Bionic flapping wing aircraft attitude tracking control method based on fuzzy state observer

Abstract

The invention 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. According to the invention, the problem that the existing control method is poor in security and stability when facing false data injection attacks of the actuator is solved. According to the method, a bionic flapping-wing aircraft attitude tracking dynamic model with actuator attack is established by using Euler angles, a virtual controller and an actual control law are designed by using a backstepping control method, and state estimation is performed by constructing a fuzzy state observer. According to the estimated state, self-adaptive safe aircraft attitude tracking control facing unknown actuator false data injection attacks is achieved, and experiments prove that under the unknown actuator false data injection attacks, safety and stability of the control method can still be guaranteed. The method can be applied to attitude tracking control of the bionic flapping-wing aircraft.

Description

Technical Field

[0001] The present invention belongs to the technical field of bionic flapping-wing aircraft attitude control, and in particular relates to a bionic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer. Background Art

[0002] With the continuous advancement of unmanned aerial vehicle (UAV) technology, bionic flapping-wing aircraft, as a new type of micro-aircraft, have gradually attracted widespread attention. Compared with traditional aircraft, bionic flapping-wing aircraft have higher maneuverability and lower energy consumption, making them suitable for a variety of missions such as environmental monitoring and disaster relief. However, the attitude control of bionic flapping-wing aircraft faces many challenges, especially the complex nonlinear dynamics and the influence of external disturbances. In practical applications, the control system of bionic flapping-wing aircraft not only needs to cope with traditional dynamic uncertainties and external environmental disturbances, but also may face threats from malicious attacks, especially false 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 publication number CN113504729A discloses a robust control method for a bionic flapping-wing aircraft based on LMI. First, a time-varying longitudinal dynamic model of the bionic flapping-wing aircraft is established, and a nonlinear longitudinal steady-state model of the bionic flapping-wing aircraft is obtained through periodic averaging. Then, a linear nominal model is obtained based on equilibrium point linearization. Next, taking into account the noise, errors, and actuator dynamics that may occur during actual control, the control system is converted to a standard form of the controller by designing weight functions. Finally, the linear matrix inequality (LMI) method is used to solve linear matrix inequalities. The resulting controller exhibits robust stability and robust performance, effectively addressing model uncertainties and external disturbances in the bionic flapping-wing aircraft system, ensuring the aircraft's stability and control performance in complex environments. However, this method does not consider the issue of system security control in the event of malicious attacks and cannot address the system's robustness against cyberattacks. Patent application publication number CN116027662A discloses a fault-tolerant control method for flapping wings and actuators of a bionic flapping-wing aircraft. This method first establishes a fault model suitable for fault-tolerant control to estimate system faults. Next, interference estimation and suppression techniques are employed to ensure system stability under various interference conditions. A fault-tolerant control strategy based on flapping wings and actuators is then proposed, effectively addressing attitude control issues caused by faults. Finally, a fault-tolerant controller is designed based on an anti-interference high-order sliding mode method, further improving the robustness and stability of the system in the event of actuator failures. This approach proposes a novel fault-tolerant control method that combines high-order sliding mode control, interference estimation techniques, and an adaptive control strategy. This method exhibits high interference rejection, good fault tolerance, and strong robustness, ensuring that the bionic flapping-wing aircraft maintains good attitude control performance even when flapping wings and actuators fail. However, the issue of system security control in the event of malicious attacks has not yet been addressed.

[0004] In summary, while existing technologies have made some progress in attitude tracking control for bionic flapping-wing aircraft, they still face security and stability issues when facing attacks such as false data injection into actuators. Therefore, developing a control method that can effectively defend against false data injection attacks and ensure the safe and stable operation of bionic flapping-wing aircraft attitude tracking systems is a challenge currently facing the bionic flapping-wing aircraft field. Summary of the Invention

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

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

[0007] Step S1: Establish a ground coordinate system, an aircraft body coordinate system, a velocity coordinate system, a left wing coordinate system, and a right wing coordinate system, and calculate the conversion relationship between the coordinate systems;

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

[0009] Step S3, combining the kinematic equation and the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass to obtain a dynamic model of the bionic flapping-wing aircraft rotating around the center of mass;

[0010] Then, the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed, and an actuator false data injection attack is introduced;

[0011] Step S4, constructing a fuzzy state observer of the bionic flapping-wing aircraft based on the fuzzy logic system;

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

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

[0014] The beneficial effects of the present invention are:

[0015] The present invention uses Euler angles to establish a bionic flapping-wing aircraft attitude tracking dynamics model with actuator attacks, uses the backstepping control method to design a virtual controller and actual control law, and constructs a fuzzy state observer to perform state estimation. Based on the estimated state, adaptive and safe aircraft attitude tracking control facing unknown actuator false data injection attacks is implemented. Experiments have shown that the method of the present invention can still ensure the security and stability of the control method under unknown actuator false data injection attacks, and has important practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a bionic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer of the present invention;

[0017] Figure 2 The curve of the difference between the output signal and the reference signal under attack in the embodiment of the present invention is Figure 1 ;

[0018] In the figure, the unit of the vertical axis is angle;

[0019] Figure 3 The curve of the difference between the output signal and the reference signal under attack in the embodiment of the present invention is Figure 2 ;

[0020] Figure 4 The curve of the difference between the output signal and the reference signal under attack in the embodiment of the present invention is Figure 3 ; DETAILED DESCRIPTION

[0021] Specific implementation method 1: Combination Figure 1 This embodiment describes a bionic flapping-wing aircraft attitude tracking control method based on a fuzzy state observer, and the method specifically includes the following steps:

[0022] Step S1: Establish a ground coordinate system, an aircraft body coordinate system, a velocity coordinate system, a left wing coordinate system, and a right wing coordinate system, and calculate the conversion relationship between the coordinate systems;

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

[0024] Step S3, combining the kinematic equation and the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass to obtain a dynamic model of the bionic flapping-wing aircraft rotating around the center of mass;

[0025] Then, the dynamic model of the bionic flapping-wing aircraft rotating around its center of mass is transformed into a general mathematical description, and an actuator false data injection attack is introduced;

[0026] Step S4, constructing a fuzzy state observer of the bionic flapping-wing aircraft based on the fuzzy logic system;

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

[0028] The control law is designed so that:

[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: Using the control law designed in step S5 to perform attitude control on the bionic flapping-wing UAV.

[0032] Specific embodiment 2: This embodiment differs from the specific embodiment 1 in that the ground coordinate system, the body coordinate system, the velocity coordinate system, the left wing coordinate system and the right wing coordinate system are respectively:

[0033] Ground coordinate system O e X e Y e Z e Also known as the inertial coordinate system, it is an absolute coordinate system fixed on the surface of the earth and is used to describe the spatial position, attitude, and speed of the bionic flapping-wing aircraft; the ground coordinate system O e X e Y e Z e Origin O e is the starting point of the bionic flapping-wing aircraft or the center of mass of the bionic flapping-wing aircraft when it takes off, X e The positive direction of the Z axis is the projection of the heading of the bionic flapping-wing aircraft on the horizontal plane when it takes off. e Axis perpendicular to X e axis, and Z e The positive direction of the Y axis is vertically upward. e Axis and O e X e Z e Plane vertical, X e Axis positive direction, Y e Axis positive 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 It is fixed to the body of the bionic flapping-wing aircraft and is a moving coordinate system; the body coordinate system O b X b Y b Z b Origin O b Coincident with the center of mass of the bionic flapping-wing aircraft, Z b The axis is parallel to the longitudinal axis of the body and the Z b The positive direction of the axis points to the head of the body, X b Axis perpendicular to Z b Axis and X b The positive direction of the axis points forward, Y b Axis and O b X b Z b The planes are vertical, and X b Axis positive direction, Y b Axis positive 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 the body coordinate system O b X b Y b Z b The origin of X v The X axis coincides with the flight velocity vector of the bionic flapping-wing aircraft in the air and v The positive direction of the axis points to the direction of flight speed, Z v Axis perpendicular to X v Axis and Z v The positive direction of the axis points upward, Y v Axis perpendicular to O v X v Z v Plane, and X v Axis positive direction, Y v Axis positive 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 O wl Located at the root of the left wing of the bionic flapping-wing aircraft, X wl The axis is parallel to the wing and X wl The positive direction of the axis points to the head of the body, Z wl The axis is perpendicular to the wing plane and the Z wl The positive direction of the axis points downward, Y wl Axis perpendicular to O wl X wl Z wl Plane, and Y wl The positive direction of the axis points to the direction of the wingspan;

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

[0038] Other steps and parameters are the same as those in the first embodiment.

[0039] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the conversion relationship between the coordinate systems is calculated as follows:

[0040] The yaw angle ψ is defined as: X b Axis in ground coordinate system O e X e Y e Projection in the plane and X e The angle between the axes, the projection points to O e X e Y e When the direction of the plane is to the right, the yaw angle is positive.

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

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

[0043] After three rotations, the body coordinate system can be obtained To ground coordinate system The conversion relationship is:

[0044]

[0045] The conversion relationship between the body coordinate system and the ground coordinate system is described by the yaw angle ψ, pitch angle θ and roll angle γ:

[0046]

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

[0048] O of the body coordinate system b Zb Axis and velocity coordinate system O v Z v The axis is always located at O in the body coordinate system. b X b Z b In the plane, the conversion relationship between the body coordinate system and the velocity coordinate system can be determined by the two angles of attack angle ζ and sideslip angle β.

[0049] The angle of attack ζ is defined as: O in the velocity coordinate system v X v Axis O in the body coordinate system 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 is at O b X b When the angle of attack is above the axis, the angle of attack is positive; the projection line is at O b X b When the axis is below the ground, the angle of attack ζ is negative;

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

[0051] Then the conversion relationship between the body coordinate system and the velocity coordinate system is described by the angle of attack ζ and the sideslip angle β:

[0052]

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

[0054] right Perform transposition and obtain the transformation matrix from the velocity coordinate system to the body coordinate system:

[0055]

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

[0057] Define the right wing flapping angle φ r Y of the right wing coordinate system wr Axis and body coordinate system O b Y b Z b The angle between the planes, when Y wr Axis by O b Y b Z b When the plane points to the front of the aircraft, the flapping angle φ r When it is positive and points to the rear of the aircraft, the flapping angle φ r is negative;

[0058] Define the right wing twist angle The wings will produce a twisting motion around the Y axis during flapping, so the twist angle of the right wing is defined as the O wr Y wr Z wr O of plane and body coordinate system b Y b Z b The angle between the planes. wr Y wr Z wr When the plane twists toward the rear of the body, the twist angle Is positive, when O wr Y wr Z wr When the plane twists toward the front of the body, the twist angle is negative;

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

[0060]

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

[0062] Similarly, define the flapping angle φ of the left wing coordinate system l and torsion angle Use the left wing flapping angle φ l and the left wing twist angle The transformation matrix from the left wing coordinate system to the body coordinate system is:

[0063]

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

[0065] Other steps and parameters are the same as those in the first or second embodiment.

[0066] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the specific process of step S2 is as follows:

[0067] Step S21: Modeling the total torque applied to the bionic flapping-wing aircraft body

[0068] Bionic flapping-wing aircraft are primarily driven and controlled by the aerodynamic forces and aerodynamic torques generated by wing motion. A flapping cycle consists of two stages: downbeat and upbeat. By adjusting the torsion angle during the upbeat and downbeat stages, the wing's angle of attack is altered to maintain a positive average lift force within the cycle, enabling the aircraft to overcome its own gravity and the damping force of the body and maintain flight.

[0069] During the flapping of the wings of a bionic 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 is the instantaneous translational force generated by the stall delay mechanism, F gyr It is the rotational circulation force generated by the rotational circulation mechanism;

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

[0073]

[0074] Among them, F' st,N is the normal force perpendicular to the wing plane per unit length in the span direction, F' st,T is the tangential force parallel to the wing plane along the chord direction per unit length in the span direction, α is the angle of attack when the wing flaps, c is the chord length of the wing, U is the translational velocity of the wing, ρ is the air density, and C 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 (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 length in the span direction is gyr,N for:

[0076]

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

[0078] According to the quasi-steady aerodynamics method, the wings of the bionic flapping-wing aircraft are infinitely divided along the wingspan direction, with a unit length of d r , then F' st,N 、F' st,T 、F' gyr,N At length d r The total aerodynamic forces on are:

[0079]

[0080] in, is the angular velocity of the wing flapping angle, c(r) is the chord length at r from the wing root, dF st,N (t,r),dF st,T (t,r) and dF gyr,N (t) are F' st,N 、F' st,T and F' gyr,N At length d r The total aerodynamic force on , t represents time;

[0081] Integrating along the span of the wing, the aerodynamic force acting on the entire wing plane is:

[0082]

[0083] Among them, A w is the area of the wing plane, L is the span of the wing, that is, the distance from the wing root to the wing tip, U cp is the velocity of the wing's center of pressure, c m is the maximum chord length of the wing, For standardized pressure center, is the normalized rotation chord length;

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

[0085]

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

[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 systems respectively, the aerodynamic force component on 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 force generated by the left wing is recorded as F Nl (t) and F Tl (t), the total aerodynamic force generated by the right wing is recorded as F Nr (t) and F Tr (t), according to formula (13), the aerodynamic force components of each axis in the left wing coordinate system and the aerodynamic force components of each axis in the right wing coordinate system are:

[0089]

[0090] Among them, -F Nr , 0, and F Tr It represents the aerodynamic force components of the total aerodynamic force of the right wing in each axis of the right wing coordinate system, F Nl , 0, and F Tl It represents the aerodynamic force components of the total aerodynamic force of the left wing in 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 are converted to the body coordinate system respectively, and the aerodynamic force components of each axis in the body coordinate system can be obtained.

[0092] The decomposition results of the aerodynamic forces generated by the left wing and the right wing of the bionic flapping-wing aircraft in the three axes of the body coordinate system are as follows:

[0093]

[0094] in, is the decomposition result of the aerodynamic force generated by the right wing in the three axes of the body coordinate system, The decomposition results of the aerodynamic force generated by the left wing in the three axes of the body coordinate system;

[0095] The decomposition results of the total aerodynamic force on the wings of the bionic flapping-wing aircraft in the three axes in the body coordinate system are:

[0096]

[0097] The wing will be located on the axis of rotation and at a distance from the wing root. The position of the wing is taken as the aerodynamic center (aerodynamic point) of the wing plane. In the left wing coordinate system and the right wing coordinate system, the coordinates of the left wing aerodynamic center and the right wing aerodynamic center are both According to the transformation matrix from the left wing coordinate system to the body coordinate system and the transformation matrix from the right wing coordinate system to the body coordinate system, the position vector of the aerodynamic center of the left wing in the body coordinate system and the position vector of the aerodynamic center of the right wing in the body coordinate system are obtained:

[0098]

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

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

[0101]

[0102] It can be seen from the above formula that when the left and right wings of the bionic flapping-wing aircraft flap symmetrically, the aerodynamic torque generated by them is in the body coordinate system X b Axis and Z b The components in the Y-axis directions are equal in magnitude but opposite in direction; b The components in the X-axis direction are equal in magnitude and in the same direction. Therefore, the X-axis can be adjusted by controlling the asymmetric flapping of the two wings. b Axis and Z b Moment in the direction of the axis.

[0103] Then, in the body coordinate system, the resultant moment of the aerodynamic force exerted on the body by the left and right wings during one flapping cycle on the aerodynamic center is:

[0104]

[0105] Among them, M w is the resultant moment;

[0106] Damping force and damping torque: When a bionic flapping-wing aircraft flies, the fuselage interacts with the incoming airflow, generating a damping force. The damping force acting on the fuselage is proportional to the incoming airflow's dynamic pressure q' and the fuselage's characteristic area S. For a bionic flapping-wing aircraft, the fuselage's characteristic area is the combined wing area of the aircraft's two wings.

[0107] The damping force of the body is decomposed into resistance 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 / m 3 , v is the velocity of the body relative to the incoming flow, S is the characteristic area of the body, c x is the drag coefficient of the bionic flapping-wing aircraft, c y is the lateral force coefficient of the bionic flapping-wing aircraft body, c z is the lift coefficient of the bionic flapping-wing aircraft, c 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 body of the bionic flapping-wing aircraft is:

[0113]

[0114] Where l is the characteristic length of the fuselage. When calculating the rolling moment and yaw moment of the fuselage of the bionic flapping-wing aircraft, the characteristic length of the fuselage is taken as the wingspan length, that is, l x =l z =R, R represents the wingspan. When calculating the pitching moment of the fuselage of the bionic flapping-wing aircraft, the fuselage characteristic length is taken as 0.25 times the chord length, l y =0.25c m ;

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

[0116]

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

[0118] The total disturbance torque caused by external interference, parameter perturbation and incomplete modeling in the body coordinate system is denoted as M d , that is, M d =[M dx ,M dy ,M dz ] T , then the total moment M of the bionic flapping-wing aircraft in the body coordinate system is:

[0119]

[0120] Step S22: Establish the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass

[0121] The movement of a bionic flapping-wing aircraft in the air is divided into translation and rotation around the center of mass of the aircraft. According to the principles of theoretical mechanics, the dynamic equation of the rotation of the aircraft around the center of mass in the aircraft coordinate system is:

[0122]

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

[0124] H=Iω (26)

[0125] Where I is the inertia matrix of the body, ω is the angular velocity vector of the body, ω=[p,q,r] T , p, q and r are the components of ω along the axis of the body coordinate system, that is, the angular momentum H is expressed as:

[0126]

[0127] Since the bionic flapping-wing aircraft has a symmetrical structure, in the inertia matrix, except for the elements on the main diagonal, all other elements are zero, that is, the angular momentum H is simplified to:

[0128]

[0129] According to the calculation method of vector derivatives in the rotating coordinate system, the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass is:

[0130]

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

[0132] Substituting formula (26) into formula (29), we can get:

[0133]

[0134] in, represents the first-order derivative of ω,

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

[0136]

[0137] Substituting Equation (24) into Equation (31), the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass is obtained by sorting out:

[0138]

[0139] Step S23: Establish the kinematic equation of the bionic flapping-wing aircraft rotating around the center of mass

[0140] In the ground coordinate system, the angular velocity vector of the bionic flapping-wing aircraft body is Angular velocity vector The angular velocity vector ω=[p,q,r] of the bionic flapping-wing aircraft rotating around the center of mass in the body coordinate system T The relationship is:

[0141]

[0142] The kinematic equation of the bionic flapping-wing aircraft in the geographic coordinate system is:

[0143]

[0144] The other steps and parameters are the same as those in the first to third embodiments.

[0145] Specific embodiment 5: This embodiment differs from specific embodiments 1 to 4 in that the C N (α) and C T The quasi-steady empirical formulas for (α) are:

[0146] C N (α)=3.4sinα (35)

[0147]

[0148] The other steps and parameters are the same as those in the first to fourth embodiments.

[0149] Specific embodiment 6: This embodiment is different from any one of the specific embodiments 1 to 5 in that the rotational force coefficient C gyr The empirical formula is:

[0150]

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

[0152] The other steps and parameters are the same as those in the first to fifth embodiments.

[0153] Specific embodiment seven: This embodiment differs from any one of the specific embodiments one to six in that and is defined as follows:

[0154]

[0155] The other steps and parameters are the same as those in the first to sixth embodiments.

[0156] and The value of depends only on the wing shape. For most insects, their value range is approximately and

[0157] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the specific process of step S3 is as follows:

[0158] The kinematic equations and dynamic equations of the bionic flapping-wing aircraft rotating around the center of mass are combined to obtain the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass:

[0159]

[0160] During the flight of a bionic flapping-wing aircraft, the sideslip angle of the fuselage is usually zero, that is, β = 0. Then, in the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass, the components of the bionic flapping-wing aircraft's body damping torque along each axis are:

[0161]

[0162] By controlling the torque acting at the center of mass of the bionic flapping-wing aircraft, the attitude of the aircraft can be controlled, so that the three attitude angles of the bionic flapping-wing aircraft can track the set target values in real time. Therefore, in this invention, the three aerodynamic torques generated by the wings are selected as the inputs of the attitude control system to design and simulate the attitude control algorithm.

[0163] In order to facilitate the design of the bionic flapping-wing aircraft attitude control algorithm, the dynamic model of the bionic flapping-wing aircraft is transformed into a general form of mathematical description. The specific transformation method is as follows:

[0164] Define the variables as follows:

[0165]

[0166] Then the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed into:

[0167]

[0168] Let x2=g'(x1)z, g(x1)=g'(x1)I -1, the external interference uncertainty d=g'(x1)d', then the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed into:

[0169]

[0170] in, represents the state vector of the bionic flapping-wing aircraft attitude system, represents the first-order derivative of x1, represents the first-order derivative of x2, represents the attitude system output vector, represents the system function vector, is the coefficient function matrix, Input vector for the attitude system, is a real number;

[0171] Because bionic flapping-wing aircraft are affected by the environment during flight, their wings will vibrate to a certain extent. This wing vibration has a significant impact on the control of the bionic flapping-wing aircraft during flight. Wing vibration not only generates lift and thrust, but also affects the stability, maneuverability, and energy consumption of the bionic flapping-wing aircraft. Due to the influence of environmental factors during flight, structural changes in the hardware during operation, etc., the system function may be unknown. Therefore, a fuzzy logic system is used to model the unknown dynamics.

[0172] When the system is attacked by false data injection from the actuator, the system state equation is transformed into:

[0173]

[0174] in, Indicates the attack signal of unknown actuator false data injection. x′1 and x1 have similar meanings, but different values. x′2 and x2 have similar meanings, but different values.

[0175] make Then, under the attack of actuator false data injection, the dynamic model of the transformed bionic flapping-wing aircraft rotating around the center of mass is:

[0176]

[0177] The other steps and parameters are the same as those in the first to seventh embodiments.

[0178] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 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 condition inequality holds:

[0180]

[0181] Among them, m is a positive parameter.

[0182] Design the 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:

[0186]

[0187] in, for estimates;

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

[0189]

[0190] Among them, σ is a positive constant, θ i is the parameter vector of the fuzzy logic system, is the fuzzy basis function, sup represents the supremum;

[0191] Use fuzzy logic system to analyze the function Make an approximation:

[0192]

[0193] Among them, the optimal parameter vector for:

[0194]

[0195] Where Ω is θ i A bounded compact set of , U is is a bounded compact set of

[0196]

[0197] The fuzzy state observer is designed as:

[0198]

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

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

[0201]

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

[0203] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0204] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the specific process of step S5 is as follows:

[0205] Define the approximation error ε i for:

[0206]

[0207] Among them, |ε i | represents ε i The absolute value of is a constant;

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

[0209]

[0210] in is the observation error vector, is the first-order derivative of e, That is, ε=[ε1,ε2,ε3] T ;

[0211] For the error system of formula (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 time derivative of V0 is:

[0214]

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

[0216] According to Young's inequality and assumption 1, we can get:

[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] Among them, ||·|| represents the 2 norm, and the external interference has a constant d * Make ||d||≤d * ;

[0222] Substituting (59)-(62) into (58), we can obtain:

[0223]

[0224] Define the error transformation of formula (64):

[0225]

[0226] Among them, z1 and z2 are errors, α1 is the virtual control signal, y d To track the signal;

[0227] Select Lyapunov function V1:

[0228]

[0229] Find the time derivative of V1:

[0230]

[0231] in, represents the first-order derivative of V1, represents y d The first derivative of According to Young's inequality:

[0232]

[0233] Combining equations (66)-(68), we can obtain:

[0234]

[0235] Design the virtual control signal as:

[0236]

[0237] Among them, p1 is a positive design parameter, represents y d The first derivative of ;

[0238] Substituting formula (70) into formula (69) yields:

[0239]

[0240] Choose the Lyapunov function V:

[0241]

[0242] Among them, γ i is a positive design parameter;

[0243] Taking the time derivative of V we get:

[0244]

[0245] in, It is y d The second-order derivative of , simplified, can be obtained:

[0246]

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

[0248] From Young's inequality we can get:

[0249]

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

[0251]

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

[0253]

[0254] Among them, p2, r i is a positive design parameter, It is y d The second derivative of .

[0255]

[0256] Depend on

[0257]

[0258] Available

[0259]

[0260] Right now:

[0261]

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

[0263]

[0264] Then we can get:

[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 Specific Embodiments 1 to 9.

[0268] This paper designs a state observer based on the attitude output vector of a bionic flapping-wing aircraft with actuator attack and a fuzzy logic system that approximates unknown nonlinearities and actuator attack signals. A virtual control law is designed based on the observer's estimated state, which is then filtered and fed into a backstepping controller to generate a control signal. This control signal controls the three-dimensional torque at the aircraft's center of mass and is compared with the desired attitude trajectory. The difference is then fed into the controller as feedback until the value converges near the origin.

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

[0270] I y =576g·mm 2 , I z =991g·mm 2 , S=1526.4mm 2 , R=53mm, c=28mm, v=5m / s, Select feedback gain K = [k1I 3×3 ,k2I 3×3 ] T , where k1 = 45 and k2 = 40. This makes 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 adaptive law are p1 = 110, p2 = 100; γ1 = 20, γ2 = 10, γ3 = 30; r1 = 100, r2 = 90, r3 = 100. The initial condition x1(0) = [0, 0, 0] T ,x2(0)=[0.1,0.1,0.1] T , the remaining initial values are all selected as 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 , when t≥20, the attack signal is introduced. The simulation results are as follows Figure 2 、 Figure 3 and Figure 4 As shown, Figures 2 to 4 shows the trajectory of the difference between the output signal under attack and the reference signal, where z1 = [z 11 ,z 12 ,z 13 ] T .

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

[0275] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A bionic flapping-wing aircraft attitude tracking control method based on fuzzy state observer, characterized in that: The method specifically comprises the following steps: Step S1: Establish a ground coordinate system, an aircraft body coordinate system, a velocity coordinate system, a left wing coordinate system, and a right wing coordinate system, and calculate the conversion relationship between the coordinate systems; Step S2: Based on the conversion relationship between the coordinate systems, establish the kinematic equation and dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass; Step S3, combining the kinematic equation and the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass to obtain a dynamic model of the bionic flapping-wing aircraft rotating around the center of mass; Then, the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed, and an actuator false data injection attack is introduced; Step S4, constructing a fuzzy state observer of the bionic flapping-wing aircraft based on the fuzzy logic system; Step S5: Based on the information observed by the fuzzy state observer, a backstepping control method is used to design a control law for the bionic flapping-wing aircraft under the attack of actuator false data injection; Step S6: Using the control law designed in step S5 to perform attitude control on the bionic flapping-wing UAV.

2. The bionic flapping-wing aircraft attitude tracking control method based on 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 O e is the starting point of the bionic flapping-wing aircraft or the center of mass of the bionic flapping-wing aircraft when it takes off, X e The positive direction of the Z axis is the projection of the heading of the bionic flapping-wing aircraft on the horizontal plane when it takes off. e Axis perpendicular to X e axis, and Z e The positive direction of the Y axis is vertically upward. e Axis and O e X e Z e Plane vertical, X e Axis positive direction, Y e Axis positive 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 O b Coincident with the center of mass of the bionic flapping-wing aircraft, Z b The axis is parallel to the longitudinal axis of the body and the Z b The positive direction of the axis points to the head of the body, X b Axis perpendicular to Z b Axis and X b The positive direction of the axis points forward, Y b Axis and O b X b Z b The planes are vertical, and X b Axis positive direction, Y b Axis positive 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 the body coordinate system O b X b Y b Z b The origin of X v The X axis coincides with the flight velocity vector of the bionic flapping-wing aircraft in the air and v The positive direction of the axis points to the direction of flight speed, Z v Axis perpendicular to X v Axis and Z v The positive direction of the axis points upward, Y v Axis perpendicular to O v X v Z v Plane, and X v Axis positive direction, Y v Axis positive 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 O wl Located at the root of the left wing of the bionic flapping-wing aircraft, X wl The axis is parallel to the wing and X wl The positive direction of the axis points to the head of the body, Z wl The axis is perpendicular to the wing plane and the Z wl The positive direction of the axis points downward, Y wl Axis perpendicular to O wl X wl Z wl Plane, and Y wl The positive direction of the axis points to the direction of the wingspan; Right wing coordinate system O wr X wr Y wr Z wr Origin O wr Located at the root of the right wing of the bionic flapping-wing aircraft, X wr The axis is parallel to the wing and X wr The positive direction of the axis points to the head of the body, Z wr The axis is perpendicular to the wing plane and the Z wr The positive direction of the axis points upward, Y wr Axis perpendicular to O wr X wr Z wr Plane, and Y wr The positive direction of the axis points in the direction of the wingspan.

3. The bionic flapping-wing aircraft attitude tracking control method based on fuzzy state observer according to claim 2, characterized in that: The calculation of the conversion relationship between the coordinate systems is specifically as follows: The conversion relationship between the body coordinate system and the velocity coordinate system is described by the angle of attack ζ and the sideslip angle β: in, Represents the transformation matrix from the body coordinate system to the velocity coordinate system; right Perform transposition and obtain the transformation matrix from the velocity coordinate system to the body coordinate system: in, Represents the transformation matrix from the velocity coordinate system to the body coordinate system; Use the right wing flapping angle φ r and right wing twist angle The transformation matrix from the right wing coordinate system to the body coordinate system is: in, Represents the transformation matrix from the right wing coordinate system to the body coordinate system; Use the left wing flapping angle φ l and the left wing twist angle The transformation matrix from the left wing coordinate system to the body coordinate system is: in, Represents the transformation matrix from the left wing coordinate system to the body coordinate system.

4. The method for attitude tracking control of a bionic flapping-wing aircraft based on a fuzzy state observer according to claim 3, characterized in that: The specific process of step S2 is: Step S21: Modeling the total torque applied to the bionic flapping-wing aircraft body During the flapping of the wings of a bionic 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 is the instantaneous translational force generated by the stall delay mechanism, F gyr It is the rotational circulation force generated by the rotational circulation mechanism; The aerodynamic force generated by the stall delay mechanism per unit length in the span direction is: Among them, F′ st,N is the normal force perpendicular to the wing plane per unit length in the span direction, F′ st,T is the tangential force parallel to the wing plane along the chord direction per unit length in the span direction, α is the angle of attack when the wing flaps, c is the chord length of the wing, U is the translational velocity of the wing, ρ is the air density, and C N (α) is the lift coefficient perpendicular to the wing plane, C T (α) is the lift coefficient parallel to the wing plane; The aerodynamic force F′ generated by the rotating circulation mechanism per unit length in the span direction gyr,N for: in, is the angular velocity of the wing's angle of attack, C gyr is the rotational force coefficient; If the wings of the bionic flapping-wing aircraft are infinitely divided along the wingspan direction, then F′ st,N , F′ st,T , F′ gyr,N At length d r The total aerodynamic forces on are: in, is the angular velocity of the wing flapping angle, c(r) is the chord length at r from the wing root, dF st,N (t,r),dF st,T (t,r) and dF gyr,N (t) are F′ st,N , F′ st,T and F′ gyr,N At length d r The total aerodynamic force on , t represents time; Integrating along the span of the wing, the aerodynamic force acting on the entire wing plane is: Among them, A w is the area of the wing plane, L is the span of the wing, that is, the distance from the wing root to the wing tip, U cp is the velocity of the wing's center of pressure, c m is the maximum chord length of the wing, For standardized pressure centers, is the normalized rotation chord length; The total aerodynamic force generated by a single wing is: Among them, F N (t) is the normal force perpendicular to the wing plane, F T (t) is the tangential force parallel to the wing plane; The aerodynamic force components of each axis in the left wing coordinate system and the aerodynamic force components of each axis in the right wing coordinate system are: Among them, -F Nr , 0, and F Tr It represents the aerodynamic force components of the total aerodynamic force of the right wing in each axis of the right wing coordinate system, F Nl , 0, and F Tl It represents the aerodynamic force components of the total aerodynamic force of the left wing in each axis of the left wing coordinate system; The decomposition results of the aerodynamic forces generated by the left wing and the right wing of the bionic flapping-wing aircraft in the three axes of the body coordinate system are as follows: in, is the decomposition result of the aerodynamic force generated by the right wing in the three axes of the body coordinate system, The decomposition results of the aerodynamic force generated by the left wing in the three axes of the body coordinate system; The wing will be located on the axis of rotation and at a distance from the wing root. The position at the left wing is taken as the aerodynamic center of the wing plane. In the left wing coordinate system and the right wing coordinate system, the coordinates of the aerodynamic center of the left wing and the aerodynamic center of the right wing are both According to the transformation matrix from the left wing coordinate system to the body coordinate system and the transformation matrix from the right wing coordinate system to the body coordinate system, the position vector of the aerodynamic center of the left wing in the body coordinate system and the position vector of the aerodynamic center of the right wing in the body coordinate system are obtained: in, is the position vector of the aerodynamic center of the right wing in the body coordinate system, is the position vector of the aerodynamic center of the left wing in the body coordinate system; In the body coordinate system, the moment of the aerodynamic force on the body during one flapping cycle of the left wing and the moment of the aerodynamic force on the aerodynamic center during one flapping cycle of the right wing are respectively: Then, in the body coordinate system, the resultant moment of the aerodynamic force exerted on the body by the left and right wings during one flapping cycle on the aerodynamic center is: Among them, M w is the resultant moment; The damping force of the body is decomposed into resistance 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 body relative to the incoming flow, S is the characteristic area of the body, c x is the drag coefficient of the bionic flapping-wing aircraft, c y is the lateral force coefficient of the bionic flapping-wing aircraft body, c z is the lift coefficient of the bionic flapping-wing aircraft, c 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 body of the bionic flapping-wing aircraft is: Among them, l x =l z =R, R represents the wingspan, l y =0.25c m ; Then the expression of the body damping torque in the body coordinate system is: Among them, M b is the damping torque of the body in the body coordinate system; The total disturbance torque caused by external interference, parameter perturbation and incomplete modeling in the body coordinate system is denoted as M d , that is, M d =[M dx ,M dy ,M dz ] T , then the total moment M of the bionic flapping-wing aircraft in the body coordinate system is: Step S22: Establish the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass In the body coordinate system, the dynamic equation of the body's rotation around the center of mass is: Where M is the total moment vector of the wing aerodynamic force and the body damping force acting on the center of mass of the bionic flapping-wing aircraft, and H is the angular momentum of the bionic flapping-wing aircraft acting on the center of mass. H=Iω (26) Where I is the inertia matrix of the body, ω is the angular velocity vector of the body, ω=[p,q,r] T , p, q and r are the components of ω along the axis of the body coordinate system, that is, the angular momentum H is expressed as: Simplify the angular momentum H to: The dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass is: in, represents the first derivative of H; Substituting formula (26) into formula (29), we can get: in, represents the first-order derivative of ω, Then, in the body coordinate system, the scalar form of the dynamic equation of the bionic flapping-wing aircraft rotating around the body's center of mass is: Substituting Equation (24) into Equation (31), the dynamic equation of the bionic flapping-wing aircraft rotating around the center of mass is obtained by sorting out: Step S23: Establish the kinematic equation of the bionic flapping-wing aircraft rotating around the center of mass In the ground coordinate system, the angular velocity vector of the bionic flapping-wing aircraft body is Angular velocity vector The angular velocity vector ω=[p,q,r] of the bionic flapping-wing aircraft rotating around the center of mass in the body coordinate system T The relationship is: The kinematic equation of the bionic flapping-wing aircraft in the geographic coordinate system is:

5. The bionic flapping-wing aircraft attitude tracking control method based on fuzzy state observer according to claim 4 is characterized in that: The C N (α) and C T (α) are: C N (a)=3.4 sinα(35) 6. The bionic flapping-wing aircraft attitude tracking control method based on 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 wing's torsion axis to the wing's leading edge to the wing's chord length.

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

8. The method for attitude tracking control of a bionic flapping-wing aircraft based on a fuzzy state observer according to claim 4, characterized in that: The specific process of step S3 is: The kinematic equations and dynamic equations of the bionic flapping-wing aircraft rotating around the center of mass are combined to obtain the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass: In the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass, the components of the bionic flapping-wing aircraft's body damping torque along each axis are: Define the variables as follows: Then the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed into: Let x2=g'(x1)z, g(x1)=g'(x1)I -1 , the external interference uncertainty term d=g'(x1)d', then the dynamic model of the bionic flapping-wing aircraft rotating around the center of mass is transformed into: in, represents the state vector of the bionic flapping-wing aircraft attitude system, represents the first-order derivative of x1, represents the first-order derivative of x2, represents the attitude system output vector, represents the system function vector, is the coefficient function matrix, Input vector for the attitude system, is a real number; When the system is attacked by false data injection from the actuator, the system state equation is transformed into: in, Indicates an unknown actuator false data injection attack signal; make Then, under the attack of actuator false data injection, the dynamic model of the transformed bionic flapping-wing aircraft rotating around the center of mass is:

9. The bionic flapping-wing aircraft attitude tracking control method based on fuzzy state observer according to claim 8, characterized in that: The specific process of step S4 is as follows: Design the 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: in, for estimates; make Function defined on the compact set Ω There exists a fuzzy logic system such that: Among them, σ is a positive constant, θ i is the parameter vector of the fuzzy logic system, is the fuzzy basis function, sup represents the supremum; Use fuzzy logic system to analyze the function Make an approximation: Among them, the optimal parameter vector for: Where Ω is θ i A bounded compact set of , U is is a bounded compact set of The fuzzy state observer is designed as: in, is the estimate of x2, is the estimate of x1, is the estimate of y, for The first derivative of for The first derivative of , k1 and k2 are both positive design parameters; According to formula (53), the state space form of the fuzzy state observer is: in, is the Hurwitz matrix, I 3×3 is the identity matrix, 0 3×3 is a 0 matrix, express The first derivative of C=[I 3×3 ,0 3×3 ].

10. The bionic flapping-wing aircraft attitude tracking control method based on fuzzy state observer according to claim 9, characterized in that: The specific process of step S5 is as follows: Define the error transformation of formula (64): Among them, z1 and z2 are errors, α1 is the virtual control signal, y d To track the signal; Design the virtual control signal as: Among them, p1 is a positive design parameter, represents y d The first derivative of ; The designed control law is: Among them, p2 is a positive design parameter, It is y d The second derivative of .

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