CN106802660A - One kind is combined strong anti-interference attitude control method - Google Patents

Abstract

One kind be combined strong anti-interference attitude control method, the method be based on non-singular terminal sliding formwork, Backstepping and observer, can realize flexibility aerocraft system quickly, high-precision attitude tracing control, while having strong interference rejection ability.Using Active Disturbance Rejection Control to quick, the accurate estimated capacity for disturbing, with reference to Reverse Step Control technology and the strong robustness and rapidity of non-singular terminal sliding formwork, high performance aircraft Attitude tracking control is realized.

Description

One kind is combined strong anti-interference attitude control method

Technical field

Strong anti-interference attitude control method is combined the present invention relates to one kind, belongs to aircraft manufacturing technology field.

Background technology

Contemporary aircraft complex structure, increasingly diversified mission requirements are to flying vehicles control performance (stability, anti-interference Property, rapidity etc.) propose requirement higher.Meanwhile, with every new technology, the continuous exploration of new method, flying vehicles control Development face many opportunities and challenges.Carrying out aircraft relation technological researching has highly important learning value, strategy meaning Justice and application prospect.How to research and develop advanced aircraft manufacturing technology technology is flying vehicles control technical foundation problem and crucial skill One of art.

Sliding mode variable structure control is the special non-linear discontinuous control method of a class.This control method is controlled with other Difference be the structure of system in dynamic process, can purposefully be changed according to the current state of system so that system is according to pre- Determine the state trajectory operation of sliding mode.Because sliding mode can be designed and unrelated with model parameter and disturbance so that Variable-structure control has the advantages that reaction speed is fast, insensitive to Parameters variation, simple to the insensitive, physics realization of disturbance, mesh Before, Sliding mode variable structure control is used widely in flying vehicles control field and SERVO CONTROL field.Backstepping has stability The good, advantage of fast convergence rate, it is allowed to retain that controlled device is non-linear or high-order feature, can process a quasi-nonlinear, not true Qualitatively influence, its concern in the application extremely researcher of aviation field.Auto Disturbances Rejection Control Technique is seen using expansion state After all of unknown outer nonlinear uncertain object Based on Nonlinear State Feedback disturbed is turned to integration tandem type by survey device, state is used Error is fed back to design preferable controller, and the inherent shortcoming of classical PID is fundamentally overcome using nonlinear organization.Together When and do not need disturbing effect outside direct measurement, it is not required that know the action rule of disturbance in advance, control can be effectively improved smart Degree.

The content of the invention

Technology solve problem of the invention is：The deficiencies in the prior art are overcome, with the attitude control system of flexible aircraft It is background, there is provided a kind of flexible attitude of flight vehicle tracing control based on non-singular terminal sliding formwork, backstepping and observer Method, realizes flexible aircraft rapid posture tracing control, and with high accuracy, strong interference rejection ability at utmost meets flexible Attitude of flight vehicle track demand.

Technical solution of the invention is：

One kind is combined strong anti-interference attitude control method, and step is as follows：

(1) flexible aerocraft system model is set up；

(2) the described flexible aerocraft system model obtained using step (1), flexible aircraft fortune is set up based on quaternary number It is dynamic to learn error equation and dynamics error equation；

(3) the flexible aerocraft system model that is obtained according to step (1), (2), flexible aircraft kinematic error equation and Dynamics error equation, based on Backstepping, determines virtual controlling amount；

(4) the flexible aircraft kinematic error equation and dynamics error equation in step (2), when setting up limited Between non-singular terminal sliding-mode surface；

(5) the flexible aerocraft system model that is obtained according to step (1), (2), flexible aircraft kinematic error equation and Dynamics error equation, total indeterminate is separated from model, determines extended state observer, estimates total indeterminate；

(6) controller based on sliding formwork and extended state observer is determined, so as to realize being combined strong anti-interference gesture stability.

Compared with the prior art, the invention has the advantages that：

(1) in flexible vibration mode, uncertain rotary inertia, external disturbance and actuator saturation influence aircraft situation Under, realize that aircraft is quick, high-precision attitude tracing control, while having strong interference rejection ability.

(2) quick, the accurate estimated capacity of Active Disturbance Rejection Control is given full play to, in conjunction with Reverse Step Control technology and nonsingular end The strong robustness and rapidity of sliding formwork are held, high performance aircraft Attitude tracking control is realized.

Brief description of the drawings

Fig. 1 is control system flow chart of the present invention based on sliding formwork and observer；

Fig. 2 is the attitude quaternion tracking error and angular speed tracking error of PID controller of the present invention；

Fig. 3 is the attitude quaternion tracking error and angular speed tracking error that the present invention is combined strong anti-interference attitude controller；

Fig. 4 is the input torque of PID controller of the present invention；

Fig. 5 is the input torque that the present invention is combined strong anti-interference attitude controller；

Fig. 6 is the simulation result of sliding-mode surface of the present invention；

Fig. 7 is estimation of the extended state observer of the present invention to disturbing；

Fig. 8 is flexible mode frequency decay curve of the present invention.

Fig. 9 is two times attitude quaternion tracking errors of situation of the present invention and angular speed tracking error；

Figure 10 is estimation of the two times extended state observers of situation of the present invention to disturbing.

Specific embodiment

Specific embodiment of the invention is further described in detail below in conjunction with the accompanying drawings.As shown in figure 1, this hair The a kind of of bright proposition is combined comprising the following steps that for strong anti-interference attitude control method：

(1) influence of the factors such as aircraft flexible nature, rotary inertia uncertain, external disturbance, actuator saturation is considered, Set up such as lower flexible aerocraft system model：

Wherein：d∈R³It is external disturbance, δ ∈ R^4×3It is rigid body and the coupling moment of flexible appendage Battle array, δ^TIt is the transposition of δ, η is flexible mode,WithThe respectively first derivative of η and second dervative；J₀∈R^3×3It is known mark Claim inertia matrix, and be positive definite matrix；Δ J is the uncertain part in inertia matrix, Ω=[Ω₁,Ω₂,Ω₃]^TIt is aircraft Angular velocity component in body coordinate system,It is the first derivative of Ω；× it is oeprator, will × it is used for vector b=[b₁, b₂,b₃]^TIt is available：

L=diag { 2 ζ_iω_ni, i=1,2 ..., N } andRespectively damping matrix and Stiffness matrix, N is rank number of mode, ω_ni, i=1,2 ..., N are vibration modal frequency matrix, ζ_i, i=1,2 ..., N is vibration Damping ratios；

U=[u₁,u₂,u₃]^TIt is the controller based on sliding formwork and extended state observer, sat (u)=[sat (u₁),sat (u₂),sat(u₃)]^TIt is the actual dominant vector of actuator generation, sat (u_i), i=1,2,3 represents the non-linear full of actuator With characteristic and meet sat (u_i)=sign (u_i)·min{u_mi,|u_i|, i=1,2,3, | | expression takes absolute value, sat (u_i) It is expressed as sat (u_i)=θ_oi+u_i, i=1, wherein 2,3, θ_oi, i=1,2,3 is：

u_mi, i=1,2,3 is actuator saturation value, is θ beyond actuator saturation value part_o=[θ_o1,θ_o2,θ_o3]^T, and it is full Foot | | θ_o||≤l_δθ, l_δθIt is arithmetic number.

(2) model obtained using step (1), flexible aircraft kinematic error equation and power are set up based on quaternary number Learn error equation：

Flexible aircraft kinematic error equation：

Wherein:(e_v,e₄)∈R³× R, e_v=[e₁,e₂,e₃]^TIt is current flight device attitude and the error quaternary for expecting attitude Number vector section, e₄It is scalar component, and meets WithIt is respectively e_v、e₄First derivative；(q_v, q₄)∈R³× R, q_v=[q₁,q₂,q₃]^TIt is the unit quaternion vector section for describing attitude of flight vehicle, q₄It is scalar component, and it is full Footq_dv=[q_d1,q_d2,q_d3]^TIt is the unit quaternion of description expectation attitude Vector section, q_d4It is scalar component, and meetsΩ_e=Ω-C Ω_d=[Ω_e1Ω_e2Ω_e3]^TIt is The angular speed error vector set up between body coordinate system and target-based coordinate system, Ω_d∈R³It is to expect angular velocity vector,It is transition matrix, and meets | | C | |=1, It is that the single order of C is led Number, I₃It is 3 × 3 unit matrixs；

Flexible vehicle dynamics error equation is：

Wherein,It is Ω_eFirst derivative, Ω_dIt is to expect angular speed,It is Ω_dFirst derivative.

(3) the flexible aerocraft system model that is obtained according to step (1), (2), flexible aircraft kinematic error equation and Dynamics error equation, based on Backstepping, determines virtual controlling amount α, specially：

α=- K₁e_v-K₂S_c (6)

Wherein, K_j=diag { k_ji}>0, i=1,2,3, j=1,2, diag (a₁,a₂,…,a_n) represent that diagonal entry is a₁,a₂,…,a_nDiagonal matrix；

Define S_c={ S_c1,S_c2,S_c3}^TIt is as follows:

WhereinP, q are positive odd numbers, and 0<q/p<1, l_1i、l_2i, i=1,2,3 are Parameter；∈_i, i=1,2,3, ι₁、ι₂It is design parameter, sign (a) is sign function, is defined as follows：

(4) the flexible aircraft kinematic error equation and dynamics error equation in step (2), when setting up limited Between non-singular terminal sliding-mode surface, specially S=[S₁ S₂ S₃]^T, wherein:

S_i=Ω_e+K₁e_v+K₂S_c, i=1,2,3 (8)

(5) the flexible aerocraft system model that is obtained according to step (1), (2), flexible aircraft kinematic error equation and Dynamics error equation, total indeterminate is separated from model, determines extended state observer, determines that expansion state is observed Device, specially：

Wherein, Z₁It is state error, F=[F₁,F₂,F₃]^T=-Ω^×J₀Ω+J₀E_Ω, E_Ω=(L₁+L₂E_q) Q (e) Ω,L₁、L₂It is arithmetic number, defines E_q：

fal(Z₁,β₁, γ) and=[fal₁(Z₁,β₁,γ),fal₂(Z₁,β₁,γ),fal₃(Z₁,β₁,γ)]^T (11)

X₁And X₂It is the output of extended state observer, S is system mode, X₁Tracking system state S, X₂Tracking system Expansion state G_δ, G_δIt is the internal disturbance of estimating system and total indeterminate of external disturbance, F is known models, and Ω is angle speed Degree, ρ₁、ρ₂It is the observing capacity coefficient of observer, Z₁It is state error, u is the control based on sliding formwork and extended state observer Device, Z_1iIt is vector Z₁I-th element, p, q are positive odd number, γ, α, β₁It is design parameter, | | expression takes absolute value；Pass through Choose appropriate ρ₁、ρ₂, γ and β₁, extended state observer output X₁And X₂S and G can be respectively traced into finite time_δ。

(6) the finite time non-singular terminal sliding-mode surface and extended state observer in step (4), (5), set up base In sliding formwork and the controller u of extended state observer, specially：

Wherein,

Controller can be considered tendency rate (J₀(-τS-σsign^r(S))), model known quantity (- J₀F), Unknown Model estimator (-J₀X₂) combination；Wherein tendency rate (J₀(-τS-σsign^r(S) controller Fast Convergent)) is realized；Model known quantity (- J₀F) Controller design is directly participated in, observer estimated pressure is reduced；For Unknown Model estimator (- J₀X₂), carried out using observer Accurately estimate and compensate, thus can different disturbances be produced with suppression, so as to keep system stabilization.

Embodiment：

In order to verify the attitude of flight vehicle tracking control unit based on observer technology and sliding formwork control technology of above-mentioned design Validity, robustness of the controller in terms of attitude of flight vehicle tracing control is demonstrated by the emulation under different condition.

Consider flexible aircraft kinematic error equation and dynamics error equation, nominal inertia matrix is

Uncertain part in inertia matrix is：

Δ J=diag (50,30,20) kgm²；

External disturbance d ∈ R³It is the function of time t, is represented by d (t), is specifically taken as：

Situation one：D (t)=0.5 [sin (t), sin (2t), sin (3t)]^T；

Situation two：D (t)=[200*sin (0.1t), 220*sin (0.2t), 300*sin (0.3t)]^T；

The quaternary number initial value of attitude of flight vehicle is q=[0.3, -0.2, -0.3,0.8832]^TIt is Ω with initial angular velocity =[0,0,0]^T, with the validity of numerical simulation access control algorithm, it is assumed that expect that attitude quaternion initial value is q_d=[0,0,0, 1]^T, expect that angular speed is the function of time t, it is represented by Ω_dT (), is specifically taken as：

Ω_d(t)=0.05 [sin (π t/100), sin (2 π t/100), sin (3 π t/100)]^T；

Have that inertia matrix is uncertain and external disturbance in the case of, Fig. 2 is tracked for the attitude quaternion of PID controller Error and angular speed tracking error；Fig. 3 be combined strong anti-interference attitude controller attitude quaternion tracking error and angular speed with Track error；Fig. 4 is the input torque of PID controller；Fig. 5 is the input torque for being combined strong anti-interference attitude controller；Can by table 1 See, compared with PID control, the controller based on sliding formwork and extended state observer proposed by the present invention more can guarantee that aircraft system System track being capable of quickly and accurately track reference attitude.

Table 1 is combined the comparative result of strong anti-interference attitude controller and PID control

Controller	Quaternary number	Angular speed
			It is combined strong anti-interference attitude controller	±9.54e-6	±2.17e-5
PID controller	±9.02e-3	±3.92e-3
			Raising ratio, %	99.8	99.4

Fig. 6 gives the simulation result of sliding-mode surface, based on parameter μ=15I₃,β₁=0.50, K₁=2I₃, K₂ =I₃Sliding-mode surface can be quickly reached with the system trajectory of q/p=0.9, extended state observer enters to uncertain and external disturbance Accurate estimation is gone, so as to effectively inhibit the chattering phenomenon that sliding formwork control is brought, Fig. 7 illustrates extended state observer to total Disturbance G_δi, the estimation performance of i=1,2,3；By choosing suitable parameter ρ₁=4.5, ρ₂=8.5 and γ=1, observer output Each component X₂I (), i=1,2,3 can effectively track each component G of disturbance_δi, i=1,2,3, it demonstrates expansion state observation Utensil has good observation performance, so that controller has Fast Convergent, high precision tracking ability.

Fig. 8 represents attitude quaternion tracking error and angular speed tracking error in disturbance situation two, and Fig. 9 and Figure 10 are represented Estimation performance of the extended state observer to total disturbance, it is seen that also be can guarantee that in the case of the sliding mode controller large disturbances of design good Convergence rate and precision, with strong interference rejection ability.It is special that the content not being described in detail in description of the invention belongs to this area The known technology of industry technical staff.

Claims (7)

1. it is a kind of to be combined strong anti-interference attitude control method, it is characterised in that step is as follows：

(1) flexible aerocraft system model is set up；

(2) the described flexible aerocraft system model obtained using step (1), flexible aircraft kinematics is set up based on quaternary number Error equation and dynamics error equation；

(3) flexible aerocraft system model, flexible aircraft kinematic error equation and the power obtained according to step (1), (2) Error equation is learned, based on Backstepping, virtual controlling amount is determined；

(4) the flexible aircraft kinematic error equation and dynamics error equation in step (2), set up finite time non- Unusual terminal sliding mode face；

(5) flexible aerocraft system model, flexible aircraft kinematic error equation and the power obtained according to step (1), (2) Error equation is learned, total indeterminate is separated from model, determine extended state observer, estimate total indeterminate；

(6) controller based on sliding formwork and extended state observer is determined, so as to realize being combined strong anti-interference gesture stability.

2. one kind according to claim 1 is combined strong anti-interference attitude control method, it is characterised in that：Flexible aerocraft system Model, specially：

$\begin{array}{c}(J_0+\mathrm{\&Delta;}J)\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=-{\mathrm{\&Omega;}}^{\&times;}(J_0+\mathrm{\&Delta;}J)\mathrm{\&Omega;}+sat\left(u\right)+\tilde{d}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}+L\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+K\mathrm{\&eta;}+\mathrm{\&delta;}\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=0\end{array};$

Wherein：d∈R³It is external disturbance, δ ∈ R^4×3It is rigid body and the coupling matrix of flexible appendage, δ^T It is the transposition of δ, η is flexible mode,WithThe respectively first derivative of η and second dervative；J₀∈R^3×3Nominally it is used to for known Moment matrix, and be positive definite matrix；Δ J is the uncertain part in inertia matrix, Ω=[Ω₁,Ω₂,Ω₃]^TIt is aircraft at this Angular velocity component in body coordinate system,It is the first derivative of Ω；× it is oeprator, will × it is used for vector b=[b₁,b₂,b₃ ]^TIt is available：

$b^{\&times;}=\left[\begin{array}{ccc}0& -b_3& b_2\\ b_3& 0& -b_1\\ -b_2& b_1& 0\end{array}\right];$

L=diag { 2 ζ_iω_ni, i=1,2 ..., N } andRespectively damping matrix and rigidity Matrix, N is rank number of mode, ω_ni, i=1,2 ..., N are vibration modal frequency matrix, ζ_i, i=1,2 ..., N is mode of oscillation Damping ratio；

U=[u₁,u₂,u₃]^TIt is the controller based on sliding formwork and extended state observer, sat (u)=[sat (u₁),sat(u₂), sat(u₃)]^TIt is the actual dominant vector of actuator generation, sat (u_i), i=1,2,3 represents the non-linear saturated characteristic of actuator And meet sat (u_i)=sign (u_i)·min{u_mi,|u_i|, i=1,2,3, sat (u_i) it is expressed as sat (u_i)=θ_oi+u_i, i= 1,2,3, wherein θ_oi, i=1,2,3 is：

u_mi, i=1,2,3 is actuator saturation value, is θ beyond actuator saturation value part_o=[θ_o1,θ_o2,θ_o3]^T, and meet | | θ_o||≤l_δθ, l_δθIt is arithmetic number.

3. one kind according to claim 2 is combined strong anti-interference attitude control method, it is characterised in that：Flexible aircraft motion Error equation and dynamics error equation are learned, specially：

Flexible aircraft kinematic error equation：

$\begin{array}{cc}{e}_v=q_{d4}{q}_v-q_{dv}^{\&times;}{q}_v-q_4{q}_{dv}& e_4=q_{dv}^T{q}_v+q_4{q}_{d4}\end{array};$

$\begin{array}{cc}{\stackrel{\&CenterDot;}{e}}_v=\frac{1}{2}(q_4{I}_3+q_v^{\&times;}){\mathrm{\&Omega;}}_e& {\stackrel{\&CenterDot;}{e}}_4=-\frac{1}{2}{q}_v^T{\mathrm{\&Omega;}}_e\end{array};$

Wherein:(e_v,e₄)∈R³× R, e_v=[e₁,e₂,e₃]^TIt is current flight device attitude and the error quaternion arrow for expecting attitude Amount part, e₄It is scalar component, and meets WithIt is respectively e_v、e₄First derivative；(q_v,q₄)∈ R³× R, q_v=[q₁,q₂,q₃]^TIt is the unit quaternion vector section for describing attitude of flight vehicle, q₄It is scalar component, and meetsq_dv=[q_d1,q_d2,q_d3]^TIt is that description expects that the unit quaternion of attitude is sweared Amount part, q_d4It is scalar component, and meetsΩ_e=Ω-C Ω_d=[Ω_e1Ω_e2Ω_e3]^TIt is to build Stand in the angular speed error vector between body coordinate system and target-based coordinate system, Ω_d∈R³It is to expect angular velocity vector,It is transition matrix, and meets | | C | |=1, It is that the single order of C is led Number, I₃It is 3 × 3 unit matrixs；

Flexible vehicle dynamics error equation is：

$\begin{array}{c}(J_0+\mathrm{\&Delta;}J){\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_e=-{({\mathrm{\&Omega;}}_e+{\mathrm{C\&Omega;}}_d)}^{\&times;}(J_0+\mathrm{\&Delta;}J)({\mathrm{\&Omega;}}_e+{\mathrm{C\&Omega;}}_d)\\ +(J_0+\mathrm{\&Delta;}J)({\mathrm{\&Omega;}}_e^{\&times;}{\mathrm{C\&Omega;}}_d-C{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_d)+sat\left(u\right)+\tilde{d}\end{array};$

Wherein,It is Ω_eFirst derivative, Ω_dIt is to expect angular speed,It is Ω_dFirst derivative.

4. one kind according to claim 3 is combined strong anti-interference attitude control method, it is characterised in that：Virtual controlling amount α has Body is：

α=- K₁e_v-K₂S_c；

Wherein, K_j=diag { k_ji}>0, i=1,2,3, j=1,2, diag (a₁,a₂,…,a_n) expression diagonal entry be a₁, a₂,…,a_nDiagonal matrix；

Define S_c={ S_c1,S_c2,S_c3}^TIt is as follows:

WhereinP, q are positive odd numbers, and 0<q/p<1, l_1i、l_2i, i=1,2,3 is parameter； ∈_i, i=1,2,3, ι₁、ι₂It is design parameter, sign (a) is sign function, is defined as follows：

$sign\left(a\right)=\left\{\begin{array}{cc}1& a>0\\ 0& a=0\\ -1& a<0\end{array}\right..$

5. one kind according to claim 4 is combined strong anti-interference attitude control method, it is characterised in that：Finite time is nonsingular Terminal sliding mode face is：S=[S₁S₂S₃]^T, wherein:

S_i=Ω_e+K₁e_v+K₂S_c, i=1,2,3.

6. one kind according to claim 5 is combined strong anti-interference attitude control method, it is characterised in that：Extended state observer Specially：

Z₁=X₁-S

${\stackrel{\&CenterDot;}{X}}_1=X_2+F-\frac{1}{2}{e}_v-{\mathrm{\&rho;}}_1{Z}_1+J_0^{-1}u;$

X₂=-ρ₂fal(Z₁,β₁,γ)

Wherein, Z₁It is state error, F=[F₁,F₂,F₃]^T=-Ω^×J₀Ω+J₀E_Ω, E_Ω=(L₁+L₂E_q) Q (e) Ω,L₁、L₂It is arithmetic number, defines E_q：

fal(Z₁,β₁, γ) and=[fal₁(Z₁,β₁,γ),fal₂(Z₁,β₁,γ),fal₃(Z₁,β₁,γ)]^T；

X₁And X₂It is the output of extended state observer, S is system mode, X₁Tracking system state S, X₂The expansion shape of tracking system State G_δ, G_δIt is the internal disturbance of estimating system and total indeterminate of external disturbance, F is known models, and Ω is angular speed, ρ₁、ρ₂ It is the observing capacity coefficient of observer, Z₁It is state error, u is the controller based on sliding formwork and extended state observer, Z_1iIt is Vector Z₁I-th element, p, q are positive odd number, γ, α, β₁It is design parameter.

7. one kind according to claim 6 is combined strong anti-interference attitude control method, it is characterised in that：Based on sliding formwork and expansion The controller u of state observer, specially：

Wherein,