Disturbance-containing nonlinear system fault estimation method based on augmented fault observer

Abstract

The invention discloses a disturbance-containing nonlinear system fault estimation method based on an augmented fault observer, relates to the technical field of disturbance-containing nonlinear system fault estimation, and aims to solve the problem of developing and designing a fault estimation method for a nonlinear system containing a sensor fault and an actuator fault at the same time. The method comprises the following steps: S1, establishing a nonlinear system model comprising an actuator fault, a sensor fault and interference; s2, designing an efficient augmented fault observer for the disturbance-containing nonlinear system in the step S1; s3, aiming at the efficient augmented fault observer in the step S2, considering nonlinearity, input interference and measurement noise, designing a group of linear matrix inequalities, and solving a gain matrix of the efficient augmented fault observer; and S4, estimating the sensor fault and the actuator fault based on the efficient augmented fault observer, and solving a fault estimation value.

Description

Technical Field

[0001] The invention relates to the technical field of fault estimation of a nonlinear system with disturbance, and in particular to a fault estimation method of a nonlinear system with disturbance based on an augmented fault observer. Background Art

[0002] As more and more process control technologies are applied to modern industry, urban transportation, electricity, and aerospace, the systems are becoming increasingly large and complex. Since the sensors and actuators in the control system are in operation for a long time, the possibility of sensor or actuator failure will be greatly increased. If the system fails and cannot be re-detected and handled as soon as possible, it may bring serious consequences. Based on the urgent need for security and reliability of the system, it is particularly important to ensure that the control system can operate safely and quickly detect and handle faults.

[0003] In the system fault diagnosis method, the adaptive fault estimation observer has the advantage of being able to estimate both state information and fault information at the same time, which is suitable for most actual system state variables that are not completely measurable. Research on systems containing only sensor faults or actuator faults has achieved certain results, but there are relatively few studies on the situation where the system contains both sensor faults and actuator faults. Therefore, it is urgent to develop a fault estimation method for nonlinear systems containing both sensor faults and actuator faults. Summary of the invention

[0004] The present invention proposes a fault estimation method for a nonlinear system with disturbance based on an augmented fault observer, which comprises the following steps: S1: Establish a nonlinear system model including actuator faults, sensor faults and disturbances; S2: Design an efficient augmented fault observer for the nonlinear system with disturbance in step S1; S3: for the efficient augmented fault observer in step S2, a set of linear matrix inequalities is designed considering nonlinearity, input interference and measurement noise, and a gain matrix of the efficient augmented fault observer is solved; S4: Estimate the sensor fault and the actuator fault based on the efficient augmented fault observer to obtain a fault estimation value.

[0005] The present invention is further configured as follows: the nonlinear system model in step S1 is: Where: x(t)∈R n ,u(t)∈R m ,y(t)∈R p ,f a (t)∈Rq ,f s (t)∈R s and d(t)∈R l are the system state vector, control input, output, actuator fault, sensor fault and unknown disturbance respectively; d s (t)∈R s represents bounded measurement noise, g[x(t),t] is a nonlinear function that satisfies the Lipschitz condition; A, B, C, D, F a ,F s ,D s denote constant matrices of appropriate dimensions respectively.

[0006] The present invention is further configured as follows: the nonlinear system model (Formula 1) satisfies the following conditions: (1) Matrix F s For the full rank of the column; (2) The actuator fault is bounded and the first-order derivative exists, satisfying (3) The input disturbance term d(t) is bounded, satisfying d(t)∈L2[0,+∞); (4) Measurement noise d s (t) is bounded and its first-order derivative exists, satisfying (5) The nonlinear term g[x(t),t] satisfies the Lipschitz condition and has Where L g is the Lipschitz constant.

[0007] The present invention is further configured as follows: the efficient augmented fault observer in step S2 is: Where: and are the state vector estimate, output vector estimate and actuator fault estimate of the augmented fault observer respectively; the observation error and Matrix L, R is the gain matrix to be designed; E = [I n 0], is a matrix with appropriate dimensions; T, N are matrices that satisfy the condition The matrix to be designed, and other coefficient matrices are defined the same as in (Formula 1).

[0008] The present invention is further configured as follows: for a certain performance index α, ε>0, a set of linear matrix inequalities are designed as follows: in,

[0009] The present invention is further configured as follows: Step S3 specifically includes the following steps: S3-1: In order to further shorten the convergence speed of the observation error of the augmented fault observer and improve the performance of the observer, the stability margin performance index ε is set; S3-2: To reduce the impact of input disturbance and measurement noise on sensor fault and actuator fault estimation, set H ∞ Performance index α; S3-3: Based on the set performance indicators α and ε, solve the matrix inequality group (Equation 3) and (Equation 4), calculate the unknown matrices X and P, and further obtain Then the gain matrix L, R is obtained, thus completing the design of the augmented fault observer.

[0010] The present invention is further configured as follows: the actuator fault estimation in step S4 can be realized by an augmented fault observer (Formula 2), and the sensor fault can be realized by accomplish.

[0011] The beneficial effects of the present invention are as follows: under the condition that the system has input disturbance and measurement noise, the present invention designs an adaptive augmented fault observer, gives the sufficient conditions for the existence of the observer in the form of linear matrix inequality, and provides a basis for realizing robust estimation of sensor faults and actuator faults of nonlinear systems. By quadratically constraining the observer gain matrix, the convergence speed of the augmented fault observer observation error is further shortened, and the performance of fault estimation is improved. At the same time, considering the disturbance in the system, by setting H ∞ Performance indicators, which weaken the impact of disturbances on fault estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flow chart of the present invention is shown.

[0013] Figure 2 A flow chart of sensor fault and actuator fault estimation in embodiment 1 of the present invention is shown.

[0014] Figure 3 A sensor failure estimation diagram in Example 2 is shown.

[0015] Figure 4 An actuator fault estimation diagram in Example 2 is shown. DETAILED DESCRIPTION

[0016] Those skilled in the art can refer to the content of this article and appropriately improve the process parameters. It is particularly important to point out that all similar replacements and modifications are obvious to those skilled in the art, and they are all considered to be included in the present invention. The methods and applications of the present invention have been described through preferred embodiments, and relevant personnel can modify or appropriately change and combine the methods and applications described herein without departing from the content, spirit and scope of the present invention to implement and apply the technology of the present invention.

[0017] The present invention proposes a fault estimation method for a nonlinear system with disturbance based on an augmented fault observer, comprising the following steps: S1: Establish a nonlinear system model including actuator faults, sensor faults and disturbances; S2: Design an efficient augmented observer for the nonlinear system with disturbance in step S2; S3: for the efficient augmented observer in step S2, a set of linear matrix inequalities is designed considering nonlinearity, input interference and measurement noise, and a gain matrix of the efficient augmented fault observer is solved; S4: Estimate the sensor fault and the actuator fault based on the efficient augmented fault observer to obtain a fault estimation value.

[0018] The nonlinear system model in step S1 is: Where: x(t)∈R n ,u(t)∈R m ,y)t)∈R p ,f a (t)∈R q ,f s (t)∈R s and d(t)∈R l are the system state vector, control input, output, actuator fault, sensor fault and unknown disturbance respectively; d s (t)∈R s represents bounded measurement noise, g[x(t),t] is a nonlinear function that satisfies the Lipschitz condition; A, B, C, D, F a ,F s ,D s denote constant matrices of appropriate dimensions respectively.

[0019] The above nonlinear system model (Equation 1) satisfies the following conditions: (1) Matrix F s For the full rank of the column; (2) The actuator fault is bounded and the first-order derivative exists, satisfying (3) The input disturbance term d(t) is bounded, satisfying d(t)∈L2[0,+∞); (4) Measurement noise d s (t) is bounded and its first-order derivative exists, satisfying (5) The nonlinear term g[x(t),t] satisfies the Lipschitz condition and has Where L g is the Lipschitz constant.

[0020] The efficient augmented fault observer in step S2 is: Where: and are the state vector estimate, output vector estimate and actuator fault estimate of the augmented fault observer respectively; the observation error and Matrix L, R is the gain matrix to be designed; E = [I n 0], is a matrix with appropriate dimensions; T, N are matrices that satisfy the condition The matrix to be designed, and other coefficient matrices are defined the same as in (Formula 1).

[0021] In step S3, for a given performance index α, ε>0, a set of linear matrix inequalities is designed as follows: in,

[0022] Wherein step S3 specifically comprises the following steps: S3-1: In order to further shorten the convergence speed of the observation error of the augmented fault observer and improve the performance of the observer, the stability margin performance index ε is set; S3-2: To reduce the impact of input disturbance and measurement noise on sensor fault and actuator fault estimation, set H ∞ Performance index α; S3-3: Based on the set performance indicators α and ε, solve the matrix inequality group (Equation 3) and (Equation 4), calculate the unknown matrices X and P, and further obtain Then the gain matrix L, R is obtained, thus completing the design of the augmented fault observer.

[0023] The actuator fault estimation in step S4 can be realized by the pipe augmentation fault observer (Equation 2). Implementation, specific process parts Figure 2 Flow chart of the method for estimating sensor fault and actuator fault during the implementation of the present invention.

[0024] Example 2

[0025] Consider a nonlinear system model with input disturbance and measurement noise. The system matrix is: d(t)=0.003sin5t The sensor fault and actuator fault functions are as follows:

[0026] Given H ∞ The performance index α = 0.2 and the stability margin ε = 0.2, using MATLAB to solve the matrix inequalities in (Equation 3) and (Equation 4), the undetermined matrix and the gain matrix of the augmented fault diagnosis observer are obtained as follows: The calculated observer gain matrix is:

[0027] refer to Figure 3 and Figure 4 The estimated values ​​and actual values ​​of sensor fault and actuator fault are shown respectively. It can be seen from the figure that the fault estimated value can quickly track the actual value of the above fault with high accuracy.

[0028] In summary, the present invention designs an adaptive augmented fault observer under the condition of input disturbance and measurement noise in the system, and gives the sufficient conditions for the existence of the observer in the form of linear matrix inequality, which provides a basis for realizing robust estimation of sensor faults and actuator faults in nonlinear systems. By quadratically constraining the observer gain matrix, the convergence speed of the augmented fault observer observation error is further shortened, and the performance of fault estimation is improved. At the same time, considering the disturbance in the system, by setting H ∞ Performance indicators, which weaken the impact of disturbances on fault estimation.

[0029] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be within the scope of protection of the present invention.

Claims

1. A method for fault estimation of a nonlinear system with disturbance based on an augmented fault observer, characterized in that: The following steps are involved: S1: Establish a nonlinear system model including actuator faults, sensor faults and disturbances; S2: Design an efficient augmented fault observer for the nonlinear system with disturbance in step S1; S3: for the efficient augmented fault observer in step S2, a set of linear matrix inequalities is designed considering nonlinearity, input interference and measurement noise, and a gain matrix of the efficient augmented fault observer is solved; S4: Estimate the sensor fault and the actuator fault based on the efficient augmented fault observer to obtain a fault estimation value.

2. The method for fault estimation of a nonlinear system with disturbance based on augmented fault observer according to claim 1, characterized in that: The nonlinear system model in step S1 is: Where: x(t)∈R n ,u(t)∈R m ,y(t)∈R p ,f a (t)∈R q ,f s (t)∈R s and d(t)∈R l are the system state vector, control input, output, actuator fault, sensor fault and unknown disturbance respectively; d s (t)∈R s represents bounded measurement noise, g[x(t),t] is a nonlinear function that satisfies the Lipschitz condition; A, B, C, D, F a ,F s ,D s denote constant matrices of appropriate dimensions respectively.

3. The method for fault estimation of a nonlinear system with disturbance based on an augmented fault observer according to claim 2, characterized in that: The nonlinear system model (Formula 1) satisfies the following conditions: (1) Matrix F s For the full rank of the column; (2) The actuator fault is bounded and the first-order derivative exists, satisfying (3) The input disturbance term d(t) is bounded, satisfying d(t)∈L2[0,+∞); (4) Measurement noise d s (t) is bounded and its first-order derivative exists, satisfying (5) The nonlinear term g[x(t),t] satisfies the Lipschitz condition and has Where L g is the Lipschitz constant.

4. The method for fault estimation of a nonlinear system with disturbance based on augmented fault observer according to claim 3, characterized in that: The efficient augmented fault observer in step S2 is: Where: and are the state vector estimate, output vector estimate and actuator fault estimate of the augmented fault observer respectively; the observation error and Matrix L, R is the gain matrix to be designed; E = [I n 0], is a matrix with appropriate dimensions; T, N are matrices that satisfy the condition The matrix to be designed, and other coefficient matrices are defined the same as in (Formula 1).

5. The method for fault estimation of a nonlinear system with disturbance based on augmented fault observer according to claim 4, characterized in that: For a certain performance index α, ε>0, a set of linear matrix inequalities are designed as follows: in, 6. The method for fault estimation of a nonlinear system with disturbance based on augmented fault observer according to claim 5, characterized in that: The step S3 specifically comprises the following steps: S3-1: In order to further shorten the convergence speed of the observation error of the augmented fault observer and improve the performance of the observer, the stability margin performance index ε is set; S3-2: To reduce the impact of input disturbance and measurement noise on sensor fault and actuator fault estimation, set H ∞ Performance index α; S3-3: Based on the set performance indicators α and ε, solve the matrix inequality group (Equation 3) and (Equation 4), calculate the unknown matrices X and P, and further obtain Then the gain matrix L, R is obtained, thus completing the design of the augmented fault observer.

7. The method for fault estimation of a nonlinear system with disturbance based on augmented fault observer according to claim 6, characterized in that: The actuator fault estimation in step S4 can be realized by the augmented fault observer (Formula 2), and the sensor fault can be accomplish.

Images