[0099] Example 1:
[0100] Using the hypersonic model of the Winged-Cone configuration published by NASA as the simulation platform, numerical simulation is carried out for its reentry flight process. In the simulation, the initial altitude is 28km, the speed is 2800m/s, the initial value of the attitude angle is [3120]deg, and the desired attitude angle is [000]deg. The initial attitude angular velocity is 0.
[0101] Because the flight conditions of the reentry aircraft vary widely, and often have uncertainties such as aerodynamic parameter perturbation, for the attitude control of the reentry aircraft, it is necessary to check not only the control performance under nominal conditions, but also the controller Can the system be controlled robustly and accurately when the environmental parameters change drastically and the system has strong uncertainty. In order to further verify the robustness of the system, a large external disturbance (directly applied to the control torque of the three axes) d=[d 1 ,d 2 ,d 3 ] T :
[0102]
[0103] The beneficial effects of the present invention are illustrated by comparing the control result given by the finite time convergence time-varying sliding mode attitude control method disclosed in this embodiment with the control result given by the traditional time-varying sliding mode control method.
[0104] A finite time convergence time-varying sliding mode attitude control method disclosed in this embodiment includes the following steps:
[0105] Step 1. Generate the state vector of the aircraft.
[0106] Combined with the actual attitude angle of the aircraft Ω = [α, β, μ] T , The attitude angular velocity ω=[p,q,r] T , Constitute the state vector x: x=[αβμpqr] T.
[0107] Step 2: Establish a dynamic model of the reentry aircraft.
[0108] Consider the attitude control problem of an unpowered reentry aircraft. It adopts the tilt turn (BTT) control, and its attitude kinematics equation is:
[0109] α · = ω z
[0110] β · = ω x s i n α + ω y c o s α - - - ( 1 )
[0111] μ · = ω x c o s α - ω y s i n α
[0112] The posture dynamic equation is:
[0113] ω · x = I y y I * M x + I x y I * M y - I y y ( I z z - I y y ) - I x y 2 I * ω y ω z - I x y ( I x x + I y y - I z z ) I * ω x ω z
[0114] ω · y = I x y I * M x + I x x I * M y - I x x ( I x x - I z z ) - I x y 2 I * ω x ω z - I x y ( I x x + I y y - I z z ) I * ω y ω z - - - ( 2 )
[0115] ω · z = 1 I z z - I y y - I x x I z z ω x ω y - I x y I z z ( ω y 2 - ω x 2 )
[0116] In the formula, α, β, μ are the angle of attack, the angle of sideslip and the angle of inclination, respectively; ω x ,ω y ,ω z They are the angular velocity of roll, yaw and pitch; I xx ,I yy ,I zz And I xy Are the moments of inertia and product of inertia about the x, y, and z axes (assuming that the aircraft is symmetric about the x-o-y plane, so I xz = I yz =0), M x ,M y ,M z They are the aerodynamic moments of roll, yaw and pitch respectively, and the calculation expressions are:
[0117] M i =qSlC mi (α,β,Ma,δ e ,δ a ,δ r ),i=x,y,z(3)
[0118] Among them, dynamic pressure q = 0.5ρV 2 , Ρ is the atmospheric density, V is the speed of the aircraft; S, l are the reference area and reference length of the aircraft, respectively; δ e ,δ a ,δ r The deflection angles of the elevator, aileron and rudder respectively; C mx ,C my ,C mz Respectively about α, β, Ma, δ e ,δ a ,δ r Moment coefficients of roll, yaw and pitch, and Ma is the Mach number of the aircraft.
[0119] Step 3. Perform feedback linearization processing on the model established in Step 1, and propose a finite-time attitude tracking task.
[0120] Write the system model as a MIMO nonlinear affine system:
[0121] { x · = f ( x ) + G ( x ) u Ω = H ( x ) - - - ( 4 )
[0122] Using feedback linearization theory, the system output is derived until the control quantity u appears in the output dynamic equation, and the auxiliary control quantity v is introduced. Decouple the system into the following uncertain second-order system:
[0123] Ω ·· = v + Δ v - - - ( 5 )
[0124] Where △v=[△v 1 ,△v 2 ,△v 3 ] T Represents the aggregate disturbance in the system during flight, assuming that the disturbance is bounded.
[0125] The finite-time attitude tracking task is proposed as: the system state starts from any initial value, and at the desired time (t f ) Tracking on the reference trajectory, and after this moment, the tracking error has been kept at 0. Namely Ω 1 -Ω 1d =0, t≥t f. The tracking error is defined as follows:
[0126] Ω ~ 1 = Ω 1 - Ω 1 d
[0127] Where Ω 1 Is the attitude angle of the reentry vehicle, Ω 1d It is the attitude angle command.
[0128] Step 4. Design a high-order sliding mode observer.
[0129] Expand the reentry aircraft model into the following form:
[0130] ζ · 0 = ζ 1
[0131] ζ · 1 = v + Δ v
[0132] According to the expansion form of the reentry vehicle model, a high-order sliding mode observer can be designed, which can simultaneously estimate the attitude angle derivative and the aggregate disturbance in the system.
[0133] ζ ^ · 0 = χ 1
[0134] χ 1 = - γ 1 ( ζ ^ 0 - ζ 0 ) 3 / 4 sgn ( ζ ^ 0 - ζ 0 ) + ζ ^ 1
[0135] ζ ^ · 1 = v + Δ v
[0136] Δ v = - γ 2 ( ζ ^ 1 - χ 1 ) 2 / 3 sgn ( ζ ^ 1 - χ 1 ) + ζ ^ 2
[0137] ζ ^ · 2 = χ 2
[0138] χ 2 = - γ 3 ( ζ ^ 2 - Δ v ) 1 / 2 sgn ( ζ ^ 2 - Δ v ) + ζ ^ 3
[0139] ζ ^ 3 = - γ 4 sgn ( ζ ^ 3 - χ 2 )
[0140] Where γ 1 ,γ 2 ,γ 3 ,γ 4 0 is the undetermined coefficient of the observer; χ 1 =[χ 11 ,χ 12 ,χ 13 ] T ,χ 2 =[χ 21 ,χ 22 ,χ 23 ] T; △v is ζ 0 ,ζ 1 , The estimated value of △v.
[0141] by Figure 7 It can be seen that the aggregate disturbance estimate converges to its true value in a finite time and satisfies the separation theorem. Therefore, the controller and the observer can be designed separately.
[0142] Step 5. Design a time-varying sliding mode control law that converges in a finite time.
[0143] Step 5.1, design a finite time convergent time-varying sliding mode function.
[0144] The time-varying sliding mode designed to converge in finite time is:
[0145] S ( t ) = Ω ~ ·· + K ( Ω ~ · 1 / p + C Ω ~ ) 2 p - 1 + W ( t ) - - - ( 6 )
[0146] The above formula satisfies q, r is a positive odd number, ε is any normal number, and satisfies 0.5 <1,c> ε,k> a, where the expression of a is:
[0147] a = 2 ( 2 - p ) 2 / p p ( 1 + p ) 1 + 1 / p ϵ + 2 1 - p ( 2 - p ) c + 2 1 + p - p 2 p p ( 2 - p ) p + 1 c ( p + 1 ) 2 ( 1 + p ) 1 + p ϵ p 2
[0148] When S(t)=0, t≥t 0 , The system state will be in a limited time t 1 Converges to 0, and:
[0149] t 1 ( t 0 ) ≤ 1 ( 1 - p ) b | x T ( t 0 ) x ( t 0 ) | ( 1 - p ) / 2
[0150] W(t) is a continuous time-varying function:
[0151] W ( t ) = W 1 ( t ) 0 t ≤ t 2 0 t t 2 - - - ( 7 )
[0152] Where t 2 Is the moment when the time-varying term W(t) converges to zero. The selection of time-varying items should satisfy condition C 1 , C 2 :
[0153] C 1 S ( 0 ) = Ω ~ ·· ( 0 ) + K ( Ω ~ · 1 / p ( 0 ) + C Ω ~ ( 0 ) ) 2 p - 1 + W ( 0 )
[0154] C2W(t 2 )=0
[0155] Condition C1 indicates that the state of the system is maintained on the sliding surface from the initial moment; condition C2 indicates that the time-varying sliding surface is at time t 2 The changes are smooth and there are no sudden changes. According to the above condition C 1 , C 2 , You can design the following time-varying function:
[0156] W 1 (t)=At+B(8)
[0157] In the formula, B=W 1 (0), A=-B/t 2. It can be seen that the sliding surface will approach the desired sliding surface at a constant speed A.
[0158] Due to the time-varying term W(t), the system state remains on the sliding mode surface from the initial moment to achieve global convergence. System performance has been improved. And we know the convergence time
[0159] t f = t 2 t 1 ( 0 ) ≤ t 2 t 1 ( t 2 ) + t 2 t 1 ( 0 ) t 2 - - - ( 9 )
[0160] Since adding a time-varying term in formula (6) can eliminate the arrival section of sliding mode control, the system enters the sliding section from the initial moment, which enhances the robustness of the system.
[0161] Step 5.2, design a finite time convergent time-varying sliding mode control law.
[0162] According to step 5.1, the output of the controller can be obtained:
[0163] v=v eq +v sw (10)
[0164] v e q = Ω ·· c - K ( Ω ~ ^ · 1 / p + C Ω ~ ) 2 p - 1 - W ( t ) - Δ v - - - ( 11 )
[0165] v sw +Tv sw = U n (12)
[0166] u n =-(K d +K t +η)sgn(S)(13)
[0167] Where K t =diag{k t,1 ,k t,2 ,k t,3 } And η=diag{η 1 ,η 2 ,η 3 } Is the matrix of undetermined positive coefficients; T=[T 1 ,T 2 ,T 3 ] T Is a constant matrix, and must satisfy K t,i ≥T i l d,i ,i=1,2,3. Equation (12) can be written as a low-pass filter:
[0168] u n = 1 s + T - - - ( 14 )
[0169] The low-pass filter can well reduce the chattering problem caused by switching items.
[0170] Equation (11) does not derive the sliding mode surface when calculating the equivalent control, so the jump problem caused by the discontinuity of the first derivative of the time-varying function can be eliminated.
[0171] Step 6, control distribution, get rudder deflection angle command δ=[δ e δ a δ r ] T
[0172] According to formulas (15) and (16), the rudder deflection angle command δ=[δ e δ a δ r ] T :
[0173] u=M=E -1 (x)(-F(x)+v)(15)
[0174] δ=G -1 u(10)(16)
[0175] Assigned to the rudder surface actuator, from the formula (16) get δ = [δ e δ a δ r ] T ,δ e ,δ a ,δ r They are the deflection angles of the elevator, aileron, and rudder. M=[M x ,M y ,M z ] Is the control torque calculated from the attitude control output v obtained in step 5.2, and G is the conversion matrix, which is determined by aerodynamic parameters.
[0176] Step 7. Input the rudder deflection command obtained in step 6 into the aircraft to control its attitude; at the same time, the aircraft outputs the current aircraft states α, β, μ, p, q, r as the input of attitude control, repeat step 1 Go to step 6, so that the aircraft realizes the actual attitude angle Ω=[α,β,μ] T Attitude angle command given by tracking guidance system Ω c =[α c ,β c ,μ c ] T the goal of.
[0177] By comparing the control results given by the time-varying sliding mode attitude control method of a reentry aircraft with finite time convergence disclosed in this embodiment with the control results given by the traditional time-varying sliding mode attitude control method, the description of this embodiment advantage.
[0178] ① It is verified that a finite time convergence time-varying sliding mode attitude control method of this embodiment can make the error converge to 0 within a finite time.
[0179] image 3 The posture angle tracking curve of the finite time convergence time-varying sliding mode posture control method of this embodiment is given when there are external disturbances and parameter perturbations. Figure 4 Yes image 3 In the 11-15s zoomed-in image, the system error remains zero. by image 3 , 4 It can be seen that using the method of this embodiment, the system error can converge to zero in a finite time. Figure 7 In the presence of external disturbances and parameter perturbations, the attitude angle tracking curve using the traditional time-varying sliding mode aircraft attitude control method and the boundary layer debounce technology is given. Picture 8 Yes Figure 7 In the 11-15s zoomed in picture, the systematic error is non-zero. by Picture 8 , 9 It can be seen that using the traditional time-varying sliding mode control method, the system error converges, but it cannot converge to zero. This shows that, compared with the traditional time-varying sliding mode control method, the time-varying sliding mode control method with finite time convergence can make the system tracking error converge to 0 in a finite time, and improve the tracking speed and accuracy.
[0180] ② It is verified that a finite time convergence time-varying sliding mode attitude control method of this embodiment can reduce the problem of control variable chattering.
[0181] Figure 5 The deflection curve of the rudder surface using the finite time convergence time-varying sliding mode attitude control method of this embodiment when there is external disturbance and parameter perturbation is given. by Figure 5 It can be seen that the deflection curve of the rudder surface is smooth without chattering. Picture 10 The deflection curve of the rudder surface using the traditional time-varying sliding mode aircraft attitude control method and the boundary layer debounce technology when there is external disturbance and parameter perturbation is given. by Picture 9 It can be seen that using the traditional time-varying sliding mode control method, the rudder surface deflection curve is smooth except for a jump in 2s. This shows that this embodiment can maintain the smooth deflection of the rudder surface while maintaining high accuracy.
[0182] ③Verify that a finite time convergence time-varying sliding mode attitude control method of this embodiment can keep the state of the system on the sliding mode surface from the beginning, and overcome the control caused by the discontinuity of the first derivative of the time-varying term The phenomenon of volume jumps enhances the robustness of the system.
[0183] Figure 5 The deflection curve of the rudder surface using the finite time convergence time-varying sliding mode attitude control method of this embodiment when there is external disturbance and parameter perturbation is given. Image 6 The sliding mode surface curve diagram of a finite time convergence time-varying sliding mode attitude control method of this embodiment is given when there is external disturbance and parameter perturbation. by Figure 5 , 6 It can be seen that the system state of this embodiment is maintained on the sliding surface from the beginning, and the control quantity does not jump. Picture 10 The deflection curve of the rudder surface using the traditional time-varying sliding mode aircraft attitude control method and the boundary layer debounce technology when there is external disturbance and parameter perturbation is given. Picture 11 In the presence of external disturbances and parameter perturbations, a sliding mode surface curve using traditional time-varying sliding mode aircraft attitude control method and using boundary layer debounce technology is given. by Picture 10 , 11 It can be seen that using the traditional time-varying sliding mode control method, the system state can be maintained on the sliding mode surface from the initial moment, however, jump phenomenon occurs when the rudder surface deflection is 2s. This shows that this embodiment can avoid the jump phenomenon caused by the discontinuity of the first derivative of the time-varying term while maintaining the advantages of the traditional time-varying sliding mode control, thereby enhancing the robustness of the system.
