Joint implementation method for failure reconfiguration and fault-tolerant control in aircraft landing phase

Abstract

The application discloses a kind of aircraft landing stage fault reconfiguration and fault-tolerant control combined implementation method, symmetric positive definite matrix P1, P2, X and matrix K, K f , L, Y1, Y2 that meet linear matrix inequality are solved, and the known quantity in the linear matrix inequality is obtained according to aircraft landing mathematical model, extended system equation, state observation equation and closed-loop control equation;The obtained matrix L, K, K f It is substituted into the state observation equation and the closed-loop control equation respectively, while achieving aircraft landing process fault reconfiguration and fault-tolerant control.The application simultaneously solves fault reconfiguration algorithm parameters and fault-tolerant control algorithm unknown parameters in a short time, reduces the amount of calculation compared with other methods, and realizes automatic landing task of aircraft.

Description

Technical Field

[0001] This invention belongs to the field of aircraft automatic control and relates to an automatic landing control method for aircraft, particularly a method for jointly implementing fault reconstruction and fault-tolerant control during the landing phase of an aircraft. Background Technology

[0002] With the increasing demand for automatic landing missions, the requirements for automatic landing functions of aircraft in different environments are constantly increasing. For example, if an actuator malfunctions during the landing process, the aircraft control system needs to be able to automatically detect the fault and effectively reconstruct the fault through a specific algorithm. Based on this, a fault-tolerant control algorithm is designed for the aircraft landing model with faults to ensure that the aircraft can still safely complete the automatic landing mission even in the presence of faults.

[0003] Currently, typical aircraft fault reconfiguration and fault-tolerant control methods often study fault reconfiguration and fault-tolerant control separately, and the aircraft landing models they target are often linear models. For example, Zhou Yang et al., in their paper "Control Allocation Method for Fault Reconfiguration of Control Surfaces Based on Controllability," proposed a method to modify the control allocation weight coefficients to complete the aircraft fault reconfiguration task, addressing the fault problem of control surfaces in aircraft actuators. Another example is Qin Tiancheng et al., in their paper "Fault-Tolerant Control Strategy for Large Civil Aircraft Based on Incremental Dynamic Inverse," who specifically studied the theory of aircraft fault-tolerant control under known aircraft fault conditions.

[0004] The above-mentioned literature has the following problems in aircraft fault reconstruction and fault-tolerant control: 1. The aircraft model is often simplified to a linear model, neglecting nonlinear terms, which does not conform to the actual situation of the aircraft; 2. The fault reconstruction problem and the fault-tolerant control problem are studied separately, which leads to the need to design fault reconstruction algorithms and fault-tolerant control algorithms separately, and calculate their respective unknown parameters, making the solution time longer. This invention proposes a joint implementation method of fault reconstruction and fault-tolerant control during the aircraft landing phase, which can effectively solve the above problems and complete the automatic landing mission under fault conditions. Summary of the Invention

[0005] In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a method for the joint implementation of fault reconstruction and fault-tolerant control during the aircraft landing phase, which completes the automatic landing task under fault conditions while considering nonlinear terms and reduces the amount of computation.

[0006] To address the aforementioned technical problems, the present invention provides a method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing, comprising:

[0007] Solving for the linear matrix inequalities yields symmetric positive definite matrices P1, P2, X and matrices K, K', satisfying the symmetric positive definite matrices P1, P2, X and K', K', K''. f L, Y1, Y2, the linear matrix inequality is:

[0008]

[0009]

[0010] in:

[0011] G 11 =A1X-B1Y2+XA1 T -(B1Y2) T

[0012]

[0013]

[0014] X = P2 -1

[0015] A2 = A1 - LC

[0016] Y1 = P1L

[0017] Y2 = KX

[0018] The known quantities in the linear matrix inequality are obtained from the aircraft landing mathematical model, the extended system equations, the state observation equations, and the closed-loop control equations.

[0019] The obtained matrices L, K, K f Substituting these equations into the state observation equation and the closed-loop control equation, respectively, simultaneously achieves fault reconstruction and fault-tolerant control during the aircraft landing process.

[0020] Furthermore, the mathematical model for the aircraft landing is as follows:

[0021]

[0022] Where x(t) is the state variable, y(t) is the output variable, u(t) represents the system control input, A, B, and C are the system matrices after equilibrium point linearization, and f a (t) represents the actuator failure state of a small aircraft, F a Let f(x,t) be the coefficient matrix of the defined fault terms, and let f(x,t) be the nonlinear term of the small aircraft landing system, satisfying:

[0023]

[0024] Where V represents the aircraft velocity, Δm is the mass uncertainty term, D represents aerodynamic drag, β represents the sideslip angle, Y represents the aerodynamic side force, T represents the engine thrust, α represents the angle of attack, L represents the aerodynamic lift, f(x,t) satisfies the Lipschitz condition, and the system fault derivative is bounded, satisfying: ρ1 is the upper bound of the fault derivative. The nonlinear term of the system is bounded, satisfying ||f(x,t)||≤ρ2, where ρ2 is the upper bound of the nonlinear term.

[0025] Furthermore, the extended system equations are as follows:

[0026]

[0027] in,

[0028] Furthermore, the state observation equation is:

[0029]

[0030] Where L is the unknown parameter of the observer matrix to be determined. and The values ​​are x1 and y1, respectively.

[0031] Furthermore, the closed-loop control equation is:

[0032]

[0033] Where K, K f Let be the coefficient matrix of the fault-tolerant controller to be determined. The system fault estimate is bounded, satisfying: ρ3 is the upper bound of the fault estimate.

[0034] The beneficial effects of this invention are as follows: This invention addresses the automatic landing problem of aircraft, especially those with malfunctions. It designs a longitudinal model of the aircraft landing process containing nonlinear terms and actuator failure terms. Compared with models established by other methods, this model is more consistent with reality. It designs aircraft fault reconstruction principles and fault-tolerant control principles. By constructing a method to solve a series of linear matrix inequalities, it can simultaneously solve the parameters of the fault reconstruction algorithm and the unknown parameters in the fault-tolerant control algorithm in a short time. Compared with other methods, it reduces the amount of computation and realizes the automatic landing task of the aircraft. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 These are the angular velocities of different systems;

[0037] Figure 3 It is angular velocity error;

[0038] Figure 4 These are the pitch angles of different systems;

[0039] Figure 5It is the pitch angle error;

[0040] Figure 6 It refers to actuator failure and reconfigured actuator failure;

[0041] Figure 7 It is the reconstruction error of the fault. Detailed Implementation

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] This invention provides a method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing, comprising:

[0044] Solving for the linear matrix inequalities yields symmetric positive definite matrices P1, P2, X and matrices K, K', satisfying the symmetric positive definite matrices P1, P2, X and K', K', K''. f L, Y1, Y2, the linear matrix inequality is:

[0045]

[0046]

[0047] in:

[0048] G 11 =A1X-B1Y2+XA1 T -(B1Y2) T

[0049]

[0050]

[0051] X = P2 -1

[0052] A2 = A1 - LC

[0053] Y1 = P1L

[0054] Y2 = KX

[0055] The known quantities in the linear matrix inequality are obtained from the aircraft landing mathematical model, the extended system equations, the state observation equations, and the closed-loop control equations.

[0056] The mathematical model for aircraft landing is:

[0057]

[0058] Where x(t) is the state variable, y(t) is the output variable, u(t) represents the system control input, A, B, and C are the system matrices after equilibrium point linearization, and f a (t) represents the aircraft actuator failure state, Fa Let f(x,t) be the coefficient matrix of the defined fault terms, and let f(x,t) be the nonlinear term of the aircraft landing system, satisfying:

[0059]

[0060] Where V represents the aircraft velocity, Δm is the mass uncertainty term, D represents aerodynamic drag, β represents the sideslip angle, Y represents the aerodynamic side force, T represents the engine thrust, α represents the angle of attack, L represents the aerodynamic lift, f(x,t) satisfies the Lipschitz condition, and the system fault derivative is bounded, satisfying: ρ1 is the upper bound of the fault derivative. The nonlinear term of the system is bounded, satisfying ||f(x,t)||≤ρ2, where ρ2 is the upper bound of the nonlinear term.

[0061] The extended system equations are:

[0062]

[0063] in,

[0064] The state observation equation is:

[0065]

[0066] Where L is the unknown parameter of the observer matrix to be determined. and The values ​​are x1 and y1, respectively.

[0067] The closed-loop control equation is:

[0068]

[0069] Where K, K f Let be the coefficient matrix of the fault-tolerant controller to be determined. The system fault estimate is bounded, satisfying: ρ3 is the upper bound of the fault estimate.

[0070] The obtained matrices L, K, K f Substituting the state observation equation and the closed-loop control equation into the equations respectively, fault reconstruction and fault-tolerant control during the aircraft landing process are achieved simultaneously.

[0071] The flowchart of the present invention is as follows Figure 1As shown, this invention mainly addresses the longitudinal automatic landing problem of aircraft. A nonlinear model of longitudinal landing is established, considering aircraft mass uncertainty and actuator failures. The nonlinear model is then transformed into a linear small-disturbance model, incorporating nonlinear terms and fault terms. Based on this, the aircraft state terms are extended to construct an extended landing system. An extended state observer is designed for this extended system, forming a state observation system. A fault-tolerant controller is also involved, forming a fault-tolerant control closed-loop system. For both the state observation system and the fault-tolerant control system, a linear matrix inequality satisfying Lyapunov stability is comprehensively designed to simultaneously solve for the unknown parameters of both the fault reconstruction algorithm and the fault-tolerant control algorithm. Finally, the effectiveness of the method is verified through simulation.

[0072] 1. Construct a longitudinal mathematical model for automatic aircraft landing.

[0073] In the geodetic coordinate system, the nonlinear equations of motion for the longitudinal descent of the aircraft are as follows:

[0074]

[0075] In the above formula: V represents aircraft speed, α represents angle of attack, β represents sideslip angle, θ represents pitch angle, φ represents roll angle, p represents roll rate, q represents pitch rate, r represents yaw rate, g represents gravitational acceleration, D represents aerodynamic drag, L represents aerodynamic lift, Y represents aerodynamic side force, T represents engine thrust, m represents aircraft mass, and I... xx I represents the moment of inertia along the x-axis. yy I represents the moment of inertia along the y-axis. zz I represents the moment of inertia along the z-axis. xz The x-axis represents the product of inertia with respect to the z-axis, and M represents the pitching moment of the aircraft.

[0076] Since the landing process often occurs after a mission, different aircraft consume different amounts of fuel after different missions, resulting in different fuselage masses. Other literature often does not consider this variation. However, the mass of an aircraft is significantly affected when it is fully fueled or about to consume all its fuel. Therefore, this invention considers the uncertainty of aircraft mass based on the above formula, so formula (1) can be further expressed as follows:

[0077]

[0078] In the above equation, Δm represents the mass uncertainty term. Separating the mass uncertainty term from the other terms, the other terms can be linearized using equilibrium point linearization to obtain a linear model. This model can be further expressed as follows:

[0079]

[0080] In the above formula: x(t) is the state variable, y(t) is the output variable, A, B, and C are the system matrices after linearization of the equilibrium point, and f a (t) represents the aircraft actuator failure state, F a Here is the coefficient matrix for the fault terms, and f(x,t) represents the nonlinear terms of the aircraft landing system, specifically as shown in the following equation:

[0081]

[0082] This invention proposes the following steps to achieve the above principle:

[0083] Step 1: Using the principle of equilibrium point linearization, transform equation (2) into equation (3), where the system matrix can be obtained using Matlab software, and the nonlinear terms are shown in equation (4).

[0084] Step 2: Customize the aircraft's actuator faults, including throttle and elevator in the longitudinal direction, and define the actuator fault term coefficient matrix F according to the actual situation. a .

[0085] The above steps construct a mathematical model for aircraft longitudinal landing that includes fault terms and nonlinear terms. This invention also makes the following assumptions:

[0086] Assumption 1: The linear term f(x,t) in equation (1) satisfies the Lipschitz condition, that is, it satisfies the following inequality:

[0087]

[0088] In the above formula: This is the Lipschitz constant.

[0089] Assumption 2: The system fault derivative is bounded, i.e., it satisfies: ρ1 is the upper bound of the fault derivative.

[0090] Assumption 3: The nonlinear terms of the system are bounded, that is, they satisfy ||f(x,t)||≤ρ2, where ρ2 is the upper bound of the nonlinear terms.

[0091] 2. Aircraft State Transition and Observer Design

[0092] According to formula (1), the present invention will determine the fault f a The system state x is merged with the system state x to form a new state variable x1, resulting in the following extended system state space:

[0093]

[0094] Define extended variables in the following form:

[0095]

[0096] Therefore, the extended system state-space equations are as follows:

[0097]

[0098] For the extended system shown in equation (8), an extended observer of the following form is designed:

[0099]

[0100] In the above formula: L is the unknown parameter of the observer matrix to be determined. and Let x1 and y1 be the observed values, and define the following error variables:

[0101]

[0102] Therefore, the dynamic equation based on the estimation bias of the state observer can be obtained:

[0103]

[0104] This invention designs a fault-tolerant control algorithm for aircraft landing under fault conditions by utilizing state feedback. The fault-tolerant control law is as follows: in Let x1 be an estimated value. f a Substituting the estimated value into the fault-tolerant control algorithm of the aircraft's longitudinal landing mathematical model, we can obtain the closed-loop control equation in the following form:

[0105]

[0106] In the above formula: K,K f Let be the coefficient matrix of the fault-tolerant controller to be determined.

[0107] This invention proposes the following steps to achieve the above principle:

[0108] Step 1: Define the extended variables as shown in Equation (7), design the state observer as shown in Equation (9), and then obtain the state and fault observation equations as shown in Equation (11);

[0109] Step 2: Design fault-tolerant control algorithm The closed-loop control equation for the longitudinal landing of the aircraft is obtained, as shown in equation (12).

[0110] Following the steps above, the state observation equations and closed-loop control equations can be obtained, and the following assumptions are made:

[0111] Assumption 4: The system fault estimate is bounded, i.e., it satisfies: ρ3 is the upper bound of the fault estimate.

[0112] 3. Design a fault reconstruction and fault-tolerant control solver

[0113] This invention innovatively designs an integrated algorithm that can simultaneously realize fault reconstruction and fault-tolerant controller solution. This approach has the following advantages: while realizing fault reconstruction, it realizes active fault-tolerant control, solves the impact of fault reconstruction error on fault-tolerant controller design, and achieves decoupling between the two.

[0114] This invention proposes the following theorem: There exist symmetric positive definite matrices P1, P2, X, and matrices K, K f Let L, Y1, and Y2 satisfy the following linear matrix inequality:

[0115]

[0116]

[0117] This allows the system to simultaneously satisfy the asymptotic stability of a bias-based state observation system and the asymptotic stability of a fault-tolerant control closed-loop system. The expressions for the other variables in the above two equations are as follows:

[0118] G 11 =A1X-B1Y2+XA1 T -(B1Y2) T (15)

[0119]

[0120]

[0121] X = P2 -1 (18)

[0122] A2 = A1 - LC (19)

[0123] Y1=P1L (20)

[0124] Y2=KX (21) Proof: This invention defines a Lyapunov function of the following form:

[0125] V(t) = e x T P1e x +x1 T P2x1 (22)

[0126] In the above formula: P1 and P2 are symmetric positive definite matrices.

[0127] Differentiating equation (22) with respect to time yields the following equation:

[0128]

[0129] This invention utilizes the following lemma:

[0130] Lemma 1: If Assumption 1 holds, then there exists a positive definite matrix P such that the following inequality holds:

[0131]

[0132] In the above formula: e represents the state estimate. x (t) represents the state estimation bias, i.e., Lemma 2: Given matrices X and Y, there exists a positive definite matrix P such that the following inequality holds:

[0133] X T Y+Y T X≤X T HX+Y T H -1 Y

[0134] Using the lemma above, the following inequality holds:

[0135]

[0136] 2x1 T P2D1f(x1,t)≤x1 T P2D1(P2D1) T x1+f(x1,t) T f(x1,t) (25)

[0137]

[0138]

[0139]

[0140] Substituting inequalities (24)-(28) into (23) yields the following equation:

[0141]

[0142] Therefore, equation (25) can be written as follows:

[0143]

[0144] Among them, E 11 E 22 They represent the following respectively:

[0145]

[0146] The matrix parameters K, L, P2 are calculated using the following LMI form:

[0147]

[0148] Considering the upper right term and E in the above equation 11 E 22 If some terms contain more than two unknowns, LMI cannot solve the problem. The following approach is used: Let X = P2 -1 Multiply the above equation by the diagonal matrix on the left and right respectively. We obtain the following formula:

[0149]

[0150] For any scalar γ, we can obtain

[0151]

[0152] That is, the following equation holds true:

[0153]

[0154] According to Schur's lemma, equation (33) can be transformed into the following equation:

[0155]

[0156] Based on assumptions 1 to 3 and equation (36), equation (30) can be expressed as follows:

[0157]

[0158] make but Therefore, equation (37) is equivalent to:

[0159]

[0160] Define the following formula:

[0161]

[0162] If the system is stable, it is necessary to Therefore, it suffices that Ω < 0, according to Schur's complement lemma:

[0163]

[0164] Define Y1 = P1L and Y2 = KX. Using Schur's complement lemma, equation (40) can be transformed into equation (13).

[0165] To ensure good convergence performance of the observer, the eigenvalues ​​of the matrix (A1-LC) need to be configured in the region D(α,r), where α and r represent the center and radius of the circle, respectively, and can be calculated using equation (14).

[0166] This invention proposes the following steps to achieve the above principle:

[0167] Step 1: Define the intermediate variables shown in equations (15) to (21). The known quantities in the above variables are all from the mathematical model of aircraft landing, state observation equations, and closed-loop control equations.

[0168] Step 2: Use the library functions in Matlab to implement the linear matrix inequalities shown in equations (13) and (14) and solve for the unknown parameters;

[0169] Step 3: Substitute the solution from the previous step into the state observation equation and the closed-loop control equation to simultaneously achieve the tasks of fault reconstruction and fault-tolerant control during the aircraft landing process.

[0170] 4. Simulation verification of automatic aircraft landing

[0171] To verify the effectiveness of the method proposed in this invention, the following simulation case is designed: a certain actuator fault is designed for the aircraft during landing, and the landing equation of the aircraft (including nonlinear terms and fault terms) is constructed according to the aforementioned principles. The fault reconstruction and fault-tolerant control algorithm of this invention is activated to solve for the fault observations and fault-tolerant control quantities. The simulation curves are shown below. Figures 2-7 As shown, the analysis is as follows:

[0172] (1) Figure 2 The figures show the pitch angular velocity of the original system, the pitch angular velocity of the faulty system, and the pitch angular velocity of the reconstructed system. It can be seen that when the actuator malfunctions, the system's angular velocity fluctuates, making it difficult to maintain equilibrium, as shown by the solid blue line. After reconstruction and fault tolerance, the system maintains pitch angular velocity equilibrium in approximately 8 seconds, as shown by the dashed black line. Figure 3 The angular velocity deviation after the fault tolerance was reached 0 in about 8 seconds.

[0173] (2) Figure 4 The figures show the pitch angles of the original system, the faulty system, and the reconstructed system. It can be seen that when the actuator malfunctions, the system's pitch angle fluctuates and becomes difficult to maintain balance, as shown by the blue solid line. After reconstruction and fault tolerance, the system reaches pitch angle equilibrium in approximately 8 seconds, as shown by the black solid line. Figure 5 The pitch angle deviation after the fault tolerance was reached 0 in about 8 seconds.

[0174] (3) Figure 6 This is an actuator fault added to the system, which generates a biased sinusoidal fault around the 5th second. Figure 7 The reconfiguration error is due to the actuator fault. At the 5th second, the reconfiguration error is relatively large due to the sudden change in the fault. After the 5th second, the reconfiguration error becomes quite small.

[0175] In summary, simulations have demonstrated the effectiveness of this method. By solving a series of linear matrix inequalities, both fault reconstruction and fault-tolerant control of the system are achieved, enabling the safe landing of the aircraft.

Claims

1. A method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing, characterized in that, include: Solving for the linear matrix inequality yields a symmetric positive definite matrix. , , sum matrix , , , , The linear matrix inequality is: ； ； in: in, The system matrix after linearization of the equilibrium point; Let be the coefficient matrix of the fault-tolerant controller to be determined; Let be the observer coefficient matrix to be determined; It is any scalar; It is the Lipschitz constant; This is the upper bound of the fault derivative; This is the upper bound of the nonlinear term; This is the upper bound of the fault estimate; The extended matrix of the state and state error is as follows: ; The known quantities in the linear matrix inequality are obtained from the aircraft landing mathematical model, the extended system equations, the state observation equations, and the closed-loop control equations. Substitute the obtained matrix L into the state observation equation, , By substituting the closed-loop control equations, fault reconstruction and fault-tolerant control during the aircraft landing process can be achieved simultaneously.

2. The method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing as described in claim 1, characterized in that: The mathematical model for the aircraft landing is as follows: ； in, For state variables, For output quantity, Indicates system control input, , The system matrix after linearization at the equilibrium point. This indicates a faulty actuator in a small aircraft. For the defined fault term coefficient matrix, For the nonlinear term of the small aircraft landing system, it satisfies: ； in, Indicates aircraft speed. For quality uncertainty, Indicates aerodynamic drag. Indicates the sideslip angle. Indicates aerodynamic lateral force. Indicates engine thrust. Indicates the angle of attack. Indicates aerodynamic lift. The system fault derivative is bounded if the Lipschitz condition is satisfied, and the following conditions are met: , Given the upper bound of the fault derivative, the nonlinear terms of the system are bounded, satisfying... , This is the upper bound of the nonlinear term.

3. The method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing as described in claim 2, characterized in that: The extended system equations are: ； in, .

4. The method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing as described in claim 3, characterized in that: The state observation equation is: ； in, The unknown parameters are the observer matrix to be determined. and They are respectively and The observed values.

5. The method for jointly implementing fault reconstruction and fault-tolerant control during aircraft landing as described in claim 4, characterized in that: The closed-loop control equation is: ； in, The system fault estimate is bounded, satisfying: , This is the upper bound of the fault estimate. This is the estimated fault value.

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