a system actuator malfunction. The problem is a sensor malfunction in the system. k For discrete-time variables; By defining augmented states and The two subsystems are transformed into: ； ； in, for The state at the next moment; for The state at the next moment; This is the output vector of subsystem 1. The output vector of subsystem 2; matrix E for , I The identity matrix; matrix for ;matrix for ;matrix for ; External interference; For system control input; It is a nonlinear term; The problem is a system actuator malfunction. The problem is a sensor malfunction in the system. k For discrete-time variables; S2. Based on two subsystems, design two iterative learning estimators 1 and 2, and the estimation errors of the two estimators respectively; apply optimization algorithms to design an integrated solution method for the parameters of the two estimators. The unknown input iterative learning estimators 1 and 2 are described as follows: ； ； in, Iteratively learn the state values ​​of estimator 1 for unknown input. for The state at the next moment; for The estimated value; for The estimated value; for The estimated value, for The state at the next time step; matrix N 1. U 1. L 1. V 1 and F These are the gain matrix parameters for estimator 1; Given unknown input, iteratively learn the state values ​​of estimator 2. for The state at the next moment; for The estimated value; for The estimated value; for The estimated value, for The state at the next time step; matrix N 2. U 2. L 2. V 2 and G The gain matrix parameters for estimator 2; Representation matrix C 11 The pseudo-inverse matrix operation, i.e. ,in Representation matrix C 11 The transpose of the matrix, k For discrete-time variables; The estimation errors of the two estimators are expressed as follows: ； ； in, The estimation error of estimator 1, for The state at the next moment; The estimation error of estimator 2, for The state at the next moment; For variables f The estimation error, i.e. ; The estimation error for the estimated nonlinear term, i.e. ;matrix N 1. U 1 represents the gain matrix parameter of estimator 1; matrix N 2. U 2 represents the gain matrix parameters of estimator 2. k For discrete-time variables; To solve for the estimator parameters, new error estimation state vectors are introduced respectively. and Then the error estimates of the two estimators dynamically become: ； ； in, The estimation error of estimator 1, for The state at the next moment; The estimation error of estimator 2, for The state at the next moment; for The state at the next moment; for The state at the next moment; Defined as ; Defined as ; The estimation error for the estimated nonlinear term, i.e. ; ; ; ; ; ; ; I It is the identity matrix. k For discrete-time variables; The method for integrating the two estimator parameters using the application optimization algorithm is as follows: The following steps are performed to solve the parameters of estimators 1 and 2, resulting in dynamic convergence of the two error estimates: a. For the two subsystems, design iterative learning estimators 1 and 2 for unknown inputs; b. If a symmetric positive definite matrix exists P 1 and P 2, and the optimal parameters This makes the following ensemble optimization problem, described by the linear matrix inequality, solvable, i.e., satisfying: = ； Then the error estimation converges dynamically; in: The symbol T represents the symmetric term of a symmetric matrix, and the matrix operation T represents the transpose of the matrix. I It is the identity matrix; This completes the design of two estimators; it also presents an estimation strategy for multiple minor faults in nonlinear systems and achieves accurate estimation when multiple faults occur concurrently.

2. The solution method for designing multiple small fault estimators for nonlinear systems according to claim 1, characterized in that, The strategy for estimating multiple minor faults in the nonlinear system is as follows: The obtained estimator parameters are used to estimate external disturbances in both subsystems. d The estimation and the newly defined state vector The estimation of minor faults in the system actuators and sensors is performed simultaneously; the estimation results of the actuator and sensor faults by the two estimators are as follows: ； ； in, Actuator failure The estimated value; For matrix The pseudo-inverse matrix, i.e. ; Actuator failure The estimated value; I It is the identity matrix. k It is a discrete-time variable.

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