CN104290919A - Direct self-repairing control method for four-rotor aircraft - Google Patents

Abstract

The invention discloses a direct self-repairing control method for a four-rotor aircraft. The direct self-repairing control method comprises the following steps that (1) feature information of an actuator failure of the four-rotor aircraft is set, and a failure model is established; (2) according to the unstability of a linearized model of the four-rotor aircraft, the optimal control law is obtained; (3) a reference model of the four-rotor aircraft is selected, in addition, the model structure of a direct self-repairing refactoring control law of the four-rotor aircraft is established, the controlled quality, obtained through calculation, of the four-rotor aircraft is output in real time, state errors are controlled in due time, and therefore the aircraft can fly in a self-repairing mode in case of a failure. Through calculation of the optimal control law based on the method, the four-rotor aircraft can still achieve satisfactory flight quality in case of the failure according to the model structure of the direct self-repairing refactoring control law of the aircraft while the four-rotor aircraft keeps stable.

Description

A kind of direct selfreparing control method of quadrotor

Technical field

The present invention relates to a kind of direct selfreparing control method of quadrotor, belong to reconstruct flight control method.

Background technology

Vehicle flight control system is the important component part of aircraft, plays very crucial effect to the airworthiness of aircraft and safety.Because vehicle flight control system parts are more, the possibility of et out of order is higher, and therefore, the Fault Tolerance Control Technology studying its flight control system is vital.When fault occurs, by reconfigurable control, ensure that aircraft recovers smooth flight in a short period of time, improve the safety of flight.

At first the research of reconstruct flight control system is inspired and come from some aircraft flight examples of breaking down or damaging awing, wherein some are had an accident because of airplane fault, other then rely on timely, the correct manipulation of chaufeur successfully to land, and avoid or reduce the generation of disaster and loss.Today that traffic is aloft day by day busy, the safety and reliability of aircraft is had higher requirement.Aeronautical chart is recognized, control system is passable, control system can and prior effect should be played wherein, also expand correlative study work afterwards.The object so reconstructing flight control system is the safety improving aircraft, when aircraft et out of order and damage, utilize remaining effective control mechanism to make up fault and the change damaging the vehicle dynamic characteristic brought, ensure the safety of aircraft and completing of task.Statistics shows, the aircraft accident caused by control inefficacy occupies significant proportion.Along with airplane design becomes increasingly complex, towards the future development of many controlsurfaces, the reconstruct increased as flight control system of control surface provides condition, and reconstruct the safety and reliability that flight control system can make full use of the remaining raising flight that many controlsurfaces bring, reduce aircraft accident incidence.Selfreparing reconfigurable control is divided into again two kinds of methods: directly selfreparing control method and indirect selfreparing control method; Indirect selfreparing control method needs first to carry out identification to the parameter of controlled object, and needs to provide multiple control program, namely first estimates flight parameter direct-on-line, determines controller parameter according to its result.

Summary of the invention

Object of the present invention, is the direct selfreparing control method providing a kind of quadrotor, the quadrotor of known fault still can be obtained and be satisfied with flight quality.

In order to reach above-mentioned purpose, solution of the present invention is:

A direct selfreparing control method for quadrotor, is characterized in that: comprise following step:

Step one: the actuator failures model of setting quadrotor is:

$\stackrel{\·}{x}=A_{p}x+B_p\mathrm{\Λu}+B_{p}f$

y＝Cx

Wherein $f=\mathrm{\Λ}(I-\mathrm{\σ})\stackrel{\‾}{u}+d,$ Then obtain:

$\stackrel{\·}{x}=A_{p}x+B_p\mathrm{\Λu}+B_p\mathrm{\Λ}(I-\mathrm{\σ})\stackrel{\‾}{u}+B_{p}d,$

y＝Cx

Here x is the state vector of quadrotor, for the derivative vector of state vector, y is the output vector of quadrotor, A _p, B _pfor the suitable dimension Constant System matrix under four-rotor helicopter fault model; I is suitable dimension identity matrix; σ=diag{ σ ₁σ ₂σ _m, Λ=diag{ λ ₁λ ₂λ _m; σ _ithe maneuverability coefficient of actr, if σ _i=1, then actr is normal, and under stuck and saturated conditions σ _i=0; λ _iactr effective coefficient, λ under degree of impairment _i∈ [0,1], wherein i=1,2 ..., m, described fault matrix Λ ∈ R ^{m × m}, σ ∈ R ^{m × m}with describe, represent the position that actr is stuck, d is external interference and modeling error, and C is the real matrix of corresponding dimension;

Step 2: for the fugitiveness of quadrotor inearized model, the expression formula of optimal control law:

u ^*(t)＝K _lqrx(t),

Here for feedback gain matrix, R ₁any positive definite matrix, P ₁unique symmetric steady-state solution for following Riccati equation:

$P_1(A_p+\mathrm{\αI})+(A_p^T+\mathrm{\αI})P_1-P_1{B}_p{R_1}^{-1}{B_p}^T{P}_1+Q_1=0$

Wherein, α is optimal control performance index and α <0, Q ₁it is any nonnegative definite matrix;

Step 3: select quadrotor reference model:

${\stackrel{\&CenterDot;}{x}}_m=A_m{x}_m+B_{m}r,$

y _m＝Cx _m

X _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, A _m, B _mwith the real matrix that C is corresponding dimension;

Model structure according to the direct selfreparing reconfigurable control rule of following quadrotor:

$u=K_1{x}_m+K_{2}r+K_3{r}_y+\hat{f}$

K ₁, K ₂, K ₃for the gain matrix of adaptive control, x _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, e _yfor the output error of quadrotor, for Fault Compensation vector; The controlling quantity u of the quadrotor calculated is exported in real time, reed time controll state error, make aircraft energy Self-repairing Flight under fault.

Further, the gain matrix K of adaptive control in the model structure of the quadrotor of described step 3 direct selfreparing reconfigurable control rule ₁, K ₂, K ₃with Fault Compensation vector meet following condition:

${\stackrel{\&CenterDot;}{K}}_1=-{\mathrm{\&Gamma;}}_1{B}_p^T{\mathrm{Pex}}_m^T,{\stackrel{\&CenterDot;}{K}}_2=-{\mathrm{\&Gamma;}}_2{B}_p^T{\mathrm{Per}}^T,{\stackrel{\&CenterDot;}{K}}_3=-{\mathrm{\&Gamma;}}_3{B}_p^T{\mathrm{Pee}}_y^T,\stackrel{\&CenterDot;}{\hat{f}}=-{\mathrm{\&Gamma;}}_4{B}_p^T\mathrm{Pe}$

Wherein, weight vector Γ _ifor diagonal angle positive definite matrix, wherein i=1 ..., 4; P is equation positive definite symmetric solution, matrix Q is any one positive definite symmetric matrices here, A _esystem matrix stable arbitrarily, the column vector of system matrix stable arbitrarily, for the row vector of the real matrix of the corresponding dimension of reality, for the row vector of the state vector of quadrotor reference model, r ^tfor the row vector of the input vector of quadrotor reference model, e is the state error of quadrotor, for the row vector of the output error of quadrotor.

Further, in above-mentioned steps two, for the fugitiveness of quadrotor inearized model, design inner ring base controller:

$J=\frac{1}{2}\underset{0}{\overset{\&infin;}{\&Integral;}}{e}^{2\mathrm{\&alpha;t}}[x^T{Q}_{1}x+u^T{R}_{1}u]\mathrm{dt},$

Wherein, J is the performance figure of optimal control law, Q ₁any nonnegative definite matrix, R ₁be any positive definite matrix, α is optimal control performance index and α <0, like this according to principle of minimum, obtains optimal control law u ^*(t).

Further, in above-mentioned steps one, the state vector x of described four-rotor helicopter is as follows:

$x^T=[\mathrm{\&epsiv;},p,\mathrm{\&lambda;},\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&epsiv;,}\frac{\&PartialD;}{\&PartialD;t}p,\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&lambda;}]$

Wherein, λ is expressed as lifting angle, roll angle, yaw angle, lifting angle cireular frequency, roll angle cireular frequency and yaw angle cireular frequency; The output vector y of described four-rotor helicopter is as follows:

y ^T＝[ε,p,λ]

Wherein, ε, p, λ are expressed as lifting angle, roll angle and yaw angle.

Further, described quadrotor meets following kinetic model when balance position:

$\frac{\text{\&PartialD;}}{\&PartialD;t}x=A_{p}x+B_{p}u,y=\mathrm{Cx}+\mathrm{Du}$

Wherein D is the real matrix of corresponding dimension, the following is the system real matrix of corresponding dimension:

$\begin{array}{c}{A}_p=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]B_p=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ \frac{{\mathrm{lK}}_f}{J_p}& -\frac{{\mathrm{lK}}_f}{J_p}& 0& 0\\ 0& 0& \frac{{\mathrm{lK}}_f}{J_r}& -\frac{{\mathrm{lK}}_f}{J_r}\\ \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}\end{array}\right]\\ C=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]D=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]\end{array}$

Wherein, K _fnclockwise propeller torque thrust constant, K _fcclockwise propeller torque thrust constant, K _fbe propeller thrust constant, l is the distance of rotor hinge to motor, J _ythe equivalent moment of inertia around yaw axis, J _pthe equivalent moment of inertia around pitch axis, J _rit is the equivalent moment of inertia around wobble shaft.

Adopt after such scheme, the present invention by calculating optimal control law make quadrotor keep stable while make quadrotor still can obtain satisfied flight quality under fault according to the model structure of aircraft direct selfreparing reconstruction and optimization control law.

Accompanying drawing explanation

Fig. 1 is the block flow diagram that the preferred embodiments of the present invention emulate for four-rotor helicopter.

Lifting angle error change figure when the real system fault of a kind of model structure for four-rotor helicopter direct selfreparing reconstruction and optimization control law that Fig. 2 designs for the preferred embodiment of the present invention occurs.

Roll angle error change figure when the real system fault of a kind of model structure for four-rotor helicopter direct selfreparing reconstruction and optimization control law that Fig. 3 designs for the preferred embodiment of the present invention occurs.

Yaw angle error change figure when the real system fault of a kind of model structure for four-rotor helicopter direct selfreparing reconstruction and optimization control law that Fig. 4 designs for the preferred embodiment of the present invention occurs.

Fig. 5 for the preferred embodiment of the present invention design a kind of occur for the model structure of four-rotor helicopter direct selfreparing reconstruction and optimization control law and the real system fault of model reference optimal control law time lifting angle error change comparison diagram.

Fig. 6 for the preferred embodiment of the present invention design a kind of occur for the model structure of four-rotor helicopter direct selfreparing reconstruction and optimization control law and the real system fault of model reference optimal control law time roll angle error change comparison diagram.

Fig. 7 for the preferred embodiment of the present invention design a kind of occur for the model structure of four-rotor helicopter direct selfreparing reconstruction and optimization control law and the real system fault of model reference optimal control law time yaw angle error change comparison diagram.

Detailed description of the invention

Below in conjunction with Figure of description, the specific embodiment of the present invention is described in further detail.

The present invention devises a kind of direct selfreparing control method of quadrotor, comprises following step:

Step one: the actuator failures model of setting quadrotor is:

$\stackrel{\&CenterDot;}{x}=A_{p}x+B_p\mathrm{\&Lambda;u}+B_{p}f$

y＝Cx

Wherein $f=\mathrm{\&Lambda;}(I-\mathrm{\&sigma;})\stackrel{\&OverBar;}{u}+d,$ Then obtain:

$\stackrel{\&CenterDot;}{x}=A_{p}x+B_p\mathrm{\&Lambda;u}+B_p\mathrm{\&Lambda;}(I-\mathrm{\&sigma;})\stackrel{\&OverBar;}{u}+B_{p}d,$

y＝Cx

Here x is the state vector of quadrotor, for the derivative vector of state vector x, y is the output vector of quadrotor, A _p, B _pfor the suitable dimension Constant System matrix under four-rotor helicopter fault model; I is suitable dimension identity matrix;

$\mathrm{\&sigma;}=\mathrm{diag}\left\{\begin{array}{cccc}{\mathrm{\&sigma;}}_1& {\mathrm{\&sigma;}}_2& ...& {\mathrm{\&sigma;}}_m\end{array}\right\}=\left[\begin{array}{ccccc}{\mathrm{\&sigma;}}_1& 0& 0& ...& 0\\ 0& {\mathrm{\&sigma;}}_2& 0& ...& 0\\ 0& 0& {\mathrm{\&sigma;}}_3& ...& 0\\ ...& ...& ...& ...& ...\\ 0& 0& 0& ...& {\mathrm{\&sigma;}}_m\end{array}\right],$

$\mathrm{\&Lambda;}=\mathrm{diag}\left\{\begin{array}{cccc}{\mathrm{\&lambda;}}_1& {\mathrm{\&lambda;}}_2& ...& {\mathrm{\&lambda;}}_m\end{array}\right\}=\left[\begin{array}{ccccc}{\mathrm{\&lambda;}}_1& 0& 0& ...& 0\\ 0& {\mathrm{\&lambda;}}_2& 0& ...& 0\\ 0& 0& {\mathrm{\&lambda;}}_3& ...& 0\\ ...& ...& ...& ...& ...\\ 0& 0& 0& ...& {\mathrm{\&lambda;}}_m\end{array}\right];$

σ _ithe maneuverability coefficient of aircraft, if σ _i=1, then aircraft is normal, and in stuck (LIP) and saturated (HOF) situation σ _i=0; λ _iaircraft effective coefficient, at damage (LOE) situation following table non ageing percentum, so λ _i∈ [0,1], wherein i=1,2, ", m, described fault matrix Λ ∈ R ^{m × m}, σ ∈ R ^{m × m}describe with u, u represents that the position that aircraft is stuck, d are external interference and modeling error, and C is the real matrix of corresponding dimension;

The state vector x of described four-rotor helicopter is as follows:

$x^T=[\mathrm{\&epsiv;},p,\mathrm{\&lambda;},\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&epsiv;,}\frac{\&PartialD;}{\&PartialD;t}p,\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&lambda;}]$

Wherein, λ is expressed as lifting angle, roll angle, yaw angle, lifting angle cireular frequency, roll angle cireular frequency and yaw angle cireular frequency; The output vector y of described four-rotor helicopter is as follows:

y ^T＝[ε,p,λ]

Wherein, ε, p, λ are expressed as lifting angle, roll angle and yaw angle.

Step 2: for the fugitiveness of quadrotor inearized model, design inner ring base controller:

$J=\frac{1}{2}\underset{0}{\overset{\&infin;}{\&Integral;}}{e}^{2\mathrm{\&alpha;t}}[x^T{Q}_{1}x+u^T{R}_{1}u]\mathrm{dt},$

Wherein, J is the performance figure of optimal control law, Q ₁any nonnegative definite matrix, R ₁be any positive definite matrix, α is optimal control performance index and α <0, and like this according to principle of minimum, obtaining optimal control law is:

u ^*(t)＝K _lqrx(t),

Here for feedback gain matrix, P ₁unique symmetric steady-state solution for following Riccati equation:

$P_1(A_p+\mathrm{\&alpha;I})+(A_p^T+\mathrm{\&alpha;I})P_1-P_1{B}_p{R_1}^{-1}{B_p}^T{P}_1+Q_1=0;$

Step 3: select quadrotor reference model:

$\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_m=A_m{x}_m+B_{m}r\\ y_m={\mathrm{Cx}}_m\end{array},$

X _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, A _m, B _mwith the real matrix that C is corresponding dimension.

Model structure according to the direct selfreparing reconfigurable control rule of following quadrotor:

$u=K_1{x}_m+K_{2}r+K_m{e}_y+\hat{f}$

K ₁, K ₂, K ₃for the gain matrix of adaptive control, x _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, e _yfor the output error of quadrotor, for Fault Compensation vector; The controlling quantity u of the quadrotor calculated is exported in real time, reed time controll state error, make aircraft energy Self-repairing Flight under fault.

The gain matrix K of adaptive control in the model structure of the direct selfreparing reconfigurable control rule of described quadrotor ₁, K ₂, K ₃with Fault Compensation vector meet following condition:

${\stackrel{\&CenterDot;}{K}}_1=-{\mathrm{\&Gamma;}}_1{B}_p^T{\mathrm{Pex}}_m^T,{\stackrel{\&CenterDot;}{K}}_2=-{\mathrm{\&Gamma;}}_2{B}_p^T{\mathrm{Per}}^T,{\stackrel{\&CenterDot;}{K}}_3=-{\mathrm{\&Gamma;}}_3{B}_p^T{\mathrm{Pee}}_y^T,\stackrel{\&CenterDot;}{\hat{f}}=-{\mathrm{\&Gamma;}}_4{B}_p^T\mathrm{Pe}$

Wherein, weight vector Γ _ifor diagonal angle positive definite matrix, wherein i=1 ..., 4, P is equation positive definite symmetric solution, matrix Q is any one positive definite symmetric matrices here, A _esystem matrix stable arbitrarily, the column vector of system matrix stable arbitrarily, for the row vector of the real matrix of the corresponding dimension of reality, for the row vector of the state vector of quadrotor reference model, r ^tfor the row vector of the input vector of quadrotor reference model, e is the state error of quadrotor, for the row vector of the output error of quadrotor.

Prove the system Existence of Global Stable how realizing quadrotor below.

The state error e of described four-rotor helicopter and the output error e of described four-rotor helicopter _yfollowing gained:

e＝x-x _m e _y＝y-y _m

Adopt the model structure of the direct selfreparing reconfigurable control rule of four-rotor helicopter, obtain the dynamic equation of the state error of four-rotor helicopter:

$\begin{array}{c}\stackrel{\&CenterDot;}{e}=\stackrel{\&CenterDot;}{x}-{\stackrel{\&CenterDot;}{x}}_m\\ =A_{p}x+B_p\mathrm{\&Lambda;u}+B_{p}f-A_m{x}_m-B_{m}r\\ =(A_p+B_p{\mathrm{\&Lambda;K}}_{3}C)e+(A_p-A_m+B_p\mathrm{\&Lambda;}{K}_1)x_m+(B_p\mathrm{\&Lambda;}{K}_2-B_m)r+B_p(\mathrm{\&Lambda;}\hat{f}+f)\end{array}$

According to model reference adaptation condition, be defined as follows:

$\begin{array}{cc}{A}_p+B_p\mathrm{\&Lambda;}{K}_3^{*}C=A_e& A_p+B_p\text{\&Lambda;}{K}_1^{*}=A_m\\ B_p\mathrm{\&Lambda;}{K}_2^{*}=B_m& \mathrm{\&Lambda;}{f}^{*}+f=0\end{array}$

Here the value of the gain matrix of direct adaptive control when representing that model mates completely, A _esystem matrix stable arbitrarily, A _p, B _pfor the real matrix of the corresponding dimension of reality, A _mfor the real matrix of the corresponding dimension of reference model.The gain matrix K of direct adaptive control rule online updating adaptive control ₁, K ₂, K ₃with Fault Compensation item vector value, make system state and export under the prerequisite of Liapunov stability, the state of track reference model and output.

Be defined as follows error matrix and error vector:

$\begin{array}{cc}{\tilde{K}}_1=K_1-K_1^{*}& {\tilde{K}}_2=K_2-K_2^{*}\\ {\tilde{K}}_3=K_3-K_3^{*}& \tilde{f}=\hat{f}-f^{*}\end{array}$

Obtain:

$\stackrel{\&CenterDot;}{e}=A_{e}e+B_p\mathrm{\&Lambda;}({\tilde{K}}_1{x}_m+{\tilde{K}}_{2}r+{\tilde{K}}_3{e}_y+\tilde{f})$

Wherein, with represent error matrix and error vector respectively;

Consider following Lyapunov function:

$V=\frac{1}{2}[e^T\mathrm{Pe}+\mathrm{Tr}\left({\tilde{K}}_1^T{\mathrm{\&Gamma;}}_1^{-1}\mathrm{\&Lambda;}{\tilde{K}}_1\right)+\mathrm{Tr}\left({\tilde{K}}_2^T{\mathrm{\&Gamma;}}_2^{-1}\mathrm{\&Lambda;}{\tilde{K}}_2\right)+\mathrm{Tr}\left({\tilde{K}}_3^T{\mathrm{\&Gamma;}}_3^{-1}\mathrm{\&Lambda;}{\tilde{K}}_3\right)+{\tilde{f}}^T{\mathrm{\&Gamma;}}_4^{-1}\mathrm{\&Lambda;}\tilde{f}]$

Its differential form is as follows:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=e^{T}P\stackrel{\&CenterDot;}{e}+\mathrm{tr}\left({\tilde{K}}_1^T{\mathrm{\&Gamma;}}_1^{-1}\mathrm{\&Lambda;}{\stackrel{\&CenterDot;}{\tilde{K}}}_1\right)+\mathrm{tr}\left({\tilde{K}}_2^T{\mathrm{\&Gamma;}}_2^{-1}\mathrm{\&Lambda;}{\stackrel{\&CenterDot;}{\tilde{K}}}_2\right)+\mathrm{tr}\left({\tilde{K}}_3^T{\mathrm{\&Gamma;}}_3^{-1}{\mathrm{\&Lambda;}\stackrel{\&CenterDot;}{\tilde{K}}}_3\right)+{\tilde{f}}^T{\mathrm{\&Gamma;}}_4^{-1}\mathrm{\&Lambda;}\stackrel{\&CenterDot;}{\tilde{f}}\\ =-\frac{1}{2}{e}^T\mathrm{Qe}+\mathrm{tr}[{\tilde{K}}_1^T{\mathrm{\&Gamma;}}_1^{-1}\mathrm{\&Lambda;}({\stackrel{\&CenterDot;}{\tilde{K}}}_1+{\mathrm{\&Gamma;}}_1{B}_p^T{\mathrm{Pex}}_m^T)+{\tilde{K}}_2^T{\mathrm{\&Gamma;}}_2^{-1}\mathrm{\&Lambda;}({\stackrel{\&CenterDot;}{\tilde{K}}}_2+{\mathrm{\&Gamma;}}_2{B}_p^T{\mathrm{Pet}}^T)+{\tilde{K}}_3^T{\mathrm{\&Gamma;}}_3^{-1}\mathrm{\&Lambda;}({\stackrel{\&CenterDot;}{K}}_3\\ +{\mathrm{\&Gamma;}}_3{B}_p^T{\mathrm{Pee}}_y^T]+{\tilde{f}}^T{\mathrm{\&Gamma;}}_4^{-1}(\stackrel{\&CenterDot;}{\hat{f}}+{\mathrm{\&Gamma;}}_4{B}_p^T\mathrm{Pe})\end{array}$

If choose: ${\stackrel{\&CenterDot;}{K}}_1=-{\mathrm{\&Gamma;}}_1{B}_p^T{\mathrm{Pex}}_m^T$

${\stackrel{\&CenterDot;}{K}}_2=-{\mathrm{\&Gamma;}}_2{B}_p^T{\mathrm{Per}}^T$

${\stackrel{\&CenterDot;}{K}}_3=-{\mathrm{\&Gamma;}}_3{B}_p^T{\mathrm{Pee}}_y^T$

$\stackrel{\&CenterDot;}{\hat{f}\text{=-}{\mathrm{\&Gamma;}}_4{B}_p^T\mathrm{Pe}}$

Then: $\stackrel{\&CenterDot;}{V}=-\frac{1}{2}{e}^T\mathrm{Qe}<0$

Realize the system Existence of Global Stable just realizing quadrotor like this.

Described quadrotor meets following kinetic model when its balance position (i.e. trouble free):

$\frac{\text{\&PartialD;}}{\&PartialD;t}x=A_{p}x+B_{p}u,y=\mathrm{Cx}+\mathrm{Du}$

Wherein D is the real matrix of corresponding dimension, the following is the system real matrix of corresponding dimension:

$\begin{array}{c}{A}_p=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]B_p=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ \frac{{\mathrm{lK}}_f}{J_p}& -\frac{{\mathrm{lK}}_f}{J_p}& 0& 0\\ 0& 0& \frac{{\mathrm{lK}}_f}{J_r}& -\frac{{\mathrm{lK}}_f}{J_r}\\ \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}\end{array}\right]\\ C=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]D=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]\end{array}$

Following table presents the design parameter value of four-rotor helicopter model:

Table 1

Symbol	Definition	Numerical value	Unit
				K fn	Clockwise propeller torque thrust constant	0.0036	N.m/V
K fc	Clockwise propeller torque thrust constant	-0.0036	N.m/V
				K f	Propeller thrust constant	0.1188	N/V
l	Rotor hinge is to the distance of motor	0.197	m
				J y	Around the equivalent moment of inertia of yaw axis	0.110	Kg.m 2
J p	Around the equivalent moment of inertia of pitch axis	0.0552	Kg.m 2
				J r	Around the equivalent moment of inertia of wobble shaft	0.0552	Kg.m 2

The preferred embodiment of the present invention adopts four-rotor helicopter, when emulating, the block process of the direct selfreparing control method of four-rotor helicopter as shown in Figure 1, comprises base controller, four-rotor helicopter, direct fault location module, selfreparing reconfigurable controller, sensor, data acquisition module, ground monitoring module and actr.

The process of emulation comprises the steps:

Step 1. sets the characteristic information of a certain fault, comprising: fault type, time of fault inception, fault end time and fault size, and described fault carries out software pouring by direct fault location module, sets up fault model;

Step 2. selfreparing reconfigurable controller calculates the controlling quantity of four-rotor helicopter according to the model structure of the direct selfreparing reconfigurable control rule of four-rotor helicopter, and the controlling quantity of the four-rotor helicopter calculated is exported to actr;

The attitude information of step 3. angle-measuring equipment Real-time Obtaining four-rotor helicopter model, and be transferred to data acquisition module, the four-rotor helicopter model attitude information measured by data acquisition module exports to selfreparing reconfigurable controller;

Step 4. selfreparing reconfigurable controller is for the four-rotor helicopter model attitude information obtained, upgrade the parameter in the model structure of the direct selfreparing reconfigurable control rule of four-rotor helicopter, and calculate the controlling quantity of four-rotor helicopter according to the model structure that the direct selfreparing reconfigurable control of four-rotor helicopter after upgrading is restrained;

Step 5. direct fault location module is at the time of fault inception of setting, according to the fault characteristic information of setting, signal transacting is carried out to the controlling quantity calculated by selfreparing reconfigurable controller in step 4, produce dummy order signal, output to actr, realize actuator failures simulation;

Step 6. ground monitoring module can the attitude information of Real-time Obtaining four-rotor helicopter each time of model, and failure message and controlling quantity information, can stop emulation at any time.

A kind of direct selfreparing control method for four-rotor helicopter of preferred embodiment of the present invention design is in the middle of specific implementation process:

1. assumed fault occurs in 5s, the loss of voltage 40% of a certain rotor motor of four-rotor helicopter;

2. the error change figure when real system fault that Fig. 2 to 4 is a kind of model structure for four-rotor helicopter direct selfreparing reconstruction and optimization control law adding preferred embodiment of the present invention design occurs; Fig. 5 to 7 for have added preferred embodiment of the present invention design a kind of occur for the model structure of four-rotor helicopter direct selfreparing reconstruction and optimization control law and the real system fault of model reference optimal control law time error change comparison diagram.

3. add the model structure of designed direct selfreparing control law, system in stable condition, weaken before not adding selfreparing reconfigurable controller with reference state error oscillation, the overshoot of error reduces, the performance of system be improved significantly.

To sum up, the direct selfreparing control method of a kind of quadrotor of the present invention, without the need to definite system parameter, has following advantage: Technical comparing is ripe, and algorithm is simple, a large class fault can be processed, the uncertainty and external interference etc. of uncertain, the structure of such as system parameter; Respond the parameter of on-line control controller by systematic error, ensure that the rapidity of faults-tolerant control; For fault, do not need independent trouble diagnosing and recognition module, the uncertainty that therefore causes can be avoided and cause the reduction of faults-tolerant control performance.

Above embodiment is only and technological thought of the present invention is described, can not limit protection scope of the present invention with this, and every technological thought proposed according to the present invention, any change that technical scheme basis is done, all falls within scope.

Claims (5)

1. a direct selfreparing control method for quadrotor, is characterized in that: comprise following step:

Step one: the actuator failures model of setting quadrotor is:

$\stackrel{\&CenterDot;}{x}=A_{p}x+B_p\mathrm{\&Lambda;u}+B_{p}f$

y＝Cx

Wherein $f=\mathrm{\&Lambda;}(I-\mathrm{\&sigma;})\stackrel{\&OverBar;}{u}+d,$ Then obtain:

$\stackrel{\&CenterDot;}{x}=A_{p}x+B_p\mathrm{\&Lambda;u}+B_p\mathrm{\&Lambda;}(I-\mathrm{\&sigma;})\stackrel{\&OverBar;}{u}+B_{p}d,$

y＝Cx

Here x is the state vector of quadrotor, for the derivative vector of state vector, y is the output vector of quadrotor, A _p, B _pfor the suitable dimension Constant System matrix under four-rotor helicopter fault model; I is suitable dimension identity matrix; σ=diag{ σ ₁σ ₂σ _m, Λ=diag{ λ ₁λ ₂λ _m; σ _ithe maneuverability coefficient of actr, if σ _i=1, then actr is normal, and under stuck and saturated conditions σ _i=0; λ _iactr effective coefficient, λ under degree of impairment _i∈ [0,1], wherein i=1,2 ..., m, described fault matrix Λ ∈ R ^{m × m}, σ ∈ R ^{m × m}describe with u, represent the position that actr is stuck, d is external interference and modeling error, and C is the real matrix of corresponding dimension;

Step 2: for the fugitiveness of quadrotor inearized model, the expression formula of optimal control law:

u ^*(t)＝K _lqrx(t),

Here for feedback gain matrix, R ₁any positive definite matrix, P ₁unique symmetric steady-state solution for following Riccati equation:

$P_1(A_p+\mathrm{\&alpha;I})+(A_p^T+\mathrm{\&alpha;I})P_1-P_1{B}_p{R_1}^{-1}{B_p}^T{P}_1+Q_1=0$

Wherein, α is optimal control performance index and α <0, Q ₁it is any nonnegative definite matrix;

Step 3: select quadrotor reference model:

${\stackrel{\&CenterDot;}{x}}_m=A_m{x}_m+B_{m}r,$

y _m＝Cx _m

X _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, A _m, B _mwith the real matrix that C is corresponding dimension;

Model structure according to the direct selfreparing reconfigurable control rule of following quadrotor:

$u=K_1{x}_m+K_{2}r+K_3{e}_y+\hat{f}$

K ₁, K ₂, K ₃for the gain matrix of adaptive control, x _mfor the state vector of quadrotor reference model, r is the input vector of quadrotor reference model, e _yfor the output error of quadrotor, for Fault Compensation vector; The controlling quantity u of the quadrotor calculated is exported in real time, reed time controll state error, make aircraft energy Self-repairing Flight under fault.

2. the direct selfreparing control method of a kind of quadrotor as claimed in claim 1, is characterized in that: the gain matrix K of adaptive control in the model structure of the direct selfreparing reconfigurable control rule of quadrotor of described step 3 ₁, K ₂, K ₃with Fault Compensation vector meet following condition:

${\stackrel{\&CenterDot;}{K}}_1=-{\mathrm{\&Gamma;}}_1{B}_p^T{\mathrm{Pex}}_m^T,{\stackrel{\&CenterDot;}{K}}_2=-{\mathrm{\&Gamma;}}_2{B}_p^T{\mathrm{Per}}^T,{\stackrel{\&CenterDot;}{K}}_3=-{\mathrm{\&Gamma;}}_3{B}_p^T{\mathrm{Pee}}_y^T,\stackrel{\&CenterDot;}{\hat{f}}=-{\mathrm{\&Gamma;}}_4{B}_p^T\mathrm{Pe}$

Wherein, weight vector Γ _ifor diagonal angle positive definite matrix, wherein i=1 ..., 4; P is equation positive definite symmetric solution, matrix Q is any one positive definite symmetric matrices here, A _esystem matrix stable arbitrarily, the column vector of system matrix stable arbitrarily, for the row vector of the real matrix of the corresponding dimension of reality, for the row vector of the state vector of quadrotor reference model, r ^tfor the row vector of the input vector of quadrotor reference model, e is the state error of quadrotor, for the row vector of the output error of quadrotor.

3. the direct selfreparing control method of a kind of quadrotor as claimed in claim 2, is characterized in that: in above-mentioned steps two, for the fugitiveness of quadrotor inearized model, and design inner ring base controller:

$J=\frac{1}{2}\underset{0}{\overset{\&infin;}{\&Integral;}}{e}^{2\mathrm{\&alpha;t}}[x^T{Q}_{1}x+u^T{R}_{1}u]\mathrm{dt},$

Wherein, J is the performance figure of optimal control law, Q ₁any nonnegative definite matrix, R ₁be any positive definite matrix, α is optimal control performance index and α <0, like this according to principle of minimum, obtains optimal control law u ^*(t).

4. the direct selfreparing control method of a kind of quadrotor as claimed in claim 3, it is characterized in that: in above-mentioned steps one, the state vector x of described four-rotor helicopter is as follows:

$x^T=[\mathrm{\&epsiv;},p,\mathrm{\&lambda;},\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&epsiv;,}\frac{\&PartialD;}{\&PartialD;t}p,\frac{\&PartialD;}{\&PartialD;t}\mathrm{\&lambda;}]$

Wherein, λ is expressed as lifting angle, roll angle, yaw angle, lifting angle cireular frequency, roll angle cireular frequency and yaw angle cireular frequency; The output vector y of described four-rotor helicopter is as follows:

y ^T＝[ε,p,λ]

Wherein, ε, p, λ are expressed as lifting angle, roll angle and yaw angle.

5. the direct selfreparing control method of a kind of quadrotor as claimed in claim 4, is characterized in that: described quadrotor meets following kinetic model when balance position:

$\frac{\text{\&PartialD;}}{\&PartialD;t}x=A_{p}x+B_{p}u,y=\mathrm{Cx}+\mathrm{Du}$

Wherein D is the real matrix of corresponding dimension, the following is the system real matrix of corresponding dimension:

$\begin{array}{c}{A}_p=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]B_p=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ \frac{{\mathrm{lK}}_f}{J_p}& -\frac{{\mathrm{lK}}_f}{J_p}& 0& 0\\ 0& 0& \frac{{\mathrm{lK}}_f}{J_r}& -\frac{{\mathrm{lK}}_f}{J_r}\\ \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fc}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}& \frac{K_{\mathrm{fn}}}{J_y}\end{array}\right]\\ C=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]D=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]\end{array}$

Wherein, K _fnclockwise propeller torque thrust constant, K _fcclockwise propeller torque thrust constant, K _fbe propeller thrust constant, l is the distance of rotor hinge to motor, J _ythe equivalent moment of inertia around yaw axis, J _pthe equivalent moment of inertia around pitch axis, J _rit is the equivalent moment of inertia around wobble shaft.