CN102736618A - Diagnosability determining method of satellite control system based on transfer functions - Google Patents

Abstract

The invention discloses a diagnosability determining method of a satellite control system based on transfer functions. The method comprises the steps of: first, establishing a failure model of the satellite control system to obtain output transfer functions of failures; obtaining detectability conditions of various failures by judging whether the output transfer functions of failures are 0 or not through the failure transfer functions, and obtaining separability conditions of various failures by judging whether transfer functions corresponding to different failures are in linear correlation or not so as to obtain a diagnosability analyzing result of the satellite control system; and finally, calculating to obtain the failure detectability and the separability as well of the system failure detectability and the separability of a failure mode of the satellite control system by a diagnosability measurement calculation method. According to the diagnosability determining method of the satellite control system based on the transfer functions, detectability and separability judgment of the failure mode of the satellite control system are realized and the diagnosability of the satellite control system is measured.

Description

A kind of satellite control system diagnosticability based on transport function is confirmed method

Technical field

The present invention relates to a kind of satellite control system diagnosticability and confirm method, relate in particular to a kind of satellite control system diagnosticability and confirm method, belong to aerospace field based on transport function.

Background technology

At present; In order to improve satellite control system fault adaptibility to response, Chinese scholars more pays close attention to Research on Fault Diagnosis Method, and has ignored one of them underlying issue--the fault diagnosability analysis; Promptly to current system configuration situation; Whether failure judgement satisfies the diagnosticability requirement, and when it did not satisfy, no matter the many advanced persons of method for diagnosing faults also were of no avail.Confirm method around satellite control system research fault diagnosticability; Can help the designer to understand some Single Point of Faliure or some needs the fault of special concern whether to have diagnosticability; The diagnosability analysis result also is the key factor that the design phase measuring point is distributed rationally needs consideration simultaneously, so the fault diagnosticability is confirmed the important prerequisite that fault diagnosis and measuring point are distributed rationally.

Document (provides one piece of document here: 1.Steven X.Ding.Model-based Fault Diagnosis Techniques:Design Schemes; Fault diagnosability analysis method based on transport function is disclosed Algorithms and Tools.Springer.2008); Weak point is that given method only is applicable to open cycle system; Do not consider as yet to have the feedback influence that brings because of controller; This method is just studied to General System simultaneously, and with respect to satellite control system, the method lacks specific aim.Because at present satellite control system has been set up comparatively precise math model, so the present invention proposes a kind of satellite control system fault diagnosticability based on transport function and confirms method.The satellite control system fault diagnosticability based on transport function for the present invention is given is confirmed method, does not have disclosed method with complete Practical significance.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes prior art; Provide a kind of diagnosticability to confirm method based on transport function; Realized detectability, separability differentiation, and the diagnosticability of satellite control system has been measured the satellite control system fault mode.

Technical solution of the present invention is: a kind of diagnosticability based on transport function is confirmed method, and step is following:

(1), sets up the fault model of satellite control system according to kinetics equation, kinematical equation, controller model and the fault effects of satellite;

(2), obtain the transport function of each fault to output according to the satellite control system fault model of step (1);

(3) according to the transport function of each fault in the step (2) to output; Through judging that whether transport function is 0 to obtain the detectability condition of various faults; Through judge the corresponding transport function of different faults whether linear dependence obtain the separability condition of various faults, with satellite control system correlation parameter substitution detectability and separability condition acquisition satellite control system fault diagnosability analysis result;

(4) utilize diagnosticability metric calculation method that the fault diagnosability analysis result that step (3) obtains is calculated, but but obtain fault degree of detection and separable degree and the system failure degree of detection and the separable degree of satellite control system fault mode.

The satellite control system fault model that said step (1) is set up is:

$\left\{\begin{array}{c}\left[\begin{array}{c}\stackrel{\·}{x}\left(t\right)\\ {\stackrel{\·}{x}}_k\left(t\right)\end{array}\right]=\left[\begin{array}{cc}A+{\mathrm{BD}}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ x_k\left(t\right)\end{array}\right]+\left[\begin{array}{c}{\mathrm{BD}}_k{F}_s\\ B_k{F}_s\end{array}\right]f_s\left(t\right)+\left[\begin{array}{c}{F}_a\\ 0\end{array}\right]f_a\left(t\right)\\ \tilde{y}\left(t\right)=\left[\begin{array}{c}y\left(t\right)\\ u\left(t\right)\end{array}\right]=\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ x_k\left(t\right)\end{array}\right]+\left[\begin{array}{c}{F}_s\\ D_k{F}_s\end{array}\right]f_s\left(t\right)\end{array}\right.$

Wherein:

θ, ψ is Eulerian angle;

x _kIntegral for x;

$u={\left[\begin{array}{ccc}{u}_x& u_y& u_z\end{array}\right]}^T;$

$\tilde{y}\left(t\right)=\left[\begin{array}{c}y\left(t\right)\\ u\left(t\right)\end{array}\right];$

Sensor failure $f_s\left(t\right)=\left[\begin{array}{c}{f}_{I,x}\\ f_{I,y}\\ f_{G,x}\\ f_{G,y}\\ f_{G,z}\end{array}\right];$

Topworks's fault $f_a\left(t\right)=\left[\begin{array}{c}{f}_{M,1}\\ f_{M,2}\\ f_{M,3}\\ f_{M,4}\end{array}\right];$

$A=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ M_{21}& 0& 0& 0& 0& M_{26}\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& M_{62}& 0& 0& M_{65}& 0\end{array}\right],$ $B={\left[\begin{array}{cccccc}0& I_x^{-1}& 0& 0& 0& 0\\ 0& 0& 0& I_y^{-1}& 0& 0\\ 0& 0& 0& 0& 0& I_z^{-1}\end{array}\right]}^T;$

$\begin{array}{c}{M}_{21}=-I_x^{-1}(I_y-I_z){\mathrm{\ω}}_0^2\\ M_{26}=-I_x^{-1}(I_y-I_z-I_x){\mathrm{\ω}}_0\end{array},$ $\begin{array}{c}{M}_{62}=-I_z^{-1}(I_z+I_x-I_y){\mathrm{\ω}}_0\\ M_{65}=-I_z^{-1}(I_y-I_x){\mathrm{\ω}}_0^2\end{array};$

I _x, I _y, I _zBe respectively rigid body around coordinate axis Ox, Oy, the moment of inertia of Oz;

ω ₀Orbit angular velocity for satellite gravitation body rotation around the center;

u _x, u _y, u _zBe the component of satellite control moment along the principal moments axle;

A _k=0, C and B _kAll be 6 rank unit matrixs, $C_k=\left[\begin{array}{cccccc}{-K}_{i,x}& 0& 0& 0& 0& 0\\ 0& 0& -K_{i,y}& 0& 0& 0\\ 0& 0& 0& 0& {-K}_{i,z}& 0\end{array}\right],$

$D_k=\left[\begin{array}{cccccc}{-K}_{p,x}& -K_{d,x}& 0& 0& 0& 0\\ 0& 0& -K_{p,y}& -K_{d,y}& 0& 0\\ 0& 0& 0& 0& -K_{p,z}& {-K}_{d,z}\end{array}\right];$

K _{P, x}, K _{P, y}, K _{P, z}The scale-up factor of expression satellite control system three direction of principal axis controllers;

K _{I, x}, K _{I, y}, K _{I, z}The integral coefficient of expression satellite control system three direction of principal axis controllers;

K _{D, x}, K _{D, y}, K _{D, z}The differential coefficient of expression satellite control system three direction of principal axis controllers;

$F_s=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1\end{array}\right];$

Be momenttum wheel allocation matrix M _{4 * 3}Pseudo inverse matrix;

Said step (2) obtains each fault:

According to the satellite control system fault model of step (1), the sensor failure that obtains to the transport function of output is:

$T_{f_s,i}=\left[\begin{array}{c}{F}_{s,i}\\ D_k{F}_{s,i}\end{array}\right]+\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{\mathrm{BD}}_k{F}_{s,i}\\ B_k{F}_{s,i}\end{array}\right]$

Wherein,

Expression sensor failure f _{S, i}To the transport function of output, f _{S, i}Expression f _sI fault, and F _{S, i}Representing matrix F _sI row, I representation unit matrix, s are the Laplace transformation coefficient;

Topworks's fault to the transport function of output is:

$T_{f_a,j}=\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{F}_{a,j}\\ 0\end{array}\right]$

Wherein,

The expression fault f of topworks _{A, j}To the transport function of output, f _{A, j}Expression f _aJ fault, F _{A, j}Representing matrix F _aJ row.

Corresponding detectability and the separability analysis condition of said various fault is:

Sensor failure f _{S, i}The condition of detectability be:

Wherein at least one element is not equal to 0 in

the expression transfer function matrix

, and all elements all equals 0 in

expression

;

The fault f of topworks _{A, j}The condition of detectability be:

The condition that N fault has separability is:

rank[T ₁T ₂…T _N]＝N

Wherein, if f _l∈ f _a, T then _lFor $\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{SI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{F}_a\\ 0\end{array}\right]$ Middle f _lCorresponding row; If f _l∈ f _s, T then _lFor $\left[\begin{array}{c}{F}_s\\ D_k{F}_s\end{array}\right]+\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{SI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{\mathrm{BD}}_k{F}_s\\ B_k{F}_s\end{array}\right]$ Middle f _lRespective column; The order computing is asked in rank () expression;

l＝1，2，…N。

Said step (5) but in the degree of detection f of fault mode _{D, i}Computing method be: $\left\{\begin{array}{cc}{f}_{d,i}=1& f_i\∈\mathrm{EF}\\ f_{d,i}=0& f_i\∈\mathrm{UF}\end{array}\right.,$

EF and UF are respectively can detect with undetectable fault and gather;

But the computing method of system failure degree of detection FDR are:

Wherein: m=|UF|+|EF| is the sum of satellite control system fault mode, λ _iBe the weighting coefficient of confirming according to fault i, | UF| representes the fault number among the undetectable fault set UF, | EF| representes the fault number among the detectable failure set EF.

The separable degree γ of fault mode in the said step (5) _iComputing method be: ${\mathrm{\γ}}_i=\left\{\begin{array}{cc}1& f_i\∈\mathrm{EI}\\ \frac{1}{\left|F_n\right|}& f_i\∈F_n,F_n\∈\mathrm{UI}\end{array}\right.,$ EI and UI are separable and inseparable failure collection, | F _n| expression F _nIn the fault number;

The computing method of the separable degree FIR of the system failure are:

M is the sum of satellite control system fault mode, λ _iBe the weighting coefficient of confirming according to fault i.

The present invention's beneficial effect compared with prior art is:

(1) at present when satellite control system is designed, lack the method that its trouble diagnosibility is carried out quantitative test, being difficult to provides guidance for the diagnosticability design of satellite control system.The present invention sets up the fault model of satellite control system, has provided fault detectability and separability Rule of judgment, but and employing degree of detection, separable degree obtain the quantitative evaluation of satellite control system.When above-mentioned quantitative target was lower than design objective, the undetectable fault pattern that can obtain according to the present invention and inseparable failure collection increased measuring point, thereby foundation were provided for the diagnosticability design of satellite control system.

(2) compared with prior art; The present invention will be generalized in the closed-loop system to the fault diagnosability analysis method of open cycle system; Through the propagation relation of analysis of failure in closed-loop system; Provide various faults corresponding detectability and separability analysis condition, make it be applicable to this closed-loop system of satellite control system.

(3) combine the satellite control system characteristics; Take into full account the probability of happening and the extent of injury of fault mode; Provide relevant diagnosticability metric and corresponding calculation method; Make the diagnosability analysis result more suit engineering reality, whether have diagnosticability the method foundation is provided for the staff estimates under the present configuring condition each fault.

(4) method of the present invention is simple, clear and definite, is suitable for engineering design.

Description of drawings

Fig. 1 is the FB(flow block) of the inventive method.

Embodiment

Fig. 1 is the FB(flow block) of the inventive method.Step of the present invention is:

(1), sets up the fault model of satellite control system according to kinetics equation, kinematical equation, controller model and the fault effects of satellite;

(2), obtain the transport function of each fault to output according to the satellite control system fault model of step (1);

(3) according to the transport function of each fault in the step (2) to output; Through judging that whether transport function is 0 to obtain the detectability condition of various faults; Through judge the corresponding transport function of different faults whether linear dependence obtain the separability condition of various faults, with satellite control system correlation parameter substitution detectability and separability condition acquisition satellite control system fault diagnosability analysis result;

(4) utilize diagnosticability metric calculation method that the fault diagnosability analysis result that step (3) obtains is calculated, but but obtain fault degree of detection and separable degree and the system failure degree of detection and the separable degree of satellite control system fault mode.

The embodiment of step (1):

1. attitude of satellite dynamics and kinematical equation

Attitude of satellite kinetics equation based on body coordinate system is:

$I_x{\stackrel{\·}{\mathrm{\ω}}}_x-(I_y-I_z){\mathrm{\ω}}_y{\mathrm{\ω}}_z=u_x$

$I_y{\stackrel{\·}{\mathrm{\ω}}}_y-(I_z-I_x){\mathrm{\ω}}_z{\mathrm{\ω}}_x=u_y---\left(1\right)$

$I_z{\stackrel{\·}{\mathrm{\ω}}}_z-(I_x-I_y){\mathrm{\ω}}_x{\mathrm{\ω}}_y=u_z$

Wherein, I _x, I _y, I _zBe respectively rigid body around coordinate axis Ox, Oy, the moment of inertia of Oz, ω _x, ω _y, ω _zBe the component of satellite spatial rotational angular velocity ω along the principal moments axle, u _x, u _y, u _zBe the component of satellite control moment along the principal moments axle.

When considering the attitude of satellite in situation of change among a small circle, the attitude motion of satellite is learned equation and is:

I.e.

Wherein,

θ, ψ are Eulerian angle, ω ₀Orbit angular velocity for satellite gravitation body rotation around the center.

Take all factors into consideration formula (1) and formula (3), the linearization attitude dynamic equations that can get satellite does

The definition status variable does

Control variable is u=[u _xu _yu _z] ^T, observed quantity does

Then following formula becomes

$\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)$ (5)

y(t)＝Cx(t)

Wherein $A=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ M_{21}& 0& 0& 0& 0& M_{26}\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& M_{62}& 0& 0& M_{65}& 0\end{array}\right],$ $B={\left[\begin{array}{cccccc}0& I_x^{-1}& 0& 0& 0& 0\\ 0& 0& 0& I_y^{-1}& 0& 0\\ 0& 0& 0& 0& 0& I_z^{-1}\end{array}\right]}^T,$ C is 6 rank unit matrixs, $\begin{array}{c}{M}_{21}=-I_x^{-1}(I_y-I_z){\mathrm{\ω}}_0^2\\ M_{26}=-I_x^{-1}(I_y-I_z-I_x){\mathrm{\ω}}_0\end{array},$ $\begin{array}{c}{M}_{62}=-I_z^{-1}(I_z+I_x-I_y){\mathrm{\ω}}_0\\ M_{65}=-I_z^{-1}(I_y-I_x){\mathrm{\ω}}_0^2\end{array}.$

2. controller model:

The PID controller model of expectation value w=0 is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_k\left(t\right)=A_k{x}_k\left(t\right)+B_{k}y\left(t\right)\\ u\left(t\right)=C_k{x}_k\left(t\right)+D_{k}y\left(t\right)\end{array}\right.---\left(6\right)$

A wherein _k=0,

Be the integral of x (t) in the formula (5), $C_k=\left[\begin{array}{cccccc}{-K}_{i,x}& 0& 0& 0& 0& 0\\ 0& 0& -K_{i,y}& 0& 0& 0\\ 0& 0& 0& 0& {-K}_{i,z}& 0\end{array}\right],$ $D_k=\left[\begin{array}{cccccc}{-K}_{p,x}& -K_{d,x}& 0& 0& 0& 0\\ 0& 0& -K_{p,y}& -K_{d,y}& 0& 0\\ 0& 0& 0& 0& -K_{p,z}& {-K}_{d,z}\end{array}\right],$ K _{P, x}, K _{P, y}, K _{P, z}The scale-up factor of expression satellite control system three direction of principal axis controllers, K _{I, x}, K _{I, y}, K _{I, z}The integral coefficient of representing three direction of principal axis controllers, and K _{D, x}, K _{D, y}, K _{D, z}The differential coefficient of representing three direction of principal axis controllers.B _kBe 6 rank unit matrixs.

For the controller model shown in the following formula, through to parameter A _k, B _k, C _kAnd D _kDifferent values is set, can describes various forms of controllers:

√ works as A _k=B _k=C _k=0, D _k=K _p, controller u (t)=K _pY (t) is a proportional controller;

√ works as A _k=0, B _k=K _i, C _kBe unit matrix, D _k=K _p, controller Be pi controller;

When √ was unit matrix as the C in the formula (5), above-mentioned controller also can be described state feedback controller.

3. satellite control system fault model

Table 1 satellite control system configuring condition

Based on the satellite control system configuring condition of table 1, consider the axis of rolling and pitch axis infrared earth sensor fault f _{I, x}f _{I, y}, three spools gyro failure f _{G, x}, f _{G, y}, f _{G, z}With momenttum wheel fault f _{M, 1}, f _{M, 2}, f _{M, 3}, f _{M, 4}, formula (5) institute representation model becomes:

$\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)+B{M}_{3*4}^{*}{f}_a\left(t\right)$ (7)

y(t)＝Cx(t)+F _sf _s(t)

Wherein $F_s=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1\end{array}\right],$ Sensor failure $f_s\left(t\right)=\left[\begin{array}{c}{f}_{I,x}\\ f_{I,y}\\ f_{G,x}\\ f_{G,y}\\ f_{G,z}\end{array}\right],$ Topworks's fault $f_a\left(t\right)=\left[\begin{array}{c}{f}_{M,1}\\ f_{M,2}\\ f_{M,3}\\ f_{M,4}\end{array}\right],$

Be momenttum wheel allocation matrix M _{4 * 3}Pseudo inverse matrix.

With y (t)=Cx (t)+F _sf _s(t) and u (t)=C _kx _k(t)+D _kY (t) is substitution formula (6) and formula (7) respectively, and the fault model that can get satellite control system is:

$\left\{\begin{array}{c}\left[\begin{array}{c}\stackrel{\·}{x}\left(t\right)\\ {\stackrel{\·}{x}}_k\left(t\right)\end{array}\right]=\left[\begin{array}{cc}A+{\mathrm{BD}}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ x_k\left(t\right)\end{array}\right]+\left[\begin{array}{c}{\mathrm{BD}}_k{F}_s\\ B_k{F}_s\end{array}\right]f_s\left(t\right)+\left[\begin{array}{c}{F}_a\\ 0\end{array}\right]f_a\left(t\right)\\ \tilde{y}\left(t\right)=\left[\begin{array}{c}y\left(t\right)\\ u\left(t\right)\end{array}\right]=\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ x_k\left(t\right)\end{array}\right]+\left[\begin{array}{c}{F}_s\\ D_k{F}_s\end{array}\right]f_s\left(t\right)\end{array}\right.---\left(8\right)$

Wherein

above-mentioned model has been contained satellite control system dynamics, kinematics, controller and various fault effects.

(2) embodiment of step 2:

According to satellite control system fault model in the step (1), the sensor failure that obtains to the transport function of output is:

$T_{f_s,i}=\left[\begin{array}{c}{F}_{s,i}\\ D_k{F}_{s,i}\end{array}\right]+\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{\mathrm{BD}}_k{F}_{s,i}\\ B_k{F}_{s,i}\end{array}\right]---\left(9\right)$

Wherein,

Expression sensor failure f _{S, i}To the transport function of output, f _{S, i}Expression f _sI fault, and F _{S, i}Representing matrix F _sI row.I representation unit matrix, s are the Laplace transformation parameter.

Topworks's fault to the transport function of output is:

$T_{f_a,j}=\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{F}_{a,j}\\ 0\end{array}\right]---\left(10\right)$

Wherein,

The expression fault f of topworks _{A, j}To the transport function of output, f _{A, j}Expression f _aJ fault, and F _{A, j}Representing matrix F _aJ row.

(3) embodiment of step 3:

The fault diagnosticability mainly comprises detectability and separability, provides analysis condition from these two aspects below.

1. fault detectability analysis condition

To satellite control system fault model shown in the formula (8), but whether in measurement information, embody, provide the detectability analysis condition to sensor and topworks's fault respectively through the failure judgement influence.

Sensor failure f in consideration formula (8) the institute representation model _{S, i}, then this fault has the condition of detectability and is:

Wherein at least one element is not equal to 0 in

expression

, and all elements all equals 0 in

expression

.

The fault f of topworks in consideration formula (8) the institute representation model _{A, j}, then this fault has the condition of detectability and is:

2. fault separability analysis condition

N fault in consideration formula (8) the institute representation model, then condition with separability of N fault is:

rank[T ₁?T ₂?…T _N]＝N

Wherein, if f _l∈ f _a, T then _lFor $\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{F}_a\\ 0\end{array}\right]$ Middle f _lCorresponding row;

If f _l∈ f _s, T then _lFor $\left[\begin{array}{c}{F}_s\\ D_k{F}_s\end{array}\right]+\left[\begin{array}{cc}C& 0\\ D_{k}C& C_k\end{array}\right]{(\mathrm{sI}-\left[\begin{array}{cc}A+B{D}_{k}C& {\mathrm{BC}}_k\\ B_{k}C& A_k\end{array}\right])}^{-1}\left[\begin{array}{c}{\mathrm{BD}}_k{F}_s\\ B_k{F}_s\end{array}\right]$ Middle f _lRespective column;

The order computing is asked in rank () expression;

l＝1，2，…N。

Based on the satellite control system fault model shown in the formula (8), but consider three measurement informations such as angle, angular velocity and controller signals (but each measurement information all is a variable independent and that can directly record), with infrared earth sensor fault f _{I, x}f _{I, y}, gyro failure f _{G, x}, f _{G, y}, f _{G, z}With momenttum wheel fault f _{M, 1}, f _{M, 2}, f _{M, 3}, f _{M, 4}Be object, fault detectability that provides above the utilization and separability analysis condition are analyzed the fault diagnosticability of satellite control system, related content (the diagnosis depth representing localization of fault degree of depth is to parts with localization of fault here) as shown in table 2.

Table 2 satellite control system diagnosticability related content

1. fault detectability analysis

According to formula (11) and formula (12); Whether is 0 through failure judgement to the transport function of exporting; Provide the detectability analysis result of various faults; As shown in table 3, can find out that therefrom all faults of consideration all have detectability (

representes empty set).

Table 3 satellite control system fault detectability analysis result

2. separability analysis

According to formula (13), as shown in table 4 through judging that various faults to the transport function of output linear dependence whether, provide the separability analysis result of various faults, can find out that therefrom all faults of consideration all have separability.

Table 4 satellite control system fault separability analysis result

The embodiment of step (4):

In order to weigh the quality of different system fault diagnosticability performance, the present invention proposes various quantitative targets and provides the corresponding calculated formula.

But the degree of detection f of fault mode _{D, i}Computing method be: $\left\{\begin{array}{cc}{f}_{d,i}=1& f_i\∈\mathrm{EF}\\ f_{d,i}=0& f_i\∈\mathrm{UF}\end{array}\right.,$ EF and UF are respectively can detect with undetectable fault and gather;

But the computing method of system failure degree of detection FDR are:

Wherein: m=|UF|+|EF| is the sum of satellite control system fault mode, λ _iBe the weighting coefficient of confirming according to fault i, | UF| representes the fault number among the undetectable fault set UF, | EF| representes the fault number among the detectable failure set EF.

The separable degree γ of fault mode _iComputing method be: ${\mathrm{\γ}}_i=\left\{\begin{array}{cc}1& f_i\∈\mathrm{EI}\\ \frac{1}{\left|F_n\right|}& f_i\∈F_n,F_n\∈\mathrm{UI}\end{array}\right.,$ EI and UI are separable and inseparable failure collection, | F _n| expression F _nIn the fault number;

The computing method of the separable degree FIR of the system failure are:

M is the sum of satellite control system fault mode, λ _iBe the weighting coefficient of confirming according to fault i.

Based on the fault diagnosability analysis result shown in table 3 and the table 4,, obtain fault mode and system diagnosability tolerance shown in table 5 and table 6 (weighting coefficient of supposing every kind of fault is 1) respectively according to the computing method of the fault diagnosticability tolerance that provides.

Table 5 fault mode fault diagnosticability tolerance

Table 6 satellite control system fault diagnosticability tolerance

But fault degree of detection	100％
		The separable degree of fault	100％

Can find out that from fault mode and the system failure diagnosticability tolerance measuring point configuring condition of satellite control system is enough at present, need not increase any measuring point again, just can satisfy the requirement of fault diagnosticability, can directly carry out Research on fault diagnosis method.

The present invention not detailed description is a technology as well known to those skilled in the art.

Claims (6)

1. the satellite control system diagnosticability based on transport function is confirmed method, it is characterized in that step is following:

(1), sets up the fault model of satellite control system according to kinetics equation, kinematical equation, controller model and the fault effects of satellite;

(2), obtain the transport function of each fault to output according to the satellite control system fault model of step (1);

(3) according to the transport function of each fault in the step (2) to output; Through judging that whether transport function is 0 to obtain the detectability condition of various faults; Through judge the corresponding transport function of different faults whether linear dependence obtain the separability condition of various faults, with satellite control system correlation parameter substitution detectability and separability condition acquisition satellite control system fault diagnosability analysis result;

(4) utilize diagnosticability metric calculation method that the fault diagnosability analysis result that step (3) obtains is calculated, but but obtain fault degree of detection and separable degree and the system failure degree of detection and the separable degree of satellite control system fault mode.

2. a kind of satellite control system diagnosticability based on transport function according to claim 1 is confirmed method, it is characterized in that: the satellite control system fault model that said step (1) is set up is:

Wherein:

θ, ψ is Eulerian angle;

x _kIntegral for x;

u＝[u _x?u _y?u _z] ^T；

Sensor failure

Topworks's fault

I _x, I _y, I _zBe respectively rigid body around coordinate axis Ox, Oy, the moment of inertia of Oz;

ω ₀Orbit angular velocity for satellite gravitation body rotation around the center;

u _x, u _y, u _zBe the component of satellite control moment along the principal moments axle;

A _k=0, C and B _kAll be 6 rank unit matrixs,

K _{P, x}, K _{P, y}, K _{P, z}The scale-up factor of expression satellite control system three direction of principal axis controllers;

K _{I, x}, K _{I, y}, K _{I, z}The integral coefficient of expression satellite control system three direction of principal axis controllers;

K _{D, x}, K _{D, y}, K _{D, z}The differential coefficient of expression satellite control system three direction of principal axis controllers;

Be momenttum wheel allocation matrix M _{4 * 3}Pseudo inverse matrix.

3. a kind of satellite control system diagnosticability based on transport function according to claim 2 is confirmed method, it is characterized in that: said step (2) obtains each fault and to the method for output-transfer function is:

According to the satellite control system fault model of step (1), the sensor failure that obtains to the transport function of output is:

Wherein,

Expression sensor failure f _{S, i}To the transport function of output, f _{S, i}Expression f _sI fault, and F _{S, i}Representing matrix F _sI row, I representation unit matrix, s are the Laplace transformation coefficient.

Topworks's fault to the transport function of output is:

Wherein,

The expression fault f of topworks _{A, j}To the transport function of output, f _{A, j}Expression f _aJ fault, F _{A, j}Representing matrix F _aJ row.

4. a kind of satellite control system diagnosticability based on transport function according to claim 3 is confirmed method, it is characterized in that: corresponding detectability and the separability analysis condition of said various faults is:

Sensor failure f _{S, i}The detectability condition be:

Wherein at least one element is not equal to 0 in

the expression transfer function matrix

, and all elements all equals 0 in

expression

;

The fault f of topworks _{A, j}The detectability condition be:

The condition that N fault has separability is:

rank[T ₁?T ₂…T _N]＝N

Wherein, if f _l∈ f _a, T then _lFor Middle f _lCorresponding row; If f _l∈ f _s, T then _lFor

Middle f _lRespective column;

The order computing is asked in rank () expression;

l＝1，2，…N。

5. a kind of satellite control system diagnosticability based on transport function according to claim 3 is confirmed method, it is characterized in that: said step (5) but in the degree of detection f of fault mode _{D, i}Computing method be:

EF and UF are respectively can detect with undetectable fault and gather;

But the computing method of system failure degree of detection FDR are:

Wherein: m=|UF|+|EF| is the sum of satellite control system fault mode, λ _iBe the weighting coefficient of confirming according to fault i, | UF| representes the fault number among the undetectable fault set UF, | EF| representes the fault number among the detectable failure set EF.

6. a kind of satellite control system diagnosticability based on transport function according to claim 3 is confirmed method, it is characterized in that: the separable degree γ of fault mode in the said step (5) _iComputing method be:

EI and UI are separable and inseparable failure collection, | F _n| expression F _nIn the fault number;

The computing method of the separable degree FIR of the system failure are:

m be satellite control

The sum of system failure pattern, λ _iBe the weighting coefficient of confirming according to fault i.

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