A bionic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer

Abstract

The application discloses a bionic flapping wing aircraft attitude tracking control method based on a fuzzy state observer, and belongs to the technical field of bionic flapping wing aircraft attitude control. The application solves the problem of poor safety and stability of an existing control method when facing a false data injection attack of an actuator. The application establishes a bionic flapping wing aircraft attitude tracking dynamics model with an actuator attack by using Euler angles, designs a virtual controller and an actual control law by using a backstepping control method, estimates states by constructing a fuzzy state observer, realizes adaptive safe aircraft attitude tracking control facing an unknown actuator false data injection attack according to the estimated states, and proves by experiments that the method can guarantee the safety and stability of the control method under the unknown actuator false data injection attack. The method can be applied to bionic flapping wing aircraft attitude tracking control.

Description

Technical Field

[0001] This invention belongs to the field of attitude control technology for biomimetic flapping-wing aircraft, specifically relating to an attitude tracking and control method for biomimetic flapping-wing aircraft based on a fuzzy state observer. Background Technology

[0002] With the continuous advancement of unmanned aerial vehicle (UAV) technology, biomimetic flapping-wing aircraft, as a novel type of micro-aircraft, have gradually attracted widespread attention. Compared with traditional aircraft, biomimetic flapping-wing aircraft possess higher maneuverability and lower energy consumption, making them suitable for various tasks such as environmental monitoring and disaster relief. However, the attitude control of biomimetic flapping-wing aircraft faces numerous challenges, especially the influence of complex nonlinear dynamics and external disturbances. In practical applications, the control system of biomimetic flapping-wing aircraft not only needs to cope with traditional dynamic uncertainties and external environmental interference, but may also face threats from malicious attacks, especially spoofed data injection attacks. Such attacks can affect the stability of the aircraft and mission execution by tampering with sensor data or control signals.

[0003] Patent application CN113504729A discloses a robust control method for a biomimetic flapping-wing aircraft based on LMI (Limited Mixture Analysis). First, a time-varying longitudinal dynamic model of the biomimetic flapping-wing aircraft is established, and a nonlinear longitudinal steady-state model is obtained through periodic averaging. Then, a linear nominal model is obtained based on the equilibrium point linearization method. Next, considering the noise, errors, and dynamic characteristics of the actuators that may occur during actual control, a weight function is designed to transform the control system into the standard form of a controller. Finally, the LMI method is used to solve the linear matrix inequality, resulting in a controller with robust stability and robust performance that can effectively cope with model uncertainties and external disturbances in the biomimetic flapping-wing aircraft system, ensuring the stability and control performance of the aircraft in complex environments. However, this method does not consider the security control problem when the system is subjected to malicious attacks and cannot solve the robustness problem of the system under cyberattacks. Patent application CN116027662A discloses a fault-tolerant control method for the flapping wings and actuators of a biomimetic flapping-wing aircraft. First, this method estimates the system's faults by establishing a fault model suitable for fault-tolerant control. Next, disturbance estimation and suppression techniques are employed to ensure the system's stability under various disturbance conditions. Then, a fault-tolerant control strategy based on the flapping wing and actuator is proposed, effectively addressing attitude control problems caused by faults. Finally, a fault-tolerant controller is designed based on an anti-disturbance high-order sliding mode method, further improving the system's robustness and stability when encountering actuator failures. Therefore, this method proposes a novel fault-tolerant control approach combining high-order sliding mode control, disturbance estimation techniques, and adaptive control strategies. This approach possesses high disturbance immunity, good fault tolerance, and strong robustness, ensuring that the biomimetic flapping-wing aircraft maintains good attitude control performance even when the flapping wing and actuator fail. However, the security control issue under malicious attacks has not yet been addressed.

[0004] In summary, although existing technologies have made some progress in attitude tracking control of biomimetic flapping-wing aircraft, security and stability issues still exist when facing spoofed data injection attacks on actuators. Therefore, developing a control method that can effectively resist spoofed data injection attacks on actuators and ensure the safe and stable operation of the attitude tracking system of a biomimetic flapping-wing aircraft is a problem that needs to be solved in the current field of biomimetic flapping-wing aircraft. Summary of the Invention

[0005] The purpose of this invention is to address the problem of poor security and stability of existing control methods when facing spoofed data injection attacks on actuators, and to propose a biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer, the method specifically including the following steps:

[0007] Step S1: Establish the ground coordinate system, body coordinate system, velocity coordinate system, left wing coordinate system, and right wing coordinate system, and calculate the transformation relationship between each coordinate system;

[0008] Step S2: Based on the transformation relationship between the coordinate systems, establish the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass;

[0009] Step S3: Combine the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass to obtain the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass.

[0010] The dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is then transformed, and a fake data injection attack on the actuator is introduced.

[0011] Step S4: Construct a fuzzy state observer for the biomimetic flapping-wing aircraft based on a fuzzy logic system;

[0012] Step S5: Based on the information observed by the fuzzy state observer, design the control law for the bionic flapping-wing aircraft under the attack of spurious data injection into the actuator using the backstepping control method;

[0013] Step S6: Use the control law designed in step S5 to perform attitude control on the biomimetic flapping-wing UAV.

[0014] The beneficial effects of this invention are:

[0015] This invention establishes a dynamic model for attitude tracking of a biomimetic flapping-wing aircraft under actuator attack using Euler angles. A virtual controller and actual control law are designed using the backstepping control method. A fuzzy state observer is constructed for state estimation. Based on the estimated state, adaptive and safe attitude tracking control of the aircraft is realized in the face of spurious data injection attacks from unknown actuators. Experiments demonstrate that the method of this invention can still guarantee the safety and stability of the control method under spurious data injection attacks from unknown actuators, which has important practical significance. Attached Figure Description

[0016] Figure 1 This is a flowchart of an attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer, according to the present invention.

[0017] Figure 2 The curve showing the difference between the output signal and the reference signal under attack according to an embodiment of the present invention. Figure 1 ;

[0018] In the graph, the vertical axis is in degrees;

[0019] Figure 3 The curve showing the difference between the output signal and the reference signal under attack according to an embodiment of the present invention. Figure 2 ;

[0020] Figure 4 The curve showing the difference between the output signal and the reference signal under attack according to an embodiment of the present invention. Figure 3 ; Detailed Implementation

[0021] Specific implementation method one: Combining Figure 1 This embodiment describes a biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer. The method specifically includes the following steps:

[0022] Step S1: Establish the ground coordinate system, body coordinate system, velocity coordinate system, left wing coordinate system, and right wing coordinate system, and calculate the transformation relationship between each coordinate system;

[0023] Step S2: Based on the transformation relationship between the coordinate systems, establish the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass;

[0024] Step S3: Combine the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass to obtain the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass.

[0025] The dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is then transformed into a general mathematical description, and a fake data injection attack on the actuator is introduced.

[0026] Step S4: Construct a fuzzy state observer for the biomimetic flapping-wing aircraft based on a fuzzy logic system;

[0027] Step S5: Based on the information observed by the fuzzy state observer, design the control law for the bionic flapping-wing aircraft under the attack of spurious data injection into the actuator using the backstepping control method;

[0028] The control law of the design makes:

[0029] (1) All signals in the entire closed-loop system are bounded;

[0030] (2) The tracking error converges to a small neighborhood containing zero;

[0031] Step S6: Use the control law designed in step S5 to perform attitude control on the biomimetic flapping-wing UAV.

[0032] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the ground coordinate system, body coordinate system, velocity coordinate system, left wing coordinate system, and right wing coordinate system are respectively:

[0033] Ground coordinate system O e X e Y e Z e Also known as an inertial coordinate system, it is an absolute coordinate system fixed on the Earth's surface, used to describe the spatial position, attitude, and velocity of a biomimetic flapping-wing aircraft; the ground coordinate system O e X e Y e Z e Origin e X is the launch point of the biomimetic flapping-wing aircraft or the center of mass of the biomimetic flapping-wing aircraft during takeoff. e The positive direction of the axis is the projection of the heading of the biomimetic flapping-wing aircraft on the horizontal plane during takeoff, Z. e The axis is perpendicular to X. e axis, and Z e The positive direction of the axis is vertically upward, Y e Shaft and O e X e Z e Plane perpendicular, X e Positive axis direction, Y e Positive axis direction and Z e The positive direction of the axis satisfies the right-hand coordinate system.

[0034] Body coordinate system O b X b Y b Z b The body of the biomimetic flapping-wing aircraft is fixed to the fuselage and is a moving coordinate system; the body coordinate system O b X b Y b Z b Origin b Z coincides with the center of mass of the biomimetic flapping-wing aircraft. b The axis is parallel to the longitudinal axis of the body and Z b The positive direction of the axis points towards the head of the aircraft, X b The axis is perpendicular to Z. b Axis and X b The positive direction of the axis points forward, Y b Shaft and O b X b Z b The plane is perpendicular, and X b Positive axis direction, Y b Positive axis direction and Z b The positive direction of the axis satisfies the right-hand coordinate system.

[0035] Velocity coordinate system Ov X v Y v Z v With body coordinate system O b X b Y b Z b The origins coincide, X v The axis coincides with the flight velocity vector of the biomimetic flapping-wing aircraft in the air, and X... v The positive direction of the axis points in the direction of flight speed, Z v The axis is perpendicular to X. v Axis and Z v The positive direction of the axis points upwards, Y v The axis is perpendicular to O v X v Z v Plane, and X v Positive axis direction, Y v Positive axis direction and Z v The positive direction of the axis satisfies the right-hand coordinate system.

[0036] Left wing coordinate system O wl X wl Y wl Z wl Origin wl Located at the wing root of the left wing of the biomimetic flapping-wing aircraft, X wl The axis is parallel to the wing and X wl The positive direction of the axis points towards the head of the fuselage, Z wl The axis is perpendicular to the wing plane and Z wl The positive direction of the axis points downwards, Y wl The axis is perpendicular to O wl X wl Z wl Plane, and Y wl The positive axis points in the direction of wingspan;

[0037] Right wing coordinate system O wr X wr Y wr Z wr Origin wr Located at the wing root of the right wing of the biomimetic flapping-wing aircraft, X wr The axis is parallel to the wing and X wr The positive direction of the axis points towards the head of the fuselage, Z wr The axis is perpendicular to the wing plane and Z wr The positive direction of the axis points upwards, Y wr The axis is perpendicular to O wr X wr Z wr Plane, and Y wr The positive axis points in the direction of the wingspan.

[0038] The other steps and parameters are the same as in Specific Implementation Method 1.

[0039] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the calculation of the transformation relationship between the coordinate systems is specifically as follows:

[0040] Define the yaw angle ψ as: the X-axis of the body coordinate system b The axis in the ground coordinate system O e X e Y e Projection in the plane and X e The angle between the axes, projected towards O e X e Y e When the plane is to the right, the yaw angle is positive.

[0041] Define the pitch angle θ as: the X-axis of the body coordinate system b Axis and ground coordinate system O e X e Y e The angle between planes, when X b The axis relative to the ground coordinate system O e X e Y e When the plane is tilted upwards, the pitch angle is positive.

[0042] Define the roll angle γ as: the Y-axis of the body coordinate system b O of the axis and the ground coordinate system e X e Y e The angle between planes, when Y b The axis relative to the ground coordinate system O e X e Y e When the plane is tilted downwards, the roll angle is positive.

[0043] The body coordinate system can be obtained after three rotations. to ground coordinate system The conversion relationship is as follows:

[0044]

[0045] The transformation relationship between the body coordinate system and the ground coordinate system can then be described using yaw angle ψ, pitch angle θ, and roll angle γ:

[0046]

[0047] in, This represents the transformation matrix from the body coordinate system to the ground coordinate system;

[0048] O of the body coordinate system b Zb O of the axis and velocity coordinate system v Z v The axes are always located at O ​​in the body coordinate system. b X b Z b Since it is in a plane, the transformation relationship between the body coordinate system and the velocity coordinate system can be determined using two angles: the angle of attack ζ and the sideslip angle β.

[0049] Define the angle of attack ζ as: O in the velocity coordinate system v X v The axis in the body coordinate system O b X b Z b Projection on the plane and O of the body coordinate system b X b The angle between the axes, the projection line at O b X b When the axis is above the y-axis, the angle of attack ζ is positive; the projection line is at O. b X b When below the axis, the angle of attack ζ is negative;

[0050] Define the sideslip angle β as: O in the velocity coordinate system v X v O of the axis and the body coordinate system b X b Z b The angle between planes, when O v X v Axis points to O b X b Z b When the plane is to the right, the sideslip angle β is positive, when O v X v Axis points to O b X b Z b When the plane is to the left, the sideslip angle β is negative;

[0051] The transformation relationship between the body coordinate system and the velocity coordinate system can then be described using the angle of attack ζ and the sideslip angle β:

[0052]

[0053] in, This represents the transformation matrix from the body coordinate system to the velocity coordinate system;

[0054] right Transpose the coordinates to obtain the transformation matrix from the velocity coordinate system to the body coordinate system:

[0055]

[0056] in, This represents the transformation matrix from the velocity coordinate system to the body coordinate system;

[0057] Define the right wing flapping angle φ r Y: the coordinate system of the right wing wr O of the axis and the body coordinate system b Y b Z b The angle between planes, when Y wr The axis is O b Y b Z b When the plane points in front of the machine body, the striking angle φ r When the direction is positive and the direction is towards the rear of the machine, the striking angle is φ. r Negative;

[0058] Define the right wing twist angle The twist angle of the right wing is defined as the angular velocity (O) of the wing during flapping, as the wings generate a torsional motion around the wing's Y-axis. wr Y wr Z wr O of the plane and the body coordinate system b Y b Z b The angle between planes. When O wr Y wr Z wr When the plane twists backward toward the rear of the machine body, the twist angle For positive, when O wr Y wr Z wr When the plane twists forward towards the body, the twist angle Negative;

[0059] Use the right wing to flap the angle φ r and right wing twist angle The transformation matrix from the right wing coordinate system to the body coordinate system is obtained as follows:

[0060]

[0061] in, This represents the transformation matrix from the right wing coordinate system to the body coordinate system;

[0062] Similarly, define the flapping angle φ in the coordinate system of the left wing. l and twist angle Use the left wing to flap at angle φ l and left wing twist angle The transformation matrix from the left wing coordinate system to the body coordinate system is obtained as follows:

[0063]

[0064] in, This represents the transformation matrix from the left wing coordinate system to the body coordinate system.

[0065] Other steps and parameters are the same as in specific implementation method one or two.

[0066] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the specific process of step S2 is as follows:

[0067] Step S21: Modeling the total torque acting on the body of the biomimetic flapping-wing aircraft

[0068] Bionic flapping-wing aircraft are primarily driven and controlled by the aerodynamic forces and torques generated by wing movement. One flapping cycle of a bionic flapping-wing aircraft consists of two processes: a downward flap and an upward flap. By adjusting the torsion angle during the upward and downward flapping processes, the angle of attack of the wing is changed, ensuring that the average lift generated within one cycle is positive. This allows the bionic flapping-wing aircraft to overcome its own weight and airframe damping forces, maintaining flight.

[0069] During the flapping of the wings of a biomimetic flapping-wing aircraft, the instantaneous aerodynamic force F generated on the surface of a single wing is:

[0070] F = F st-dl +F gyr (7)

[0071] Among them, F st-dl The instantaneous translational force F is generated by the stall delay mechanism. gyr It is the rotating circulation force generated by the rotating circulation mechanism;

[0072] According to aerodynamic theory, under steady-state conditions, the aerodynamic force generated per unit length in the wingspan by the stall delay mechanism is:

[0073]

[0074] Among them, F' st,N F' is the normal force per unit length of span perpendicular to the wing plane. st,T Let α be the tangential force per unit length of span, forward along the wing chord direction and parallel to the wing plane, α be the angle of attack during wing flapping, c be the wing chord length, U be the wing translational velocity, ρ be the air density, and C be the tangential force. N (α) is the lift coefficient perpendicular to the wing plane, C T (α) is the lift coefficient parallel to the wing plane;

[0075] The aerodynamic force (a normal force) generated by the rotating circulation mechanism is always perpendicular to the wing plane. The aerodynamic force F' generated by the rotating circulation mechanism per unit span is... gyr,N for:

[0076]

[0077] in, C is the angular velocity of the wing's angle of attack. gyr This is the rotational force coefficient;

[0078] Based on quasi-steady aerodynamics, the wings of the biomimetic flapping-wing aircraft are infinitely divided along the wingspan, with a unit length of d. r Then F' st,N F' st,T F' gyr,N In length d r The total aerodynamic forces on the surface are as follows:

[0079]

[0080] in, Let c(r) be the angular velocity of the wing flapping angle, and c(r) be the chord length at a distance r from the wing root. dF st,N (t,r), dF st,T (t,r) and dF gyr,N (t) are respectively F' st,N F' st,T and F' gyr,N In length d r The total aerodynamic force on the surface, where t represents time;

[0081] Integrating along the span of the wing, we obtain the aerodynamic force acting on the entire wing plane as follows:

[0082]

[0083] Among them, A w U is the area of ​​the wing plane, L is the wing span, which is the distance from the wing root to the wingtip, and U is the wing length. cp c is the velocity at the center of pressure of the wing. m The maximum chord length of the wing. As a standardized pressure center, For standardized rotational chord length;

[0084] The total aerodynamic force generated by a single wing is:

[0085]

[0086] Among them, F N (t) represents the normal force perpendicular to the wing plane, F T (t) represents the tangential force parallel to the plane of the wing;

[0087] By projecting the total aerodynamic force generated by the movement of the left and right wings onto the three axes of the left and right wing coordinate system, the aerodynamic force components in each axis can be obtained. The normal force is opposite to the flight direction of the aircraft.

[0088] Formula (13) applies to both the left and right wings, so the total aerodynamic resultant force generated by the left wing is denoted as F. Nl (t) and F Tl (t), let F be the total aerodynamic force generated by the right wing. Nr (t) and F Tr (t), according to formula (13), the aerodynamic components of each axis of the left wing coordinate system and the aerodynamic components of each axis of the right wing coordinate system are respectively:

[0089]

[0090] Among them, -F Nr 0 and F Tr F represents the aerodynamic components of the total aerodynamic resultant force of the right wing along each axis of the right wing coordinate system. Nl 0 and F Tl This represents the aerodynamic components of the total aerodynamic force of the left wing along each axis of the left wing coordinate system;

[0091] By using the transformation matrix from the wing coordinate system to the body coordinate system, the aerodynamic forces generated by the left and right wings can be transformed into the body coordinate system, and the aerodynamic force components in each axis under the body coordinate system can be obtained.

[0092] The aerodynamic forces generated by the left and right wings of the biomimetic flapping-wing aircraft are decomposed along the three axes of the body coordinate system as follows:

[0093]

[0094] in, The aerodynamic force generated by the right wing is decomposed along the three axes of the body coordinate system. The aerodynamic force generated by the left wing is decomposed along the three axes of the body coordinate system;

[0095] The decomposition of the total aerodynamic force on the wings of the biomimetic flapping-wing aircraft along the three axes in the body coordinate system is as follows:

[0096]

[0097] Located on the axis of rotation of the wing and at a distance from the wing root If the position is taken as the aerodynamic center (point of aerodynamic force application) of the wing plane, then the coordinates of the aerodynamic center of the left wing and the aerodynamic center of the right wing in the left wing coordinate system and the right wing coordinate system are both... Based on the transformation matrices from the left wing coordinate system to the body coordinate system and from the right wing coordinate system to the body coordinate system, the position vectors of the aerodynamic center of the left wing and the right wing in the body coordinate system are obtained:

[0098]

[0099] in, Let be the position vector of the aerodynamic center of the right wing in the body coordinate system. This is the position vector of the aerodynamic center of the left wing in the body coordinate system;

[0100] In the body coordinate system, the torque of the aerodynamic force acting on the body about the aerodynamic center during one flapping cycle of the left wing and the torque of the aerodynamic force acting on the body about the aerodynamic center during one flapping cycle of the right wing are respectively:

[0101]

[0102] As can be seen from the above formula, when the left and right wings of the biomimetic flapping-wing aircraft flap symmetrically, the aerodynamic torque generated is in the body coordinate system X b Axis and Z b The components along the axial direction are equal in magnitude but opposite in direction; in the Y... b The components along the axial direction are equal in magnitude and have the same direction. Therefore, X can be adjusted by controlling the asymmetrical flapping of the two wings. b Axis and Z b Torque in the axial direction.

[0103] In the body coordinate system, the resultant torque of the aerodynamic forces acting on the body about the aerodynamic center during one flapping cycle of the left and right wings is:

[0104]

[0105] Among them, M w The resultant torque;

[0106] Airframe damping force and damping moment: When a biomimetic flapping-wing aircraft flies in the air, the airframe interacts with the incoming airflow, generating damping force. The damping force acting on the airframe is proportional to the dynamic pressure q′ of the incoming airflow and the characteristic area S of the fuselage. For a biomimetic flapping-wing aircraft, the characteristic area of ​​the fuselage is the wing area of ​​the aircraft's two wings.

[0107] The damping force of the body is decomposed into drag force F along each axis of the velocity coordinate system. vx Lateral force F vy and lift F vz :

[0108]

[0109] Where q′ represents the dynamic pressure of the incoming flow;

[0110]

[0111] Where ρ is the air density, ρ = 1.225 kg / m³ 3 v is the velocity of the body relative to the incoming flow, S is the characteristic area of ​​the body, and c x For the drag coefficient of the biomimetic flapping-wing aircraft, c y c is the lateral force coefficient of the biomimetic flapping-wing aircraft. z c is the lift coefficient of the biomimetic flapping-wing aircraft. x =2cos 2 ζ, c y = -sin(2β), c z =sin(2ζ);

[0112] In the velocity coordinate system, the damping torque of the body damping force acting on the biomimetic flapping-wing aircraft body is:

[0113]

[0114] Where l is the characteristic length of the fuselage. When calculating the roll moment and yaw moment of the biomimetic flapping-wing aircraft fuselage, the characteristic length of the fuselage is taken as the wingspan, i.e., l x =l z =R, where R represents the wingspan. When calculating the pitch moment of the biomimetic flapping-wing aircraft fuselage, the characteristic length of the fuselage is taken as 0.25 times the chord length. y =0.25c m ;

[0115] The expression for the damping torque of the body in the body coordinate system is:

[0116]

[0117] Among them, M b The damping moment of the body in the body coordinate system;

[0118] Let M be the total disturbance torque caused by external disturbances, parameter perturbations, and incomplete modeling in the body coordinate system. d M d =[M dx M dy M dz ] T Then the total torque M experienced by the biomimetic flapping-wing aircraft in the body coordinate system is:

[0119]

[0120] Step S22: Establish the dynamic equations for the biomimetic flapping-wing aircraft's rotation around its center of mass.

[0121] The motion of a biomimetic flapping-wing aircraft in the air consists of translation and rotation around its center of mass. According to the principles of theoretical mechanics, the dynamic equation for the rotation of the aircraft around its center of mass in the body coordinate system is:

[0122]

[0123] Where M is the total torque vector of the wing aerodynamic force and the body damping force acting on the center of mass of the biomimetic flapping-wing aircraft, and H is the angular momentum of the biomimetic flapping-wing aircraft acting on the center of mass.

[0124] H=Iω (26)

[0125] Where I is the inertia matrix of the organism, ω is the angular velocity vector of the organism, and ω = [p, q, r] T Let p, q, and r be the components of ω along each axis of the body coordinate system, i.e., the angular momentum H is expressed as:

[0126]

[0127] Since the biomimetic flapping-wing aircraft has a symmetrical structure, all elements in the inertial matrix except for those on the main diagonal are zero, which simplifies the angular momentum H to:

[0128]

[0129] Based on the method for calculating the vector derivative in a rotating coordinate system, the dynamic equation of the biomimetic flapping-wing aircraft rotating about its center of mass is:

[0130]

[0131] in, This represents the first derivative of H;

[0132] Substituting equation (26) into equation (29) and rearranging, we get:

[0133]

[0134] in, This represents the first derivative of ω.

[0135] Then, in the body coordinate system, the scalar form of the dynamic equation of the biomimetic flapping-wing aircraft rotating around its center of mass is:

[0136]

[0137] Substituting equation (24) into equation (31), and rearranging, we obtain the dynamic equation for the biomimetic flapping-wing aircraft rotating around its center of mass as follows:

[0138]

[0139] Step S23: Establish the kinematic equations of motion of the biomimetic flapping-wing aircraft around its center of mass.

[0140] In the ground coordinate system, the angular velocity vector of the biomimetic flapping-wing aircraft's body rotation is: angular velocity vector The angular velocity vector ω = [p, q, r] of the biomimetic flapping-wing aircraft rotating around its center of mass in the body coordinate system. T The relationship is:

[0141]

[0142] The kinematic equations of the biomimetic flapping-wing aircraft in the geographic coordinate system are:

[0143]

[0144] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0145] Specific Implementation Method Five: This implementation method differs from one of Specific Implementation Methods One to Four in that the C... N (α) and C T The quasi-steady empirical formulas for (α) are as follows:

[0146] C N (α)=3.4sinα (35)

[0147]

[0148] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0149] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the rotational force coefficient C... gyr The empirical formula is:

[0150]

[0151] in, It is the ratio of the distance from the axis of twist of the wing to the leading edge of the wing to the wing chord length. For most insects, its value is about 1 / 4.

[0152] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0153] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the... and The definition is as follows:

[0154]

[0155] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0156] and The value is only related to the wing morphology, and for most insects, their value range is approximately [value missing]. and

[0157] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step S3 is as follows:

[0158] By combining the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass, a dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is obtained:

[0159]

[0160] During the flight of a biomimetic flapping-wing aircraft, the sideslip angle is usually zero, i.e., β = 0. Therefore, in the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass, the components of the damping torque of the aircraft along each axis are as follows:

[0161]

[0162] The attitude of a biomimetic flapping-wing aircraft can be controlled by adjusting the torque acting on its center of mass, enabling the aircraft's three attitude angles to track the set target values ​​in real time. Therefore, this invention selects the three aerodynamic torques generated by the wings as inputs to the attitude control system for the design and simulation of the attitude control algorithm.

[0163] To facilitate the design of attitude control algorithms for biomimetic flapping-wing aircraft, the dynamic model of the biomimetic flapping-wing aircraft is transformed into a general mathematical description. The specific transformation method is as follows:

[0164] Define the variables as follows:

[0165]

[0166] The dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is then transformed as follows:

[0167]

[0168] Let x2 = g'(x1)z, g(x1)=g'(x1)I -1Given the external disturbance uncertainty term d = g'(x1)d', the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is transformed as follows:

[0169]

[0170] in, This represents the state vector of the attitude system of a biomimetic flapping-wing aircraft. Denotes the first derivative of x1. This represents the first derivative of x². This represents the output vector of the attitude system. Represents the system function vector. The coefficient function matrix, Let be the input vector of the attitude system. It is a real number;

[0171] Because biomimetic flapping-wing aircraft are affected by the environment during flight, causing wing vibrations, these vibrations significantly impact flight control. Wing vibrations not only generate lift and thrust but also affect the aircraft's stability, maneuverability, and energy consumption. Due to environmental factors and structural changes in the aircraft's hardware during operation, leading to wing vibrations, the system function may be unknown. Therefore, a fuzzy logic system will be used to model these unknown dynamics.

[0172] When subjected to an executor-based spoofed data injection attack, the system state equation transforms into:

[0173]

[0174] in, This indicates an unknown executor spoofing data injection attack signal. x′1 and x1 have similar meanings but different values, and x′2 and x2 have similar meanings but different values.

[0175] make Under an actuator spoofing data injection attack, the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass after form transformation is as follows:

[0176]

[0177] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0178] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the specific process of step S4 is as follows:

[0179] Assumption 1: There exists a positive constant m such that the following Lipschitz conditional inequality holds:

[0180]

[0181] Where m is a positive parameter.

[0182] Design a filter signal u f for:

[0183] u f =H L (s)u≈u (47)

[0184] Among them, H L (s) is a Butterworth low-pass filter;

[0185] Reconstruct equation (45) as follows:

[0186]

[0187] in, for The estimate;

[0188] make Functions defined on compact set Ω There exists a fuzzy logic system such that:

[0189]

[0190] Where σ is a positive constant, θ i For the parameter vector of the fuzzy logic system, Let suprem be a fuzzy basis function;

[0191] Using fuzzy logic systems to analyze functions Approximation:

[0192]

[0193] Wherein, the optimal parameter vector for:

[0194]

[0195] Where Ω is θ i A bounded compact set, U is A bounded compact set; then

[0196]

[0197] The fuzzy state observer is designed as follows:

[0198]

[0199] in, For the estimate of x2, For the estimate of x1, For the estimate of y, for The first derivative, for The first derivative of k1 and k2 are both positive design parameters;

[0200] According to equation (53), the state space form of the fuzzy state observer is as follows:

[0201]

[0202] in, It is the Herwitz matrix, I 3×3 It is the identity matrix, 0 3×3 It is a 0 matrix. express The first derivative, C = [I 3×3 ,0 3×3 ].

[0203] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0204] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the specific process of step S5 is as follows:

[0205] Define the approximation error ε i for:

[0206]

[0207] Where, |ε i | represents ε i The absolute value, It is a constant;

[0208] From equations (48) and (55), we get:

[0209]

[0210] in For the observation error vector, Let e ​​be the first derivative. That is, ε = [ε1, ε2, ε3] T ;

[0211] For the error system of equation (56), the positive definite symmetric matrix P satisfies: P T =P>0, construct the Lyapunov function V0 as:

[0212] V0 = e TPe(57)

[0213] The derivative of V0 with respect to time is:

[0214]

[0215] in, Given the first derivative of V0, and matrix Q T =Q>0, satisfying A T P + PA = -Q;

[0216] From Young's inequality and Assumption 1, we can obtain:

[0217]

[0218] 2e T PBε≤||e|| 2 +||P|| 2 ε *2 (60)

[0219]

[0220] 2e T PBd≤||e|| 2 +||P|| 2 d *2 (62)

[0221] Where ||·|| represents the 2-norm, and the external disturbance has a constant d. * Make ||d||≤d * ;

[0222] Substituting (59)-(62) into (58) yields:

[0223]

[0224] Error transformation of equation (64):

[0225]

[0226] Where z1 and z2 are errors, α1 is the virtual control signal, and y d For tracking signals;

[0227] Choose the Lyapunov function V1:

[0228]

[0229] Taking the derivative of V1 with respect to time, we get:

[0230]

[0231] in, This represents the first derivative of V1. Indicates y d The first derivative, By Young's inequality:

[0232]

[0233] Combining equations (66) and (68), we get:

[0234]

[0235] The virtual control signal is designed as follows:

[0236]

[0237] Where p1 is a positive design parameter. Indicates y d The first derivative;

[0238] Substituting equation (70) into equation (69), we get:

[0239]

[0240] Choose the Lyapunov function V:

[0241]

[0242] Where, γ i Positive design parameters;

[0243] Taking the derivative of V with respect to time, we get:

[0244]

[0245] in, It is y d The second derivative, simplified, yields:

[0246]

[0247] Among them, z 2i Let i be the i-th element in z2;

[0248] From Young's inequality, we can obtain:

[0249]

[0250] Substituting equation (75) into equation (74), we get:

[0251]

[0252] The actual control law and adaptive law are designed as follows:

[0253]

[0254] Where p2, r i Positive design parameters It is y d The second derivative of .

[0255]

[0256] Depend on

[0257]

[0258] achievable

[0259]

[0260] Right now:

[0261]

[0262] in, λ min (Q) is the smallest eigenvalue of matrix Q, λ max (P) represents the largest eigenvalue of matrix P.

[0263]

[0264] Therefore, we can conclude that:

[0265]

[0266] Therefore, all signals in the entire closed-loop system are bounded, and the tracking error converges to a small neighborhood containing zero.

[0267] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0268] This invention combines the attitude output vector of a biomimetic flapping-wing aircraft with actuator attack capabilities with a fuzzy logic system designing an unknown nonlinearity and actuator attack signal to design a state observer. A virtual control law is designed for the observer's estimated state, and then filtered and fed into a backstepping controller to generate a control signal. The control signal controls the three-dimensional torque at the aircraft's center of mass and compares it with the desired attitude trajectory. The difference is fed back to the controller as a feedback signal until the values ​​converge to near the origin.

[0269] The feasibility and control performance of the method proposed in this invention will be verified below. The model parameters include moment of inertia, wing area, wingspan, and chord length, which are estimated based on the body characteristics of the red-throated hummingbird. The parameters are I... x =575g·mm 2 ,

[0270] I y =576g·mm 2 I z =991g·mm 2 S = 1526.4 mm 2 , R=53mm, c=28mm, v=5m / s, Choose the feedback gain K = [k1I 3×3 k2I 3×3 ] T Where k1 = 45 and k2 = 40. This ensures that the roots of the characteristic polynomial of A all have negative real parts. In the above adaptive control scheme, the parameters of the actual controller and the adaptive law are p1 = 110, p2 = 100; γ1 = 20, γ2 = 10, γ3 = 30; r1 = 100, r2 = 90, r3 = 100. Initial condition x1(0) = [0,0,0] T x2(0) = [0.1, 0.1, 0.1] T The remaining initial values ​​are all chosen to be zero, given the reference signal y. d =[sin(t),sin(t),sin(t)] T The attack signal is:

[0271] ρ(x1,x2,t)=

[0272] 0.5[x 11 +x 12 +x 13 x 21 +x 22 +x 23 x 11 +x 12 +x 13 +x 21 +x 22 x 23 x 11 x 12 +x 13 +x 21 +x 22 +x 23 ] T

[0273] Where, x1=[x 11 ,x 12 ,x 13 ] T , x2=[x 21 ,x 22 ,x 23 ] T An attack signal is introduced when t≥20. The simulation results are as follows: Figure 2 , Figure 3 and Figure 4 As shown, Figures 2 to 4 This illustrates the trajectory of the difference between the output signal and the reference signal under attack, where z1 = [z 11 ,z 12 ,z 13 ] T .

[0274] from Figures 2 to 4 It can be seen that the control method proposed in this invention can achieve good tracking performance. When the actuator components of the system are attacked, the controller designed in this invention can ensure the normal operation of the system and guarantee the boundedness of signals within the system, thereby achieving the control objective requirements.

[0275] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer, characterized in that, The method specifically includes the following steps: Step S1: Establish the ground coordinate system, body coordinate system, velocity coordinate system, left wing coordinate system, and right wing coordinate system, and calculate the transformation relationship between each coordinate system; Step S2: Based on the transformation relationship between the coordinate systems, establish the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass; Step S3: Combine the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass to obtain the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass. The dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is then transformed, and a fake data injection attack on the actuator is introduced. Step S4: Construct a fuzzy state observer for the biomimetic flapping-wing aircraft based on a fuzzy logic system; Step S5: Based on the information observed by the fuzzy state observer, design the control law for the bionic flapping-wing aircraft under the attack of spurious data injection into the actuator using the backstepping control method; Step S6: Use the control law designed in step S5 to perform attitude control on the biomimetic flapping-wing UAV.

2. The biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer according to claim 1, characterized in that, The ground coordinate system, body coordinate system, velocity coordinate system, left wing coordinate system, and right wing coordinate system are respectively: Ground coordinate system O e X e Y e Z e Origin e X is the launch point of the biomimetic flapping-wing aircraft or the center of mass of the biomimetic flapping-wing aircraft during takeoff. e The positive direction of the axis is the projection of the heading of the biomimetic flapping-wing aircraft on the horizontal plane during takeoff, Z. e The axis is perpendicular to X. e axis, and Z e The positive direction of the axis is vertically upward, Y e Shaft and O e X e Z e Plane perpendicular, X e Positive axis direction, Y e Positive axis direction and Z e The positive direction of the axis satisfies the right-hand coordinate system. Body coordinate system O b X b Y b Z b Origin b Z coincides with the center of mass of the biomimetic flapping-wing aircraft. b The axis is parallel to the longitudinal axis of the body and Z b The positive direction of the axis points towards the head of the aircraft, X b The axis is perpendicular to Z. b Axis and X b The positive direction of the axis points forward, Y b Shaft and O b X b Z b The plane is perpendicular, and X b Positive axis direction, Y b Positive axis direction and Z b The positive direction of the axis satisfies the right-hand coordinate system. Velocity coordinate system O v X v Y v Z v With body coordinate system O b X b Y b Z b The origins coincide, X v The axis coincides with the flight velocity vector of the biomimetic flapping-wing aircraft in the air, and X... v The positive direction of the axis points in the direction of flight speed, Z v The axis is perpendicular to X. v Axis and Z v The positive direction of the axis points upwards, Y v The axis is perpendicular to O v X v Z v Plane, and X v Positive axis direction, Y v Positive axis direction and Z v The positive direction of the axis satisfies the right-hand coordinate system. Left wing coordinate system O wl X wl Y wl Z wl Origin wl Located at the wing root of the left wing of the biomimetic flapping-wing aircraft, X wl The axis is parallel to the wing and X wl The positive direction of the axis points towards the head of the fuselage, Z wl The axis is perpendicular to the wing plane and Z wl The positive direction of the axis points downwards, Y wl The axis is perpendicular to O wl X wl Z wl Plane, and Y wl The positive axis points in the direction of wingspan; Right wing coordinate system O wr X wr Y wr Z wr Origin wr Located at the wing root of the right wing of the biomimetic flapping-wing aircraft, X wr The axis is parallel to the wing and X wr The positive direction of the axis points towards the head of the fuselage, Z wr The axis is perpendicular to the wing plane and Z wr The positive direction of the axis points upwards, Y wr The axis is perpendicular to O wr X wr Z wr Plane, and Y wr The positive axis points in the direction of the wingspan.

3. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 2, characterized in that, The calculation of the transformation relationship between the coordinate systems is specifically as follows: The transformation relationship between the body coordinate system and the velocity coordinate system can be described using the angle of attack ζ and the sideslip angle β as follows: in, This represents the transformation matrix from the body coordinate system to the velocity coordinate system; right Transpose the coordinates to obtain the transformation matrix from the velocity coordinate system to the body coordinate system: in, This represents the transformation matrix from the velocity coordinate system to the body coordinate system; Use the right wing to flap the angle φ r and right wing twist angle The transformation matrix from the right wing coordinate system to the body coordinate system is obtained as follows: in, This represents the transformation matrix from the right wing coordinate system to the body coordinate system; Use the left wing to flap at angle φ l and left wing twist angle The transformation matrix from the left wing coordinate system to the body coordinate system is obtained as follows: in, This represents the transformation matrix from the left wing coordinate system to the body coordinate system.

4. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 3, characterized in that, The specific process of step S2 is as follows: Step S21: Modeling the total torque acting on the body of the biomimetic flapping-wing aircraft During the flapping of the wings of a biomimetic flapping-wing aircraft, the instantaneous aerodynamic force F generated on the surface of a single wing is: F=F st-dl +F gyr (7) Among them, F st-dl The instantaneous translational force F is generated by the stall delay mechanism. gyr It is the rotating circulation force generated by the rotating circulation mechanism; The aerodynamic force per unit length in the wingspan generated by the stall delay mechanism is: Among them, F′ st,N F′ is the normal force per unit length of span perpendicular to the wing plane. st,T Let α be the tangential force per unit length of span, forward along the wing chord direction and parallel to the wing plane, α be the angle of attack during wing flapping, c be the wing chord length, U be the wing translational velocity, ρ be the air density, and C be the tangential force. N (α) is the lift coefficient perpendicular to the wing plane, C T (α) is the lift coefficient parallel to the wing plane; Aerodynamic force F′ generated per unit span by the rotating circulation mechanism gyr,N for: in, C is the angular velocity of the wing's angle of attack. gyr This is the rotational force coefficient; If the wings of a biomimetic flapping-wing aircraft are infinitely divided along the wingspan, then F′ st,N F′ st,T F′ gyr,N In length d r The total aerodynamic forces on the surface are as follows: in, Let c(r) be the angular velocity of the wing flapping angle, and c(r) be the chord length at a distance r from the wing root. dF st,N (t,r), dF st,T (t,r) and dF gyr,N (t) are respectively F′ st,N F′ st,T and F′ gyr,N In length d r The total aerodynamic force on the surface, where t represents time; Integrating along the span of the wing, we obtain the aerodynamic force acting on the entire wing plane as follows: Among them, A w U is the area of ​​the wing plane, L is the wing span, which is the distance from the wing root to the wingtip, and U is the wing length. cp c is the velocity at the center of pressure of the wing. m The maximum chord length of the wing. As a standardized pressure center, For standardized rotational chord length; The total aerodynamic force generated by a single wing is: Among them, F N (t) represents the normal force perpendicular to the wing plane, F T (t) represents the tangential force parallel to the plane of the wing; The aerodynamic components along each axis of the left wing coordinate system and the aerodynamic components along each axis of the right wing coordinate system are as follows: Among them, -F Nr 0 and F Tr F represents the aerodynamic components of the total aerodynamic resultant force of the right wing along each axis of the right wing coordinate system. Nl 0 and F Tl This represents the aerodynamic components of the total aerodynamic force of the left wing along each axis of the left wing coordinate system; The aerodynamic forces generated by the left and right wings of the biomimetic flapping-wing aircraft are decomposed along the three axes of the body coordinate system as follows: in, The aerodynamic force generated by the right wing is decomposed along the three axes of the body coordinate system. The aerodynamic force generated by the left wing is decomposed along the three axes of the body coordinate system; Located on the axis of rotation of the wing and at a distance from the wing root If the position is taken as the aerodynamic center of the wing plane, then the coordinates of the aerodynamic center of the left wing and the aerodynamic center of the right wing in the left wing coordinate system and the right wing coordinate system are both... Based on the transformation matrices from the left wing coordinate system to the body coordinate system and from the right wing coordinate system to the body coordinate system, the position vectors of the aerodynamic center of the left wing and the right wing in the body coordinate system are obtained: in, Let be the position vector of the aerodynamic center of the right wing in the body coordinate system. This is the position vector of the aerodynamic center of the left wing in the body coordinate system; In the body coordinate system, the torque of the aerodynamic force acting on the body about the aerodynamic center during one flapping cycle of the left wing and the torque of the aerodynamic force acting on the body about the aerodynamic center during one flapping cycle of the right wing are respectively: In the body coordinate system, the resultant torque of the aerodynamic forces acting on the body about the aerodynamic center during one flapping cycle of the left and right wings is: Among them, M w The resultant torque; The damping force of the body is decomposed into drag force F along each axis of the velocity coordinate system. vx Lateral force F vy and lift F vz : Where q′ represents the dynamic pressure of the incoming flow; Where ρ is the air density, v is the velocity of the aircraft relative to the incoming flow, S is the characteristic area of ​​the aircraft, and c x c is the drag coefficient of the biomimetic flapping-wing aircraft. y c is the lateral force coefficient of the biomimetic flapping-wing aircraft. z c is the lift coefficient of the biomimetic flapping-wing aircraft. x =2cos 2 ζ, c y = -sin(2β), c z =sin(2ζ); In the velocity coordinate system, the damping torque of the body damping force acting on the biomimetic flapping-wing aircraft body is: Among them, l x =l z =R, where R represents wingspan, l y =0.25c m ; The expression for the damping torque of the body in the body coordinate system is: Among them, M b The damping moment of the body in the body coordinate system; Let M be the total disturbance torque caused by external disturbances, parameter perturbations, and incomplete modeling in the body coordinate system. d M d =[M dx M dy M dz ] T Then the total torque M experienced by the biomimetic flapping-wing aircraft in the body coordinate system is: Step S22: Establish the dynamic equations for the biomimetic flapping-wing aircraft's rotation around its center of mass. In the body coordinate system, the dynamic equation for the body's rotation about its center of mass is: Where M is the total torque vector of the wing aerodynamic force and the body damping force acting on the center of mass of the biomimetic flapping-wing aircraft, and H is the angular momentum of the biomimetic flapping-wing aircraft acting on the center of mass. H=Iω (26) Where I is the inertia matrix of the organism, ω is the angular velocity vector of the organism, and ω = [p, q, r] T Let p, q, and r be the components of ω along each axis of the body coordinate system, i.e., the angular momentum H is expressed as: The angular momentum H can be simplified to: The dynamic equation of motion for a biomimetic flapping-wing aircraft rotating around its center of mass is: in, This represents the first derivative of H; Substituting equation (26) into equation (29) and rearranging, we get: in, This represents the first derivative of ω. Then, in the body coordinate system, the scalar form of the dynamic equation of the biomimetic flapping-wing aircraft rotating around its center of mass is: Substituting equation (24) into equation (31), and rearranging, we obtain the dynamic equation for the biomimetic flapping-wing aircraft rotating around its center of mass as follows: Step S23: Establish the kinematic equations of motion of the biomimetic flapping-wing aircraft around its center of mass. In the ground coordinate system, the angular velocity vector of the biomimetic flapping-wing aircraft's body rotation is: angular velocity vector The angular velocity vector ω = [p, q, r] of the biomimetic flapping-wing aircraft rotating around its center of mass in the body coordinate system. T The relationship is: The kinematic equations of the biomimetic flapping-wing aircraft in the geographic coordinate system are:

5. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 4, characterized in that, The C N (α) and C T (α) are respectively: C N (a)=3.4 sinα(35) 6. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 4, characterized in that, The rotational force coefficient C gyr for: in, It is the ratio of the distance from the axis of twist of the wing to the leading edge of the wing to the wing chord length.

7. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 4, characterized in that, The and The definition is as follows:

8. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 4, characterized in that, The specific process of step S3 is as follows: By combining the kinematic and dynamic equations of the biomimetic flapping-wing aircraft rotating around its center of mass, a dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is obtained: In the dynamic model of a biomimetic flapping-wing aircraft rotating around its center of mass, the components of the damping torque of the aircraft along each axis are as follows: Define the variables as follows: The dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is then transformed as follows: Let x2 = g'(x1)z, g(x1)=g'(x1)I -1 Given the external disturbance uncertainty term d = g'(x1)d', the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass is transformed as follows: in, This represents the state vector of the attitude system of a biomimetic flapping-wing aircraft. Denotes the first derivative of x1. This represents the first derivative of x². This represents the output vector of the attitude system. Represents the system function vector. The coefficient function matrix, Let be the input vector of the attitude system. It is a real number; When subjected to an executor-based spoofed data injection attack, the system state equation transforms into: in, This indicates an attack signal injecting false data into an unknown actuator; make Under an actuator spoofing data injection attack, the dynamic model of the biomimetic flapping-wing aircraft rotating around its center of mass after form transformation is as follows:

9. The attitude tracking control method for a biomimetic flapping-wing aircraft based on a fuzzy state observer according to claim 8, characterized in that, The specific process of step S4 is as follows: Design a filter signal u f for: u f =H L (s)u≈u(47) Among them, H L (s) is a Butterworth low-pass filter; Reconstruct equation (45) as follows: in, for The estimate; make Functions defined on compact set Ω There exists a fuzzy logic system such that: Where σ is a positive constant, θ i For the parameter vector of the fuzzy logic system, Let suprem be a fuzzy basis function; Using fuzzy logic systems to analyze functions Approximation: Wherein, the optimal parameter vector for: Where Ω is θ i A bounded compact set, U is A bounded compact set; then The fuzzy state observer is designed as follows: in, For the estimate of x2, For the estimate of x1, For the estimate of y, for The first derivative, for The first derivative of k1 and k2 are both positive design parameters; According to equation (53), the state space form of the fuzzy state observer is as follows: in, It is the Herwitz matrix, I 3×3 It is the identity matrix, 0 3×3 It is a 0 matrix. express The first derivative, C = [I 3×3 ,0 3×3 ].

10. The biomimetic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer according to claim 9, characterized in that, The specific process of step S5 is as follows: Error transformation of equation (64): Where z1 and z2 are errors, α1 is the virtual control signal, and y d For tracking signals; The virtual control signal is designed as follows: Where p1 is a positive design parameter. Indicates y d The first derivative; The control law is designed as follows: Where p2 is a positive design parameter, It is y d The second derivative of .

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