A parameter uncertainty aero-engine system fault-tolerant control method based on a sliding mode method

Abstract

The application provides a parameter uncertainty aero-engine system fault-tolerant control method based on a sliding mode method, and belongs to the field of engine system fault-tolerant control. The application considers the influence of parameter uncertainty on aero-engine system actuator fault-tolerant control, constructs a fault observer to estimate system states and fault signals, and provides a basis for the design of a subsequent sliding mode fault-tolerant controller. Further, a fault-tolerant controller based on the sliding mode method is designed based on the estimated system states and fault signals to compensate for the fault of the system in real time, so that the system can still maintain stability and achieve the expected H ∞ performance index, so as to improve the reliability of the system when a fault occurs.

Description

TECHNICAL FIELD

[0001] The application relates to a parameter uncertainty aero-engine system fault-tolerant control method based on a sliding mode method and belongs to the field of engine system fault-tolerant control. BACKGROUND

[0002] Modern control systems are increasingly complex in the fields of aerospace, chemical industry, nuclear power and the like, and often need to work for a long time under different environments and high loads, which will inevitably cause failure of the control system. Minimizing the influence of faults on the system is a necessary way to avoid economic losses and casualties. Therefore, the research on fault-tolerant control (FTC) methods has attracted widespread attention from scholars.

[0003] At present, FTC is divided into passive FTC and active FTC. The passive FTC method mainly regards system faults as disturbances and designs a controller on this basis. The control objective and robust control are achieved in the case of system health or failure. Therefore, passive FTC is closely related to robust control systems. However, passive FTC is only effective for some small faults. On the other hand, active FTC uses the estimated information of states and faults to reconstruct the controller, and then adjusts or reconfigures the parameters to compensate for the influence of faults. Therefore, fault estimation plays an important role in active fault-tolerant control. So far, the methods used for active FTC include the sliding mode observer (SMO) based method, the proportional integral observer (PIO) based method, the unknown input observer (UIO) based method, the adaptive observer (AO) based method and the H ∞ In recent years, sliding mode control has attracted more and more attention in fault-tolerant control systems due to its excellent control performance. Especially for systems containing parameter uncertainties, sliding mode control has strong robustness. The aero-engine control system needs to rely on a large number of actuators to ensure the stable operation of the system within the entire flight envelope. Due to the extremely harsh working environment, these actuators are prone to failure during system operation, and once the failure occurs, the entire control system may fail, which may cause serious consequences. Therefore, it is an important measure to improve the safety and reliability of the system to estimate the actuator faults of the aero-engine control system with parameter uncertainties and implement fault-tolerant control, which has important significance for practical engineering. SUMMARY

[0004] For the fault-tolerant control problem of the aero-engine system with parameter uncertainties, the application provides an aero-engine system fault-tolerant control method based on a sliding mode method.

[0005] In order to achieve the above purpose, the technical scheme adopted by the application is as follows:

[0006] A fault-tolerant control method for aero-engine system based on sliding mode method, comprising the following steps:

[0007] S1. Establishing an aero-engine state space model with parameter uncertainty:

[0008] Considering that the system is affected by parameter uncertainty, disturbance and noise and an actuator fault occurs, the state space of the system can be written as follows:

[0009]

[0010] Wherein, x, u, y are the state vector, control input vector and measured output vector of the system respectively. w represents the process disturbance. v represents the measurement noise, and f represents the actuator fault. A, B, C, D ω ,D v are matrices with appropriate dimensions. F is a known fault matrix. ΔA and ΔB are uncertainty matrices, which are unknown but bounded, satisfying the following:

[0011] ΔA = M1Δ1N1, ΔB = M2Δ2N2, (2)

[0012] Wherein, the matrices M1, N1, M2 and N2 are known, and Δ1 and Δ2 are unknown matrices satisfying And I1 and I2 are unit matrices with appropriate dimensions.

[0013] In addition, without loss of generality, it is assumed that the initial state, process disturbance and measurement noise are unknown, but satisfy the following conditions:

[0014]

[0015] Wherein, is the estimated value of the state, and are known vectors.

[0016] S1.1 In order to realize the estimation of the actuator fault f(k), the actuator fault f(k) is regarded as an additional state of the system, and the state space model of the system is represented as:

[0017]

[0018] Wherein, ξ(k) = [x T (k) f T (k)] T , h(k) = f(k+1) - f(k),

[0019] S2. Using the extended fault observer on the state-space model (4) obtained in S1.1, the dynamic error system is obtained:

[0020] Using the extended fault observer for model (4), consider the following observer:

[0021]

[0022] in, and These are the estimated values ​​of the augmented state vector ξ(k) and the measurement output y(k), respectively. It is the gain of the discrete-time fault observer, L x and L f These are the gain matrices for the state observer and the fault observer, respectively.

[0023] Define the estimation error as Combining (4) and (5), the error dynamic system is obtained as follows:

[0024]

[0025] according to The error dynamic system can be rewritten as:

[0026]

[0027] in, It is a process matrix.

[0028] From the above equation regarding the error dynamic system, it can be seen that due to the influence of parameter uncertainty, the state estimation... Both the system's control input u(k) and the parameter uncertainty matrices ΔA and ΔB are unknown, thus affecting the state estimation. If the influence of the system's control input u(k) can be considered as an unknown disturbance, then the error dynamic system can be simplified as follows:

[0029] e(k+1)=A d e(k)+B d d(k) (8)

[0030] in B d =D x +ΔD, D y =[0 D v 0 0 0]. H ∞ Technology is one of the most studied methods for dealing with disturbances and noise, H ∞ The technical assumption is that the energy of interference and noise signals is bounded throughout the entire time domain. Next, we will use H...∞ techniques to handle disturbances and noises.

[0031] S3. Apply Lyapunov's second method to the dynamic error system (8) obtained in S2 to obtain the observer gain matrix L that satisfies H ∞ performance of the observer gain matrix:

[0032] The designed observer gain matrix is L = G -1 W, G represent a known given matrix, and the parameters W, P, γ need to satisfy the following linear matrix inequality conditions, and the specific numerical value can be obtained by using the optimization toolbox for calculation:

[0033]

[0034] where ψ = φ + ∈N T N,

[0035]

[0036] S4. Establish a parameter uncertainty system fault-tolerant controller based on sliding mode control using the state observation value and fault estimation value obtained by the fault observer designed in S3.

[0037] According to (5), the observation results of state and fault can be expressed as:

[0038]

[0039] where, and are divided into state and fault estimation values, L x and L f are the state observer gain and fault observer gain, respectively.

[0040] The state estimation error is expressed as:

[0041] e x (k+1) = (A - L x C) e x (k) + Fe f (k) + ΔAx(k) + ΔBu(k) + D w w(k) - L x D v v(k) (11)

[0042] where e x (k) and e f (k) are the state estimation error and fault estimation error, respectively.

[0043] Next, in order to realize fault-tolerant control, the following sliding surface is designed:

[0044]

[0045] Where G is a known given matrix, and GB is invertible.

[0046] because The sliding surface can be rewritten as:

[0047] S(k)=Gx(k)-Ge x (k) (13)

[0048] To ensure the designed sliding surface reaches its ideal state and to reduce the impact of faults and uncertainties on the system, the following control law is designed:

[0049]

[0050] in, and They are The upper and lower bounds, and They are The upper and lower bounds of q are given, and q > 0 is a constant.

[0051] Proof: Consider the following condition for the quasi-sliding mode inequality of a sliding mode controller for an aero-engine system with parameter uncertainties:

[0052]

[0053] Where ΔS(k)=S(k+1)-S(k) is the difference of the sliding surface, and η>0 is a constant.

[0054] Combining (1) and (11), the sliding surface (13) can be written as:

[0055]

[0056] Because ξ(0), the process disturbance w(k) and the measurement noise v(k) are bounded. Therefore and The upper and lower bounds can also be obtained using set membership estimation, i.e.

[0057]

[0058] Substituting the control law (14) into the sliding surface (15), we obtain the arrival law of the sliding surface as follows:

[0059]

[0060] in,

[0061]

[0062]

[0063]

[0064]

[0065] We can see that, regardless and The sign of ΔS(k) is always opposite to the sign of S(k), meaning that the closed-loop system (1) satisfies the sliding mode arrival condition (15). After the arrival condition is met, the system state moves in a zigzag pattern on the quasi-sliding surface, achieving stable fault-tolerant control.

[0066] The beneficial effects of this invention are as follows: It considers the impact of parameter uncertainty on fault-tolerant control of aero-engine system actuators, constructs a fault observer to estimate system state and fault signals, and provides a basis for the subsequent design of a sliding mode fault-tolerant controller. Furthermore, based on the estimated system state and fault signals, a fault-tolerant controller based on the sliding mode method is designed to compensate for system faults in real time, enabling the system to remain stable and achieve the expected H even when a fault occurs. ∞ Performance metrics are used to improve the reliability of the system in the event of a failure. Attached Figure Description

[0067] Figure 1 Block diagram of fault-tolerant control for aero-engine systems based on sliding mode method

[0068] Figure 2 A diagram showing the state observation results of an aero-engine under an expanded fault observer;

[0069] Figure 3 A diagram showing the results of aero-engine fault observation under an expanded fault observer;

[0070] Figure 4 The control input diagram for the sliding mode fault-tolerant controller;

[0071] Figure 5 The diagram shows the state results after sliding mode fault-tolerant control of an aero-engine. Detailed Implementation

[0072] The Euler one-step method was used to discretize the continuous system model of an aero-engine of a certain research institute, with a sampling time interval T. s =0.025s. Then, taking parameter uncertainty, faults, and noise interference into account in system (1), the corresponding parameter matrix is ​​as follows:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] in, It is a random signal with a magnitude between 0 and 1.

[0079] By solving the linear matrix inequality (9), we obtain the result based on H. ∞ The observer gain matrix of the technology is:

[0080]

[0081] Next, to demonstrate the significant performance of the proposed method in fault-tolerant control, we perform simulation verification. The simulation results are as follows: Figures 2-5 As shown, Figure 2 and Figure 3 The figures show the observer's observations of the state and fault when an aero-engine malfunctions. As can be seen, the state is estimated relatively well, and the fault can also be estimated, although with slightly lower accuracy than the state estimate. This is because a delay occurs when the observer provides negative feedback to the fault signal. These state and fault estimations lay the foundation for the subsequent design of a sliding mode fault-tolerant controller. Figure 4 The diagram shows the control inputs of a sliding mode fault-tolerant controller. It can be seen that the control inputs change accordingly at the location of the fault to reduce the impact of the fault on the system. Figure 5 The figure shows the results of the fault-tolerant control. It can be seen from the figure that the designed sliding mode fault-tolerant controller can achieve fault-tolerant control of the failed aero-engine system, and the results are significantly improved compared to the case without fault-tolerant control. This demonstrates the effectiveness of the proposed sliding mode fault-tolerant control method. In summary, the proposed sliding mode fault-tolerant control method can effectively handle aero-engine failures affected by parameter uncertainties, ensuring system reliability.

[0082] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A fault-tolerant control method for aero-engine systems with parameter uncertainties based on sliding mode method, characterized in that, Includes the following steps: S1. Establish a state-space model of an aero-engine with parameter uncertainties: Considering the system's effects of parameter uncertainty, disturbances, and noise, and the occurrence of actuator failure, the system's state space can be written in the following form: (1) ； in, , , These are the system's state vector, control input vector, and measurement output vector, respectively. This includes process interference; Represents measurement noise. This indicates an actuator malfunction; It is a known matrix; It is a known fault matrix; and It is an uncertainty matrix, which is unknown but bounded, and satisfies the following: (2) ； Among them, matrix , , and It is known. and An unknown matrix satisfies , and It is the identity matrix; Furthermore, without loss of generality, we assume that the initial state, process disturbances, and measurement noise are unknown, but satisfy the following conditions: (3)； in, This is an estimate of the state. , and It is a known vector; S1.1 In order to achieve actuator failure The estimate is that the actuator will fail. If we consider it as an additional state of the system, then the system state-space model is represented as: (4)； in, , , , , , , , , ; S2. Using the extended fault observer on the state-space model (4) obtained in S1.1, the dynamic error system is obtained: Using the extended fault observer for model (4), consider the following observer: (5) ； in, and These are the augmented state vectors. and measurement output The estimated value; It is the gain of the discrete-time fault observer. and These are the gain matrices of the state observer and the fault observer, respectively. Define the estimation error as Combining (4) and (5), the error dynamic system is obtained as follows: (6) ； according to The error dynamic system is rewritten as: (7) ； in, It is a process matrix; From the above equation, we can see that due to the influence of parameter uncertainty, the state estimation... and system control input All of these affect the error system; in addition, the parameter uncertainty matrix and Since they are unknown, they are unsuitable for state estimation. and system control input If the resulting impact is considered as an unknown disturbance, then the error dynamic system simplifies to: (8)； in , , , , , ; Technology is one of the most studied methods for dealing with disturbances and noise. The technology assumes that the energy of interference and noise signals is bounded throughout the entire time domain. The following steps will employ... Technology to handle disturbances and noise; S3. Apply Lyapunov's second method to the dynamic error system (8) obtained in S2, and find the condition that satisfies... Observer gain matrix for performance: The designed observer gain matrix is , Represents a known, given matrix, with parameters , , The following linear matrix inequality conditions must be met. Use the optimization toolbox to calculate the specific values: (9) ； in, , ; ； S4. Using the state observations and fault estimates obtained from the fault observer designed in S3, establish a fault-tolerant controller for the parameter uncertainty system based on sliding mode control; According to (5), the observation results of the state and fault are expressed as follows: (10) ； in, and The estimates are divided into status and fault estimates. and These are the state observer gain and the fault observer gain, respectively. The state estimation error is expressed as: (11) ； in, and These are the state estimation error and the fault estimation error, respectively. Next, in order to achieve fault-tolerant control, the following sliding mold surface is designed: (12) ； in, It is a known, given matrix, and It is reversible; because The sliding surface is rewritten as: (13) ； To ensure the designed sliding surface reaches its ideal state and to reduce the impact of faults and uncertainties on the system, the following control law is designed: (14) ； in, , , , , ; and They are The upper and lower bounds, and They are The upper and lower bounds, It is a constant; Proof: Consider the following condition for the quasi-sliding mode inequality of a sliding mode controller for an aero-engine system with parameter uncertainties: (15) ； in, It is the difference between the sliding surfaces. It is a constant; Combining (1) and (11), the sliding surface (13) can be written as: (16) ； because, Process interference and measuring noise It is bounded; therefore and The upper and lower bounds are also obtained by estimating the set members, i.e. (17) ； Substituting the control law (14) into the sliding surface (15), the arrival law of the sliding surface is obtained as follows: (18) ； in, ； So, regardless , and How does the value change? The symbol is always with The signs are opposite, meaning that the closed-loop system (1) satisfies the sliding mode arrival condition (15); after the arrival condition is achieved, the system state makes a zigzag motion on the quasi-sliding surface, thus achieving stable fault-tolerant control.

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