Aircraft landing control method based on L1 adaptive control

Abstract

The invention belongs to the technical field of aircraft landing control, and relates to an aircraft landing control method based on L1 self-adaptive control, landing control of an aircraft is realized by designing an attack angle loop, a height loop, a direct force loop and a speed loop, L1 self-adaptive control is introduced into attack angle loop control, and other loops are PID (Proportion Integration Differentiation) controllers. And the height error is input into a PID controller of the height ring to calculate and obtain a reference track angular rate instruction. An L1 self-adaptive controller is used for enabling an attack angle to track an input reference attack angle instruction, and self-adaptive compensation control is carried out. A reference track angular rate instruction generated by the height outer ring is subtracted from a feedback track angular rate to obtain a track angular rate error at the moment, and then the track angular rate error is input into a PID controller of the direct force ring to obtain a flap control instruction through calculation. And the speed error at the moment is obtained by subtracting the reference speed rate instruction from the feedback speed, and then the speed error is input into a PID controller of a speed ring to calculate and obtain a control instruction of an accelerator. Therefore, aircraft landing control is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft landing control, and relates to an aircraft landing control method based on L1 adaptive control. Background Art

[0002] Problems such as near-ground airflow disorder, large flight speed variation range, and complex operation procedures exist during the aircraft approach and landing phase. Therefore, the approach and landing phase is a stage with frequent accidents in flight missions. Long landings and hard landings are the most frequent unsafe events in this stage. Hard landings can cause fatigue damage to the structure of the aircraft itself, especially the landing gear, and reduce the service life of the aircraft. Long landings will reduce the available proportion of the runway and increase the difficulty of air traffic controller's command and release at the same time. Therefore, it has very important research significance for the aircraft to land safely within the limited length and space of the runway.

[0003] In recent years, adaptive control technologies (such as model reference adaptive control, MRAC) have been introduced into the field of flight control, which can estimate system parameters online and adjust the controller to cope with model uncertainties. However, traditional adaptive control methods have the following limitations. Slow parameter convergence speed: within the short time window of the landing process, the adaptive law may not be able to converge to the true parameters quickly, resulting in a lag in the control response; Insufficient robustness: the high-frequency unmodeled dynamics and external disturbances are not fully considered, which is likely to cause system instability; Verification complexity: the stability proof usually relies on ideal assumptions (such as slow time-varying parameters), making it difficult to meet the actual engineering requirements. Many domestic scholars have conducted extensive research on the flight control direction based on the above characteristics of L1 adaptive control. Scholars such as Huang Jin designed an L1 adaptive state feedback controller in "Longitudinal L1 Adaptive Control of Unmanned Airships", built the pitch and altitude control loops of the unmanned airship, gave different types of input signals and added disturbances in the two control loops respectively, and compared its control effect with that of traditional PID control. Scholars such as Ma Hanrong proposed an L1 adaptive flight control method based on nonlinear dynamic inversion in "Research on L1 Adaptive Flight Control Method Based on Dynamic Inversion", which improved the dynamic performance and robustness of the system by introducing PI-type dynamic inversion control and L1 adaptive structure. Scholars such as Hu Runchang designed corresponding inner-loop stability augmentation controllers and control allocation strategies in "L1 Adaptive Augmentation Control for Thrust Vectoring V / STOL Aircraft" for the problems of control quantity coupling and redundancy during the power system conversion process in the takeoff and landing transition stages of thrust vectoring V / STOL aircraft. Scholars such as Zhang Bicong designed corresponding L1 adaptive controllers in "L1 Adaptive Control Considering Actuator Dead Zone" for problems such as the presence of dead zones in actuators, uncertainties in system models, and bounded disturbances during the attitude control of aircraft. Based on the above research foundation, the present invention proposes an aircraft landing control method based on L1 adaptive control, which can effectively suppress the influence of high-frequency uncertainties on the system while ensuring rapid parameter estimation, and significantly improves the transient performance and robustness of angle-of-attack control. Summary of the Invention

[0004] To solve the above problems, the present invention provides an aircraft landing control method based on L1 adaptive control, aiming to achieve high-precision landing control under complex disturbances through adaptive law design and multi-loop cooperative control, filling the technical gap in this field.

[0005] The technical solution of the present invention:

[0006] An aircraft landing control method based on L1 adaptive control includes aircraft dynamics control modeling and optimization design of an aircraft landing controller combined with PID and L1 adaptive control. Based on the aircraft dynamics model, the system is optimized and designed using the PID algorithm and the L1 adaptive control algorithm. The specific steps are as follows:

[0007] Step (1) Aircraft Dynamics Control Modeling

[0008] The coordinate systems in aircraft landing control simulation are defined as follows:

[0009] (1.1) Ground Coordinate System

[0010] Origin O e Take the take-off point of the aircraft, o e x e The axis points in the direction of the initial flight path of the aircraft, o e y e Perpendicular to the ground and upward, o e z e Perpendicular to o e x e y e To the right. Generally, the ground coordinate system is used to describe the position relationship of the aircraft.

[0011] (1.2) Body Coordinate System

[0012] Origin O b Take it at the center of mass of the aircraft. The three coordinate axes are fixed to the aircraft. o b x b The axis is located in the symmetry plane of the aircraft. It is aligned with the fuselage axis and points forward; o b y b Located in the symmetry plane of the aircraft and perpendicular to o b x b , upward is positive, o b z b Perpendicular to o b x b y b Plane, to the right is positive.

[0013] (1.3) Velocity Coordinate System

[0014] Origin O a Take it at the center of mass of the aircraft, o a x a The axis coincides with the instantaneous airspeed direction of the aircraft's center of mass, o a y a The axis is in the symmetry plane of the aircraft and perpendicular to o a x a axis, upward is positive, o a z a The axis is perpendicular to o a x a y b Plane, to the right is positive.

[0015] The parameters related to the motion state of the aircraft and their direction definitions are as follows:

[0016] Velocity V: In the velocity coordinate system, along o a x a Forward is positive;

[0017] Forward velocity V x : In the body coordinate system, along o b x b Forward is positive;

[0018] Vertical velocity V y : In the body coordinate system, along o b y b Upward is positive;

[0019] Lateral velocity V z : In the body coordinate system, along o b z b Rightward is positive;

[0020] Angle of attack α: The airspeed is positive below the aircraft body system, and its expression is:

[0021]

[0022] Sideslip angle β: The airspeed is positive on the right side of the aircraft body system, and its expression is:

[0023]

[0024] Roll angle γ: In the body coordinate system, rolling to the right is positive;

[0025] Roll rate ω x : The positive direction is defined in the same way as the positive direction of the roll angle;

[0026] Yaw angle ψ: In the body coordinate system, the nose of the aircraft deflecting to the left is positive;

[0027] Yaw rate ω y : The positive direction is defined in the same way as the positive direction of the yaw angle;

[0028] Pitch angle In the body coordinate system, the aircraft pitching up is positive;

[0029] Pitch rate ω z : The positive direction is defined in the same way as the positive direction of the pitch angle;

[0030] Forward flight distance S g : In the ground coordinate system, along o e x e Forward is positive;

[0031] Altitude h: In the ground coordinate system, along o e y e Upward is positive;

[0032] Lateral distance z: In the ground coordinate system, along o e z e Positive to the right.

[0033] In the ground coordinate system, the expression of the gravity G:

[0034] G = [0 -mg 0] T (3)

[0035] Where m is the current mass of the aircraft and g is the local acceleration due to gravity.

[0036] Thrust T and thrust moment M T Expression:

[0037]

[0038] Where z T is the coordinate of the projection point of the thrust line on the body coordinate system o b z b .

[0039] During the flight of the aircraft, the aerodynamic force R acting on it is decomposed into three components along the velocity coordinate system, which are respectively called drag D, lift L and side force Z. Due to the position relationship between the center of pressure and the center of mass, the aerodynamic moments M generated by the aerodynamic force in the body coordinate system can be distinguished according to their rotation axes, and are respectively called roll moment M x , pitch moment M y and yaw moment M z , and their definitions are:

[0040]

[0041] Experimental analysis shows that: The forces acting on the aircraft are related to the dynamic pressure q of the oncoming flow, the characteristic area S of the aircraft body, and the characteristic length l (when analyzing the pitch moment, the characteristic length is taken as the mean aerodynamic chord length b a , when analyzing the roll and yaw moments, the characteristic length is taken as the wingspan l), so the above aerodynamic forces and moments can be expressed as:

[0042]

[0043] Where c x represents the dimensionless drag coefficient, c y represents the dimensionless lift coefficient, c z represents the dimensionless side force coefficient, m x represents the dimensionless roll moment coefficient, m y represents the dimensionless pitch moment coefficient, m z represents the dimensionless yaw moment coefficient. When the aircraft is in cruise and normal maneuvering conditions, the dimensionless coefficients are defined as:

[0044]

[0045] In the formula, δ a represents the aileron deflection angle, δ r represents the rudder deflection angle, δ e is the elevator deflection angle, c x0 represents the reference value of the dimensionless drag coefficient, represents the dimensionless coefficient of the drag derivative with respect to the angle of attack, represents the dimensionless drag coefficient of the drag derivative with respect to the elevator, represents the dimensionless coefficient of the drag derivative with respect to the roll rate, c y0 represents the reference value of the dimensionless lift coefficient, represents the dimensionless coefficient of the lift derivative with respect to the angle of attack, represents the dimensionless coefficient of the lift derivative with respect to the sideslip angle, represents the dimensionless drag coefficient of the lift derivative with respect to the elevator, represents the dimensionless coefficient of the lift derivative with respect to the pitch rate, c z0 represents the reference value of the dimensionless side force coefficient, represents the dimensionless coefficient of the side force derivative with respect to the sideslip angle, represents the dimensionless coefficient of the side force derivative with respect to the roll rate, represents the dimensionless coefficient of the side force derivative with respect to the yaw rate, represents the dimensionless coefficient of the side force derivative with respect to the aileron, represents the dimensionless coefficient of the side force derivative with respect to the rudder, m x0 represents the reference value of the dimensionless roll moment coefficient, represents the dimensionless coefficient of the roll moment derivative with respect to the sideslip angle, represents the dimensionless coefficient of the roll moment derivative with respect to the roll rate, represents the dimensionless coefficient of the roll moment derivative with respect to the yaw rate, represents the dimensionless coefficient of the roll moment derivative with respect to the aileron, represents the dimensionless coefficient of the roll moment derivative with respect to the rudder, m y0 represents the reference value of the dimensionless pitch moment coefficient, represents the dimensionless coefficient of the pitch moment derivative with respect to the sideslip angle, represents the dimensionless coefficient of the pitch moment derivative with respect to the roll rate, represents the dimensionless coefficient of the pitch moment derivative with respect to the pitch rate, represents the dimensionless coefficient of the pitch moment derivative with respect to the aileron, represents the dimensionless coefficient of the pitch moment derivative with respect to the rudder, m z0 represents the dimensionless yaw moment coefficient, The dimensionless coefficient representing the partial derivative of the yaw moment with respect to the angle of attack, The dimensionless coefficient representing the partial derivative of the yaw moment with respect to the elevator, The dimensionless coefficient representing the partial derivative of the yaw moment with respect to the yaw angular rate.

[0046] The dynamic equation established in the moving coordinate system, referring to the relationship between the absolute derivative and the relative derivative of a vector: The difference between the derivative of a certain vector with respect to time (absolute derivative) in the inertial coordinate system and the derivative of the same vector with respect to time in the moving coordinate system is equal to the vector product of this vector itself and the angular velocity of the moving coordinate system, that is:

[0047]

[0048] In the formula, Represents the absolute derivative of the velocity vector V in the inertial coordinate system, Represents the relative derivative of the velocity vector V in the moving coordinate system. Between the ground coordinate system and the body coordinate system, Ω represents the three-axis angular rate (ω x , ω y , ω z ).

[0049] Therefore, in the body coordinate system, the translational motion equation of the center of mass is established:

[0050]

[0051] In the formula, L ba Represents the coordinate transformation matrix from the velocity system to the body system, and L bg Represents the coordinate transformation matrix from the ground system to the body system. To simplify the modeling process and the formula writing process, let dL ba R = F = [F x F y F z T , and substituting it into the translational motion equation of the center of mass, the expression of the velocity components in the body system can be obtained as follows:

[0052]

[0053] In the formula, V x Represents the velocity in the x-axis direction in the body system, Represents the derivative of the velocity in the x-axis direction in the body system, and V y Represents the velocity in the y-axis direction in the body system, Represents the derivative of the velocity in the y-axis direction in the body system, and V z Represents the velocity in the z-axis direction in the body system, Represents the derivative of the velocity in the z-axis direction in the body system.

[0054] ​Similarly, the dynamic equations of the aircraft's rotation about the center of mass in the moving coordinate system are established as follows:

[0055]

[0056] In the formula, H represents the angular momentum, expressed as H = I·Ω, I is the inertia tensor, and M T represents the thrust moment.

[0057] The inertia tensor of the aircraft is:

[0058]

[0059] In the formula, I xx is the moment of inertia about the x-axis, I yy is the moment of inertia about the y-axis, I zz is the moment of inertia about the z-axis, I xy is the product of inertia between the x-axis and the y-axis.

[0060] It can be obtained that the expressions of the three-axis angular velocity components of the aircraft's rotation about the center of mass are as shown in Equation (13):

[0061]

[0062] In the formula, is the derivative of the roll rate, is the derivative of the pitch rate, is the derivative of the yaw rate.

[0063] After obtaining the above angular rate and velocity component equations, the angular displacement and linear displacement equations are described in the ground coordinate system and the body coordinate system respectively, and the expressions are as shown in Equation (14) and Equation (15).

[0064] Ground coordinate system linear displacement motion equation:

[0065]

[0066] In the formula, is the derivative of the forward displacement, is the derivative of the altitude, is the derivative of the lateral displacement.

[0067] Body coordinate system angular displacement motion equation:

[0068]

[0069] In the formula, is the derivative of the roll angle, is the derivative of the pitch angle, is the derivative of the yaw angle.

[0070] Step (2) Optimization Design of Aircraft Landing Controller Based on the Combination of PID and L1 Adaptive Control

[0071] Overall idea: During the aircraft landing process, affected by various interference factors such as wind disturbance, there are problems in the longitudinal attitude control of the aircraft, that is, the angle of attack loop control, such as high control difficulty, low control accuracy, and slow convergence time. And the L1 adaptive control has the characteristics of fast convergence speed and strong robustness. Therefore, it is considered to introduce it into the angle of attack loop control of landing. The control loop design includes three parts: the design of the angle of attack loop controller based on the combination of L1 adaptive control, the design of the altitude outer loop and direct force loop controller based on PID control, and the design of the speed loop controller based on PID control. The angle of attack loop uses the L1 adaptive controller to make the angle of attack track the input reference angle of attack command. The altitude loop subtracts the input reference altitude from the feedback current altitude to obtain the altitude error at this time. The altitude error is input into the PID controller of the altitude loop to calculate the reference trajectory angular rate command. The direct force loop subtracts the reference trajectory angular rate command generated by the altitude outer loop from the feedback trajectory angular rate to obtain the trajectory angular rate error at this time, and then inputs it into the PID controller of the direct force loop to calculate the flap control command. The speed loop subtracts the input reference speed rate command from the feedback speed to obtain the speed error at this time, and then inputs it into the PID controller of the speed loop to calculate the throttle control command. Based on the above control design, the aircraft landing control is completed.

[0072] The specific steps are as follows:

[0073] (2.1) Design of Angle of Attack Loop Controller Based on L1 Adaptive Control:

[0074] The control structure is: The L1 adaptive controller enables the current angle of attack to track the input reference angle of attack command, thereby completing the angle of attack control.

[0075] The L1 adaptive control method is as follows:

[0076] The L1 adaptive algorithm is an improved algorithm of model reference adaptive control and is a fast and robust adaptive control algorithm. This algorithm adds a low-pass filter in the control law link to make its performance better. It adds a low-pass filter in the control law link to filter out the high-frequency oscillation signals caused by the continuous increase of the adaptive gain and ensures the separation of the control law and the adaptive law. It consists of a controlled object, a state observer, a control law module, an adaptive law, and a low-pass filter module.

[0077] ① Controlled Object

[0078] The mathematical model of the controlled object with uncertain parameters is:

[0079]

[0080] where is the system desired output, y is the system output, A is the uncertainty of the structure of the controlled object itself, B is the uncertainty caused by the input, c is the output matrix, and σ′ is the disturbance existing in the system.

[0081] The desired output of the control system is:[[]]

[0082]

[0083] where A m ∈R n×n is a Hurwitz matrix designed based on the desired conditions of aircraft landing, b is the control matrix, r′ = ωu + θx + σ is the system input, where ω, θ, and σ are the uncertainties of the system, input, and disturbance.

[0084] The state - space equation of the controlled object is described as:[[]]

[0085]

[0086] Letting Equation (16) be equal to Equation (18) gives

[0087]

[0088] ② State observer

[0089] The state - space equation of the state observer is the same as the structure of the controlled object and can be described as

[0090]

[0091] where are the estimated values of x, y, ω, θ, and σ in Equation (18). When the controlled object changes, the state observer can model it and solve for the numerical values.

[0092] ③ Control law

[0093] The adaptive - law module aims to calculate the estimated parameter values so that when the controlled object changes, the model established by the state observer can still follow the changed controlled object. Its working principle is as follows:[[]]

[0094] Letting Equation (18) minus Equation (20), the error expression can be obtained:[[]]

[0095]

[0096] where

[0097] Lemma: Lyapunov's second method

[0098] For the scalar Lyapunov quadratic function V(x) with continuous first-order partial derivatives

[0099] V(x) = x T Px (22)

[0100] where x T is the transpose of the input matrix.

[0101] If it satisfies

[0102]

[0103] then the system equilibrium point x 0 = 0 is an asymptotically stable equilibrium point.

[0104] The Lyapunov function constructed by this lemma is as follows:

[0105]

[0106] where Γ is the adaptive gain and P is a positive definite matrix that makes hold.

[0107] According to the above lemma, to make this Lyapunov function asymptotically stable, the following conditions need to be satisfied:

[0108]

[0109] Substituting all the above parameters into the above formula, we get:

[0110]

[0111] Therefore, the Lyapunov stability condition of equation (25) can be satisfied.

[0112] Substitute each parameter into the above formula:

[0113]

[0114] Because and are both 1*1 matrices, and P is positive definite and symmetric, so we have Similarly, we can get Satisfying both

[0115]

[0116] Therefore, the above formula can be simplified:

[0117]

[0118] Since the first term of equation (28) already satisfies being less than 0, to satisfy equation (28), we only need to make

[0119]

[0120] Finally, the adaptation law is as follows:

[0121]

[0122] where: Proj is the projection operator, and its purpose is to make the adaptation parameters bounded.

[0123] Definition: For a convex set: where, τ max is the norm boundary value of the parameter vector τ, ε is the step size for updating the adaptation parameters each time, and the calculation formula of the projection operator is as follows:

[0124]

[0125] ④ Adaptation law

[0126] Under the condition of a given input, a state observer is used for controller design. If the adaptation law module can ensure that the state observer model can effectively track the state of the controlled object, and under steady-state conditions, the reference signal and the output of the state observer can be made equal, then the controlled object can be controlled according to the given signal. By this method, the controlled object can be tracked, so that the controlled object can track the previous reference input, thus achieving tracking.

[0127] According to Equation (18), from the transfer function expression, we can obtain:

[0128]

[0129] When time t → ∞

[0130]

[0131] To make equal to the input r, we have:

[0132]

[0133] where,

[0134] ⑤ Low-pass filter

[0135] Since a low-pass filter is introduced, the control law can be rewritten as

[0136]

[0137]

[0138] Where C(s) is the transfer function of the low-pass filter, Equation (36) is the expression form of the low-pass filter, and the bandwidth of the filter is represented by k. Its selection principle must meet the requirements of the L1 small gain theorem.

[0139] Lemma: L1 small gain theorem

[0140] In closed-loop control, a new control strategy - the small gain theorem is adopted. In the L1 adaptive controller, as the adaptive gain increases, the parameters of the system can converge rapidly, but large vibrations will also occur, causing large oscillations in the system. In response to this situation, the present invention proposes to add a low-pass filter to the system design to eliminate high-frequency vibrations of the system. However, if a low-pass filter is added, due to the difference in its frequency bandwidth, it has a great impact on the output of the system. After adding the low-pass filter, to determine the overall stability, the "small gain" principle must be used.

[0141] In a system with an input of w 1 (s), an output of w 2 (s), a feedforward transfer function of N(s), and a feedback transfer function of M(s), the mathematical expression of its small gain theorem is

[0142] w 2 (s) = N(s)[w 1 (s) - M(s)w 2 (s)] (37)

[0143] Then the sufficient condition for the system to be stable is

[0144]

[0145] Describe the controlled object with parameter uncertainties in state space form:

[0146]

[0147] The control signal is constructed by combining the input signal r, the feedforward gain K g and the adaptive parameters. Then, this signal is processed by a low-pass filter to obtain the actual control signal u.

[0148] The design of the linear feedback law K must ensure that the transfer function of the formed closed-loop system has the properties of a Hurwitz matrix.

[0149] Definition:

[0150] N(s) = H 0 (s)*C(s) (40)

[0151]

[0152] Therefore, it is only necessary to judge (38), and when it is satisfied, the bandwidth k can be obtained:

[0153]

[0154] After applying the design of the low-pass filter in the control law, the adaptive gain can be significantly increased, and at the same time, the oscillation of the control law can be avoided, thereby optimizing the disadvantages of the model reference adaptive control (MRAC).

[0155] (2.2) Design of the altitude outer loop and direct force loop controller based on PID control:

[0156] The control structure is as follows: The altitude error at this time is obtained by subtracting the input reference altitude from the feedback current altitude, and the altitude error is input to the PID controller of the altitude loop to calculate the reference trajectory angular velocity command; The reference trajectory angular velocity command generated by the altitude outer loop is subtracted from the feedback trajectory angular velocity to obtain the trajectory angular velocity error at this time, and then the trajectory angular velocity error is input to the PID controller of the direct force loop to calculate the flap control command. The control law is as follows:

[0157]

[0158] In the formula, is the command value of the trajectory angular velocity, is the proportional term coefficient of the altitude loop PID controller, is the differential term coefficient of the altitude loop PID controller, is the integral term coefficient of the altitude loop PID controller, h c is the reference altitude.

[0159] The trajectory angular velocity can be obtained by the following formula:

[0160]

[0161] In the formula, n z is the longitudinal overload, θ T is the engine mounting angle, and in the present invention, it is assumed that θ T is 0.

[0162]

[0163] In the formula, δ f is the command value of the flap, δ f0 is the trim value of the flap, is the proportional term coefficient of the direct force loop PID controller, is the differential term coefficient of the direct force loop PID controller.

[0164] (2.3) Design of the speed loop controller based on PID control:

[0165] The control structure is as follows: the reference speed rate command input to the speed loop is subtracted from the feedback speed to obtain the current speed error, and then the speed error is input to the PID controller of the speed loop to calculate the throttle control command. The control law is as follows:

[0166]

[0167] In the formula, δ T is the command value of the throttle, and δ T0 is the trim value of the throttle. is the proportional term coefficient of the speed loop PID controller. is the differential term coefficient of the speed loop PID controller, and V c is the speed reference value.

[0168] Based on the above control design, the aircraft landing control is completed.

[0169] Advantages of the present invention:

[0170] The present invention considers the problems of slow convergence speed, low control accuracy, and long convergence time in the aircraft angle of attack control during the aircraft landing process, and determines to adopt an aircraft landing control method combining PID and L1 adaptive control. The L1 adaptive control algorithm is used for the control of the angle of attack loop, which has high control accuracy, good control effect, good angle of attack control performance, and broad application prospects. Brief description of the drawings

[0171] Figure 1 is the overall flowchart of the aircraft landing control based on L1 adaptive control of the present invention;

[0172] Figure 2 is the altitude simulation result in the embodiment;

[0173] Figure 3 is the speed simulation result in the embodiment;

[0174] Figure 4 is the angle of attack simulation result in the embodiment;

[0175] Figure 5 is the trajectory angle simulation result in the embodiment. Specific implementation manners

[0176] The following further describes the specific implementation manners of the present invention in combination with the drawings and technical solutions.

[0177] The simulation implemented in the present invention is carried out according to the Figure 1 control algorithm flow, and an aircraft landing simulation combining PID and L1 adaptive control is carried out with the aircraft landing control as the background.

[0178] (1) Input the initial state and specify the target state

[0179] ① Altitude control: The altitude descends uniformly from 500 m until it lands on the ground.

[0180] ② Forward flight speed control: The forward flight speed remains constant until it lands on the ground.

[0181] ③ Angle of attack control: The angle of attack of the aircraft remains constant until it lands on the ground.

[0182] Table 1 Simulation parameters

[0183]

[0184]

[0185] Use the linmod statement of the numerical simulation software to identify the state - space equation of the aircraft model, and thus the system matrix and control matrix of the aircraft model can be obtained.

[0186] After identification, the system matrix of the aircraft

[0187] A = -0.5562 (47)

[0188] The control matrix of the aircraft

[0189] B = -0.0168 (48)

[0190] For simplicity of design, the output matrix of the aircraft is taken as 1, i.e., C = 1.

[0191] Based on the above design, it can be ensured that the Lyapunov function constructed in the L1 adaptive control algorithm is asymptotically stable.

[0192] Table 2 Initial values of adaptive parameters and selection of adaptive gains

[0193]

[0194] The bandwidth k of the low - pass filter is selected as 50.

[0195] (2) Establish the dynamic model

[0196] In order to accurately describe the motion state of the aircraft and facilitate the force analysis of the aircraft, it is necessary to select an appropriate coordinate system. In the modeling process of the present invention, the ground coordinate system, body coordinate system, velocity coordinate system and flight path coordinate system are mainly used, and the definitions of each coordinate system are all in the American coordinate system. The dynamic model used in the simulation is detailed in the part of the invention content.

[0197] (3) Aircraft landing control simulation based on the combination of PID and L1 adaptive control

[0198] The angle of attack loop uses an L1 adaptive controller to make the angle of attack track the input reference angle of attack command. The altitude loop subtracts the feedback of the current altitude from the input reference altitude to obtain the altitude error at this time. The altitude error is input into the PID controller of the altitude loop to calculate the reference trajectory angular rate command. The direct force loop subtracts the feedback of the trajectory angular rate from the reference trajectory angular rate command generated by the outer altitude loop to obtain the trajectory angular rate error at this time, and then inputs it into the PID controller of the direct force loop to calculate the control command of the flap. The reference speed rate command input into the speed loop subtracts the feedback speed to obtain the speed error at this time, and then inputs it into the PID controller of the speed loop to calculate the control command of the throttle.

[0199] It can be seen from Figures 2 to 5 that the tracking effects of altitude, forward speed, angle of attack and trajectory angle are good. The overshoot of altitude control is 2.38%, the overshoot of forward speed is 0.87%, the overshoot of angle of attack is 20.2%, and the overshoot of trajectory angle is 83.8%. After the convergence of each parameter, the altitude control error is within ±0.6, the speed control error is within ±0.1, the angle of attack control error is within ±0.1°, and the trajectory angle control error is within 0.1°. It can be seen from the simulation analysis that the controller combining PID and L1 adaptive control can achieve landing control.

[0200] In summary, the simulation results show that the L1 adaptive control based on the present invention converges the tracking of altitude, forward speed, angle of attack and trajectory angle within the control error during the landing process. The convergence time is 20 s, and its convergence speed is fast, showing certain advantages in terms of rapidity and stability.

Claims

1. An aircraft landing control method based on L1 adaptive control, characterized in that: The specific steps are as follows: Step (1) Aircraft dynamics control modeling The coordinate system in the aircraft landing control simulation is defined as follows: (1.1) Ground coordinate system Origin O e Take the take-off point of the aircraft, o e x e The axis points to the direction of the aircraft's initial flight path, o e y e Vertically upward from the ground, o e z e Perpendicular to o e x e y e To the right; (1.2) Body coordinate system Origin O b Take the center of mass of the aircraft, and the three coordinate axes are fixed to the aircraft; o b x b The axis lies in the plane of symmetry of the aircraft; The fuselage axis is consistent and points forward; b y b Located in the plane of symmetry of the aircraft and perpendicular to o b x b , upward is positive, o b z b Perpendicular to o b x b y b For a plane, rightward is positive; (1.3) Velocity coordinate system Origin O a Taken at the center of mass of the aircraft, o a x a The axis coincides with the instantaneous airspeed direction of the aircraft's center of mass, o a y a The axis is in the plane of symmetry of the aircraft and is perpendicular to o a x a Axis is positive, o a z a Axis perpendicular to o a x a y b For a plane, rightward is positive; The relevant parameters of the aircraft motion state and their directions are defined as follows: Speed ​​V: In the speed coordinate system, along o a x a Forward is positive; Forward speed V x : In the body coordinate system, along o b x b Forward is positive; Vertical speed V y : In the body coordinate system, along o b y b Upward is positive; Lateral speed V z : In the body coordinate system, along o b z b Rightward is positive; Angle of attack α: The airspeed is positive below the aircraft system, and its expression is: Sideslip angle β: The airspeed is positive on the right side of the aircraft system, and its expression is: Roll angle γ: In the body coordinate system, rolling to the right is positive; Roll angular rate ω x : The positive direction is consistent with the positive direction of the roll angle; Yaw angle ψ: In the body coordinate system, the nose is tilted to the left as positive; Yaw angular rate ω y : The positive direction is consistent with the positive direction of the yaw angle; Pitch angle θ: In the body coordinate system, the pitch angle is positive when the aircraft is tilted up; Pitch rate ω z : The positive direction is consistent with the positive direction of the pitch angle; Forward flight distance S g : In the ground coordinate system, along o e x e Forward is positive; Height h: In the ground coordinate system, along o e y e Upward is positive; Lateral distance z: in the ground coordinate system, along o e z e Rightward is positive; In the ground coordinate system, the expression of gravity G is: G=[0 -mg 0] T (3) Where m is the current mass of the aircraft, and g is the local gravitational acceleration; Thrust T and thrust moment M T expression: In the formula, z T is the thrust line in the body coordinate system o b z b The coordinates of the projection point on ; During the flight, the aerodynamic force R is decomposed into three components along the velocity coordinate system, namely, drag D, lift L and lateral force Z. The aerodynamic moments M generated by the aerodynamic force in the body coordinate system are distinguished according to their rotation axes, namely, rolling moments M and x , pitch moment M y and yaw moment M z , which is defined as: The force acting on the aircraft is related to the dynamic pressure q of the incoming flow, the characteristic area S of the fuselage, and the characteristic length l. When analyzing the pitch moment, the characteristic length is the average aerodynamic chord length b. a ; When analyzing the rolling and yaw moments, the characteristic length is taken as the wingspan l; therefore, the aerodynamic force and moment are expressed as: In the formula, c x represents the dimensionless drag coefficient, c y represents the dimensionless lift coefficient, c z represents the dimensionless lateral force coefficient, m x represents the dimensionless rolling moment coefficient, m y represents the dimensionless pitching moment coefficient, m z Represents the dimensionless yaw moment coefficient. When the aircraft is in cruise and normal maneuvering conditions, the dimensionless coefficient is defined as: In the formula, δ a represents the aileron deflection angle, δ r represents the rudder deflection angle, δ e is the elevator deflection angle, c x0 represents the dimensionless drag coefficient reference value, is the dimensionless coefficient of the derivative of drag with respect to angle of attack, The dimensionless drag coefficient representing the drag on the elevator deflection, The dimensionless coefficient representing the derivative of the drag with respect to the roll angular rate, c y0 represents the dimensionless lift coefficient reference value, is the dimensionless coefficient of the derivative of lift with respect to the angle of attack, is the dimensionless coefficient of the derivative of lift with respect to the sideslip angle, The dimensionless drag coefficient representing the lift force acting on the elevator deflection, The dimensionless coefficient representing the derivative of lift with respect to pitch rate, c z0 represents the dimensionless lateral force coefficient reference value, is the dimensionless coefficient of the derivative of the lateral force with respect to the sideslip angle, is the dimensionless coefficient representing the derivative of the lateral force with respect to the rolling angular rate, is the dimensionless coefficient of the derivative of the lateral force with respect to the yaw rate, is the dimensionless coefficient of the lateral force on the aileron deflection, The dimensionless coefficient of the lateral force on the rudder deflection, m x0 represents the dimensionless rolling moment coefficient reference value, is the dimensionless coefficient representing the derivative of the rolling moment with respect to the sideslip angle, is the dimensionless coefficient representing the derivative of the rolling moment with respect to the rolling angular rate, is the dimensionless coefficient of the derivative of the rolling moment with respect to the yaw rate, is the dimensionless coefficient of the rolling moment derivative on the aileron, The dimensionless coefficient of the rolling moment on the rudder deflection, m y0 represents the reference value of the dimensionless coefficient of the pitching moment, represents the dimensionless coefficient of the derivative of the pitching moment with respect to the sideslip angle, represents the dimensionless coefficient of the derivative of the pitch moment with respect to the roll angular rate, represents the dimensionless coefficient of the partial derivative of the pitch moment with respect to the pitch angular rate, is the dimensionless coefficient of the pitch moment derivative on the aileron, The dimensionless coefficient of the pitch moment on the rudder deflection, m z0 represents the dimensionless yaw moment coefficient, is the dimensionless coefficient of the derivative of the yaw moment with respect to the angle of attack, represents the dimensionless coefficient of the yaw moment on the elevator, It represents the dimensionless coefficient of yaw moment to yaw rate; The dynamic equation established in the moving coordinate system refers to the relationship between the absolute derivative and the relative derivative of the vector: the difference between the derivative of a vector with respect to time in the inertial coordinate system and the derivative of the same vector with respect to time in the moving coordinate system is equal to the vector product of the vector itself and the angular velocity of the moving coordinate system, that is: In the formula, represents the absolute derivative of the velocity vector V in the inertial coordinate system, represents the relative derivative of the velocity vector V in the moving coordinate system, between the ground coordinate system and the body coordinate system, Ω represents the three-axis angular rate (ω x ,ω y ,ω z ); Therefore, in the body coordinate system, the center of mass translation motion equation is established: Where, L ba represents the coordinate transformation matrix from the velocity system to the machine system, L bg Represents the coordinate transformation matrix from the ground system to the aircraft system; to simplify the modeling process and formula writing process, let dL ba R=F=[F x F y F z ] T , substituting into the center of mass translation motion equation, the velocity component expression of the machine system is as follows: Where V x Indicates the x-axis speed of the machine system. It represents the derivative of the velocity in the x-axis direction of the machine system, V y Indicates the y-axis speed of the machine system. It represents the derivative of the velocity in the y-axis direction of the machine system, V z It indicates the speed in the z-axis direction of the machine system. It represents the derivative of the velocity in the z-axis direction of the machine system; Similarly, the dynamic equation of the aircraft rotating around the center of mass in the moving coordinate system is as follows: In the formula, H represents the momentum, expressed as H = I Ω, I is the inertia tensor, M T represents thrust torque; The inertia tensor of the aircraft is: In the formula, I xx is the moment of inertia about the x-axis, I yy is the moment of inertia of the y-axis, I zz is the moment of inertia along the z axis, I xy is the inertia product of the x-axis and the y-axis; The expressions of the three-axis angular velocity components of the aircraft rotating around the center of mass are as follows: In the formula, is the derivative of the roll angular rate, is the derivative of the pitch angular rate, is the derivative of the yaw rate; The angular displacement and linear displacement equations are described in the ground coordinate system and the body coordinate system respectively, as shown in equations (14) and (15); The linear displacement motion equation of the ground coordinate system is: In the formula, is the derivative of the forward displacement, is the derivative of a higher number, is the derivative of the lateral displacement; The motion equation of angular displacement in the body coordinate system: In the formula, is the derivative of the roll angle, is the derivative of the pitch angle, is the derivative of the yaw angle; Step (2) Optimization design of aircraft landing controller based on the combination of PID and L1 adaptive control It includes three parts: the design of an angle of attack loop controller based on L1 adaptive control, the design of an altitude outer loop and a direct force loop controller based on PID control, and the design of a speed loop controller based on PID control; the angle of attack loop uses an L1 adaptive controller to make the angle of attack track the input reference angle of attack instruction; the altitude loop is obtained by subtracting the input reference altitude from the feedback current altitude to obtain the altitude error at this time, and the altitude error is input to the PID controller of the altitude loop to calculate the reference trajectory angular rate instruction; the direct force loop is obtained by subtracting the reference trajectory angular rate instruction generated by the altitude outer loop from the feedback trajectory angular rate to obtain the trajectory angular rate error at this time, and then inputting it into the PID controller of the direct force loop to calculate the flap control instruction; the reference speed rate instruction input by the speed loop is subtracted from the feedback speed to obtain the speed error at this time, and then inputting it into the PID controller of the speed loop to calculate the throttle control instruction; the aircraft landing control is completed based on the above control design.

2. The aircraft landing control method based on L1 adaptive control according to claim 1, characterized in that: Step (2) is as follows: (2.1) Design of angle of attack loop controller based on L1 adaptive control: The control structure is as follows: the L1 adaptive controller makes the current angle of attack track the input reference angle of attack command to complete the angle of attack control; The L1 adaptive control method consists of a controlled object, a state observer, a control law module, an adaptive law, and a low-pass filter module; ① The accused The mathematical model of the controlled object with uncertain parameters is: In the formula, is the expected output of the system, y is the system output, A is the uncertainty of the structure of the controlled object itself, B is the uncertainty caused by the input, c is the output matrix, and σ′ is the disturbance existing in the system; The expected output of the control system is: In the formula, A m ∈R n×n is the Hurwitz matrix designed based on the expected conditions for aircraft landing, b is the control matrix, r′=ωu+θx+σ is the system input, where ω, θ, σ are the uncertainties of the system, input, and disturbance; The state space equation of the controlled object is described as: Let equation (16) be equal to equation (18) and we get ②State Observer The state space equation of the state observer has the same structure as the controlled object and is described as In the formula, are the estimated values ​​of x, y, ω, θ, and σ in equation (18). When the controlled object changes, the state observer models it and solves the value; ③Control law Subtract equation (18) from equation (20) to get the error The expression is: In the formula Lemma: Lyapunov's Second Method For a scalar Lyapunov quadratic function V(x) with continuous first-order partial derivatives V(x)=x T Px (22) Where x T is the transpose of the input matrix; If satisfied Then the system equilibrium point x0 = 0 is the asymptotically stable equilibrium point; The Lyapunov function constructed using this lemma is as follows: In the formula, Γ is the adaptive gain, P is the A positive definite matrix is ​​established; For the Lyapunov function to be asymptotically stable, the following conditions need to be met: Substituting all the above parameters into the above formula, we get: Therefore, the Lyapunov stability condition of equation (25) is satisfied; Substitute the parameters into the above formula: because and are all 1*1 matrices, and P is positive definite and symmetric, so we have The same goes for Satisfy at the same time Therefore, the simplified formula is: Since the first term of formula (28) is less than 0, to satisfy formula (28), we only need to set The final adaptive law is as follows: Where: Proj is the projection operator; Definition: For a convex set: Among them, τ max is the norm boundary value of the parameter vector τ, ε is the step size for updating the adaptive parameters each time, and the calculation formula of the projection operator is as follows: ④ Adaptive law According to formula (18), the transfer function expression is obtained: When time t→∞ To make Equal to input r, we have: In the formula, ⑤Low-pass filter Due to the introduction of the low-pass filter, the control law is rewritten as In the formula, C(s) is the transfer function of the low-pass filter, formula (36) is the expression of the low-pass filter, and the bandwidth of the filter is represented by k. Its selection principle must comply with the requirements of the L1 small gain theorem; Lemma: L1 Small Gain Theorem In a system with input w1(s), output w2(s), feedforward transfer function N(s), and feedback transfer function M(s), the mathematical expression of the small gain theorem is: w2(s)=N(s)[w1(s)-M(s)w2(s)] (37) Then the sufficient condition for the stability of the system is The controlled object with parameter uncertainty is described in state space form: The control signal is obtained by combining the input signal r, the feedforward gain K g and adaptive parameters; then, this signal is processed by a low-pass filter to obtain the actual control signal u; The design of the linear feedback law K must ensure that the transfer function of the closed-loop system has the properties of a Hurwitz matrix; definition: N(s)=H0(s)*C(s) (40) So we only need to judge (38), and when it satisfies, we can get the bandwidth k: (2.2) Design of high outer loop and direct force loop controller based on PID control: The control structure is as follows: the height error is obtained by subtracting the input reference height from the feedback current height, and the height error is input to the reference trajectory angular rate command calculated by the PID controller of the height loop; the trajectory angular rate error is obtained by subtracting the reference trajectory angular rate command generated by the height outer loop from the feedback trajectory angular rate, and then the trajectory angular rate error is input to the PID controller of the direct force loop to calculate the flap control command; the control law is as follows: In the formula, is the command value of the trajectory angular rate, is the proportional term coefficient of the height loop PID controller, is the differential term coefficient of the height loop PID controller, is the integral term coefficient of the height loop PID controller, h c is the base height; The trajectory angular rate is obtained by the following formula: Where n z is the longitudinal overload, θ T Mounting angles for the engine; In the formula, δ f is the command value of the flap, δ f0 is the trim value of the flaps, is the proportional term coefficient of the direct force loop PID controller, is the differential term coefficient of the direct force loop PID controller; (2.3) Design of speed loop controller based on PID control: The control structure is: the reference speed rate command input by the speed loop is subtracted from the feedback speed to obtain the speed error at this time, and then the speed error is input to the PID controller of the speed loop to calculate the throttle control command; the control law is as follows: In the formula, δ T is the command value of the throttle, δ T0 is the throttle trim value, is the proportional term coefficient of the speed loop PID controller, is the differential term coefficient of the speed loop PID controller, V c The speed reference value.

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