CN114237266A - Flapping wing flight attitude control method based on L1 self-adaption - Google Patents

Abstract

The application discloses a flapping wing flight attitude control method based on L1 self-adaptation, which comprises the following steps: firstly, establishing a flapping wing flying motion model; step two, constructing an L1AC self-adaptive controller; step three, self-adaptive control is carried out on the bionic flapping wing flight L1, and a built actual flapping wing flight dynamics model is verified; and fourthly, performing simulation analysis and calculation, inputting actual parameters of the flapping wing aircraft into a control model, and verifying the effectiveness of the constructed L1AC adaptive controller in platform application. Has the following advantages: in the flapping wing flight attitude control applied to the L1 self-adaptive control method, the established flapping wing dynamic model is combined to establish a flapping wing flight attitude control system, the self-adaptive control adjusts parameter estimation according to the control law, the output error of the state predictor and the controlled object is ensured to be stable under the Lyapunov meaning, and the control law is obtained.

Description

A L1 Adaptive Attitude Control Method for Flapping-wing Flight

technical field

The invention is a flapping-wing attitude control method based on L1 self-adaptation, and belongs to the field of unmanned aerial vehicle control.

Background technique

Flapping-wing flight control is a typical high-order uncertain nonlinear control problem. A flapping-wing aircraft relies on the rapid flapping of the wings to generate the power required for flight. The aircraft itself needs to use flexible and lightweight materials to improve flight efficiency. The fuselage is easily disturbed by external forces, resulting in unstable flight. At the same time, the rapid flapping of the wing during flapping flight will cause a large vibration of the whole system. Self-vibration and external force disturbance will cause the performance of the sensor and the actuator to decrease, and the measurement error of the motion parameter will increase. Therefore, the attitude control of the flapping-wing aircraft requires a control algorithm that matches the flight characteristics of the flapping-wing aircraft to achieve its system stability.

Traditional fixed-wing and rotary-wing flight control algorithms cannot meet the control requirements of flapping-wing flight. In order to solve the nonlinear and unsteady flight control problem of flapping-wing, many scholars at home and abroad have carried out research on it. On the basis of the traditional control method, the sliding mode, fuzzy and other control theories are introduced and applied to the flight control of flapping wings.

The following control methods are adopted in the prior art:

1. Use the generalized mixed sensitivity ladder design method to model and control the flapping wing aircraft. Since the lift generated by the flapping wing has a certain periodicity, the average theory is used to convert the nonlinear time-varying model into a nonlinear time-invariant model. The model is then linearized under different flight conditions, and a novel H-infinity control method based on convex optimization is proposed to deal with multiple possibly conflicting control parameters (such as the frequency and time-domain closed-loop characteristics of the system's input and output).

Second, a nonlinear control strategy that uses a differential plane controller to simulate the control of flapping wings in the pitch plane, while flying a circular trajectory and maintaining a constant orientation relative to the horizon.

3. The sliding mode control method is used to verify the effectiveness of two different types of sliding mode control strategies in maintaining the flapping-wing pitch plane when it is disturbed by external wind and damaged.

4. The longitudinal control method of flapping-wing aircraft is based on the control model of conventional aircraft, introduces the influence of wing inertia on the system model, and adopts the combination of vibration and feedback control to control the longitudinal dynamic equation of flapping-wing.

5. Three nonlinear flapping-wing flight control models are established, and the complexity of the models continues to increase. The first model includes only rigid body dynamics and ignores wing dynamics, the second model includes rigid body dynamics and wing dynamics, and the third model includes full rigid body and rigid wing dynamics. At the same time, in order to improve the accuracy of the model, the linear quadratic regulation (LQR) is used as the design method of the main control system, combined with the nonlinear parameter optimization algorithm, the flapping flight control algorithm is given.

Most of the above flight control methods for flapping wing only solve the attitude control problem of flapping flight in one dimension, and do not adjust the flight attitude in time according to the changes of the external environment, and the established dynamic model does not consider the external wind disturbance and itself. Vibration problem.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to aim at the above deficiencies, and to provide a flapping-wing attitude control method based on L1 self-adaptation. , build a flapping-wing flight attitude control system, and the adaptive control adjusts the parameter estimation according to the control law to ensure that the output error between the state predictor and the controlled object is stable in the sense of Lyapunov, and the control law is obtained from this. According to the adjusted parameters and the predetermined control signal, the control amount is adjusted according to the control law. When the adaptive gain is large enough, it is proved by mathematical method that the system has better transient response characteristics. At the same time, in order to test the robustness of the control system, parameter uncertainty is increased. The boundary of flight control control parameters is optimized by combining the Monte Carlo-Support Vector Machine method, and the control parameters that meet the control expectations of the flapping aircraft are obtained and classified and judged, which can be transplanted to the embedded system for the subsequent L1AC-based flapping flight control algorithm. and provide a theoretical basis for further development.

In order to solve the above technical problems, the present invention adopts the following technical solutions:

A flapping flight attitude control method based on L1 adaptation, comprising the following steps:

Step 1, establish a flapping flight motion model;

Step 2, construct the L1AC adaptive controller;

Step 3: L1 adaptive control of bionic flapping-wing flight to verify the built actual flapping-wing flight dynamics model;

Step 4, simulation analysis and calculation, input the actual flapping aircraft parameters into the control model to verify the effectiveness of the constructed L1AC adaptive controller in the platform application.

Further, the concrete steps of establishing the flapping flight motion model are as follows:

Step 1, establish the dynamic equation of the centroid motion of the flapping wing;

Step 2, establish the dynamic equation of the flapping wing rotating around the center of mass;

Step 3, establish the kinematic equation of the centroid motion of the flapping wing;

Step 4, establish the kinematics equation for the rotation of the flapping wing's center of mass;

Step 5, establish the dynamic model of the flapping-wing flight system.

Further, the L1AC adaptive controller includes a controlled object, a state predictor, an adaptive law and a control law, and a low-pass filter D(s) is added to the control law to separate the control law and the adaptive law, and Only low frequency signals are allowed into the system.

Further, the construction of the L1AC adaptive controller specifically includes the following steps

Step 1, build a state predictor;

Step 2, build an adaptive law;

Step 3, construct the control law.

The present invention adopts the above technical scheme, compared with the prior art, has the following technical effects:

Apply the L1 adaptive control method to the flapping-wing attitude control, combine the established flapping-wing dynamics model, and build a flapping-wing attitude control system. The adaptive control adjusts the parameter estimation according to the control law to ensure the state predictor and the controlled object. The output error is stable in the Lyapunov sense, and thus the control law is obtained. According to the adjusted parameters and the predetermined control signal, the control amount is adjusted according to the control law. When the adaptive gain is large enough, it is proved by mathematical method that the system has better transient response characteristics. At the same time, in order to test the robustness of the control system, parameter uncertainty is increased. The boundary of the flight control control parameters is optimized by combining the Monte Carlo-Support Vector Machine method, and the control parameters that meet the control expectations of the flapping aircraft are obtained and classified and judged, which can be transplanted to the embedded system for the subsequent L1AC-based flapping flight control algorithm. and provide a theoretical basis for further development.

Description of drawings

In order to illustrate the specific embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that are required to be used in the description of the specific embodiments or the prior art. Similar elements or parts are generally identified by similar reference numerals throughout the drawings. In the drawings, each element or section is not necessarily drawn to actual scale.

Fig. 1 is the definition diagram of flapping flight coordinate system in the present invention;

Fig. 2 is the positional relationship diagram of the wing and the fuselage in the present invention;

FIG. 3 is a diagram of the force acting on the fuselage in the present invention;

Fig. 4 is the structural block diagram of L1AC adaptive controller in the present invention;

5 is a structural diagram of an L1AC adaptive controller in the present invention;

Fig. 6 is the simulation block diagram of L1AC adaptive controller in the present invention;

Fig. 7 is the curve diagram of L1 adaptive controller control output tracking result when unknown parameters are different in the present invention;

Fig. 8 is a control variable response curve diagram when unknown parameters are different in the present invention;

Fig. 9 is the curve diagram of L1 controller control output tracking result when different interference signals in the present invention;

Fig. 10 is the change curve diagram of control amount when different interference signals in the present invention;

FIG. 11 is a graph showing the variation curve of estimation error when different interference signals in the present invention;

12 is a schematic diagram of the flapping-wing attitude control system in the present invention;

13 is a block diagram of the L1 adaptive attitude control system for flapping wing flight in the present invention;

Fig. 14 is the simulation flow chart of flapping attitude control system in the present invention;

Fig. 15 is the response curve diagram of flapping flight attitude angle in the present invention;

16 is a classification prediction diagram of input control parameters based on Monte Carlo-Support Vector Machine in the present invention;

Fig. 17 is the objective function model diagram in the present invention;

FIG. 18 is a diagram of positive and negative samples and a hyperplane in the present invention.

Detailed ways

Embodiment 1, a kind of flapping flight attitude control method based on L1 adaptation, comprises the following steps:

The first step is to establish a flapping flight motion model.

The specific introduction of the flapping flight motion model is as follows:

1. Definition of the coordinate system of the flapping flight motion model

The flapping-wing bionic ammunition imitates birds to generate the power required for flight by flapping their wings. In order to establish a flapping-wing flight motion model, it is necessary to define a set of coordinate systems for the process of flapping-wing flight motion. During the flapping flight, the center of mass and inertia moment of the entire flight system will change due to the flapping up and down. Therefore, it is necessary to describe the motion equations of each link part of the flapping-wing flight system separately. When describing the system motion model, the motion parameters of each component are described in the same coordinate system through coordinate transformation. To this end, according to the flight requirements of flapping-wing bionic ammunition, the following are established respectively: ground coordinate system, track coordinate system, velocity coordinate system, fuselage coordinate system and wing coordinate system, as shown in Figure 1.

(1) Ground coordinate system

The system ground coordinate system OX _e Y _e Z _e , whose coordinate origin is fixed on the surface of the earth, the OX _e axis is the intersection of the track plane and the horizontal plane during flapping flight, and the flying direction is positive; the OY _e axis is perpendicular to the OX _e Axis, pointing upward is positive; OZ _e -axis is perpendicular to the two axes and conforms to the right-hand rule.

(2) Fuselage coordinate system

The origin o of the fuselage coordinate system ox _a y _a z _a is taken on the center of mass of the fuselage, the ox _b axis is parallel to the fuselage axis, and the direction from the tail of the fuselage to the head is positive; the oy _b axis is located in the longitudinal symmetry plane of the fuselage and The ox _b axis is vertical, pointing upward is positive; the oz _b axis is perpendicular to the ox _b z _b plane, and the direction is determined by the right-hand coordinate system.

(3) Speed coordinate system

The velocity coordinate system ox _{a y a} za , the origin is located at the center of mass of the flapping-wing flight platform, the ox _a axis is along the direction of the flight speed vector, the oy _a axis is located in the longitudinal plane of the body, perpendicular to the ox _a axis, pointing upward is positive, the oz _a axis It is perpendicular to the other two axes and obeys the right-hand rule.

(4) Track coordinate system

The track coordinate system ox _k y _k z _k , the origin is fixed to the instantaneous center of mass of the flapping flight platform, the ox _k axis coincides with the ground speed vector direction of the aircraft, the oy _k axis is located in the vertical plane containing the ox _k axis, and is perpendicular to the The ox _k -axis is positive pointing upward, and the oz _k -axis is perpendicular to the other two axes in accordance with the right-hand rule. In the track coordinate system, it is relatively simple to establish the motion equation of the center of mass during flapping flight. Therefore, when establishing the motion equation of the center of mass of the flapping wing, each parameter of the flapping wing is converted to the track coordinate system.

(5) Wing coordinate system

The origin of the wing coordinate system ox _w y _w z _w o _w is fixed at the connection between the wing and the fuselage, and the o _w x _w axis is parallel to the chordwise direction of the wing, and it is positive from the trailing edge of the wing to the leading edge of the wing. ; o _w y _w axis is perpendicular to the airfoil, pointing upward is positive; o _w z _w axis is perpendicular to the other two axes and conforms to the right-hand rule. The flapping flight platform of this patent can realize up and down flapping and chordwise twisting motion. When the wing does not twist, its wing chord is parallel to the fuselage axis.

2. Conversion between coordinate systems of flapping-wing bionic ammunition

During flapping flight, the ground coordinate system, speed coordinate system, track coordinate system, fuselage coordinate system and wing coordinate system have their own directions in space, and there is a certain relationship between them, which acts on the fuselage. The forces and moments on the wings and their corresponding motion parameters are generally defined in their independent coordinate systems. In order to accurately describe the motion and dynamic model of flapping wing flight, it is necessary to The parameters are converted from the defined coordinate system to the same coordinate system, which requires the conversion of each coordinate system.

2.2 Conversion relationship between ground coordinate system and track coordinate system

The relationship between the ground coordinate system and the track coordinate system can be represented by two Euler angles: the track declination angle Ψ and the track inclination angle Θ. The two Euler angles are defined as follows:

Track declination Ψ: The velocity vector of flapping flight, that is, the angle between the ox _a axis in the track coordinate system and the OX _e in the ground coordinate system. If the ox _a axis is above the horizontal plane, then Ψ is positive; otherwise, it is negative.

Track inclination Θ: The angle between the velocity vector of the flapping fuselage and the OX _e Y _e surface. When the head of the fuselage speed is in the positive direction of the OZ _e -axis, the track inclination is positive; otherwise, it is negative.

2.3 Conversion relationship between velocity coordinate system and fuselage coordinate system

Since the oy _{a of the velocity coordinate system and the oy b axis} of the fuselage coordinate system are both in the longitudinal symmetry plane of the fuselage, two Euler angles can be used between the velocity coordinate system and the fuselage coordinate system: the angle of attack α and the sideslip angle β, which are defined as:

Angle of attack α: the angle between the projection of the fuselage velocity vector on the longitudinal symmetry plane ox _b y _b of the fuselage and the ox _b axis. If the velocity vector is projected in the negative direction of the oy _b axis, the angle of attack is positive; otherwise, it is negative.

Side slip angle β: the angle between the fuselage velocity vector and the fuselage longitudinal symmetry plane ox _b y _b . If the velocity vector is projected in the positive direction of the oz _b axis, the sideslip angle is positive.

2.4 Conversion relationship between track coordinate system and speed coordinate system

Under no wind conditions, the ox _k axis of the track coordinate system coincides with the ox _a of the speed coordinate system, and the track coordinate system coincides with the speed vector of the fuselage, so the conversion relationship between the track coordinate system and the speed coordinate system is described. There is only one velocity roll angle γ _a .

Speed roll angle γ _a : the angle between the oy _a axis in the speed coordinate system and the ox _k y _k in the track coordinate system. Viewed from the same direction as the flight speed direction, if the longitudinal symmetry plane of the fuselage is inclined to the right, the speed roll angle γ _a is positive; otherwise, it is negative. According to the same derivation method as above, the transformation matrix from the track coordinate system to the velocity coordinate system can be obtained as:

2.5 Conversion relationship between the fuselage coordinate system and the wing coordinate system

The motion of the wing is time-varying and independent. The wing of the flapping flight platform designed in this paper can realize the up and down flapping and chordwise twisting motion. Therefore, in the wing coordinate system, the relationship between the wing and the fuselage can be described by the flapping amplitude angle φ and the twist angle Φ of the wing, as shown in Figure 2.

Flutter amplitude angle φ: the angle between the wing oy _w axis and the fuselage ox _b y _b plane, the axis oy _w is above the plane, then φ is positive, and when oy _w is below the plane, then φ is burden.

Torsion angle Φ: the angle between the ox _w axis and the fuselage plane ox _b y _b , if the ox _w axis is above the ox _b y _b plane, then Φ is positive, and below the ox _b y _b plane, then Φ is negative.

3. Analysis of aerodynamic parameters of flapping wings

Before establishing the kinematics and dynamics mathematical model of flapping flight, it is necessary to analyze the forces acting on the fuselage and wing during flapping flight. Since the flapping wing is a complex nonlinear system with multiple inputs and multiple outputs, it is subject to many external and self-disturbing factors during its flight. Therefore, in the aerodynamic analysis of the flapping wing, some limitations need to be made on the bionic flapping wing model.

(1) The mass characteristics and motion characteristics of each component of the bionic flapping wing system are measurable and constant.

(2) The wings on both sides flap symmetrically around the fuselage axis, and the flapping speed is constant.

(3) The change of the system center of gravity, moment of inertia and product of inertia caused by the mass of the wing during flapping is not considered.

(4) The system is rigid, with no flexible deformation and uniform mass distribution.

The flapping flight system can be divided into two parts: the fuselage and the wing. The wing is the main source of power for the lift required for flight, while the fuselage generates a portion of the lift and withstands air resistance. Therefore, when analyzing the aerodynamic parameters of the flapping wing system, it is also carried out according to these two parts.

3.1 Analysis of the force and moment of the fuselage

During flapping flight, there are three main external forces on the fuselage: gravity G, external aerodynamic force Q and force T acting on the fuselage by the flapping of the wings, as shown in Figure 3.

3.2 Determination of wing aerodynamic parameters

During the flapping flight, the external gust and the airflow disturbance during the flapping process will affect the stability of the flapping flight. Therefore, in the attitude control of flapping wing flight, it is necessary to consider the influence of external disturbance force on the attitude of the moment generated by the flapping wing. Assuming that the moment generated by the external disturbance force is _{MG, the components along the body coordinate system can be expressed as: MGx, MGy, MGz , then according} to the above separation, the total moment on the body is:

In the formula,

The establishment of the flapping flight motion model includes the following steps:

Step 1, establish the dynamic equation of the centroid motion of the flapping wing.

When establishing the dynamic model of the center of mass motion of the flapping wing, the selection of the reference frame directly affects the complexity of the equation of motion of the center of mass of the flapping wing. Through the dynamic problem of flapping-wing mass center motion, the established flapping-wing flight mechanics vector equation is projected into the track coordinate system ox _k y _k z _k , and the corresponding dynamic equation is obtained.

The track coordinate system ox _k y _k z _k is a moving coordinate system, which has both displacement motion (its velocity is V) and rotational motion (its angular velocity is Ω) relative to the ground coordinate system. The dynamic equation is established in the moving coordinate system, and the relationship between the absolute speed during flapping flight and its implicated speed is:

为速度矢量V在地面坐标系中的绝对导数，

为速度矢量在航迹坐标系中的相对导数。in,

is the absolute derivative of the velocity vector V in the ground coordinate system,

is the relative derivative of the velocity vector in the track coordinate system.

The equation of motion of the center of mass in flapping flight can be expressed as:

In the formula, the projection of each vector on each axis of the track coordinate system oxkykzk can be written as:

According to the definition in the track coordinate system ox _k y _k z _k , the velocity vector V coincides with the ox _a axis in the track coordinate system, so the projected component of the velocity vector in the track coordinate system can be written as:

According to formula (1.49)～(1.50), we can get:

Ω×V=[0 VΩ _za −VΩ _ya ] ^T (1.53).

则航迹坐标系相对地面坐标系的旋转角速度为两次旋转的角速度合成。根据两个坐标系之间的变换矩阵可得：It takes two rotations to switch from the ground coordinate system to the track coordinate system, and the angular velocities of the two rotations are

Then the rotational angular velocity of the track coordinate system relative to the ground coordinate system is the composite of the angular velocity of the two rotations. According to the transformation matrix between the two coordinate systems, we can get:

Bringing formulas (1.51) and (1.52) into (1.50), the kinetic equation of the center of mass motion of flapping flight is finally obtained as:

为航迹切向加速度，

为航迹法向加速度，

为航迹测向加速度，

为扑翼飞行平台质心所受合力在航迹坐标系下各轴分量。In the formula,

is the track tangential acceleration,

is the normal acceleration of the track,

is the track direction finding acceleration,

It is the component of each axis in the track coordinate system of the resultant force on the center of mass of the flapping-wing flight platform.

Step 2, establish the dynamic equation of the flapping wing rotating around the center of mass.

The scalar form of the dynamic equation of the flapping wing rotating around the center of mass is clearest in the fuselage coordinate system. The fuselage coordinate system ox _b y _b z _b is the moving coordinate system, assuming that the rotational angular velocity of the fuselage coordinate system relative to the ground coordinate system is ω, H is the moment of momentum acting on the center of mass of the fuselage, and M is the moment at the center of mass. In the fuselage coordinate system, the dynamic equation of the flapping wing rotating around the center of mass is:

分别为动量矩的绝对、相对导数。In the formula,

are the absolute and relative derivatives of the moment of momentum, respectively.

Assuming that i, j, and k are the unit vectors along each axis of the fuselage coordinate system, respectively, and p, q, r are the components of the rotational angular velocity ω along each axis of the fuselage coordinate system under the fuselage coordinate system, then the moment of fuselage momentum can be expressed as for:

H=J·ω (1.57).

In the formula, J is the inertia tensor, and its matrix expression is:

J _x , J _y , J _z represent the moment of inertia of the flapping-wing flight platform to each axis of the fuselage coordinate system, and J _xy , J _yz , J _zx represent the inertial product of the flapping-wing flight platform to each axis of the fuselage coordinate system. In order to simplify the rotation equation, the inertial product of the flapping-wing flight platform to each axis of the fuselage coordinate system is zero, then the components of the momentum moment H along each axis of the fuselage coordinate system are:

and,

According to formula (1.58), we can get:

Taking formulas (1.59) and (1.60) into (1.55), the dynamic equation of flapping flight rotating around the center of mass can be expressed as:

In the formula, M _x , My _y , and M _z are the components of all external forces acting on the flapping flight platform to the moment on the center of mass on each axis of the fuselage coordinate system ox _b y _b z _b . Formula (1.61) can also be written as :

The expressions of M _x , _My , and M _z in the formula are shown in formulas (1.44) to (1.46).

Step 3, establish the kinematic equation of the centroid motion of the flapping wing

The kinematics equation of the center of mass of the flapping wing describes the real-time coordinate position of the flapping wing. Let u, v, and w be the components of the flapping wing velocity vector along each axis in the ground coordinate system, respectively.

According to the definition of the track coordinate system ox _a y _a z _a , the velocity vector V coincides with the ox _a axis. According to the conversion relationship between the track coordinate system and the ground coordinate system, we can get:

According to the above analysis, the kinematic equation of the centroid of the flapping wing is obtained as:

Step 4, establish the kinematic equation for the rotation of the flapping wing's center of mass

To determine the attitude change of the flapping wing in space during flight, it is necessary to establish the kinematic equation of the attitude change of the flapping wing relative to the ground coordinate system, that is, to establish the derivative and rotation of the flapping wing yaw angle ψ, pitch angle θ, and roll angle γ to time Correspondence between angular velocity components p, q, r.

According to the transformation relationship between the fuselage coordinate system and the ground coordinate system,

After changing the above formula, the kinematics equation for the rotation of the flapping wing around the center of mass is obtained:

Step 5, establish the dynamic model of the flapping flight system

According to the above analysis, the dynamic model of the whole system during flapping flight can be obtained as shown in formula (1.69):

Since the mass of the wing and the flexible deformation factors of the wing flapping process are ignored when establishing the dynamic model of the flapping flight system, the influence of the inertial force of the wing and the flexible deformation on the overall force and moment of the system is not considered in the model. As a result, the established dynamic model of the flapping-wing attitude control system is not very accurate, and there is a modeling error with the attitude change of the actual flapping-wing flight. At the same time, because the flapping of the wing during flapping flight will cause a large vibration of the overall system, the dynamic parameters in the model will change, and the disturbance of external gusts and incoming flow will also affect the attitude stability during flapping flight. Therefore, in designing the flapping flight control system, it is necessary to consider the influence of various factors on flapping flight.

Step 2, construct the L1AC adaptive controller.

The dynamic equation of flapping-wing flight is established, and the aerodynamic characteristics of the rigid-flexible flapping-wing are analyzed, and the changes of lift, drag and moment under different parameters are obtained. From the attitude control equation of flapping wing and the unsteady aerodynamic characteristics of flapping wing, it can be known that the attitude control of flapping wing is greatly disturbed by external disturbance factors, and it is a nonlinear system with multiple inputs and multiple outputs with uncertainty. For the stability design of flapping-wing flight attitude, due to modeling errors, parameter changes, external disturbances and unmodeled dynamics, the control system generally has uncertainties. In order to ensure the stability of flapping flight and the controllability of the system, its feedback control must be robust. Generally speaking, for a nonlinear system, if it can still show stable controllability under the conditions of parameter changes, external disturbances, and unmodeled dynamics, the system can be considered robust. Flapping wing flight dynamics are mainly affected by parameter uncertainty. A common way to deal with uncertainty is to adjust the gain, but this method is complex and time-consuming. Various types of robust and adaptive control techniques have been applied by many researchers in the past to such uncertain nonlinear systems, but these techniques have not been possible until recently with the maturity of computational power and theoretical knowledge in stability. applied to the actual flight control.

For flapping-wing flight attitude control system, a fast and robust adaptive control (L1AC) method is proposed. By adding a low-pass filter to the control law, the control rate and the design of the adaptive law are separated. By designing a state predictor, the uncertain parameters in the flapping-wing attitude control model are estimated and monitored, and the parameter estimation is adjusted by the adaptive law, so as to ensure that the output error between the state predictor and the controlled object is stable in the sense of Lyapunov. Adaptive control law. According to the adjusted parameters and the predetermined control signal, the control amount is adjusted according to the control law. When the adaptive gain is large enough, it is proved by mathematical method that the system has better transient response characteristics. At the same time, in order to test the robustness of the control system, parameter uncertainty is increased. The Monte Carlo-support vector machine method is used to optimize the control parameter boundaries in the flight control, and the control parameters that can meet the control expectations are obtained, and the obtained parameters are classified and judged according to the stable level flight conditions.

1. Composition of L1AC adaptive controller

The L1AC adaptive controller is a fast and robust adaptive control, which is different from the traditional model reference adaptive control (MRAC), as shown in Fig. Adaptive law and control law. The control law adds a low-pass filter D(s) to separate the control law and the adaptive law, and only allow low-frequency signals to enter the system. The L1AC algorithm can not only ensure the asymptotic stability of the system output, but also make the control signal, input and output signals of the system have good transient response characteristics.

The state predictor in the L1AC adaptive controller estimates the uncertain parameters of the system, which is consistent with the traditional MRAC, but differs from the MRAC in that the L1AC adaptive controller introduces a low-pass filter C(s), Make the error signal of the L1AC adaptive controller and the flapping flight attitude controller independent of each other. This method can ensure that the closed-loop state predictor is bounded, and the controller can be arbitrarily designed, through the low-pass filter C ( s) Filter the control signal, adjust the cut-off bandwidth of C(s), thereby control the frequency of the system, ensure that the amplitude margin and phase margin of the L1AC adaptive controller are not affected by high gain, and improve the L1AC self-efficacy. To adapt to the robustness of the controller, the L1AC adaptive controller can have a large adaptive gain, reduce the error of the system, and ensure that the system still has good transient performance and steady-state performance when the dynamic characteristics of the system are not modeled.

According to the established dynamic equation of flapping flight, the state equation of flapping attitude is established, and its expression can be written as:

In the formula, x(t)∈R is the state variable of the system, which can be measured by sensors, u(t)∈R is the control signal of the system; y(t)∈R is the output value of the system; b∈R, c∈ R is a known constant, Am is an n×n square matrix, and requires (Am,b). θ∈R is the uncertainty item of the system, and σ∈R is the disturbance item of the system. ω, θ, σ describe the parameter uncertainty of the plant.

According to the model of the controlled object, the state predictor of the system is established, and its state space expression can be written as:

分别时对x、ω、θ、σ的估计值，当时间区域无穷时，被控对象与状态预测器具有一致的动力学模型，估计偏差在李雅普诺夫意义下稳定。In the formula,

When the estimated values of x, ω, θ, σ are respectively, when the time area is infinite, the controlled object and the state predictor have the same dynamic model, and the estimated deviation is stable in the sense of Lyapunov.

可以表示为：State variable error between plant and state predictor

It can be expressed as:

为主要输入，且误差在李雅普诺夫定理下稳定，得到了对估计参量的

数学表达式，即公式(2.16)。同时为保证闭环控制系统的输入输出稳定性，估计参量在控制律中也会应用。Adaptive Control with State Variable Error

is the main input, and the error is stable under the Lyapunov theorem, the estimated parameters are obtained

Mathematical expression, ie formula (2.16). At the same time, in order to ensure the input and output stability of the closed-loop control system, the estimated parameters are also used in the control law.

The control law consists of two parts, one is the reconstruction of the reference input matched with the state predictor; the other is the low-pass filtering link, through the reconstruction of the reference matched with the state predictor, to ensure that the reference input is used to predict the state The output of the L1AC controller is stable, and the adaptive law and state predictor are designed to ensure that the system error x ~ is stable in the sense of Lyapunov, the L1AC control system is also stable in input and output. The parameter estimation is decoupled from the control link, so that a faster convergence rate of parameter estimation can be obtained under the condition of large adaptive gain, so as to obtain better control performance, and at the same time, it also avoids the large adaptive gain in traditional MRAC. The system is sensitive to noise and delay, and can theoretically guarantee the tracking error bound of the controlled system to the reference model.

2. The construction of the L1AC adaptive controller includes the following steps:

Step 1, build a state predictor

所代替，状态预测器建模为：In order to obtain the state response of the L1AC adaptive controller when there is an unknown disturbance, a state predictor structure is constructed, as shown in Equation (2.34), to realize the state estimation of the controlled object. The state predictor is similar to the state space expression of the controlled object. , but the input gain, unknown uncertain parameters, interference terms, etc. in the L1AC adaptive controller adopt adaptive estimation parameters

Instead, the state predictor is modeled as:

Define the error vector:

的状态空间表达式：The difference between equations (2.34) and (2.8) can be obtained to obtain the system error from the control input u(t) to the L1AC adaptive controller

The state space expression for :

According to the relationship between the control input and the error, the state predictor and the controlled object have consistent dynamic responses. In order to ensure that the system error between the input and the L1AC adaptive controller is asymptotically stable, a quadratic scalar function is selected as Lyapunov function:

的解，I＝IT＞0，Γ为 L1AC自适应控制器的自适应增益，通过增大系统增益Γ，可以提高被控对象的追踪控制精度。In the formula, P=P ^T > 0 is a positive definite symmetric matrix and is

The solution of , I=IT>0, Γ is the adaptive gain of the L1AC adaptive controller. By increasing the system gain Γ, the tracking control accuracy of the controlled object can be improved.

对式(2.34)求导可得：In order to make the closed-loop system asymptotically stable, it is necessary to satisfy

Taking the derivative of equation (2.34), we can get:

According to equation (2.38), when the derivative of the defined Lyapunov function is negative, it can be proved that the system error of the L1AC adaptive controller is stable in the Lyapunov sense.

Step 2, build the adaptive law

和

均存在连续边界，则参数的估计值可以根据基于投影算子的自适应律得到，如式(2.39)～(2.41) 所示：The construction of the adaptive law needs to obtain the model of the adaptive law according to the estimated parameters. To ensure that the system error of the L1AC adaptive controller is stable in the sense of Lyapunov, it is necessary to make the defined scalar function negative definite, that is, formula (2.38) is less than zero, due to the unknown parameters x(t),

and

There are continuous boundaries, the estimated values of the parameters can be obtained according to the adaptive law based on the projection operator, as shown in equations (2.39) to (2.41):

分别为ω(t)、θ(t)和σ(t)的估计值，Γ_ω＝Γ_θ＝Γ_σ＝Γ，Γ＞0&Γ∈R⁺为自适应增益，Γ与

的边界成反比，即增大Γ的值能够有效降低L1AC自适应控制器的系统误差，提高被控对象的追踪精度。 Proj(·,·)为投影算子，Proj(·,·)投影算子的计算公式为公知技术，此处不再赘述。In the formula,

are the estimated values of ω(t), θ(t) and σ(t), respectively, Γ _ω = Γ _θ = Γ _σ = Γ, Γ>0 & Γ∈R ⁺ is the adaptive gain, Γ and

The boundary is inversely proportional to , that is, increasing the value of Γ can effectively reduce the system error of the L1AC adaptive controller and improve the tracking accuracy of the controlled object. Proj(·,·) is a projection operator, and the calculation formula of the Proj(·,·) projection operator is a well-known technique, and will not be repeated here.

Step 3, build the control law

The purpose of the control law design is to compensate the uncertainty in the system through the control signal, and to ensure that the actual output of the system quickly tracks the reference input. According to the ideal controller and parameter estimates, the given L1 adaptive initial control law is as follows:

为

的拉氏变换，

可以表示为：where K>0 is the feedback gain, D(s) is a strictly true function, r(s) is the reference control input, r(s) is the Laplace transform of the control input signal r(t),

for

The Laplace transform of ,

It can be expressed as:

Since the L1 adaptive control will have high frequency oscillation, a low-pass filter is introduced to filter the high frequency signal generated by the adaptive control. By controlling the cut-off frequency of the filter, the amplitude margin and phase margin of the system are not affected by the change of the system gain, so as to achieve the decoupling of parameter estimation and control law, and improve the robustness of the system. The definition of kg in the final control law is shown in formula (2.11), and the selection of K is related to the filter design in the controller. Design a low-pass filter whose expression is:

For the convenience of designing the controller, define D(s)=1/s, then the final designed low-pass filter can be expressed as:

The necessary condition for the stability of L1 gain is that the designed low-pass filter needs to satisfy the L1 small gain theorem (Lemma 1), so that the transient and steady-state performance of the closed-loop control system are consistent and bounded. Define,

H(s)=(sI-A _m ) ^-1 B (2.47).

G(s)=H(s)(1-C(s)) (5.48).

The L1 gain of the system is stable and the conditions that need to be met to obtain the desired performance are:

To sum up, the attitude control system designed according to L1 adaptive theory includes state predictor (2.36), adaptive law (2.39)～(2.41) and control law (2.42). When the system satisfies the condition of equation (2.49), The system has better stability. The structure of the L1 adaptive control system is shown in Figure 5.

3. Simulation and verification of L1AC adaptive controller

The L1AC adaptive controller is used to control the attitude during flapping flight, and the above-designed control system simulation module is constructed through Matlab/Simulink, and its control system performance is analyzed.

The constructed simulation module performs simulation analysis on the following second-order system.

in,

c＝[1 0]

c=[1 0]

u(t) represents the control input and σ(t) represents the system disturbance.

Assume that the uncertainty vector and disturbance vector in the system model are:

σ(t)＝sin(πt)ω=1;

σ(t)=sin(πt)

The bounds of uncertain parameters are defined as:

Δ＝[-10,10]Ω=[0.5,2];

Δ=[-10,10]

求得矩阵P为：According to the Lyapunov equation

The matrix P is obtained as:

In order to ensure that the system output tracks the ideal system output with zero stable error, the adaptive gain Γ = 10000 is selected, then.

y _id =c ^T H(s)k _g r(s) (2.69).

where r(t)=cos(2t/π).

则有：select

Then there are:

The L1 adaptive norm stability condition is:

According to the form of the G(s) function, under the closed-loop performance condition of the system corresponding to the state matrix Am, appropriately increasing the bandwidth of the low-pass filter can ensure that the system satisfies the norm stability condition and the closed-loop adaptive system has good tracking performance. However, an excessively large filter bandwidth will also cause the control signal to be sensitive to external disturbances, resulting in reduced system robustness. In order to verify the performance of the designed controller, the bandwidth of the low-pass filter selected here is ωK=60.

Modeling and simulation analysis are carried out in the matlab/simulink compilation environment. The designed L1AC adaptive controller simulation framework is shown in Figure 6.

In this controller design, the robustness and adaptability of the controller are analyzed separately for different signals of the unknown parameters θ(t) and σ(t) of the system. simulation:

Among them, awgn(x, 0.1) is the Gaussian white noise added to the signal, chrip(0, 0.1, 100, 1) is the swept-frequency interference signal, and a 10-fold gain is applied during the simulation process.

In this controller design, the robustness and adaptability of the controller are analyzed for different signals of the system unknown parameters θ(t) and σ(t), respectively. First, for the parameter θ(t), select different signals for simulation:

Among them, awgn(x, 0.1) is the Gaussian white noise added to the signal, chrip(0, 0.1, 100, 1) is the swept-frequency interference signal, and a 10-fold gain is applied during the simulation process. Figure 7 shows the response of θ(t) between the output of the system and the reference input under different signals, and Figure 8 shows the variation of the control amount.

As shown in Figure 9 to Figure 11, for the interference signal σ(t), the following signals are used for simulation:

σ₄(t)＝2。

σ ₄ (t)=2.

According to the above simulation results, it can be seen that for the system with time-varying parameters and disturbances, the control signal and system response of the designed L1AC controller can track the reference signal with bounds in the case of fast self-adaptation. When the system considers time-varying parameters and interference, the adjustment time of the system is within 10s, the overshoot is less than 5%, and the estimation error is less than 0.02. The above simulation results show that the designed L1AC controller can maintain good robustness under the condition of fast self-adaptation to meet the dynamic performance to avoid the interference of time-varying parameters and external disturbances.

Step 3: L1 adaptive control of bionic flapping-wing flight to verify the actual flapping-wing flight dynamics model built.

When flapping-wing bionic ammunition performs specific combat missions, the stable control of its flight attitude is the premise to ensure the effective completion of the mission. The flapping-wing flight dynamics model was established above, but due to the limitation of theoretical level and technical conditions, the established flapping-wing attitude control model cannot very accurately describe the attitude changes caused by the flexible deformation of the wing and its own vibration during the flapping-wing flight. , so there is inevitably a systematic modeling error. At the same time, because flapping flight is easily affected by external environmental factors, such as gusts, eddy currents and other factors, it will inevitably affect the flapping attitude control parameters, so it is necessary to consider the influence of these factors when performing flapping flight attitude control. .

System energy index and parameter design of flapping wing attitude control system

During the control process, the flapping-wing flight control system actually corrects the attitude angle of flapping-wing flight in real time to ensure that the attitude angle deviation is within a reasonable range. The attitude control principle is shown in Figure 12.

θ _r , ψ _r and γ _r are the given quantities of pitch angle, yaw angle and roll angle, respectively, and e _θ , e _ψ , and e _γ are the deviations between the actual attitude angle and the given quantities. The flapping-wing flight control system realizes the stable flight of flapping-wing bionic ammunition by reducing the difference between the actual attitude angle and the input given value.

In order to realize the ability of flapping-wing bionic ammunition to perform combat tasks, its flight control system must have good robustness and anti-interference ability, and at the same time have high reliability, so that its own system parameters are affected by factors affected by the model. reduced to a minimum. The transient characteristics of flapping-wing flight control system require correspondingly fast, stable and small overshoot.

When building a flapping flight control system, for a given initial condition and a given disturbance, the time for the system to reach a stable condition does not exceed 5s, and the overshoot of the system does not exceed 5°. It can overcome the interference of external gusts, assuming the external wind speed is 5m/s. Due to the different flight parameters of flapping-wing aircraft of different sizes, the design parameters are only defined for the flapping-wing bionic ammunition designed in this paper. At the same time, due to the different mechanical design, system vibration and selected material properties during the actual flight, the achieved control performance indicators will also change to a certain extent.

Step 4, simulation analysis and calculation, input the actual flapping aircraft parameters into the control model, and verify the validity of the constructed L1AC adaptive controller in the platform application.

1. Parameters of flapping flight attitude control system

The parameters used by the flapping-wing flight attitude control system are shown in Table 1.

Table 1 Design parameters of flapping wings

In the simulation process, the moment of inertia used for flapping flight is selected as: Jx=112.57×10-6 (kg·m2), Jy=3799.3×10-6 (kg·m2), Jz=3739.4×10-6 (kg·m2) m2). Due to the differences in the shape, structure and applicable environment of various flapping-wing aircraft, the design parameters of the actual flapping-wing aircraft will also be different. The design parameters given in Table 1 are mainly used for the subsequent flight attitude control simulation, and the specific design should be determined according to the characteristics of the actual object.

2. Construction and simulation analysis of flapping wing control system

According to the above analysis, the L1AC adaptive attitude control system for flapping wing flight is established. Considering that the state equation of the flapping flight control system is relatively complex; the system convergence is affected by many time-varying parameters; the flight state convergence speed is slow, while establishing the flight control simulation system, it is necessary to impose certain constraints on the input control parameters, and predict the control parameters. state. Therefore, the system includes system dynamics model, L1AC adaptive controller, flapping flight controller and Monte Carlo-SVM parameter boundary prediction and classification module.

系统的干扰向量σ_i(t)＝[0.3°sint 0.2°sint 0.1°sint]^T，飞行速度V_ini＝5m/s，设控制器目标飞行状态：θ_r＝0°，ψ_r＝0°，γ_r＝0°。以 Matlab2018b为平台建立仿真系统建立扑翼飞行器L1自适应姿态控制仿真系统，如图13所示。According to the actual flight situation of the flapping wing, the uncertainty vector of the system is set

System disturbance vector σ _i (t)=[0.3°sint 0.2°sint 0.1°sint] ^T , flight speed V _ini =5m/s, set the controller target flight state: θ _r =0°, ψ _r =0° , γ _r =0°. Using Matlab2018b as the platform to establish a simulation system, the L1 adaptive attitude control simulation system of the flapping-wing aircraft is established, as shown in Figure 13.

The overall simulation of the system consists of two parts: the L1AC-based flapping-wing flight control simulation system and the Monte Carlo-support vector machine input control parameter prediction and classification simulation. The complete system workflow of flapping-wing aircraft simulation is shown in Figure 14. At the beginning of the simulation, the parameters of the simulation system need to be initialized, including the system parameters of the flapping aircraft, the external environment parameters, and the simulation control parameters. After the initialization is completed, the dynamics module of the flapping-wing aircraft is solved, and the minimum value of the nonlinear multivariate function of flapping-wing flight is obtained, and then the initial conditions of stable flapping-wing flight are obtained. Linearize the system model and complete the pole configuration, calculate the adaptive controller parameter matrix, complete the horizontal and vertical simulation analysis of the flapper flight, and output the response curve of the flapper's roll, pitch and heading with time when the target setting is achieved , as shown in Figure 15.

It can be seen from Figure 15 that the roll (γ), pitch (θ) and yaw (ψ) parameters of the flapper L1AC controller can track the preset target values. When random interference of control variables is introduced into the simulation system, the pitch angle and yaw angle adjustment time of the system can be stabilized within 5s, and the roll angle can also be stabilized within 10s, the control steady-state error is small, and the overshoot after stabilization is not large. It can meet the performance requirements of the control system.

Considering the Monte Carlo-SVM-based flight control parameter boundary optimization simulation, the Monte Carlo method is used to calculate the roll (γ)/pitch (θ) variable boundary. As shown in Figure 14, using the random function that comes with matlab, the roll and pitch target flight states (target point) are randomly incremented, and the attitude angle is calculated by the L1AC controller, and the attitude parameters are output after 14s of calculation The simulation terminates when any of the following conditions are still not met:

(1) The pitch angle variance is greater than 3;

(2) The roll angle variance is greater than 3;

(3) The elevation difference is greater than 5m.

The program enters the next iterative calculation, and the state where theta, phi, and elevation difference parameters still cannot converge after the system stabilization time of more than 14s is defined as the control preset target (target point) exceeding the flight control redundancy limit, which is included in the failure parameter set. Similarly, The successful data set of system control parameters is completed, which provides a data set basis for the next step of classification and prediction of control parameters.

As shown in Figure 16, the support vector machine (SVM) module in matlab is used to classify and train the control input θ and γ states. Generally, after passing the cross-validation, it is necessary to adjust the kernel function parameters to achieve better prediction accuracy. For this reason, the OptimizeHyperparameters variable is used for hyperparameter optimization, and the kernel function scale parameter (KernelScale) and the box constraint (BoxConstraint) scale are adjusted to easily find the minimization Hyperparameters for 5-fold cross-validation loss. Here, on the one hand, try the geometric sequence of box constraint parameters. Increasing the box constraint scale may reduce the number of support vectors, but may also increase the training time. On the other hand try a geometric sequence of RBF sigma parameters scaled by the original kernel. Iterative calculation and cross-validation can obtain the model with the lowest classification error, as shown in Figure 17.

As shown in Figure 18, it can be seen that through the training of positive and negative sample sets of input expected states provided by Monte Carlo simulation and the adjustment of hyperparameters, a relatively clear hyperplane can be found to classify the targetpoints that meet the expected control parameters of the flapping aircraft. Judging, this provides the basis for the subsequent transplantation and further development of the flapping flight control algorithm based on L1AC to the embedded system.

The description of the present invention has been presented for purposes of illustration and description, and is not intended to be exhaustive or to limit the invention to the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiment was chosen and described in order to better explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use.

Claims (10)

1. An L1 self-adaptive flapping wing flight attitude control method is characterized in that: the method comprises the following steps:

firstly, establishing a flapping wing flying motion model;

step two, constructing an L1AC self-adaptive controller;

step three, self-adaptive control is carried out on the bionic flapping wing flight L1, and a built actual flapping wing flight dynamics model is verified;

and fourthly, performing simulation analysis and calculation, inputting actual parameters of the flapping wing aircraft into a control model, and verifying the effectiveness of the constructed L1AC adaptive controller in platform application.

2. The adaptive flapping wing flight attitude control method of claim 1 based on L1, wherein: the specific steps of establishing the flapping wing flying motion model are as follows:

step 1, establishing a dynamic equation of flapping wing mass center motion;

step 2, establishing a kinetic equation of the flapping wings rotating around the mass center;

step 3, establishing a kinematic equation of flapping wing mass center motion;

step 4, establishing a kinematic equation of flapping wing centroid rotation;

and 5, establishing a power model of the flapping wing flight system.

3. The adaptive flapping wing flight attitude control method of claim 1 based on L1, wherein: the L1AC adaptive controller comprises a controlled object, a state predictor, an adaptive law and a control law, wherein a low-pass filter D(s) is added in the control law, the control law and the adaptive law are separated, and only low-frequency signals are allowed to enter the system.

4. The adaptive flapping wing flight attitude control method of claim 1 based on L1, wherein: the construction of the L1AC adaptive controller specifically comprises the following steps

Step 1, constructing a state predictor;

step 2, constructing a self-adaptive law;

and 3, constructing a control law.

5. The adaptive flapping wing flight attitude control method of claim 4 based on L1, wherein: step 1, constructing a state predictor

In order to obtain the state response of the L1AC adaptive controller in the presence of unknown disturbance, a state predictor structure is constructed, as shown in an expression (2.34), the state estimation of a controlled object is realized, the state predictor is similar to the state space expression of the controlled object, and only the input gain, unknown uncertain parameters, interference items and the like in the L1AC adaptive controller adopt adaptive estimation parameters

Instead, the state predictor is modeled as:

defining an error vector:

the system error of the adaptive controller from the control input u (t) to L1AC is obtained by subtracting the equations (2.34) and (2.8)

The state space expression of (1):

according to the method, a relation between a control input and an error is established, so that a state predictor and a controlled object have consistent dynamic response, and in order to ensure that the system error of the input and an L1AC self-adaptive controller is asymptotically stable, a quadratic scalar function is selected as a Lyapunov function:

wherein P is P^T> 0 is a positive definite symmetric matrix and is

The solution of (1) is that I is more than IT and gamma is the adaptive gain of the L1AC adaptive controller, and the tracking control precision of the controlled object can be improved by increasing the system gain gamma;

to make the closed loop system progressively stable, it is necessary to satisfy

The derivation of equation (2.34) can be:

according to the formula (2.38), when the derivative of the defined lyapunov function is negative timing, it can be proved that the system error of the L1AC adaptive controller is stable in the lyapunov sense;

step 2, constructing an adaptive law

The construction of the adaptive law needs to obtain a model of the adaptive law according to estimated parameters, and to ensure that the system error of the L1AC adaptive controller is stable in the Lyapunov sense, a defined scalar function needs to be negative definite, namely, the formula (2.38) is less than zero, because of unknown parameters x (t),

And

if continuous boundaries exist, the estimated values of the parameters can be obtained according to the self-adaptation law based on the projection operator, as shown in formulas (2.39) - (2.41):

in the formula,

estimated values of ω (t), θ (t) and σ (t), Γ, respectively_ω＝Γ_θ＝Γ_σ＝Γ，Γ＞0&Γ∈R⁺For adaptive gain, Γ is

The boundary of (A) is in inverse proportion, namely the system error of the L1AC self-adaptive controller can be effectively reduced by increasing the value of gamma, the tracking precision of the controlled object is improved, and the Proj (·) is a projection operator;

step 3, constructing a control law

The purpose of control law design is to compensate uncertainty in the system through control signals and ensure that the actual output of the system tracks the reference input quickly, and according to an ideal controller and parameter estimation values, an L1 self-adaptive initial control law is given as follows:

where K > 0 is the feedback gain, D(s) is a strictly true function, r(s) is the reference control input, r(s) is the Laplace transform of the control input signal r (t),

is composed of

The change of the number of the cells in the cell is changed,

can be expressed as:

because the L1 adaptive control can generate high-frequency oscillation, a low-pass filtering link is introduced to filter the high-frequency signal generated by the adaptive control, and the amplitude margin and the phase margin of the system are not influenced by the gain change of the system by controlling the cut-off frequency of the filter, so that the decoupling of parameter estimation and control law is achieved, and the robustness of the system is improved. The definition of kg in the final control law is shown as equation (2.11), and the selection of K is related to the filter design in the controller, so as to design a low-pass filter, whose expression is:

for the convenience of designing the controller, defining d(s) to be 1/s, the finally designed low-pass filter can be expressed as:

the necessary condition for the gain stabilization of L1 is that the designed low-pass filter needs to satisfy the L1 small gain theorem (theorem 1), so that the transient and steady-state performance of the closed-loop control system are consistently bounded, defined,

H(s)＝(sI-A_m)^-1B (2.47)；

G(s)＝H(s)(1-C(s)) (5.48)；

the system L1 has stable gain and the conditions that need to be met to achieve the desired performance are:

in summary, the attitude control system designed according to the L1 adaptive theory includes a state predictor (2.36), adaptive laws (2.39) - (2.41), and a control law (2.42), and when the system satisfies the condition of equation (2.49), the system has better stability.

6. The flapping wing flight attitude control method based on L1 self-adaptation of claim 2, wherein: the process of establishing the dynamic equation of the flapping wing centroid motion is as follows:

establishing a dynamic equation in a moving coordinate system, wherein the relation between the absolute speed of the flapping wing in flight and the involvement speed thereof is as follows:

wherein,

being the absolute derivative of the velocity vector V in the ground coordinate system,

is the relative derivative of the velocity vector in the track coordinate system;

the mass-center motion equation during flapping flight can be expressed as:

in the formula, the projection of each vector on each axis of the trajectory coordinate system oxkykzk can be written as:

according to the track coordinate system ox_ky_kz_kDefinition of (1), velocity vector V and ox in track coordinate system_aThe axes are coincident, so the projected component of the velocity vector in the trajectory coordinate system can be written as:

according to the formulae (1.49) to (1.50), it is possible to obtain:

Ω×V＝[0 VΩ_za -VΩ_ya]^T (1.53)；

the conversion from the ground coordinate system to the track coordinate system needs to be carried out by two rotations, and the angular speeds of the two rotations are respectively

The rotation angular velocity of the track coordinate system relative to the ground coordinate system is the angular velocity composition of the two rotations. From the transformation matrix between the two coordinate systems:

substituting the equations (1.51) and (1.52) into (1.50), the final equation of the motion dynamics of the center of mass of the flapping wing flight is:

in the formula,

in order to provide a track tangential acceleration,

is the normal acceleration of the flight path,

the direction-finding acceleration of the flight path is taken as the acceleration,

the resultant force of the mass centers of the flapping wing flight platforms is the component of each axis in the track coordinate system.

7. The flapping wing flight attitude control method based on L1 self-adaptation of claim 2, wherein: the process of establishing the kinetic equation of the flapping wing rotating around the center of mass is as follows:

fuselage coordinate system ox_by_bz_bThe flapping wing flapping:

in the formula,

absolute and relative derivatives of the moment of momentum, respectively;

assuming that i, j, and k are unit vectors along each axis of the fuselage coordinate system, and p, q, and r are components of the rotational angular velocity ω along each axis of the fuselage coordinate system under the fuselage coordinate system, the moment of fuselage momentum can be expressed as:

H＝J·ω (1.57)；

in the formula, J is the inertia tensor, and the matrix expression form is as follows:

J_x、J_y、J_zrepresenting the moment of inertia of the flapping flight platform about each axis of the fuselage coordinate system, J_xy、J_yz、J_zxRepresenting the product of inertia of the flapping flight platform on each axis of the fuselage coordinate system. In order to simplify the rotational equation, the product of inertia of the flapping wing flight platform on each axis of the fuselage coordinate system is zero, and then the component of the momentum moment H along each axis of the fuselage coordinate system is:

and, instead,

from equation (1.58), one can obtain:

by substituting equations (1.59) and (1.60) into (1.55), the kinetic equation for flapping flight rotation about the center of mass can be expressed as:

in the formula, M_x、M_y、M_zActing on the coordinate system ox of the fuselage of all external forces acting on the flapping-wing flying platform respectively_by_bz_bThe components on each axis, equation (1.61), can also be written as:

8. the flapping wing flight attitude control method based on L1 self-adaptation of claim 2, wherein: the process of establishing the kinematic equation of the flapping wing centroid motion is as follows:

the flapping wing mass center kinematic equation describes the flight real-time coordinate position of the flapping wing, and u, v and w are respectively set as the components of the velocity vector of the flapping wing along each axis in the ground coordinate system;

from the track coordinate system ox_ay_az_aThe velocity vectors V and ox are defined_aThe axes are overlapped, and the following can be obtained according to the conversion relation between the track coordinate system and the ground coordinate system:

according to the analysis, the kinematic equation of the flapping wing centroid is obtained as follows:

9. the flapping wing flight attitude control method based on L1 self-adaptation of claim 2, wherein: the process of establishing the kinematics equation of the flapping wing centroid rotation is as follows:

to determine the attitude change of the flapping wings in the space during flying, a kinematic equation of the attitude change of the flapping wings relative to a ground coordinate system needs to be established, namely, the corresponding relation between time derivatives of the yaw angle psi, the pitch angle theta and the roll angle gamma of the flapping wings and the rotating angular velocity components p, q and r is established;

according to the transformation relationship between the coordinate system of the body and the coordinate system of the ground,

after the above formula is changed, a kinematic equation of the flapping wing rotating around the mass center is obtained:

10. the flapping wing flight attitude control method based on L1 self-adaptation of claim 2, wherein: the process of establishing the power model of the flapping wing flight system comprises the following steps:

according to the analysis, a dynamic model of the whole system in flapping-wing flight can be obtained, which is shown as the formula (1.69):

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