CN106843254A - One kind actively reconstructs fault tolerant control method in real time - Google Patents

Abstract

A kind of actively to reconstruct fault tolerant control method in real time, the method is based on sliding formwork control, finite-time control technology and Chebyshev neural network, can meet real-time active tolerant control of the flexible aerocraft system when actuator failure and saturation.Introducing only needs to the Chebyshev neural network of desired signal and always disturbs estimating the system comprising failure and saturation, design nominal control law and compensation control law, the influence that compensation failure and saturation are caused, weakens the intrinsic buffeting of sliding mode system, improves the precision of posture tracing system.

Description

One kind actively reconstructs fault tolerant control method in real time

Technical field

Fault tolerant control method is actively reconstructed in real time the present invention relates to one kind, belongs to aircraft manufacturing technology field.

Background technology

With the continuous expansion continued to develop with application field of science and technology, the structure and task of all kinds of aircraft are increasingly Complicated and huge, flight environment of vehicle is badly changeable, and its reliability has become the major issue in Design of Flight Control.Pass through The requirement of aircraft minimum safe is realized in the reconstruct of control system or restructuring, this for ensure aircraft smoothly complete task or Avoid crashing significant.How to research and develop has compared with the flight control system of strong fault tolerance ability to meet high reliability request With important learning value and application prospect.

Fault Tolerance Control Technology is a kind of significant change for adapting to environment, may be allowed to one or more portions in control system The control system of part failure.The guiding theory of faults-tolerant control is that a control system once breaks down, and system can still be tieed up Hold its own and operate in safe condition, and certain performance indications are met under conditions permit.Sliding mode variable structure control is a kind of Special non-linear discontinuous control method, this control method structure for being system different from other controls is in dynamic process In, can be according to the current state of system so that system is run according to the state trajectory of predetermined sliding mode.Its design and model ginseng Number and disturb unrelated so that variable-structure control have reaction speed it is fast, insensitive to Parameters variation, to disturbance insensitive, physics The advantages of realizing simple.Chebyshev neural network with arbitrary accuracy Nonlinear Function Approximation, and can have under certain condition Stronger self study, self adaptation and self organization ability.Chebyshev neural network is combined with Sliding mode variable structure control, to mould Type uncertainty and non-linear partial estimation compensation, can eliminate the buffeting problem of sliding formwork control to a certain extent.Finite time Control method is a kind of nonlinear control method, is time optimal control method, compared with asymptotically stable system, when limited Between stabilization system exist external disturbance and it is internal it is uncertain in the case of not only there is faster convergence rate, also more preferably Robustness and interference rejection ability.

The content of the invention

Technology solve problem of the invention is：The deficiencies in the prior art are overcome, with the active tolerant control of flexible aircraft It is background, proposes a kind of aircraft reality based on sliding formwork control technology, finite-time control technology and Chebyshev neural network When actively reconstruct fault tolerant control method.Flexible aircraft real-time fault tolerance control is realized, multiplying property or additivity event occurs in actuator Under barrier, attitude of flight vehicle tracing control demand is at utmost met.

Technical solution of the invention is：

One kind actively reconstructs fault tolerant control method in real time, 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 aircraft kinematic error equation and dynamics error equation in step (2), when setting up limited Between non-singular terminal sliding-mode surface；

(4) according to the finite time non-singular terminal sliding-mode surface set up in Chebyshev neural network and step (3), really Calibration claims control law u_nWith compensation control law u_a, so as to obtain it is complete actively reconstruct fault-tolerant controller, and then realize real-time master Dynamic reconstruct faults-tolerant control.

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

1st, control method of the present invention can realize that flexible aircraft actively reconstructs faults-tolerant control in real time.

2nd, non-strange fast terminal sliding formwork control is applied to flexible attitude of flight vehicle tracing control neck by control method of the present invention Domain, makes system fast and stable and avoid singular problem in finite time

3rd, with sliding formwork control be combined neutral net by control method of the present invention, and proposition basic function only relies upon expectation letter Number Chebyshev neural network carry out the unknown total disturbance of efficiently approximation system.

Brief description of the drawings

Fig. 1 actively reconstructs fault-tolerant controller structured flowchart for the present invention；

Fig. 2 actively reconstructs faults-tolerant control attitude error and angular speed error for the present invention；

Fig. 3 is PID control attitude error of the present invention and angular speed error；

Fig. 4 is attitude angle of the present invention and angular speed curve；

Fig. 5 is sliding-mode surface of the present invention and control moment curve；

Fig. 6 is the curve of output of Chebyshev neural network pilot controller of the present invention；

Fig. 7 is flexible mode frequency decay curve of the present invention.

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 bright one kind that proposes actively reconstructs fault tolerant control method in real time, comprises the following steps that：

(1) factors such as uncertain aircraft flexible nature, rotary inertia, external disturbance, actuator failures and saturation are considered Influence, 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 actively to reconstruct fault-tolerant controller, sat (u)=[sat (u₁),sat(u₂),sat(u₃)]^TIt is The actual dominant vector that actuator is produced, sat (u_i), i=1,2,3 represents the non-linear saturated characteristic of actuator and meets 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, its Middle 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 Sufficient ‖ θ_o‖≤l_δθ, l_δθIt is arithmetic number, G_δ=[G_δ1,G_δ2,G_δ3]^TIt is that additivity failure, i.e. failure influence system and expire with additive way Sufficient ‖ G_δ‖≤l_δf, l_δfIt is arithmetic number；D=diag { δ_o1,δ_o2,δ_o3It is actuator efficiency index value and satisfaction 0<ε_τi≤δ_oi≤1, I=1,2,3；0<ε_τi≤ 1, i=1,2,3 represent the minimum executive capability of actuator, δ_oi=1, i=1,2,3 represent i-th execution Device is working properly；0<ε_τi≤δ_oi≤ 1, i=1,2,3 represent i-th actuator partial failure, but the actuator remains to provide Part executive capability.

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

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 meetsWithIt 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 meetq_dv=[q_d1,q_d2,q_d3]^TIt is the unit four of description expectation attitude First number vector section, q_d4It is scalar component, and meetsΩ_e=Ω-C Ω_d=[Ω_e1Ω_e2Ω_e3 ]^TIt is built upon 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 the first derivative of C, 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；

Flexible vehicle dynamics error equation is rewritten as：

Wherein：F determines part for model, and R is unknown total disturbance；

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

S=Ω_e+K₁e_v+K₂S_c (9)

Wherein S=[S₁,S₂,S₃]^T∈R³, K_j=diag { k_ji}>0, i=1,2,3, j=1,2, diag (a₁,a₂,…,a_n) Expression diagonal entry is a₁,a₂,…,a_nDiagonal matrix；And define S_c=[S_c1,S_c2,S_c3]^TIt is as follows：

Whereinr₁,r₂It is positive odd number, and 0<r<1, l_1i、l_2i, i=1, 2,3 is parameter；ε_i, i=1,2,3, ι₁、ι₂It is design parameter, sign (a) is sign function, is defined as follows：

Based on finite time non-singular terminal sliding-mode surface, such as shown in formula (9), suitable parameter is designed, work as satisfactionWhen, control targe { e is capable of achieving in finite time_v≡0,e₄≡1,Ω_e≡0}。

(4) according to the finite time non-singular terminal sliding-mode surface set up in Chebyshev neural network and step (3), really Calibration claims control law u_nWith compensation control law u_a, so as to obtain it is complete actively reconstruct fault-tolerant controller, it is specific as follows：

U=u_n+u_a (11)

u_n=[u_n1,u_n2,u_n3]^T=-ρ S- β sig^λ(S)-F (12)

Wherein, ρ=diag (ρ₁,ρ₂,ρ₃),ρ_i>0, i=1,2,3, β=diag (β₁,β₂,β₃), β_i>0, i=1,2,3；sig^λ(S)=[| S₁|^λsign(S₁),|S₂|^λsign(S₂),|S₃|^λsign(S₃)]^T, F determines part for model, and λ ∈ (0,1) are designs Parameter；

M weight matrixs, μ=μ (X)=(1, T₁(x₁),...,T_n(x₁),...,T_n(x_m))^T, wherein T_i(x_j), i= 1 ..., n, j=1 ..., m represent Chebyshev polynomials, m is the input number of Chebyshev neural network, and n is Qie Bixue The polynomial exponent number of husband；It is robust control, the convergence error for compensating Chebyshev neural network is defined as follows：

Wherein i=1,2,3, χ₁For positive normal real number and meet χ₁≥ε_M, ε_MIt is convergence upper error, κ is positive scalar； Tanh () is hyperbolic tangent function.For middle weight matrix M, using following ADAPTIVE CONTROL：

In formulaIt is normal number.Compensation control law u_aBy Chebyshev neural network control item M μ And robust controlTwo parts are constituted.Wherein Chebyshev neural network control item M μ are used to total disturbance of approximation system, And robust controlThen it is used to compensate the approximate error of Chebyshev neural network.Nonlinear feedback-ρ S- β sig^λ(S) it is used to Realize attitude of flight vehicle state variable incoming terminal sliding mode in finite time.

Embodiment：

Be checking flexible attitude of flight vehicle Adjusted Option proposed by the present invention reasonability and design controller to not It is determined that, disturbance the problems such as validity, numerical simulation is carried out under present Matlab environment to it, nominal rotational 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：

D (t)=[10*sin (0.1t), 15*sin (0.2t), 20*sin (0.2t)]^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, 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；

Actuator failures parameter D and G_δIt is the function of time t, respectively：

D=diag (δ_o1(t),δ_o2(t),δ_o3(t))

G=diag (G_δ1(t),G_δ2(t),G_δ3(t))

Flexible appendage parameter：

ω_n=(1.0973 1.2761 1.6538 2.2893)；

η=(0.01242 0.01584-0.01749 0.01125)；

ζ_n=(0.05 0.06 0.08 0.025)；

Specific controller parameter is as follows：

The input of Chebyshev neural network isIt isFirst derivative.

The comparative result of this patent control method of table 1 and PID control

Fig. 2 gives attitude quaternion error with attitude angular velocity error in Finite-time convergence characteristic；Fig. 3 gives PID control attitude error and angular speed error under equal conditions；Fig. 4 is the attitude and angular speed variation characteristic of aircraft；Fig. 5 is Sliding-mode surface and control moment curve；Fig. 6 is the curve of output of Chebyshev neural network pilot controller；Fig. 7 is flexible mode Frequency decay curve.From simulation result it can be seen that：With reference to the nonsingular fast terminal sliding formwork control of Chebyshev neural network System chatter phenomenon is almost cancelled completely, and angular speed error is strictly controlled at 5 × 10^-3.Interior, precision has reached expected wanting Ask.Compared with PID control, the controller performance of present invention design is more superior, illustrates that Chebyshev neural network can be effective Ground approximation system is always disturbed, so as to suppress interference, improves control accuracy.

Claims (6)

1. one kind actively reconstructs fault tolerant control method in real time, 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) the flexible aircraft kinematic error equation and dynamics error equation in step (2), set up finite time non- Unusual terminal sliding mode face；

(4) according to the finite time non-singular terminal sliding-mode surface set up in Chebyshev neural network and step (3), it is determined that mark Claim control law u_nWith compensation control law u_a, so as to obtain it is complete actively reconstruct fault-tolerant controller, and then realize actively weight in real time Structure faults-tolerant control.

2. one kind according to claim 1 actively reconstructs fault tolerant control method in real time, it is characterised in that：It is described to set up flexible Aerocraft system model, specially：

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

Wherein：d∈R³It is external disturbance, δ ∈ R^3×3It 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 ]^TObtain：

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

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 actively to reconstruct fault-tolerant controller, sat (u)=[sat (u₁),sat(u₂),sat(u₃)]^TIt is to perform The actual dominant vector that device is produced, sat (u_i), i=1,2,3 represents the non-linear saturated characteristic of actuator and meets 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, wherein 2,3, θ_oiFor：

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, G_δ=[G_δ1,G_δ2,G_δ3]^TIt is that additivity failure, i.e. failure influence system and meet ‖ with additive way G_δ‖≤l_δf, l_δfIt is arithmetic number；D=diag { δ_o1,δ_o2,δ_o3It is actuator efficiency index value and satisfaction 0<ε_τi≤δ_oi≤ 1, i= 1,2,3；0<ε_τi≤ 1, i=1,2,3 represent the minimum executive capability of actuator, δ_oi=1, i=1,2,3 represent i-th actuator work Make normal；0<ε_τi≤δ_oi≤ 1, i=1,2,3 represent i-th actuator partial failure, but the actuator remains to provide part Executive capability.

3. one kind according to claim 2 actively reconstructs fault tolerant control method in real time, it is characterised in that：Set up flexible flight Device kinematic error equation and dynamics error equation are 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 the first derivative of C, I₃ It is 3 × 3 unit matrixs；

Flexible vehicle dynamics error equation is：

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

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

Flexible vehicle dynamics error equation is rewritten as：

${\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_e=F+J_0^{-1}u+R;$

Wherein：F determines part for model, and R is unknown total disturbance；

$F={J_0}^{-1}(-{\mathrm{\&Omega;}}^{\&times;}{J}_0\mathrm{\&Omega;})+({\mathrm{\&Omega;}}_e^{\&times;}{\mathrm{C\&Omega;}}_d-C{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_d);$

$R={J_0}^{-1}(-{\mathrm{\&Omega;}}^{\&times;}\mathrm{\&Delta;}J\mathrm{\&Omega;})+\mathrm{\&Delta;}J(-{\mathrm{\&Omega;}}^{\&times;}\mathrm{\&Delta;}J\mathrm{\&Omega;}+Dsat(u\left)\right)+G_{\mathrm{\&delta;}}+{(J_0+\mathrm{\&Delta;}J)}^{-1}\tilde{d}.$

4. one kind according to claim 3 actively reconstructs fault tolerant control method in real time, it is characterised in that：Finite time is non-strange Different terminal sliding mode face S, specially：

S=Ω_e+K₁e_v+K₂S_c；

Wherein S=[S₁,S₂,S₃]^T∈R³, K_j=diag { k_ji}>0, i=1,2,3, j=1,2, diag (a₁,a₂,…,a_n) represent Diagonal entry is a₁,a₂,…,a_nDiagonal matrix；And define S_c=[S_c1,S_c2,S_c3]^TIt is as follows：

Whereinr₁,r₂It is positive odd number, and 0<r<1, l_1i、l_2i, i=1,2,3 are Parameter；ε_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 actively reconstructs fault tolerant control method in real time, it is characterised in that：Nominal control law u_n With compensation control law u_a, specially：

U=u_n+u_a；

u_n=[u_n1,u_n2,u_n3]^T=-ρ S- β sig^λ(S)-F；

Wherein, ρ=diag (ρ₁,ρ₂,ρ₃),ρ_i>0, i=1,2,3, β=diag (β₁,β₂,β₃), β_i>0, i=1,2,3；sig^λ(S) =[| S₁|^λsign(S₁),|S₂|^λsign(S₂),|S₃|^λsign(S₃)]^T, F determines part for model, and λ ∈ (0,1) are design ginsengs Number；

M weight matrixs, μ=μ (X)=(1, T₁(x₁),...,T_n(x₁),...,T_n(x_m))^T, wherein

T_i(x_j), i=1 ..., n, j=1 ..., m represent Chebyshev polynomials, and m is the input of Chebyshev neural network Number, n is the exponent number of Chebyshev polynomials；It is robust control, the convergence for compensating Chebyshev neural network is missed Difference, is defined as follows：

$\mathrm{\&theta;}={\mathrm{\&chi;}}_1\tanh \left(\frac{3{\mathrm{\&nu;\&chi;}}_1{S}_i}{\mathrm{\&kappa;}}\right),\mathrm{\&nu;}=0.25;$

Wherein i=1,2,3, χ₁For positive normal real number and meet χ₁≥ε_M, ε_MIt is the convergence error upper limit, κ is positive scalar；tanh () is hyperbolic tangent function.

6. one kind according to claim 5 actively reconstructs fault tolerant control method in real time, it is characterised in that：The step (5) Middle weight matrix M, meets following ADAPTIVE CONTROL：

$\stackrel{\&CenterDot;}{M}=({\stackrel{\&RightArrow;}{d}}_1{\mathrm{S\&mu;}}^T-{\stackrel{\&RightArrow;}{d}}_1{\stackrel{\&RightArrow;}{d}}_{2}M);$

In formula, It is arithmetic number.