Sliding mode control-based fault-tolerant control method for preset performance of morphing aircraft

Abstract

The invention provides a fault-tolerant control method for preset performance of a morphing aircraft based on sliding-mode control. The fault-tolerant control method comprises the following steps: establishing a longitudinal nonlinear dynamic model of the morphing aircraft; based on the longitudinal nonlinear dynamic model of the morphing aircraft, establishing a longitudinal nonlinear dynamic model of the morphing aircraft under the fault condition of the execution mechanism; the method comprises the following steps: extracting a speed subsystem and an attitude subsystem aiming at a longitudinal nonlinear dynamic model of a morphing aircraft under an execution mechanism fault condition; carrying out sliding-mode control-based preset performance fault-tolerant controller design on the attitude subsystem; aiming at a speed subsystem, combining an attitude subsystem controller, and carrying out sliding mode control-based preset performance fault-tolerant controller design; the two designed controllers are utilized to realize the fault-tolerant control of the variant aircraft under the condition of executing mechanism fault. The sliding mode control and the preset performance control are combined, so that the conservative property is improved by quick response, the fault-tolerant capability is enhanced by switching the control law, and the stability is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control of variable aircraft, and particularly to a preset performance fault-tolerant control method for variable aircraft based on sliding mode control. Background Technique

[0002] The problem of fault-tolerant control of variable aircraft is one of the key and difficult problems in the research of variable aircraft. Ensuring the safe and stable flight of the aircraft under the condition of actuator failure has great practical significance and also has a profound impact on theoretical research.

[0003] At present, variable aircraft can change their external structures according to flight environments and mission requirements, showing great application potential in both military and civilian fields, and have become the current forefront hotspots in the research of new aircraft control technologies. However, the problem of fault-tolerant control of variable aircraft remains an unsolved key and difficult problem. Especially, how to ensure the attitude stable control of variable aircraft under the condition of sudden actuator failure is still a very challenging problem. The actuator herein refers to the drive mechanism of the aircraft's control surfaces (such as rudders, elevators, ailerons, etc.).

[0004] The goal of fault-tolerant control of variable aircraft is to ensure that the variable aircraft still has safe and stable flight and strong robustness performance under the condition of failure in a complex flight environment. Existing fault-tolerant control methods can be divided into two categories: active fault-tolerant control and passive fault-tolerant control. Although the active control method has lower conservatism, the control structure needs to be switched, and there is a time delay in the fault detection and isolation structure, which reduces the reliability of the control system during actual flight. Therefore, for the sudden actuator failure of variable aircraft, a passive fault-tolerant control method is considered. Passive fault-tolerant control itself does not rely on the fault information of the system. This kind of controller is preset in advance and will not be changed due to system failure. Therefore, it does not need to design a fault diagnosis scheme and can ensure that the system has a certain robustness regardless of whether the system fails or not. Most of the existing passive fault-tolerant control methods are based on the Lyapunov function, based on traditional control methods such as backstepping control method and sliding mode control method, and apply the traditional control method to the fault of the aircraft attitude control system to study the fault-tolerant control law.

[0005] In recent years, due to the increasing requirements for the transient and steady-state performance of the system in the fault-tolerant control problem of morphing aircraft, the use of preset performance control to solve this problem has gradually attracted more and more researchers' attention. The core idea of the preset performance control method is to artificially design a performance constraint envelope for the system state (usually the system error), and characterize the transient and steady-state performance of the controlled system through the convergence characteristics of the performance constraint function. This method has strong robustness, can cope with various types of faults and uncertainties, and can also flexibly design the control law according to different performance requirements and system characteristics to meet specific performance indicators. However, inaccurate models may affect the control effect, and to ensure performance in the worst case, the design is relatively conservative, making the system unable to achieve the best performance under normal conditions. The sliding mode control method can enhance the robustness of the attitude control system of morphing aircraft under model uncertainty and external disturbance. Therefore, how to combine the sliding mode control with the preset performance control method, aiming at the morphing aircraft with actuator faults, overcome the adverse effects of composite disturbances, actuator effectiveness loss faults and time-varying offset faults, and ensure that the tracking error meets the preset performance constraints is an urgent problem to be solved at present. Summary of the Invention

[0006] Aiming at the above-mentioned shortcomings of the prior art, the present invention proposes a preset performance fault-tolerant control method for morphing aircraft based on sliding mode control, which combines sliding mode control with preset performance control, can quickly respond to improve conservativeness, enhance the fault-tolerant ability by switching the control law, and improve stability.

[0007] The present invention discloses a preset performance fault-tolerant control method for morphing aircraft based on sliding mode control, including the following steps:

[0008] Step 1: Establish a longitudinal nonlinear dynamic model of the morphing aircraft;

[0009] Step 2: Based on the established longitudinal nonlinear dynamic model of the morphing aircraft, considering partial actuator failure faults and time-varying offset faults, establish a longitudinal nonlinear dynamic model of the morphing aircraft under actuator fault conditions;

[0010] Step 3: For the longitudinal nonlinear dynamic model of the morphing aircraft under actuator fault conditions, extract the velocity subsystem and the attitude subsystem;

[0011] Step 4: Design a preset performance fault-tolerant controller based on sliding mode control for the extracted attitude subsystem to obtain a well-designed attitude subsystem controller;

[0012] Step 5: For the extracted velocity subsystem, combined with the attitude subsystem controller, design a preset performance fault-tolerant controller based on sliding mode control to obtain a well-designed velocity subsystem controller;

[0013] Step 6: Use the attitude subsystem controller and the speed subsystem controller to achieve fault-tolerant control of the morphing aircraft under the condition of actuator failure.

[0014] Furthermore, the specific steps of Step 1 are as follows: For the variable wingspan aircraft, establish the longitudinal non-linear dynamic model of the variable wingspan aircraft, and then simplify the longitudinal non-linear dynamic model of the variable wingspan aircraft to finally obtain a simplified control-oriented system model:

[0015]

[0016] Where, is the state vector, V and h are the aircraft speed and altitude, α, are the angle of attack and pitch angle of the aircraft respectively, and q is the component of the rotational angular velocity of the body coordinate system relative to the ground coordinate system on the z-axis of the body coordinate system; u = [δ e , δ t T is the input vector, δ e is the rudder deflection angle, and δ t is the engine throttle opening; ξ ∈ [0, 1] is the wingspan deformation rate, d is the composite disturbance, and f(x, ξ) and g(x, ξ) are system functions;

[0017] And:

[0018]

[0019]

[0020] Where, Q = 0.5ρV 2 represents the dynamic pressure, where ρ is the atmospheric density, S w is the wing reference area, m is the aircraft mass, and I y is the component of the aircraft moment of inertia about the z-axis of the body coordinate system, is the engine thrust coefficient, C D0 , C L0 , C m0 are the drag coefficient, lift coefficient, and pitch moment coefficient at zero angle of attack respectively, are the aerodynamic coefficients of lift and pitch moment with respect to the angle of attack, are the second aerodynamic derivatives of drag and lift with respect to the angle of attack, c A is the mean geometric chord length of the wing, are the aerodynamic derivatives of lift, drag, and pitch moment with respect to the elevator deflection angle.

[0021] Furthermore, the specific steps of Step 2 are as follows:

[0022] Step 2.1: Establish the fault model of the i-th actuator:​

[0023]

[0024] Among them, λ i and r i are the indication factors of different faults. λ i is the indication factor of the partial benefit loss fault, and r i is the indication factor of the time-varying offset fault. And 0 ≤ λ i ≤ 1, r i is 0 or 1. According to different combinations of λ i and r i , different working states of the actuator can be obtained: when λ i = 1 and r i = 0, it means that the actuator has no fault; when 0 < λ i < 1 and r i = 0, it means that the actuator has a partial benefit loss fault; when λ i = 0 and r i = 1, it means that the actuator has a time-varying offset fault; when 0 < λ i < 1 and r i = 1, it means that the actuator has both a partial benefit loss and a time-varying offset fault;

[0025] Step 2.2: Based on the above fault model, represent the actual control input vector u′(t) as:

[0026]

[0027] Among them, the matrix λ = diag{λ1, λ2} represents the unknown control benefit loss faults occurring in the engine throttle opening δ t and the rudder deflection angle δ e among the two control inputs. r = diag{r1, r2}, v(t) = [δ t , δ e T , t f represents the fault occurrence time;

[0028] Step 2.3: Replace the input vector u in the simplified control-oriented system model with the actual control input vector u′(t) to obtain the variant aircraft model under the actuator fault condition:

[0029]

[0030] Furthermore, the speed subsystem and the attitude subsystem extracted in Step 3 are respectively:

[0031] ​

[0032] In the formula, the system functions f1(x1, ξ), g1(x1, ξ), f2(x2, ξ), and g2(x2, ξ) are respectively:

[0033]

[0034] where d1 is the composite disturbance of the velocity subsystem; d2 is the composite disturbance of the attitude subsystem.

[0035] Furthermore, the controller of the attitude subsystem designed in step 4 is:

[0036]

[0037] where k2 > 0 is a parameter to be designed, c2 is a parameter to be designed, s2 is the sliding mode surface function, is the pitch angle reference signal;

[0038] and the sliding mode surface function s2 is:

[0039]

[0040] In the formula, ε2 is the inverse function of the hyperbolic tangent function S(ε2);

[0041]

[0042] In the formula, M1, M2, and M3 are respectively:

[0043]

[0044] In the formula, δ 21 , δ 22 are positive real numbers to be designed, representing the performance envelope boundary, μ2(t) is the performance function, and e2 is the pitch angle tracking error.

[0045] Furthermore, the controller of the velocity subsystem designed in step 5 is:

[0046]

[0047] where k1 > 0 is a parameter to be designed, c1 is a parameter to be designed, μ1 is the performance function, e1 is the velocity tracking error, s1 is the sliding mode surface function, V d is the velocity reference signal, δ 11 , δ 12 are positive real numbers to be designed, representing the performance envelope boundary;

[0048] and the sliding mode surface function s1 is:

[0049] s1 = c1ε1

[0050] In the formula, ε1 is the inverse function of the hyperbolic tangent function S(ε1);

[0051]

[0052] where S represents the hyperbolic tangent function.

[0053] Therefore, the present invention adopts the above-mentioned method for fault-tolerant control of a variable aircraft with preset performance based on sliding mode control, and has the following beneficial effects:

[0054] First, the present invention decomposes the complex dynamic model of the variable aircraft into two relatively independent speed subsystems and attitude subsystems, designs controllers respectively, simplifies the controller design, reduces the complexity brought by system coupling, improves the design efficiency and performance of the controller, and is convenient for fault-tolerant control;

[0055] Second, the present invention adopts the preset performance control method to solve the fault-tolerant control problem of the variable aircraft, so that the tracking error meets the preset performance constraints, thereby ensuring the transient and steady-state performance of the system. Directly embedding the performance requirements into the controller design simplifies the control design process. By adjusting the parameters of the performance function, the transient and steady-state performance indexes of the system can be flexibly set to meet different control requirements;

[0056] Third, the preset performance control method may affect the control effect in the case of inaccurate modeling, and in order to ensure the performance in the worst case, the design is relatively conservative, so that the system cannot reach the best performance under normal conditions. The sliding mode control method can enhance the robustness of the attitude control system of the variable aircraft under the influence of model uncertainty and external interference. The present invention combines the two, can overcome the adverse effects of composite interference, actuator effectiveness loss faults and time-varying offset faults, and ensure that the tracking error meets the preset performance constraints;

[0057] In summary, the present invention simplifies the controller design, improves the control performance, and is convenient for fault-tolerant control; adopts the preset performance control method to solve the fault-tolerant control problem of the variable aircraft, and the tracking error meets the preset performance constraints, so that the transient and steady-state performance of the system is ensured; combines the sliding mode control with the preset performance control to improve the conservativeness with fast response, enhance the fault-tolerant ability with the switching control law, improve the stability, and has important engineering significance for the fault-tolerant control of the variable aircraft.

[0058] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0059] Figure 1 is the flow chart of the method proposed by the present invention;

[0060] Figure 2The curve graph of the speed tracking error obtained by the method proposed in the present invention;

[0061] Figure 3 The curve graph of the pitch angle tracking error obtained by the method proposed in the present invention. Detailed implementation manners

[0062] In the description of the present invention, it should also be noted that unless otherwise clearly specified and limited, these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0063] The present invention proposes a preset performance fault-tolerant control method for a morphing aircraft based on sliding mode control, which includes the following steps:

[0064] Step 1: Establish a longitudinal nonlinear dynamic model of the morphing aircraft in the geocentric rectangular coordinate system;

[0065] Step 2: Based on the longitudinal nonlinear dynamic model of the morphing aircraft constructed in Step 1, considering partial actuator failures and time-varying offset faults, establish a longitudinal nonlinear dynamic model of the morphing aircraft under actuator fault conditions;

[0066] Step 3: For the longitudinal nonlinear dynamic model of the morphing aircraft under actuator fault conditions constructed in Step 2, extract the speed subsystem and the attitude subsystem;

[0067] Step 4: Design a preset performance fault-tolerant controller based on sliding mode control for the attitude subsystem extracted in Step 3, and prove its stability;

[0068] Step 5: For the speed subsystem extracted in Step 3, combined with the attitude subsystem controller designed in Step 4, design a preset performance fault-tolerant controller based on sliding mode control, and prove its stability;

[0069] Step 6: Utilize the attitude subsystem controller and the speed subsystem controller designed in Step 4 and Step 5 to achieve fault-tolerant control of the morphing aircraft under actuator fault conditions.

[0070] The construction processes of the respective models in the above steps are introduced separately below.

[0071] 1. Longitudinal nonlinear dynamic model of the morphing aircraft

[0072] For a variable wingspan aircraft, it can autonomously change the length of the wingspan during flight, and the two wingspans extend or shorten symmetrically. Define its wingspan deformation rate as:

[0073]

[0074] where b is the current wingspan, b min and b max are the shortest and longest wingspans respectively, and ξ ∈ [0, 1];

[0075] Referring to the dynamic model of a conventional aircraft, the longitudinal nonlinear dynamic model of the variable-wingspan aircraft is established as follows:

[0076]

[0077] where m is the mass of the aircraft, V and h are the speed and altitude of the aircraft, L(ξ), D(ξ), T are the drag, lift and thrust respectively, α, θ, are the angle of attack, flight path angle and pitch angle of the aircraft respectively, I y is the component of the moment of inertia of the aircraft about the z-axis of the body coordinate system, q is the component of the angular velocity of the body coordinate system relative to the ground coordinate system on the z-axis of the body coordinate system, M y (ξ) is the pitch moment, and g is the acceleration due to gravity.

[0078] Among them, the aerodynamic forces (drag, lift) and aerodynamic moments (pitch moment) are all related to the wingspan deformation rate. In addition, the thrust T of the aircraft is described by a linear relationship:

[0079]

[0080] where, is the engine thrust coefficient, and δ t is the engine throttle opening.

[0081] The above longitudinal motion equations of the aircraft are described in the form of the following affine nonlinear system:

[0082]

[0083] In the formula, is the state vector, u = [δ e , δ t T is the input vector, δ e is the rudder deflection angle, and f(x, ξ), g(x, ξ), g1(x, ξ), g2(x, ξ) are system functions;

[0084] Next, considering the model uncertainties caused by model simplification and channel coupling, the aerodynamic parameter errors in the model, the external unknown disturbances, and the additional forces and additional moments that may be generated by the deformation of the aircraft, etc., the nonlinear model of the variable aircraft is corrected as:

[0085] ​

[0086] where Δf(x, ξ), Δg(x, ξ), Δg1(x, ξ), Δg2(x, ξ) are internal uncertainty disturbances; d' is model uncertainty; d'' is external disturbance.

[0087] For the convenience of control law design, d1 and d2 are combined into a composite disturbance d, and g1(x, ξ) and g2(x, ξ) are ignored when solving the control law subsequently, obtaining a simplified control-oriented system model:

[0088]

[0089] The system functions f(x, ξ) and g(x, ξ) in the formula are as follows:

[0090]

[0091] where Q = 0.5ρV 2 represents the dynamic pressure, where ρ is the atmospheric density, S w is the wing reference area, C D0 , C L0 , C m0 are the drag coefficient, lift coefficient, and pitching moment coefficient at zero angle of attack, respectively, are the aerodynamic coefficients of lift and pitching moment with respect to the angle of attack, respectively, are the second aerodynamic derivatives of drag and lift with respect to the angle of attack, c A is the mean geometric chord length of the wing, are the aerodynamic derivatives of lift, drag, and pitching moment with respect to the elevator deflection angle, respectively.

[0092] 2. Longitudinal Nonlinear Dynamics Model of a Variable Aircraft under Actuator Fault Conditions

[0093] Considering partial failure faults and time-varying offset faults of the actuator, let v i (t) be the input of the i-th actuator at time t, is an unknown time-varying function, and the following fault model of the i-th actuator is established:

[0094]

[0095] where λ i and r i are indication factors for different faults, λ i is the indication factor for partial benefit loss faults, r i is the indication factor for time-varying offset faults, and 0 ≤ λ i ≤ 1, r i is 0 or 1; according to λ i and r iDifferent combinations can result in different working states of the actuator: λ i = 1, r i = 0 indicates that the actuator has no fault; 0 < λ i < 1, r i = 0 indicates that the actuator has a partial benefit loss fault; λ i = 0, r i = 1 indicates that the actuator has a time-varying offset fault; 0 < λ i < 1, r i = 1 indicates that the actuator has both a partial benefit loss and a time-varying offset fault simultaneously.

[0096] To simplify the expression, in the control-oriented system (Equation 6) obtained in Step 1, replace the input vector u with the actual control input vector u′(t):

[0097]

[0098] where the matrix λ = diag{λ1, λ2} represents the unknown control benefit loss faults occurring in the engine throttle opening δ t and the rudder deflection angle δ e among these two control inputs, r = diag{r1, r2}, v(t) = [δ t , δ e T , t f represents the fault occurrence time.

[0099] Based on Equation (10), the variant aircraft model under actuator fault conditions can be obtained:

[0100]

[0101] 3. Extract the velocity subsystem and the attitude subsystem

[0102] For the variant aircraft model under actuator fault conditions shown in Equation (11), extract the velocity subsystem and the attitude subsystem, as shown in Equations (12) and (13) respectively:

[0103]

[0104] where d1 and d2 represent the composite disturbances of the velocity subsystem and the attitude subsystem respectively, and the system functions f1(x1, ξ), g1(x1, ξ), f2(x2, ξ), g2(x2, ξ) are respectively

[0105]

[0106] ​Define the reference command signals for the velocity subsystem and the attitude subsystem as x id (i = 1, 2), and make the following assumptions:

[0107] (1) The reference command signal x id has second-order continuous derivatives and and x id 、 and are all bounded;

[0108] (2) g1(x1, ξ), g2(x2, ξ) are invertible.

[0109] Although the velocity subsystem is affected by both the rudder deflection angle and the throttle opening, since the attitude subsystem is only controlled by the rudder deflection angle, the rudder deflection angle command can be obtained by preferentially designing the attitude control system, and thus the rudder deflection angle in the velocity subsystem can be regarded as a constant.

[0110] 4. Controller design of the attitude subsystem

[0111] First, define the pitch angle tracking error as:

[0112]

[0113] where x 2d is the reference command signal of the attitude subsystem, is the pitch angle reference signal, and is generated from the desired altitude signal, i.e.:

[0114] where h d is the desired altitude signal, k p , k i are all parameters to be designed.

[0115] Secondly, the error in Equation (16) can be transformed into:

[0116] e2 = μ2(t)S(ε2)(18)

[0117] where S(ε2) is the hyperbolic tangent function, satisfying:

[0118]

[0119] where δ 21 , δ 22 are positive real numbers to be designed, representing the performance envelope boundary; and μ2(t) is the performance function, which can be expressed as:

[0120] μ2(t) = (μ 20 - μ 2∞ )exp(-κ20 t) + μ 2∞ (20)

[0121] Wherein, is the initial value of μ2(t) (i.e., μ2(0) = μ 20 ); is the final value of μ2(t), μ 20 > μ 2∞ > 0, μ 20 exponentially decays to μ 2∞ ; κ 20 > 0 is a parameter to be designed, representing the exponential convergence rate;

[0122] According to the properties of the hyperbolic tangent function, the inverse function ε2 of S(ε2) is:

[0123]

[0124] Taking the derivative of Equation (21) gives:

[0125]

[0126] Wherein, M1, M2, and M3 are respectively:

[0127]

[0128] Then, for the attitude subsystem, select the sliding mode surface function:

[0129]

[0130] Wherein, c2 is a parameter to be designed.

[0131] Taking the derivative of the sliding mode surface function s2 with respect to time gives:

[0132]

[0133] Next, design the preset performance fault-tolerant controller for the attitude subsystem based on sliding mode control as:

[0134]

[0135] Wherein, k2 > 0 is a parameter to be designed.

[0136] Finally, prove the stability of the attitude subsystem: Substitute the designed controller into the sliding mode surface derivative, and we get:

[0137]

[0138] Define and take the derivative of V2, and we get:

[0139]

[0140] Integrating the above equation, we get:

[0141]

[0142] where \(k_2>0\). According to Barbalat's lemma, when \(t\rightarrow\infty\), \(s_2\rightarrow0\), and thus \(e_2\rightarrow0\). Then it is proved that the subsystem is Lyapunov asymptotically stable.

[0143] 5. Controller Design of the Velocity Subsystem

[0144] First, define the velocity tracking error as:

[0145] \(e_1 = x_1 - x\) 1d \(= V - \hat{V}\) d (27)

[0146] where the velocity reference signal \(\hat{V}\) d is the desired velocity signal, and \(x\) 1d is the reference command signal of the velocity subsystem;

[0147] Secondly, transform the error \(e_1\) in Equation (27) into:

[0148] \(e_1=\mu_1(t)S(\varepsilon_1)\) (28)

[0149] where \(S(\varepsilon_1)\) is the hyperbolic tangent function, satisfying:

[0150]

[0151] where \(\delta\) 11 , \(\delta\) 12 are positive real numbers to be designed, representing the performance envelope boundary; and \(\mu_1(t)\) is the performance function, which can be expressed as:

[0152] \(\mu_1(t)=(\mu\) 10 -\mu\) 1∞ )\exp(-\kappa\) 10 t)+\mu\) 1∞ (30)

[0153] In the formula, is the initial value of \(\mu_1(t)\) (i.e., \(\mu_1(0)=\mu\) 10 ); is the final value of \(\mu_1(t)\), \(\mu\) 10 >\(\mu\) 1∞ >0, \(\mu\) 10 exponentially decays to \(\mu\) 1∞ ; \(\kappa\) 10 >0 is a parameter to be designed, representing the exponential convergence rate.

[0154] Taking the derivative of the performance function μ1(t), we can obtain:

[0155]

[0156] According to the properties of the hyperbolic tangent function, the inverse function ε1 of S(ε1) is:

[0157]

[0158] Taking the derivative of Equation (32), we can obtain:

[0159]

[0160] Then, for the velocity subsystem, select the sliding mode surface function:

[0161] s1 = c1ε1 (34)

[0162] where c1 is a parameter to be designed.

[0163] Taking the derivative of the sliding mode surface function s1 with respect to time, we can obtain:

[0164]

[0165] Next, design the preset performance fault-tolerant controller for the velocity subsystem based on sliding mode control as:

[0166]

[0167] where k1 > 0 is a parameter to be designed.

[0168] Finally, prove the stability of the velocity subsystem: Substitute the designed controller into the sliding mode surface derivative, and we can obtain

[0169] Define and take the derivative of V1, we can obtain:

[0170]

[0171] Integrating the above equation, we can obtain:

[0172]

[0173] where k1 > 0. According to Barbalat's lemma, when t → ∞, s1 → 0, and we can also obtain e1 → 0. Then it is proved that the subsystem is Lyapunov asymptotically stable.

[0174] 6. Fault-tolerant control of a morphing aircraft under actuator faults

[0175] By using the controllers of the above-mentioned attitude subsystem and velocity subsystem, namely, Equation (26) and Equation (36), the fault-tolerant control problem of the morphing aircraft under actuator failure conditions can be solved. The specific fault-tolerant control steps are as follows: First, given appropriate initial values of the state vector , given the time, type, and degree of the sudden fault of the actuator; Second, gradually adjust the performance envelope parameters (δ 21 , δ 22 and δ 11 , δ 12 ), the parameters of the performance function (the parameters of μ1(t) and μ2(t)), the sliding mode surface parameters, and the controller parameters, and execute the above Steps 1-Step 5; Then, check whether the tracking error is within the performance envelope and whether the morphing aircraft can fly stably at the desired speed and altitude. If satisfied, check whether the generated control law u1 satisfies the constraint condition 0% ≤ u1 ≤ 100%, and whether u2 satisfies the constraint condition -40° ≤ u2 ≤ 40°. If the conditions are satisfied, obtain the tracking error that meets the preset performance constraints, stop adjusting the parameters, and thus realize the fault-tolerant control of the morphing aircraft.

[0176] Embodiment

[0177] To prove the effectiveness of the method proposed in the present invention, the following simulation experiments are carried out. A variable wingspan aircraft model as shown in Equations (1)-(5) is adopted, with the goal of the variable wingspan aircraft flying stably at the desired altitude and speed under actuator failure conditions and the tracking error meeting the preset performance constraints.

[0178] First, the present invention conducts experiments with a general variable wingspan aircraft model, and the basic data of the variable wingspan aircraft are shown in Table 1.

[0179] Table 1 Basic Attributes of Variable Wingspan Aircraft

[0180]

[0181] Second, use Simulink to build the fault-tolerant control framework of this paper, and obtain the tracking error of the method proposed in the present invention after repeatedly adjusting the parameters.

[0182] According to the method proposed in the present invention, the velocity tracking error curve as shown in Figure 2 is obtained. It can be seen from Figure 2 that the velocity tracking error converges relatively fast in the early stage and can be maintained within the preset performance envelope in the presence of compound disturbances and actuator efficiency loss and time-varying offset faults; Similarly, it can be seen from the pitch angle tracking error curve shown in Figure 3 that the pitch angle tracking error can also converge quickly in the early stage, and the error can also be maintained within the preset performance envelope after the fault occurs.

[0183] In summary, the proposed fault-tolerant control method for a variant aircraft with preset performance based on sliding mode control can overcome the adverse effects of compound disturbances, actuator effectiveness loss faults, and time-varying offset faults, and ensure that the tracking error meets the preset performance constraints.

[0184] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for fault-tolerant control of preset performance of a variant aircraft based on sliding mode control, characterized in that: The method comprises the following steps: Step 1: Establish a longitudinal nonlinear dynamic model of the variant aircraft; Step 2: Based on the constructed longitudinal nonlinear dynamic model of the variant aircraft, the longitudinal nonlinear dynamic model of the variant aircraft under the condition of actuator failure is established by considering the partial failure of the actuator and the time-varying offset failure; Step 3: Extract the velocity subsystem and attitude subsystem for the longitudinal nonlinear dynamic model of the variant aircraft under the condition of actuator failure; Step 4: Design a controller with preset performance tolerance based on sliding mode control for the extracted attitude subsystem to obtain a designed attitude subsystem controller; Step 5: For the extracted speed subsystem, combined with the attitude subsystem controller, a controller with preset performance tolerance based on sliding mode control is designed to obtain the designed speed subsystem controller; Step 6: Use the attitude subsystem controller and the speed subsystem controller to achieve fault-tolerant control of the variant aircraft under actuator failure conditions.

2. A method for controlling a variant aircraft with preset performance based on sliding mode control according to claim 1, characterized in that: The specific steps of step 1 are as follows: For a variable-span aircraft, a longitudinal nonlinear dynamic model of the variable-span aircraft is established, and then the longitudinal nonlinear dynamic model of the variable-span aircraft is simplified to finally obtain a simplified control-oriented system model: Where x = [V, α, θ, q, h] T is the state vector, V and h are the speed and altitude of the aircraft, α and θ are the attack angle and pitch angle of the aircraft respectively, and q is the component of the angular velocity of the missile body coordinate system relative to the ground coordinate system on the z-axis of the missile body coordinate system; u = [δ e ,δ t ] T is the input vector, δ e is the rudder deflection angle, δ t is the engine throttle opening; ξ∈[0,1] is the wingspan deformation rate, d is the composite disturbance, f(x,ξ) and g(x,ξ) are system functions; and: Where, Q = 0.5ρV 2 represents the dynamic pressure, where ρ is the atmospheric density, S w is the reference area of ​​the wing, m is the mass of the aircraft, I y is the component of the vehicle's moment of inertia with respect to the z-axis of the missile body coordinate system, is the engine thrust coefficient, C D0 ,C L0 ,C m0 are the drag coefficient, lift coefficient and pitch moment coefficient at zero angle of attack, are the aerodynamic coefficients of lift and pitch moment with respect to the angle of attack, are the secondary aerodynamic derivatives of drag and lift with respect to the angle of attack, c A is the average geometric chord length of the wing, are the aerodynamic derivatives of lift, drag and pitching moment with respect to the elevator deflection angle, respectively.

3. A method for controlling a variant aircraft with preset performance based on sliding mode control as claimed in claim 2, characterized in that: The specific steps of step 2 are: Step 2.1: Establish the fault model of the i-th actuator: Among them, λ i and r i is the indicator factor of different faults, λ i is the indicator factor of partial benefit loss failure, r i is the indicator factor of time-varying offset fault, and 0≤λ i ≤1, r i is 0 or 1, depending on λ i and r i Different combinations of can get different working states of the actuator: i =1, r i =0, it means that the actuator has no fault; 0<λ i <1, r i =0, it means that the actuator has a partial benefit loss failure; i =0, r i =1, it indicates that the actuator has a time-varying offset fault; 0<λ i <1, r i =1, it means that the actuator has a partial benefit loss and a time-varying offset fault at the same time; Step 2.2: Based on the above fault model, the actual control input vector u′(t) is expressed as: Among them, the matrix λ = diag{λ1,λ2} represents the engine throttle opening δ of the variant aircraft t and rudder angle δ e The unknown control benefit loss fault occurs in these two control inputs, r = diag{r1,r2}, v(t) = [δ t ,δ e ] T , t f Indicates the time when the fault occurred; Step 2.3: Replace the input vector u in the simplified control-oriented system model with the actual control input vector u′(t) to obtain the variant aircraft model under the actuator failure condition:

4. A method for controlling a variant aircraft with preset performance based on sliding mode control as claimed in claim 3, characterized in that: The velocity subsystem and attitude subsystem extracted in step 3 are: Where, the system functions f1(x1,ξ), g1(x1,ξ), f2(x2,ξ), g2(x2,ξ) are: Among them, d1 is the composite disturbance of the velocity subsystem; d2 is the composite disturbance of the attitude subsystem.

5. The method for controlling a variant aircraft with preset performance based on sliding mode control according to claim 4, characterized in that: The controller of the attitude subsystem designed in step 4 is: Among them, k2>0 is the parameter to be designed, c2 is the parameter to be designed, s2 is the sliding surface function, θ d is the pitch angle reference signal; And the sliding surface function s2 is: Where ε2 is the inverse function of the hyperbolic tangent function S(ε2); Where M1, M2, and M3 are: In the formula, δ 21 ,δ 22 is a positive real number to be designed, representing the performance envelope boundary, μ2(t) is the performance function, and e2 is the pitch angle tracking error.

6. A method for fault-tolerant control of a variant aircraft with preset performance based on sliding mode control as claimed in claim 5, characterized in that: The controller of the speed subsystem designed in step 5 is: Among them, k1>0 is the parameter to be designed, c1 is the parameter to be designed, μ1 is the performance function, e1 is the speed tracking error, s1 is the sliding surface function, V d is the speed reference signal, δ 11 ,δ 12 is a positive real number to be designed, representing the performance envelope boundary; And the sliding surface function s1 is: s1=c1ε1 Where ε1 is the inverse function of the hyperbolic tangent function S(ε1); Wherein, S represents the hyperbolic tangent function.

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