Fault-tolerant control method for aero-engine actuator based on set-membership estimation and tube MPC

Abstract

This invention relates to a fault-tolerant control method for aero-engine actuators based on member estimation and Tube MPC, belonging to the field of fault-tolerant control for aero-engine systems. First, an augmented state observer is designed to simultaneously estimate the state and actuator faults; then, using H... ∞ The observer gain and state feedback gain are obtained using the LQR method, respectively, making the estimation and control errors robust to disturbances and noise. Furthermore, fault membership is estimated through centrosymmetric polyhedral analysis. Then, a fault-tolerant controller is designed based on the obtained observer gain, state feedback gain, and Tube MPC method. The fault-tolerant control method designed in this invention enables the controller to be robust to unknown disturbances and measurement noise, and, based on the Tube MPC method, ensures that the state strictly meets the control constraints of the aero-engine while compensating for actuator faults.

Description

TECHNICAL FIELD

[0001] The application relates to a fault-tolerant control method for an aero-engine actuator based on set membership estimation and Tube MPC, and belongs to the field of fault-tolerant control of an aero-engine system. BACKGROUND

[0002] Modern flight missions have higher and higher requirements for the control precision and stability of aero-engines. The working process of the aero-engine is extremely complex, and the flight conditions and working environment are always changing. For example, the working conditions of the aero-engine are different during taxiing, taking off, climbing, cruising, descending and maneuvering. The aero-engine control system needs to control the aero-engine to meet the requirements of the flight mission, and also needs to ensure that the aero-engine can work safely to avoid dangerous situations. The limit protection control function is introduced to meet the latter requirement, so that the aero-engine can work within the safety parameter range set under extreme working conditions, that is, the working state of the aero-engine is ensured to be not overheated, not over-speeded and not in surge. Meanwhile, due to the extremely complex structure, high load continuous work and other reasons, the system built by hardware is prone to various problems, and is affected by factors such as inherent life during long-time work. Light problems reduce performance, and heavy problems damage components. Therefore, reducing the influence of faults on the system is a necessary way to avoid economic losses and casualties. Therefore, the research on fault-tolerant control methods has attracted widespread attention from scholars.

[0003] On the other hand, MPC (Model Predictive Control) proposes an effective control method to deal with system constraints in control design. The basic idea of Tube MPC is to restrict all possible state trajectories within a pre-designed tube to ensure that the constraint conditions of all possible disturbances in the optimization problem are met. Due to the use of feedback control law, Tube MPC reduces the conservatism while maintaining similar computational load to traditional model predictive control. By constructing a positive invariant set to realize the tube, and taking the tube parameters as the decision variables of the optimization problem, the online design and update of the tube section are realized.

[0004] The actuator changes the oil supply, the fan or compressor stator guide vane angle, the geometric passage area of the tail nozzle, etc. of the engine according to the instructions of the controller to achieve the purpose of controlling the state of the engine. The failure of the actuator will interrupt or change the control output of the controller, so that the controlled object cannot obtain the required controlled input quantity. The failure of the actuator represents partial or complete failure of the control action. Actuator sticking is an example of complete failure, at this time it will not produce any action to the input signal, and damage, line burning, short circuit, foreign matter may cause complete failure of the actuator. The actuator failure can also be divided into sticking, constant gain change, constant deviation failure, etc. according to the manifestation.

[0005] Therefore, it is important to estimate the actuator fault of the aero-engine control system and implement fault-tolerant control to improve the safety and reliability of the system, and it has important significance for actual engineering. SUMMARY

[0006] In view of the problem that the output and state variables of the aero-engine may exceed the limit boundary when the actuator fails and is subjected to certain disturbance and noise, the application provides an aero-engine actuator fault-tolerant control method based on set membership estimation and Tube MPC.

[0007] To achieve the above purpose, the technical scheme adopted by the application is as follows:

[0008] An aero-engine actuator fault-tolerant control method based on set membership estimation and Tube MPC comprises the following steps:

[0009] S1. Considering that the system is subjected to disturbance and noise and the actuator fails, the state space of the system can be written as follows:

[0010]

[0011] where x is the state vector of the system, u is the control input vector of the system, y is the measured output vector of the system, y l is the limit output vector of the system, w is the process disturbance vector, v is the limit noise vector, v e is the measurement noise vector, f is the fault, A, B, C, C l , D l are known matrices with appropriate dimensions, D1, D, D2 are process disturbance, measurement noise and limit noise matrices respectively, and F is a known fault matrix.

[0012] It is assumed that the initial state, initial fault, process disturbance, measurement noise and limit noise are unknown, but satisfy the following conditions:

[0013]

[0014] where p0, q0, are known vectors.

[0015] S1.1 To estimate 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:

[0016] The augmented system can be written as follows:

[0017]

[0018] where,

[0019] h k = f k+1 - f k

[0020] S2. Construct the Luenberger observer for the augmented system obtained in S1:

[0021]

[0022] is the estimation of the augmented state, and L is the gain of the Luenberger observer.

[0023] S3. Based on the invariance set theory, separate the perturbation of the model, and obtain the nominal system:

[0024]

[0025] and are the state vector and input vector of the nominal system, respectively.

[0026] S4. Define the state estimation error: Combining (3) and (4), the estimation error dynamic system is obtained as:

[0027]

[0028] Define where L satisfies ρ(A L ) < 1. The estimation error dynamic system can be simplified as:

[0029]

[0030] where

[0031] Define the state control error: Combining (4) and (5), the control error dynamic system of the estimation system and the nominal system is obtained as:

[0032]

[0033] Define A K = A + BK, where K satisfies ρ(A K ) < 1, and K is the state feedback gain obtained by the LQR (Linear Quadratic Regulator) method.

[0034] The control error dynamic system can be simplified as:

[0035]

[0036] where

[0037] S5. Next we adopt H ∞ performance to deal with the disturbance and noise, and design the robust observer. The observer gain L and state feedback gain K are obtained by H ∞ and LQR method respectively:

[0038] H ∞ technique is a method that attracts most attention to deal with the disturbance and noise, H ∞ technique assumes that the disturbance and noise signals are bounded in the whole time domain, and then H ∞ technique is adopted to deal with the disturbance and noise;

[0039] For the obtained state estimation error dynamic system, the observer gain matrix L is solved to satisfy H ∞ performance:

[0040] The designed observer gain matrix is L = P -1 Y, P represents the given known positive definite matrix, and the parameters Y and γ need to satisfy the following linear matrix inequality condition. The specific numerical value can be obtained by using the optimization toolbox for calculation:

[0041]

[0042] where, The evaluation function and constraint function of LQR control are designed as:

[0043]

[0044] where Q and R are semi-positive and positive definite parameter matrices respectively, and the state feedback matrix K is solved.

[0045] S6. Solve the minimum robust positive invariant set, i.e. Tube size:

[0046] First, for the obtained estimation error system of the estimation system and the actual system, the disturbance set located in the set is defined as:

[0047]

[0048] Further, we get:

[0049]

[0050] Similarly, for the control error system of the obtained estimation system and the nominal system:

[0051] the disturbance set located in the set is defined as

[0052]

[0053] Further, we have

[0054]

[0055] Then the set S is defined as

[0056]

[0057] The minimal invariant set is calculated by repeatedly applying the Minkowski sum The set S is obtained.

[0058] S7. Next, the set-membership estimation of the fault is solved by using the central symmetric polytope method:

[0059] Augmented state The upper bound and the lower bound of the augmented state are given by

[0060]

[0061] where

[0062] |H k (i,j) | represents the absolute value of the element in the i-th row and j-th column of the matrix H k .

[0063] Finally, the upper bound and the lower bound of the fault f k are given by

[0064]

[0065] The upper bound and the lower bound of the state x k are given by

[0066]

[0067] where α = [I nx 0], β = [0 I nf ], nx is the dimension of the state x, nf is the dimension of the fault, I nx represents the identity matrix with dimension nx, and I nf represents the identity matrix with dimension nf.

[0068] S8. Next, the standard Tube MPC problem is solved to obtain the control input, and the estimated value of the fault is fed back to the control law for fault tolerance:

[0069] The optimization objective function is expressed as:

[0070]

[0071] where P, Q, R are weight matrices corresponding to the penalty functions, and are positive definite.

[0072] Considering the safety of the aero-engine and the saturation of the actuators, define the state constraint set X and the input constraint set U, symbol is the Pontryagin difference of the set.

[0073] The nominal state constraint and the nominal input constraint can be expressed as:

[0074]

[0075] The initial state and the final state of the nominal system satisfy

[0076] Therefore, the following quadratic output feedback Tube MPC problem is proposed:

[0077]

[0078] s.t.

[0079]

[0080]

[0081]

[0082] At each time, solve and use the first quantity of the control sequence obtained by solving as the control input

[0083] In order to offset the disturbance and compensate for the fault, the real control law is designed as follows:

[0084]

[0085] where Define A K = A + BK, where K satisfies ρ(A K ) < 1.

[0086] is the estimated value of the fault, is the control input of the nominal system, and K is the state feedback gain obtained by the LQR method.

[0087] Input the calculated u k into the system and execute.

[0088] Advantages of the present application:

[0089] In view of the problem that the output and state variables may exceed the limit boundary when the traditional aero-engine control method is affected by certain disturbance and noise or the actuator fails, the aero-engine actuator fault-tolerant control method based on set membership estimation and Tube MPC provided in the present application can effectively compensate the influence of the fault and ensure the engine to work within the safe range in the presence of disturbance and noise, and has high robustness. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 Fig. 1 is a block diagram of the aero-engine actuator fault-tolerant control method based on set membership estimation and Tube MPC;

[0091] Figure 2 Fig. 2 is a Tube MPC result diagram of robust output feedback;

[0092] Figure 3 Fig. 3 is a comparison result diagram of the output variables of the traditional MPC and Tube MPC;

[0093] Fig. 4(a) is a comparison result diagram of the output and state variables considering fault-tolerant control;

[0094] Fig. 4(b) is a comparison result diagram of the output and state variables without considering fault;

[0095] Fig. 4(c) is a comparison result diagram of the output and state variables without considering fault-tolerant control;

[0096] Figure 5 Fig. 5 is a set membership estimation result diagram of the fault. DETAILED DESCRIPTION

[0097] The aero-engine continuous system model in the book "Advanced Control of Turbofan Engine" by Hanz Richter is discretized by using Euler one-step method, and the sampling time interval Ts = 0.015s. Then, the fault and disturbance noise are considered in the system, and the corresponding parameter matrix is as follows:

[0098]

[0099]

[0100]

[0101] The observer gain L and the state feedback gain K are obtained by using H ∞ and LQR method respectively:

[0102]

[0103] w(t) is an unknown but bounded disturbance |w(t)|≤ [0.0025 0.0025] T v(t) is an unknown but bounded noise |v(t)|≤ [0.0025 0.0025] T and v e (t) is an unknown but bounded noise |v e (t)|≤ [0.1 0.1] T h(t) is also unknown but bounded |h(t)|≤ [0.05 0.05] T The reference value of the state is chosen as r = [50 50] T The initial state of the target is set as x0= [0 0] T The initial value of the estimate is set as the same as the true value, i.e. The initial value of the fault estimate is set as the same as the true value The weight matrix is taken as Q = diag(1, 1), R = diag(3000, 3000) respectively.

[0104] The output variable high-pressure turbine inlet temperature T 48 and the high-pressure compressor surge margin SmHPC are limited in the following ranges:

[0105] -150≤ΔT 48 ≤300, -10≤ΔSmHPC≤20

[0106] The input variable fuel flow W F , variable stator vane VSV, variable bleed valve VBV are limited in the following ranges:

[0107] -1≤ΔW F ≤2, -20≤ΔVSV≤15, -0.5≤ΔVBV≤0.4

[0108] The state variable fan speed ΔN f , compressor speed ΔN c are limited in the following ranges:

[0109] -300≤ΔN f ≤300, -300≤ΔN c ≤300

[0110] S9. The following considers the case that the actuator has a slow drift fault at the sampling time k = 40:

[0111]

[0112] The prediction horizon and the control horizon are taken as equal, i.e. 15, the sampling step is set as 100, and the simulation sampling period T is 15 milliseconds.

[0113] Next, to demonstrate the significant performance of the proposed method in fault-tolerant control, we perform simulation verification. The simulation results are shown in FIG. 6. Figures 2-5 Figure 2 show the behavior of Tube MPC. The Tube defines the unknown state trajectory, which converges to its reference value from the initial state for a random initial state where and a random sequence of acceptable state extreme values and output disturbances, the final state is contained in the terminal set. As shown in FIG. 7, the red solid line is the actual trajectory of the unknown disturbance sequence, and the green solid line is the optimal initial state sequence. Figure 1 shows the curve of the output variable ΔSmHPC. The red dashed line is the lower bound, and the green dashed line is the upper bound. We can see that under the influence of disturbances and noises, the output variable ΔSmHPC does not exceed the constraint range, but if we compare it with the traditional MPC, we can find that it seems to exceed the constraint range. Figure 3

[0114] As shown in FIG. 4, if we compare the actuator failure under the same disturbance and noise influence, after considering the fault-tolerant control strategy proposed in this patent, when the actuator has a slowly varying fault, neither the state nor the output will exceed the constraint range. In addition, both the state and the output variable satisfy their respective constraint conditions. After considering fault-tolerant control, the changes in state and output values are not significantly different from those without faults, which demonstrates the effectiveness of our fault-tolerant control method. In contrast, if the fault-tolerant control strategy is not considered, as the sampling step k gradually increases, the output variables ΔT 48 and ΔSmHPC may exceed their limit range. Because we can see from the figure that they are divergent. Similarly, as the sampling step k gradually increases, the state variable ΔN f may also exceed its limit range. Because we can see from the figure that they are divergent. Figure 5 The figure describes the set-membership estimation result of the fault, and it can be seen that the fault can be accurately enclosed by the upper and lower bounds. In summary, the fault-tolerant control method based on the central-symmetrical polyhedron and Tube MPC can effectively protect the system to operate within the safe range. Even in the presence of faults, unknown disturbances, and noises, the fault-tolerant control method can still achieve robust stability. The fault-tolerant control method is crucial for ensuring the safety and reliability of the system, reducing the risk related to actuator failure, and improving the performance of the entire system.

[0115] ​​The above embodiments only express the implementation ways of the present application, and cannot be understood as the limitation to the scope of the present application patent. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application.

Claims

1. A fault-tolerant control method for aeroengine actuators based on set-membership estimation and Tube MPC, characterized in that, The steps are as follows: S1, establishing an augmented state, forming a new augmented state vector with the actuator fault and the state vector; A discrete system state space model: ； wherein , , , , , ; xk+1denotes the augmented state vector at time k + 1, denotes the fault rate of change at time k, xkdenotes the augmented state vector at time k, T denotes the transpose; S2, constructing a Luenberger observer for the augmented system; The constructed Luenberger observer: ； denotes the estimate of the augmented state vector at time k + 1, denotes the estimate of the augmented state vector at time k, L denotes the gain of the Luenberger observer; S3, separating the disturbance from the model based on the invariant set theory, and establishing a nominal model; S4, establishing an estimation error dynamic system and a control error dynamic system; S5 utilizes and the LQR method to obtain the observer gain L and the state feedback gain K; S6 solving the minimum robust positive invariant set, i.e. the Tube size; ​ ； ； wherein, is a robust positive invariant set of the augmented state estimation error system, is a robust positive invariant set of the augmented state control error system, S is also a robust positive invariant set; W, Ve, H are polytopic sets to which process disturbance, measurement noise and fault rate of change belong; the minimum robust positive invariant set is calculated by applying Minkowski sum through repeated iteration set, and then the S set is obtained; S7 uses the central symmetric polytope method to solve the set member estimation of the fault; augmented state upper bound and lower bound expressed as: ； wherein ; representative matrix absolute value of the element in the i-th row and j-th column H k The calculation process is given by the following equation: ； Finally, the upper bound and the lower bound of the fault are expressed as: ； State upper bound and lower bound expressed as: ； wherein, nx is the dimension of the state variable x, and nf is the dimension of the fault; S8, solving a standard Tube MPC problem to obtain a control input, and feeding back the estimated value of the fault to the control law for fault tolerance; ； ； wherein, represents a cost function, N represents a time domain, P, Q, R are weight matrices corresponding to penalty functions, and are all positive definite; is represented as an equality constraint, is represented as a nominal state constraint, is represented as a nominal input constraint, the initial state and the final state of the nominal system respectively satisfy , constraints, are all inequality constraints; and at each time instant, the first quantity of the control sequence obtained by solving is used as the control input ; The real control law is designed as follows: ； wherein, represents the input of the nominal system at time k, K represents the state feedback gain, represents the augmented state control error at time k, represents the fault estimate at time k; The calculated u k The input system and executes.

2. The set-membership estimation and Tube MPC based fault-tolerant control method for a propulsion actuator according to claim 1, wherein, In the step S3, the disturbance is separated from the model based on the invariant set theory, and a nominal model is established: ； xkand ukdenote the state vector and input vector of the nominal system at time k, respectively.

3. The set-membership estimation and Tube MPC based fault-tolerant control method for a propulsion actuator according to claim 1 or 2, characterized in that, In the step S4, an estimation error dynamic system and a control error dynamic system of the augmented state are established: ； wherein ; ； wherein ; , , , ； where w k is the process disturbance vector, v k is the measurement noise vector, v ek is the limit noise vector, A, C, I, , is a known constant matrix, D1, D, D2 are the process disturbance, measurement noise and limit noise matrices, respectively, F is a known fault matrix; and L represents the gain of the Luenberger observer.

4. The set-membership estimation and Tube MPC based fault-tolerant control method for a propulsion actuator according to claim 1 or 2, characterized in that, In the step S5, the observer gain L and the state feedback gain K are obtained by using and LQR method, respectively. The designed observer gain matrix is P denotes a given positive definite matrix, and the parameter Y, The following linear matrix inequality condition needs to be satisfied, and the specific numerical value can be obtained by calculation using the optimization toolbox: ； wherein ; The evaluation function and the constraint function of the LQR control are designed as follows: ； Wherein Q and R are semi-positive and positive definite parameter matrices respectively, and the state feedback matrix K is solved.

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