Flexible preset performance anti-saturation control method based on high-order fixed time observer

Abstract

The invention discloses a flexible preset performance anti-saturation control method based on a high-order fixed time observer. The method comprises the following steps: establishing an aircraft dynamics model; a high-order fixed time disturbance observer is arranged to estimate disturbance of the kinetic model; setting a preset finite time function to restrain the system state; setting an anti-saturation auxiliary function, and constructing a flexible preset performance function based on a flexible relationship between the anti-saturation auxiliary function and a preset finite time performance function; constructing a constraint relationship between the flexible preset performance function and the tracking error; setting an anti-saturation controller by taking the attitude angle as an outer ring and the attitude angular speed as an inner ring; and according to the guidance instruction, an anti-saturation controller is adopted to control the aircraft. According to the flexible preset performance anti-saturation control method based on the high-order fixed time observer, the performance constraint requirement can be met at the same time, and the influence of execution mechanism saturation on a control system is reduced.

Description

[0001] The present invention relates to a flexible preset performance anti-saturation control method based on a high-order fixed-time observer, and belongs to the technical field of aircraft control. Background Art

[0002] During the re-entry process, the complex aerodynamic environment and strong disturbance conditions place extremely high demands on the control performance of the aircraft. When the aircraft encounters strong disturbances, the control system often needs to make significant adjustments to the actuators to maintain flight attitude stability, which will lead to two interrelated technical problems:

[0003] First, drastic changes in the aircraft's attitude will exceed the preset performance constraint boundaries, posing a potential threat to flight stability and thermal protection systems; second, actuator saturation will not only weaken control efficiency, but may also increase the risk of attitude instability.

[0004] To address the above issues, existing technologies typically use performance constraint methods to limit the amplitude of attitude angle changes and design anti-saturation auxiliary functions to mitigate the impact of actuator saturation on the control system. However, existing technologies have the following limitations:

[0005] 1) When the attitude angle approaches the constraint boundary, the performance constraint method needs to adjust the attitude by increasing the control amount. When the actuator is saturated, this will aggravate the saturation of the actuator, and the actual control amount has no room for further improvement.

[0006] 2) Anti-saturation algorithms often introduce auxiliary systems to reduce the control amount after the actuator is saturated, which has the opposite effect of the performance constraint method. Especially when the aircraft encounters strong disturbances, the preset performance anti-saturation algorithm is difficult to effectively control the attitude angle within the constraint boundary and cannot achieve the expected anti-saturation effect.

[0007] Therefore, it is necessary to conduct more in-depth research on the existing aircraft anti-saturation control methods to solve the above problems. Summary of the Invention

[0008] In order to overcome the above problems, an in-depth study was conducted and a flexible preset performance anti-saturation control method based on a high-order fixed-time observer was proposed, which includes the following steps:

[0009] S1. Establish aircraft dynamics model;

[0010] S2. Set up a high-order fixed-time disturbance observer to estimate the disturbance of the dynamic model;

[0011] S3. Setting a preset finite time function to constrain the system state;

[0012] S4. Setting an anti-saturation auxiliary function, and constructing a flexible preset performance function based on a flexible relationship between the anti-saturation auxiliary function and the preset finite time performance function;

[0013] S5. Constructing a constraint relationship between the flexible preset performance function and the tracking error;

[0014] S6. Setting an anti-saturation controller with the attitude angle as the outer loop and the attitude angular velocity as the inner loop;

[0015] S7. According to the guidance instructions, the anti-saturation controller is used to control the aircraft.

[0016] In a preferred embodiment, in S1, the aircraft system model is represented as:

[0017]

[0018]

[0019] where x1 = [α, β, γ] T ,x2=[ω x ,ω y ,ω z ] T ,u=[δ x ,δ y ,δ z ] T

[0020] x1 and x2 are system state variables, x1 represents the aircraft attitude angle, x2 represents the aircraft attitude angular velocity, u is the system control variable, the superscript T represents the transpose, d1 and d2 are disturbances, f1, f2, g1, g2, u s , J, C are all intermediate variables, u s is a control variable with saturation characteristics, α, β, γ are respectively the angle of attack, sideslip angle and velocity inclination of the aircraft, m, V, θ are respectively the mass, velocity and ballistic inclination of the aircraft, ω x 、ω y 、ω z is the component of the aircraft's angular velocity in the x, y, and z directions, J x 、J y 、J z is the component of the main moment of inertia of the aircraft in the x, y, and z directions, J xy is the inertia product of the aircraft, L is the aerodynamic lift of the aircraft, N is the lateral force of the aircraft, S ref is the characteristic area of ​​the aircraft, is the dynamic pressure, L ref is the characteristic length of the aircraft, C mx 、C my 、C mzare the roll, yaw, and pitch moment coefficients, δ x is the roll equivalent rudder angle, δ y is the equivalent rudder angle of yaw, δ z is the pitch equivalent rudder angle, C mx0 Represents δ x =δ y =δ z = 0 when the rolling moment coefficient, C my0 Represents δ x =δ y =δ z = 0 when the yaw moment coefficient, C mz0 Represents δ x =δ y =δ z = 0 when the pitching moment coefficient, equivalent rudder deflection angle δ x , δ y , δ z When used as a superscript of a moment coefficient, it indicates the partial derivative of the moment coefficient with respect to the equivalent rudder deflection angle, u max is the maximum rudder angle allowed by the aircraft, u min The minimum rudder deflection angle allowed for the aircraft;

[0021] In S2, the high-order fixed-time disturbance observer is set as:

[0022]

[0023] in, represents the estimate of the system state x = [x1, x2], represents the estimation of the disturbance d = [d1, d2], f(x), g(x) represent the known items of the system, is the state observation error; Δ1 and Δ2 are auxiliary variables, λ1, λ2, λ3, λ4, λ5, λ6, λ7, and λ8 are gain parameters, and p1, p2, p3, p4, q1, q2, q3, and q4 are all configurable parameters.

[0024] In a preferred embodiment, in S3, the preset finite time function ρ i (t) is set to:

[0025]

[0026] Where T is the predefined finite time, t represents the current flight time, μ i and b i is a normal number, and N is a positive integer.

[0027] In a preferred embodiment, in S4, the anti-saturation auxiliary function is set to:

[0028]

[0029] g u =diag(g u,1 ,g u,2 ,g u,3 ), g l =diag(g l,1 ,g l,2 ,g l,3 )

[0030]

[0031] Δu=u s -u

[0032] Δu=[Δu1,Δu2,Δu3] T =[Δδ x ,Δδ y ,Δδ z ] T

[0033] Among them, Λ 1,l , Λ 2,l , Λ 3,l , Λ 1,u , Λ 2,u , Λ 3,u is an auxiliary term, R 1,l 、R 2,l 、R 1,u 、R 2,u 、w 1,l 、w 2,l 、w 1,u 、w 2,u are intermediate variables, a1, a2, a3, a4, c1, c2, c3, c4, m1, m2, m3, m4, n1, n2, n3, n4 are constants, is the matrix composed of non-negative elements in the g1 matrix, is the matrix composed of non-negative elements in the g2 matrix, g u 、g l is an intermediate variable.

[0034] In a preferred embodiment, the flexible preset performance function E is expressed as:

[0035] E=ρ+Λ 1,u +Λ 1,l

[0036] Where ρ represents the preset finite-time performance function, ρ=[ρ1,ρ2,ρ3] T , ρ1 represents the constraint value of the angle of attack, ρ2 represents the constraint value of the sideslip angle, and ρ3 represents the constraint value of the velocity inclination angle.

[0037] In a preferred embodiment, in S5, the tracking error is expressed as:

[0038]

[0039] Among them, z1 represents the attitude angle tracking error, z2 represents the attitude angular velocity tracking error, and x 1d represents the desired attitude angle, x 2d Indicates the command signal.

[0040] In a preferred embodiment, a fractional barrier Lyapunov function is set as the constraint relationship between the flexible preset performance function and the tracking error. The constraint relationship between the flexible preset performance function and the tracking error is expressed as:

[0041]

[0042] E=[E1,E2,E3] T

[0043] z1=[z 1,1 ,z 1,2 ,z 1,3 ] T

[0044] Among them, L a1 represents the fractional barrier Lyapunov function.

[0045] In a preferred embodiment, in S6, the outer loop of the controller is configured as follows:

[0046]

[0047] Among them, x 2c Indicates the virtual control rate of attitude angle, k1=diag(k 1,1 ,k 1,2 ,k 1,3 ) is the controller outer loop parameter diagonal matrix, Estimation of the comprehensive disturbance of the outer loop attitude angle, ε1 is an intermediate variable.

[0048] In a preferred embodiment, in the outer loop of the controller, the estimation of the integrated disturbance And the attitude angle estimation in z1 Obtained through observation by the outer loop disturbance observer,

[0049] The outer loop disturbance observer is set as:

[0050]

[0051] Among them, p1, p2, p3, p4, q1, q2, q3, q4 are configurable parameters, λ 1,1 ,λ 1,2 ,λ 1,3 ,λ 1,4 ,λ 1,5 ,λ 1,6 ,λ 1,7 ,λ 1,8 is a configurable parameter, Δ 1,1 , Δ 1,2 is an intermediate variable, is the estimation error of the state quantity of the outer loop disturbance observer.

[0052] In a preferred embodiment, the controller inner loop is configured as follows:

[0053]

[0054] Where k2=diag(k 2,1 ,k 2,2 ,k 2,3 ) is the diagonal matrix of the controller inner loop parameters, is the estimation of the comprehensive disturbance of the inner loop attitude angular velocity.

[0055] The beneficial effects of the present invention include:

[0056] (1) Simultaneously meet performance constraints and reduce the impact of actuator saturation on the control system;

[0057] (2) The fixed-time disturbance observer has a higher estimation accuracy for disturbances;

[0058] (3) Under strong disturbances, the maximum change amplitude of the attitude angle is greatly reduced, and the saturation time of the actuator is greatly shortened. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A schematic flow chart of a flexible preset performance anti-saturation control method based on a high-order fixed-time observer according to a preferred embodiment of the present invention is shown;

[0060] Figure 2 The attack angle tracking curves of Example 1 and Comparative Example 1;

[0061] Figure 3 The sideslip angle tracking curves of Example 1 and Comparative Example 1;

[0062] Figure 4 The speed and inclination angle tracking curves of Example 1 and Comparative Example 1 are shown;

[0063] Figure 5 This is a simulation diagram of the flexible constraint of the angle of attack tracking error in Example 1;

[0064] Figure 6 This is a simulation diagram of the flexible constraint of the sideslip angle tracking error in Example 1;

[0065] Figure 7 This is a simulation diagram of the flexible constraint of the velocity and inclination angle tracking error in Example 1;

[0066] Figure 8 The three-channel attitude angular velocity curves of Example 1 and Comparative Example 1;

[0067] Figure 9 The three-channel rudder deflection angle curves of Example 1 and Comparative Example 1;

[0068] Figure 10 1 is an estimated simulation diagram of the outer loop disturbance d1 of Example 1 and Comparative Example 1;

[0069] Figure 11 2 is a simulation diagram of the estimated inner loop disturbance d2 of Example 1 and Comparative Example 1. DETAILED DESCRIPTION

[0070] The present invention will be described in further detail below with reference to the accompanying drawings and examples, through which the features and advantages of the present invention will become more clearly understood.

[0071] The word "exemplary" is used exclusively herein to mean "serving as an example, example, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0072] The present invention provides a flexible preset performance anti-saturation control method based on a high-order fixed-time observer, such as Figure 1 As shown, the following steps are included:

[0073] S1. Establish aircraft dynamics model;

[0074] S2. Set up a high-order fixed-time disturbance observer to estimate the disturbance of the dynamic model;

[0075] S3. Setting a preset finite time function to constrain the system state;

[0076] S4. Setting an anti-saturation auxiliary function, and constructing a flexible preset performance function based on a flexible relationship between the anti-saturation auxiliary function and the preset finite time performance function;

[0077] S5. Constructing a constraint relationship between the flexible preset performance function and the tracking error;

[0078] S6. Setting an anti-saturation controller with the attitude angle as the outer loop and the attitude angular velocity as the inner loop;

[0079] S7. According to the guidance instructions, the anti-saturation controller is used to control the aircraft.

[0080] In S1, the aircraft system model is expressed as:

[0081]

[0082]

[0083] where x1 = [α, β, γ] T ,x2=[ω x ,ω y ,ω z ] T ,u=[δ x ,δ y ,δ z ] T

[0084] x1 and x2 are system state variables, x1 represents the aircraft attitude angle, x2 represents the aircraft attitude angular velocity, u is the system control variable, the superscript T represents the transpose, d1 and d2 are disturbances, f1, f2, g1, g2, u s , J, C are all intermediate variables, u s is a control variable with saturation characteristics, α, β, γ are respectively the angle of attack, sideslip angle and velocity inclination of the aircraft, m, V, θ are respectively the mass, velocity and ballistic inclination of the aircraft, ω x 、ω y 、ω z is the component of the aircraft's angular velocity in the x, y, and z directions, J x 、J y 、J z is the component of the main moment of inertia of the aircraft in the x, y, and z directions, J xy is the inertia product of the aircraft, L is the aerodynamic lift of the aircraft, N is the lateral force of the aircraft, S ref is the characteristic area of ​​the aircraft, is the dynamic pressure, L ref is the characteristic length of the aircraft, C mx 、C my 、C mz are the roll, yaw, and pitch moment coefficients, δ x is the roll equivalent rudder angle, δ y is the equivalent rudder angle of yaw, δ z is the pitch equivalent rudder angle, C mx0 Represents δ x =δ y =δ z = 0 when the rolling moment coefficient, C my0 Represents δ x=δ y =δ z = 0 when the yaw moment coefficient, C mz0 Represents δ x =δ y =δ z = 0 when the pitching moment coefficient, equivalent rudder deflection angle δ x , δ y , δ z When used as a superscript of a moment coefficient, it indicates the partial derivative of the moment coefficient with respect to the equivalent rudder deflection angle, u max is the maximum rudder angle allowed by the aircraft, u min The minimum rudder angle allowed by the aircraft.

[0085] In S2, the high-order fixed-time disturbance observer is set as:

[0086]

[0087] in, represents the estimate of the system state x = [x1, x2], represents the estimation of the disturbance d = [d1, d2], f(x), g(x) represent the known items of the system, is the state observation error; Δ1 and Δ2 are auxiliary variables, λ1, λ2, λ3, λ4, λ5, λ6, λ7, and λ8 are gain parameters, and p1, p2, p3, p4, q1, q2, q3, and q4 are all configurable parameters.

[0088] In S3, the preset finite time function ρ i (t) is set to:

[0089]

[0090] Where T is the predefined finite time, t represents the current flight time, μ i and b i is a normal number, and N is a positive integer.

[0091] In S4, the anti-saturation auxiliary function is set to:

[0092]

[0093] Among them, Λ 1,l , Λ 2,l , Λ 3,l , Λ 1,u , Λ 2,u , Λ 3,u is an auxiliary term, R 1,l 、R 2,l 、R 1,u 、R 2,u 、w 1,l、w 2,l 、w 1,u 、w 2,u are intermediate variables, a1, a2, a3, a4, c1, c2, c3, c4, m1, m2, m3, m4, n1, n2, n3, n4 are constants, is the matrix composed of non-negative elements in the g1 matrix, is the matrix composed of non-negative elements in the g2 matrix,

[0094] Preferably, a1, a2, a3, a4, c1, c2, c3, c4 are positive numbers, m1, m2, m3, m4 are constants greater than 1, and n1, n2, n3, n4 are positive numbers less than 1.

[0095] Preferably, g u =diag(g u,1 ,g u,2 ,g u,3 ), g l =diag(g l,1 ,g l,2 ,g l,3 )

[0096] Each element is represented as:

[0097]

[0098] Where Δu=u s -u

[0099] Decomposed into: Δu=[Δu1,Δu2,Δu3] T =[Δδ x ,Δδ y ,Δδ z ] T , Δu1 represents the difference between the actual roll rudder angle and the expected roll rudder angle, Δu2 represents the difference between the actual yaw rudder angle and the expected yaw rudder angle, and Δu3 represents the difference between the actual pitch rudder angle and the expected pitch rudder angle.

[0100] In the present invention, the anti-saturation auxiliary function satisfies the fixed-time convergence theory. Furthermore, by setting the above-mentioned anti-saturation auxiliary function, the influence of actuator saturation on the control system is reduced. By constructing a convergence function containing double power terms, it is ensured that the anti-saturation auxiliary variable converges to an arbitrarily small neighborhood range within a fixed time, thereby improving the desaturation speed of the actuator.

[0101] The preset finite time performance function ρ is expressed as:

[0102] ρ=[ρ1,ρ2,ρ3] T

[0103] Where ρ1 represents the constraint value of the angle of attack, ρ2 represents the constraint value of the sideslip angle, ρ3 represents the constraint value of the velocity inclination angle, and the superscript T represents transposition.

[0104] The flexible preset performance function E is expressed as:

[0105] E=ρ+Λ 1,u +Λ 1,l

[0106] In S5, the tracking error is expressed as:

[0107]

[0108] Among them, z1 represents the attitude angle tracking error, z2 represents the attitude angular velocity tracking error, and x 1d represents the desired attitude angle, x 2d Indicates the command signal.

[0109] Preferably, the command signal is filtered, and the filtered command signal x 2d Expressed as:

[0110]

[0111] Where τ = diag (τ1, τ2, τ3) is a diagonal matrix of filter parameters with positive elements, and the command filter error χ is: χ = x 2d -x 2c , x 2d (0) = x 2c (0).

[0112] A fractional barrier Lyapunov function is set as the constraint relationship between the flexible preset performance function and the tracking error. The constraint relationship between the flexible preset performance function and the tracking error is expressed as:

[0113]

[0114] E=[E1,E2,E3] T

[0115] z1=[z 1,1 ,z 1,2 ,z 1,3 ] T

[0116] Among them, L a1 represents the fractional barrier Lyapunov function.

[0117] According to the present invention, when there is a constraint boundary, z1 approaches the constraint boundary E, which will cause the control amount to increase under the action of the fractional barrier Lyapunov function to prevent the tracking error from exceeding the constraint boundary; when there is no constraint boundary, the fractional barrier Lyapunov function can be changed to a traditional quadratic Lyapunov function, and the fractional barrier Lyapunov function can be adjusted by adjusting the flexible preset performance function E i The design satisfies the Lyapunov function functions of both constrained and unconstrained cases.

[0118] Traditional constraints generally use a logarithmic barrier Lyapunov function for constraints. In the present invention, a fractional barrier Lyapunov function is used as the constraint relationship between the flexible preset performance function and the tracking error. Compared with the traditional logarithmic barrier Lyapunov function, it has the following advantages:

[0119] 1) When there is no constraint boundary, the traditional logarithmic barrier Lyapunov function cannot handle both constrained and unconstrained situations. However, the fractional barrier Lyapunov function can adjust the flexible preset performance function E i The design can handle both systems with constrained characteristics and systems without constrained characteristics, which expands the constraint range of the control system to a certain extent;

[0120] 2) The performance constraint feedback term of the fractional barrier Lyapunov function is relatively reduced due to the addition of the power term, which is more suitable for dealing with the contradictory relationship between the preset performance constraint and the anti-saturation function.

[0121] In S6, the controller adopts backstepping control, with the attitude angle as the outer loop and the attitude angular velocity as the inner loop.

[0122] Furthermore, the outer loop of the controller is set as:

[0123]

[0124]

[0125] Among them, x 2c Indicates the virtual control rate of attitude angle, k1=diag(k 1,1 ,k 1,2 ,k 1,3 ) is the controller outer loop parameter diagonal matrix, Estimation of the comprehensive disturbance of the outer loop attitude angle, ε1 is an intermediate variable.

[0126] In the present invention, ε1 is a feedback term that constrains the performance of the tracking error, which can stabilize the extreme changes in the system caused by the tracking error and improve the stability of the control system.

[0127] According to the present invention, in the outer loop of the controller, the estimation of the integrated disturbance And the attitude angle estimation in z1 Obtained through observation by the outer loop disturbance observer.

[0128] Preferably, the outer loop disturbance observer is configured as follows:

[0129]

[0130] Among them, p1, p2, p3, p4, q1, q2, q3, q4 are configurable parameters, λ 1,1 ,λ 1,2 ,λ 1,3 ,λ 1,4 ,λ 1,5 ,λ 1,6 ,λ 1,7 ,λ 1,8 is a configurable parameter, Δ 1,1 , Δ 1,2 is the intermediate variable, is the estimation error of the state quantity of the outer loop disturbance observer.

[0131] The controller inner loop is set as:

[0132]

[0133] Where k2=diag(k 2,1 ,k 2,2 ,k 2,3 ) is the diagonal matrix of the controller inner loop parameters, is the estimation of the comprehensive disturbance of the inner loop attitude angular velocity.

[0134] According to the present invention, in the inner loop of the controller, the estimation of the integrated disturbance And the attitude angular velocity estimation in z2 Obtained through inner loop disturbance observer observation.

[0135] Preferably, the inner-loop disturbance observer is configured as follows:

[0136]

[0137] Among them, λ 2,1 ,λ 2,2 ,λ 2,3 ,λ 2,4 ,λ 2,5 ,λ 2,6 ,λ 2,7 ,λ 2,8 is a configurable parameter, Δ 2,1 , Δ 2,2 is the intermediate variable, is the estimation error of the state quantity of the inner loop disturbance observer.

[0138] Preferably, a filter is further provided in the controller, and the outer loop attitude angle virtual control rate is filtered by the filter, thereby avoiding the "computational explosion" problem caused by continuous derivation of the virtual control law in traditional backstepping control.

[0139] More preferably, the filter is a first-order filter.

[0140] Example

[0141] Example 1

[0142] The simulation experiment was carried out under the following conditions: the initial value of the aircraft attitude angle tracking control simulation was set to [α0, β0, γ0] T =[15°,2°,0°] T , the initial values ​​of attitude angular velocity are all 0° / s, the initial flight altitude is h0=30km, the initial flight speed is V0=2500m / s. The simulation time is 30s, and the attitude angle command is set to [α d ,β d ,γ d ] T =[10°,0°,10°] T The three-channel rudder angle limit is: |δ x |≤20°, |δ y |≤20°, |δ z |≤30°. The aircraft sweep angle changes from 30° to 90° in 15 seconds, and the change process takes 2 seconds.

[0143] During the simulation, a flexible preset performance anti-saturation control method based on a high-order fixed-time observer is used, which includes the following steps:

[0144] S1. Establish aircraft dynamics model;

[0145] S2. Set up a high-order fixed-time disturbance observer to estimate the disturbance of the dynamic model;

[0146] S3, setting a preset finite time function to constrain the system state; S4, setting an anti-saturation auxiliary function, and constructing a flexible preset performance function based on the flexible relationship between the anti-saturation auxiliary function and the preset finite time performance function;

[0147] S5. Constructing a constraint relationship between the flexible preset performance function and the tracking error;

[0148] S6. Setting an anti-saturation controller with the attitude angle as the outer loop and the attitude angular velocity as the inner loop;

[0149] S7, according to the guidance instructions, use the anti-saturation controller to control the aircraft. In S1, the aircraft system model is expressed as:

[0150]

[0151]

[0152] In S2, the high-order fixed-time disturbance observer is set as:

[0153]

[0154] In S3, the preset finite time function ρ i (t) is set to:

[0155]

[0156] In S4, the anti-saturation auxiliary function is set to:

[0157]

[0158]

[0159] The flexible preset performance function E is expressed as:

[0160] E=ρ+Λ 1,u +Λ 1,l

[0161] In S6, the tracking error is expressed as:

[0162]

[0163] A fractional barrier Lyapunov function is set as the constraint relationship between the flexible preset performance function and the tracking error. The constraint relationship between the flexible preset performance function and the tracking error is expressed as:

[0164]

[0165] E=[E1,E2,E3] T

[0166] z1=[z 1,1 ,z 1,2 ,z 1,3 ] T

[0167] In S7, the outer loop of the controller is set to:

[0168]

[0169] In the outer loop of the controller, the estimation of the integrated disturbance And the attitude angle estimation in z1 Obtained through observation by the outer loop disturbance observer,

[0170] The outer loop disturbance observer is set as:

[0171]

[0172] The controller inner loop is set as:

[0173]

[0174] In the inner loop of the controller, the estimation of the integrated disturbance And the attitude angular velocity estimation in z2 Obtained through the inner loop disturbance observer,

[0175] The inner loop disturbance observer is set as:

[0176]

[0177] The control parameters involved are:

[0178] k1=diag(1,1,1), k2=diag(5,5,5), τ=diag(0.01,0.01,0.01), p1=0.8, p2=0.6, p3=0.4, p4=0.2, q1=1.2, q2=1.4, q3=1.6, q4=1.8,

[0179] T=5s, N=3, b1=b2=b3=0.1°, μ1=0.49rad, μ2=0.39rad, μ3=0.69rad, a1=a2=a3=a4=1, c1=c3=0.5, c2=c4=1, m1=m2=m3=m4=1.1, n1=n2=n3=n4=0.9.

[0180] During the simulation, the simulation duration is 30 seconds. When the simulation time is between 20 seconds and 25 seconds, a strong disturbance of 80 sin (πt / 5) degrees is added to the inner loop yaw channel. The external disturbance is set as:

[0181] d1=[0.5sin(0.1πt),0.5sin(πt / 30),0.5sin(πt / 30)] T (° / s)

[0182]

[0183] Comparative Example 1

[0184] The same experiment as in Example 1 was performed, except that a backstepping control method with a fixed-time disturbance observer was used.

[0185] In the backstepping control method with fixed-time disturbance observer, the outer loop virtual control law is set as:

[0186]

[0187] Disturbance Estimation for Outer Loop Fixed-Time Disturbance Observer Designed to:

[0188]

[0189] The inner loop control law is set as:

[0190]

[0191] Disturbance Estimation for Inner-Loop Fixed-Time Disturbance Observer Designed to:

[0192]

[0193] in, is the state observation error, k3=diag(1,1,1), k4=diag(5,5,5), a 11 =a 21 =0.25, a 21 =a 22 =1.1, a 13 =a 23 =5.5, b 11 =b 21 =0.65, b 21 =b 22 =1.2.

[0194] Comparing Example 1 with Comparative Example 1, the results are as follows Figure 2-11 As shown. Among them, Figure 2 The attack angle tracking curves of Example 1 and Comparative Example 1 are shown as follows: Figure 3 are the sideslip angle tracking curves of Example 1 and Comparative Example 1, Figure 4 The speed angle tracking curves of Example 1 and Comparative Example 1 are as follows: Figure 5 This is a simulation diagram of the flexible constraint of the angle of attack tracking error in Example 1. Figure 6 This is a simulation diagram of the flexible constraint of the sideslip angle tracking error in Example 1. Figure 7 This is a simulation diagram of the flexible constraint of the velocity angle tracking error in Example 1. Figure 8 The three-channel attitude angular velocity curves of Example 1 and Comparative Example 1 are: Figure 9 The three-channel rudder deflection curves of Example 1 and Comparative Example 1 are: Figure 10: This is the estimated simulation diagram of the outer loop disturbance d1 of Example 1 and Comparative Example 1, Figure 11 2 is a simulation diagram of the estimated inner loop disturbance d2 of Example 1 and Comparative Example 1.

[0195] from Figure 2-Figure 4 It can be seen that under strong disturbance, the change amplitude of the attitude angle in Example 1 is significantly smaller than that in Comparative Example 1, and the tracking error convergence speed is significantly faster than that of the method in Comparative Example 1. At the same time, the angle of attack tracking curve produces a slight fluctuation at 15s due to the influence of the swept wing change. In addition, due to the strong coupling characteristics between the yaw and roll channels, when a strong disturbance is added to the yaw channel at 20s, both the sideslip angle and the velocity inclination angle undergo significant changes, among which the amplitude of the velocity inclination angle changes the most.

[0196] from Figure 5-Figure 7 It can be seen from FIG1 that under strong disturbance, the flexible preset performance function in Example 1 dynamically adjusts the constraint boundary according to the saturation of the actuator, so that the attitude angle tracking error of Example 1 is kept within the constraint boundary.

[0197] from Figure 8-Figure 9 It can be seen from the figure that, under the influence of strong disturbance, the attitude angular velocity in Example 1 fluctuates greatly, while the attitude angular velocity changes less under the action of the flexible preset performance function in the method of Example 1; from the three-channel rudder deflection angle curve, it can be seen that, under the influence of strong disturbance, the yaw rudder deflection angle of Example 1 and Comparative Example 1 saturates at around 22s. From the local enlarged diagram, it can be seen that the saturation time of the actuator in Example 1 is shortened by about 30% compared with Comparative Example 1 under the action of the fixed-time anti-saturation auxiliary function, and the pitch rudder deflection angle decreases significantly when the sweep angle changes at t=15s, indicating that the deformation additional torque has a significant impact on the pitch channel.

[0198] from Figure 10-11 From the locally enlarged diagram, it can be seen that the high-order fixed-time disturbance observer of Example 1 has a significantly higher estimation accuracy for disturbances than the method of Comparative Example 1.

[0199] Table II shows the comparison of the maximum change amplitude of the attitude angle and the saturation time of the actuator under strong disturbance.

[0200] Table 2

[0201]

[0202] As shown in Table 2, the maximum change amplitude of the attitude angle under strong disturbances in Example 1 is reduced by approximately 80% compared to Comparative Example 1, and the actuator saturation time is shortened by approximately 30% compared to Comparative Example 1. The flexible preset performance anti-saturation control method of Example 1 can simultaneously meet performance constraints and anti-saturation requirements under strong disturbances. It not only expands the constraint boundary when the actuator is saturated, keeping the change amplitude of its tracking error within a certain range; it also shortens the actuator saturation time under the action of the fixed-time anti-saturation auxiliary function, achieving better control results.

[0203] The present invention has been described above with reference to preferred embodiments, but these embodiments are merely exemplary and serve only as illustrations. On this basis, various replacements and improvements can be made to the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A flexible preset performance anti-saturation control method based on a high-order fixed-time observer, characterized in that: The following steps are involved: S1. Establish aircraft dynamics model; S2. Set up a high-order fixed-time disturbance observer to estimate the disturbance of the dynamic model; S3. Setting a preset finite time function to constrain the system state; S4. Setting an anti-saturation auxiliary function, and constructing a flexible preset performance function based on a flexible relationship between the anti-saturation auxiliary function and the preset finite time performance function; S5. Constructing a constraint relationship between the flexible preset performance function and the tracking error; S6. Setting an anti-saturation controller with the attitude angle as the outer loop and the attitude angular velocity as the inner loop; S7. According to the guidance instructions, the anti-saturation controller is used to control the aircraft.

2. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 1 is characterized in that: In S1, the aircraft system model is expressed as: g2=qS r L r JC Where, x1=[a,b,c] T ,x2=[ω x ,oh y ,oh z ] T ,u=[δ x ,d y ,d z ] T x1 and x2 are system state variables, x1 represents the aircraft attitude angle, x2 represents the aircraft attitude angular velocity, u is the system control variable, the superscript T represents the transpose, d1 and d2 are disturbances, f1, f2, g1, g2, u s , J, C are all intermediate variables, u s is a control variable with saturation characteristics, α, β, γ are respectively the angle of attack, sideslip angle and velocity inclination of the aircraft, m, V, θ are respectively the mass, velocity and ballistic inclination of the aircraft, ω x 、ω y 、ω z is the component of the aircraft's angular velocity in the x, y, and z directions, J x 、J y 、J z is the component of the main moment of inertia of the aircraft in the x, y, and z directions, J xy is the inertia product of the aircraft, L is the aerodynamic lift of the aircraft, N is the lateral force of the aircraft, S ref is the characteristic area of ​​the aircraft, is the dynamic pressure, L ref is the characteristic length of the aircraft, C mx 、C my 、C mz are the roll, yaw, and pitch moment coefficients, δ x is the roll equivalent rudder angle, δ y is the equivalent rudder angle of yaw, δ z is the pitch equivalent rudder angle, C mx0 Represents δ x =δ y =δ z = 0 when the rolling moment coefficient, C my0 Represents δ x =δ y =δ z = 0 when the yaw moment coefficient, C mz0 Represents δ x =δ y =δ z = 0 when the pitching moment coefficient, equivalent rudder deflection angle δ x , δ y , δ z When used as a superscript of a moment coefficient, it indicates the partial derivative of the moment coefficient with respect to the equivalent rudder deflection angle, u max is the maximum rudder angle allowed by the aircraft, u min The minimum rudder deflection angle allowed for the aircraft; In S2, the high-order fixed-time disturbance observer is set as: sig(σ)=sign(σ).|σ| in, represents the estimate of the system state x = [x1, x2], represents the estimation of the disturbance d = [d1, d2], f(x), g(x) represent the known items of the system, is the state observation error; Δ1 and Δ2 are auxiliary variables, λ1, λ2, λ3, λ4, λ5, λ6, λ7, and λ8 are gain parameters, and p1, p2, p3, p4, q1, q2, q3, and q4 are all configurable parameters.

3. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 1 is characterized in that: In S3, the preset finite time function ρ i (t) is set to: Where T is the predefined finite time, t represents the current flight time, μ i and b i is a normal number, and N is a positive integer.

4. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 2 is characterized in that: In S4, the anti-saturation auxiliary function is set to: g u =diag(g u,1 ,g u,2 ,g u,3 ),g l =diag(g l,1 ,g l,2 ,g l,3 ) Δu=u s -u Δu=[Δu1,Δu2,Δu3] T =[Dδ x ,Dd y ,Dd z ] T Among them, Λ 1,l , Λ 2,l , Λ 3,l , Λ 1,u , Λ 2,u , Λ 3,u is an auxiliary term, R 1,l 、R 2,l 、R 1,u 、R 2,u 、w 1,l 、w 2,l 、w 1,u 、w 2,u are intermediate variables, a1, a2, a3, a4, c1, c2, c3, c4, m1, m2, m3, m4, n1, n2, n3, n4 are constants, is the matrix composed of non-negative elements in the g1 matrix, is the matrix composed of non-negative elements in the g2 matrix, g u 、g l is an intermediate variable.

5. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 4 is characterized in that: The flexible preset performance function E is expressed as: E=ρ+Λ 1,u +L 1,l Where ρ represents the preset finite-time performance function, ρ=[ρ1,ρ2,ρ3] T , ρ1 represents the constraint value of the angle of attack, ρ2 represents the constraint value of the sideslip angle, and ρ3 represents the constraint value of the velocity inclination angle.

6. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 4 is characterized in that: In S5, the tracking error is expressed as: Among them, z1 represents the attitude angle tracking error, z2 represents the attitude angular velocity tracking error, and x 1d represents the desired attitude angle, x 2d Indicates the command signal.

7. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 6 is characterized in that: A fractional barrier Lyapunov function is set as the constraint relationship between the flexible preset performance function and the tracking error. The constraint relationship between the flexible preset performance function and the tracking error is expressed as: <h2 style=";text-align:left;direction:ltr">E=[E1,E2,E3]<h2 style=";text-align:left;direction:ltr"> T z1=[z 1,1 ,With 1,2 ,With 1,3 ] T Among them, L a1 represents the fractional barrier Lyapunov function.

8. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 7 is characterized in that: In S6, the outer loop of the controller is set to: Among them, x 2c Indicates the virtual control rate of attitude angle, k1=diag(k 1,1 ,k 1,2 ,k 1,3 ) is the controller outer loop parameter diagonal matrix, Estimation of the comprehensive disturbance of the outer loop attitude angle, ε1 is an intermediate variable.

9. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 8, characterized in that: In the outer loop of the controller, the estimation of the integrated disturbance And the attitude angle estimation in z1 Obtained through observation by the outer loop disturbance observer, The outer loop disturbance observer is set as: Among them, p1, p2, p3, p4, q1, q2, q3, q4 are configurable parameters, λ 1,1 ,λ 1,2 ,λ 1,3 ,λ 1,4 ,λ 1,5 ,λ 1,6 ,λ 1,7 ,λ 1,8 is a configurable parameter, Δ 1,1 , Δ 1,2 is an intermediate variable, is the estimation error of the state quantity of the outer loop disturbance observer.

10. The flexible preset performance anti-saturation control method based on high-order fixed-time observer according to claim 7, characterized in that: The controller inner loop is set to: Where k2=diag(k 2,1 ,k 2,2 ,k 2,3 ) is the diagonal matrix of the controller inner loop parameters, is the estimation of the comprehensive disturbance of the inner loop attitude angular velocity.

Images