CN102778889B - The intermittent defect robust parsing method of spacecraft attitude control system - Google Patents

Abstract

The present invention discloses a kind of intermittent defect robust parsing method of spacecraft attitude control system, and step is: first set up spacecraft attitude control system mathematical model; Next sets up the mathematical model of intermittency check device fault; Use Lyapunov method design controller, and portray the behavior of posture control system under normal condition and failure condition respectively, describe the operation overall process with the attitude control system of the spacecraft of intermittent defect with stochastic systems model; And then the robust parsing problem of posture control system is converted into the stability analysis problem of the switched system with unstable mode, there is provided a kind of fault tolerance judgment criterion to judge whether current system is stablized in real time, as long as meet this criterion, then do not need to take any faults-tolerant control measure, system still can keep stable under the equilibrium activity of normal condition and malfunction.This invention can be avoided adopting the height produced in faults-tolerant control and faults-tolerant control implementation process to control energy consumption, high computation complexity and risk.

Description

The intermittent defect robust parsing method of spacecraft attitude control system

Technical field

The invention belongs to spacecraft attitude faults-tolerant control field, particularly a kind of robust parsing method of the intermittent defect for Spacecraft Control device.

Background technology

Spacecraft Attitude Control problem, the engineering important because of it and learning value, caused the great interest of people.Attitude control system of the spacecraft has high requirement to security, and the controller of posture control system, actuator, sensor and internal system all likely break down, and these faults can have a strong impact on the performance of system, even make system crash.Therefore posture control system needs to have certain fault-tolerant ability, guarantee its stability run and reliability.Method and Technology about spacecraft faults-tolerant control has had a lot of achievement, such as document (IEEE Transactions on Control Systems Technology, 2008,16 (4), 799-808), (Journal of Guidance, Control and Dynamics, 2008,31 (5), 1456-1463), (IET Control Theory & Applications, 2011,5 (2), 271-282) etc.These faults-tolerant control schemes only consider the failure condition of actuator and sensor mostly, and fault-tolerant core concept is after fault occurs, and by the impact regulated or reconfigurable controller produces system with compensate for failed, thus make failure system still stable operation.

Produce when occurring in the intermittent defect self of the controller of attitude control system of the spacecraft, time and disappear.When it happens, system works can be made to occur abnormal; When it disappears, system gets back to again normal duty.Intermittent defect is the main cause causing Circuits System to lose efficacy, and the probability of happening that this kind of fault mentioned by document (IEEE Transactions on Reliability, 1997,46, (2), 269-274) is 10 to 30 times of permanent fault.For the control circuit unit of attitude control system of the spacecraft, As time goes on the pad on each electrical equipment and circuit board can produce physical abrasion and break, or produces connection phenomenon off and on.This loose connection is the intermittent defect of a quasi-representative, directly can have influence on the output of controller, i.e. torque instruction voltage, and then affect the output of motor.Therefore, it is very necessary for carrying out robust parsing to the controller intermittent defect of posture control system.

But, rarely have report for the robust parsing of spacecraft intermittent defect and the achievement of design.As everyone knows, need the regular hour according to failure condition adjustment control to realize faults-tolerant control target, and consume certain control energy, this method is difficult to the intermittent defect being applicable to controller, and reason has three:

1) intermittent defect occurrence frequency is higher, if all remove adjustment control when these faults occur at every turn, certainly will will expend a lot of control energy consumptions;

2) adjustment control too continually, can produce serious overshoot, make the hydraulic performance decline of system, even unstable;

3) when controller itself fail, be difficult to go adjustment control to realize fault-tolerant target again.

Therefore, the present inventor attempts to propose a kind of easy controller intermittent defect robust parsing method, and this case produces thus.

Summary of the invention

Object of the present invention, be a kind of intermittent defect robust parsing method that spacecraft attitude control system is provided, it is for the intermittent defect of controller, the generation analyzing intermittent defect and the impact disappeared on system stability, obtain a fault tolerance judgment criterion, make when intermittent defect meets certain condition, do not need to take any faults-tolerant control measure, with the attitude control system of the spacecraft still stable operation of controller intermittent defect, thus avoid taking faults-tolerant control, and the height produced in faults-tolerant control implementation process controls energy consumption, high computation complexity and risk.

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

An intermittent defect robust parsing method for spacecraft attitude control system, comprises the steps:

(1) the attitude control system mathematical model of spacecraft is set up:

$J\stackrel{\·}{\mathrm{\ω}}=-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+\mathrm{\μ}+d$

$\stackrel{\·}{q}=\frac{1}{2}(q_4\mathrm{\ω}+{\mathrm{\ω}}^{\×}q)$

${\stackrel{\·}{q}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q$

Wherein, represent inertia angular velocity; q ₄scalar, q ₁, q ₂, q ₃, q ₄be expressed as hypercomplex number; J=J ^trepresent positive definite inertial matrix, μ represents that controller exports, i.e. control torque; D represents the uncertain of system and disturbance;

The equilibrium point of selection posture control system is: ω=q=0, q ₄=1, then have:

$\stackrel{\·}{q}=\frac{1}{2}({\tilde{q}}_4+1)\mathrm{\ω}+\frac{1}{2}{\mathrm{\ω}}^{\×}q$

${\stackrel{\·}{\tilde{q}}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q$

Wherein, ${\tilde{q}}_4\stackrel{\mathrm{\Δ}}{=}{q}_4-1;$

(2) the controller mathematical model with intermittent defect is set up:

Use μ _σrepresent that the controller with intermittent defect exports, wherein subscript σ (t) is a time dependent switching function, { 0, value in 1}, wherein 0 represents that controller is in normal condition, and 1 represents that controller is in intermittent defect situation, according to the occurrence characteristic of intermittent defect, this switching function Markov chain describes, namely

$P\{\mathrm{\σ}(t+\mathrm{\Δ})=j|\mathrm{\σ}\left(t\right)=i\}=\left\{\begin{array}{cc}{\mathrm{\ρ}}_{\mathrm{ij}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right),& i\≠j\\ 1+{\mathrm{\ρ}}_{\mathrm{ii}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right)& i=j\end{array}\right.$

Wherein, 0≤ρ _ij≤ 1 represents from pattern i to pattern j the rate of transform of (i ≠ j), ρ _ii=-∑ _{j ≠ i}ρ _ij; △ >0 is Infinite-dimensional interval transfer time, and ο (△) is higher-order shear deformation;

According to attitude control system model, the calm state controller μ of design ₀, this controller is changed to μ in case of a fault ₁;

(3) with the stochastic systems descriptive system operational process with unstable mode:

Attitude control system model is at μ _σeffect under be written as switched system:

dx(t)=f _σ(t)(x(t))dt

Wherein state f _σobtained by attitude control system model;

(4) fault tolerance judgment criterion is set up:

Define symbol η ₀and η ₁the state convergency factor of the system that is respectively under normal condition and failure condition and diverging rate, definition △ t ₁for system work T.T. under normal circumstances in the time period [0, t], △ t ₂for the work T.T. under system fault conditions in the time period [0, t], $\stackrel{\‾}{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{\right|{\mathrm{\ρ}}_{\mathrm{ii}}\left|\right|i\∈M\},$ $\widetilde{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{{\mathrm{\ρ}}_{\mathrm{ij}}\right|i,j\∈M\};$

The design of fault tolerance judgment criterion is as follows:

In t, make if there is a constant beta >0

$e^{-{\mathrm{\η}}_0\mathrm{\Δ}{t}_1+{\mathrm{\η}}_1\mathrm{\Δ}{t}_2}\≤\mathrm{\β}{e}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t},$ $\∀t\≥0$

So spacecraft attitude control system is stable under the effect of intermittent defect.

In above-mentioned steps (1), indeterminate is unknown function d (x) of system state, meets Lipschitz condition, namely for known positive number.

In above-mentioned steps (2), Controller gain variations is under normal circumstances as follows:

${\mathrm{\μ}}_0={\mathrm{\ω}}^{\×}\mathrm{J\ω}-k_1\mathrm{J\ω}-\frac{1}{2}\mathrm{Jq}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)$

Wherein, k ₁>0, k ₂>0, k ₃>0, ε >0 is an arbitrarily small constant;

Under failure condition, the circuit performance of controller is abnormal, causes gain amplifier to change, controller μ ₀become

${\mathrm{\μ}}_1={\mathrm{\ω}}^{\×}\mathrm{J\ω}{k}_1^f\mathrm{J\ω}-\frac{1}{2}\mathrm{Jq}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)$

Wherein, all represent the gain coefficient under fault, this makes the output of controller depart from normal value.

In above-mentioned steps (3), ask for state convergency factor η under normal circumstances by the following method ₀with the state emission rate η under failure condition ₁:

Under normal circumstances, a Liapunov conditional function is defined definition: ${\mathrm{LV}}_p\left(x\right)\stackrel{\mathrm{\Δ}}{=}\frac{\∂V_p\left(x\right)}{\∂x}{f}_p\left(x\right),p=\mathrm{0,1}$

By selecting suitable k ₁, k ₂, k ₃, have

${\mathrm{LV}}_0=2{\mathrm{\ω}}^T{J}^{-1}(-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+{\mathrm{\μ}}_0)+q^T({\tilde{q}}_4+1)\mathrm{\ω}-{\tilde{q}}_4^T{\mathrm{\ω}}^{T}q+\stackrel{\‾}{d}{V}_0$

$=-2k_1{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}(-k_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0$

$\≤-{\mathrm{\η}}_0{V}_0$

Wherein, η ₀be greater than 0, show the system that controller can be calmed under normal circumstances, V ₀exponential convergence;

In case of a fault, have

${\mathrm{LV}}_0=2k_1^f{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}(-k_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0\≤{\mathrm{\η}}_1{V}_0$

Wherein η ₁>0, under showing failure condition, system is no longer stable, function V ₀index is dispersed.

In above-mentioned steps (4), fault tolerance judgment criterion is applicable to any time, namely in any t, if there is a constant beta >0, makes

$e^{-{\mathrm{\η}}_0\mathrm{\Δ}{t}_1+{\mathrm{\η}}_1\mathrm{\Δ}{t}_2}\≤\mathrm{\β}{e}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t},$ $\∀t\≥0$

So spacecraft attitude control system is still stable under the effect of intermittent defect.

After adopting such scheme, the present invention make full use of intermittent defect time and occur with time and the feature disappeared, as long as meet the fault tolerance judgment criterion that the present invention proposes, posture control system still can keep stable under the equilibrium activity of normal condition and malfunction, in this case, do not need to take any faults-tolerant control measure, system still can keep stable under the equilibrium activity of normal condition and malfunction, namely do not need as traditional fault tolerant control method, controller is reconstructed.This method avoid the height produced in faults-tolerant control implementation process and control energy consumption, high computation complexity and risk, require high reliability for spacecraft is this and needs the complication system of high energy consumption to have important practical significance.

Accompanying drawing explanation

Fig. 1 is the structured flowchart of attitude control system in the present invention;

Fig. 2 is the fault-tolerance approach schematic diagram that the present invention is based on switched system;

Fig. 3 is the trajectory diagram of first switching function;

Fig. 4 is the state trajectory figure of attitude control system corresponding diagram 3;

Fig. 5 is the trajectory diagram of second switching function;

Fig. 6 is the state trajectory figure of attitude control system corresponding diagram 5.

Embodiment

Below with reference to accompanying drawing, technical scheme of the present invention and beneficial effect are described in detail.

The invention provides a kind of intermittent defect robust parsing method of spacecraft attitude control system, comprise the steps:

(1) set up the attitude control system mathematical model of spacecraft, be spacecraft body module, executor module and sensor assembly in Fig. 1;

$J\stackrel{\·}{\mathrm{\ω}}=-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+\mathrm{\μ}+d---\left(1\right)$

$\stackrel{\·}{q}=\frac{1}{2}(q_4\mathrm{\ω}+{\mathrm{\ω}}^{\×}q)---\left(2\right)$

${\stackrel{\·}{q}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q---\left(3\right)$

Wherein, represent inertia angular velocity; q ₄scalar, q ₁, q ₂, q ₃, q ₄be expressed as hypercomplex number; J=J ^trepresent positive definite inertial matrix, μ represents that controller exports, i.e. control torque.Indeterminate is unknown function d (x) of system state, d (x) meets Lipschitz condition, namely for known positive number.Cross product form is:

${\mathrm{\ω}}^{\×}=\left[\begin{array}{ccc}0& -{\mathrm{\ω}}_3& {\mathrm{\ω}}_2\\ {\mathrm{\ω}}_3& 0& -{\mathrm{\ω}}_1\\ -{\mathrm{\ω}}_2& {\mathrm{\ω}}_1& 0\end{array}\right]$

The equilibrium point of selection posture control system is: ω=q=0, q ₄=1, then (2)-(3) formula can be rewritten as:

$\stackrel{\·}{q}=\frac{1}{2}({\tilde{q}}_4+1)\mathrm{\ω}+\frac{1}{2}{\mathrm{\ω}}^{\×}q---\left(4\right)$

${\stackrel{\·}{\tilde{q}}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q---\left(5\right)$

Wherein, ${\tilde{q}}_4\stackrel{\mathrm{\Δ}}{=}{q}_4-1.$

(2) set up intermittency check device fault mathematical model, determine markovian rate of transform ρ ₁₀(i.e. the probability of intermittent defect disappearance) and ρ ₀₁(probability that intermittence fault occurs);

Use μ _σrepresent that the controller adopting State Feedback Design exports, i.e. control torque.Wherein subscript σ (t) is a time dependent switching function, value in 0,1}, wherein 0 represents that controller is in normal condition, 1 represents that controller is in intermittent defect situation, this means that the output valve of controller may the saltus step because of failure condition.According to the occurrence characteristic of intermittent defect, this switching function Markov chain describes, namely

$P\{\mathrm{\σ}(t+\mathrm{\Δ})=j|\mathrm{\σ}\left(t\right)=i\}=\left\{\begin{array}{cc}{\mathrm{\ρ}}_{\mathrm{ij}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right),& i\≠j\\ 1+{\mathrm{\ρ}}_{\mathrm{ii}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right)& i=j\end{array}\right.$

Wherein, 0≤ρ _ij≤ 1 represents from pattern i to pattern j the rate of transform of (i ≠ j), ρ _ii=-∑ _{j ≠ i}ρ _ij.△ >0 is the time interval without the transition by means of the spirit of being poor, and ο (△) is higher-order shear deformation.

Controller gain variations is under normal circumstances as follows:

${\mathrm{\μ}}_0={\mathrm{\ω}}^{\×}\mathrm{J\ω}-k_1\mathrm{J\ω}-\frac{1}{2}\mathrm{Jq}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)---\left(6\right)$

Wherein, k ₁>0, k ₂>0, k ₃>0, ε >0 is an arbitrarily small constant.

The controller intermittent defect considered is physical abrasion because each pad in control circuit chip produces due to the passing of time and breaks or loosen and cause.This loose connection is a typical intermittent fault, can make the property abnormality of control circuit, causes gain amplifier to change.Under failure condition, controller μ ₀(6) become

${\mathrm{\μ}}_1={\mathrm{\ω}}^{\×}\mathrm{J\ω}{k}_1^f\mathrm{J\ω}-\frac{1}{2}\mathrm{Jq}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)---\left(7\right)$

Wherein, all represent the gain coefficient under fault, this makes the output of controller depart from normal value.

(3) based on Lyapunov function (Lyapunov function) method design canonical controller μ ₀, be the controller module in Fig. 1, and calculate Lyapunov function V ₀convergency factor η ₀, passed to robust parsing module;

Attitude control system model (1) (4) (5) are at μ _σeffect under can be written as switched system:

dx(t)=f _σ(t)(x(t))dt

Wherein, state f _σcan be obtained by attitude control system model.

Under normal circumstances, a Liapunov conditional function is defined definition: ${\mathrm{LV}}_p\left(x\right)\stackrel{\mathrm{\Δ}}{=}\frac{\∂V_p\left(x\right)}{\∂x}{f}_p\left(x\right),p=\mathrm{0,1}$

By selecting suitable k ₁, k ₂, k ₃, have

${\mathrm{LV}}_0=2{\mathrm{\ω}}^T{J}^{-1}(-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+{\mathrm{\μ}}_0)+q^T({\tilde{q}}_4+1)\mathrm{\ω}-{\tilde{q}}_4^T{\mathrm{\ω}}^{T}q+\stackrel{\‾}{d}{V}_0$

$=-2k_1{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}(-k_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0$

$\≤-{\mathrm{\η}}_0{V}_0$

Wherein, η ₀be greater than 0, under the effect of controller formula (6) as can be seen from the above equation, Liapunov conditional function V ₀with exponential form convergence, convergency factor is η ₀.

In case of a fault, have

${\mathrm{LV}}_0=2k_1^f{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}(-k_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0\≤{\mathrm{\η}}_1{V}_0$

Wherein η ₁>0, after breaking down as can be seen from the above equation, controller formula (7) no longer can be calmed system, function V ₀disperse with exponential form, convergency factor is η ₁.

Therefore switched system dx (t)=f _{σ (t)}the mode 0 of (x (t)) dt is stablized, and mode 1 is unstable.

This stochastic systems is used to have two advantages:

1) behavior of the whole process of posture control system can be analyzed easily, instead of study the situation before fault and after fault separately.This is very important for the system action analyzed under intermittent defect;

2) Fault-Tolerant Problems of posture control system can be converted into the stability problem of the switched system with unstable mode, can use the analysis tool that some are very useful to switched system.

(4) fault tolerance judgment criterion is set up:

Definition △ t ₁for the work T.T. under system normal condition (pattern 0 is run) in the time period [0, t], △ t ₂for the work T.T. under system fault conditions (pattern 1) in the time period [0, t], definition

$\stackrel{\‾}{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{\right|{\mathrm{\ρ}}_{\mathrm{ii}}\left|\right|i\∈M\},$ $\widetilde{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{{\mathrm{\ρ}}_{\mathrm{ij}}\right|i,j\∈M\};$

The design of fault tolerance judgment criterion is as follows:

In t, make if there is a constant beta >0

$e^{-{\mathrm{\η}}_0\mathrm{\Δ}{t}_1+{\mathrm{\η}}_1\mathrm{\Δ}{t}_2}\≤\mathrm{\β}{e}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t},$ $\∀t\≥0---\left(8\right)$

So spacecraft attitude control system is stable under the effect of intermittent defect.

For simplicity, η is replaced with common η below ₀and η ₁.Use mark N _{σ (t)}expression system is at [0, the t] switching times in the time period.Use t _kthe kth time switching instant of representative system.

Suppose to have switched j time at moment t, i.e. t>=t _j.By obtain:

$E\left[V_0\left(x\left(t\right)\right)\right]\≤E\left[e^{\mathrm{\η}(t-t_j)}{V}_0\left(x\left(t_j\right)\right)\right]$

$\≤E\left[e^{\mathrm{\η}(t-t_{j-1})}{V}_0\left(x\left(t_{j-1}\right)\right)\right]$

$\begin{array}{c}.\\ .\\ .\end{array}$

$\≤E\left[e^{\mathrm{\ηt}}{V}_0\left(x\left(0\right)\right)\right]$

$\≤\underset{j=0}{\overset{\∞}{\mathrm{\Σ}}}P(N_{\mathrm{\σ}\left(t\right)}=j)e^{\mathrm{\ηt}}{V}_0\left(x\left(0\right)\right)$

$\≤\underset{j=0}{\overset{\∞}{\mathrm{\Σ}}}\frac{e^{-\widetilde{\mathrm{\λ}}t}{\left(\stackrel{\‾}{\mathrm{\λ}}t\right)}^j}{j!}\mathrm{\β}{e}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t}{V}_0\left(x\left(0\right)\right)$

$\≤\mathrm{\β}{V}_0\left(x\left(0\right)\right)$

As can be seen from the above equation, in whole system operational process, if fault-tolerant condition (8) meets, then under the impact of intermittent defect, the mathematical expectation of state x (t) is still bounded all the time, and is tending towards initial point and trends towards initial point along with x (0).

Fault tolerance judgment criterion (8) take full advantage of intermittent defect time and occur with time and the feature disappeared.The core of this criterion is to use the balance between unstable mode and stable mode to go calm system.If the working time long enough of system under normal condition (failure vanishes), and when fault occurs the working time enough short, so system still can ensure to stablize, and system performance and β have chosen much relations, and this value is selected according to the demand of posture control system usually.

The Detection and diagnosis mechanism of design intermittent defect, is fault diagnosis module, according to being

LV ₀≤-η ₀V ₀（9）

If in t, above-mentioned inequality (9) does not meet, then think and have fault to occur in t.If some fault there occurs, inequality (9) still meets, then think that this fault does not destroy the stability of system, without the need to detecting.

In the process of system cloud gray model, operation troubles diagnostic module all the time, the input of this module real-time acquisition system and status information, after detecting that intermittent defect occurs, calculate the diverging rate η of failure condition minor function ₁, by time of failure and value η ₁pass to robust parsing module.If at certain moment failure vanishes, the moment of failure vanishes is also passed to robust parsing module by fault diagnosis module;

(5) robust parsing module receives time of failure, diverging rate η ₁and after the failure vanishes time; according to fault tolerance judgment criterion (8); the stability that judgement system is current; if met, system continues to run, and does not take any faults-tolerant control or safeguard measure, because in the time in the past; the working time long enough of system under normal condition (failure vanishes); and when fault occurs the working time enough short, therefore system still can ensure to stablize, as shown in Figure 2.If judge that current system is unstable, then report to the police, now must take faults-tolerant control measure.

Below with the validity of simulating, verifying the inventive method.

When emulating, select inertial matrix:

$J=\left[\begin{array}{ccc}1200& 100& -200\\ 100& 2200& 300\\ -200& 300& 3100\end{array}\right]\mathrm{kg}\·m^2$

Assuming that indeterminate is d=0.1W ω, wherein W is the Brownian movement of standard, represents noise.Initial parameter is elected as

(ω ₁ω ₂ω ₃)=(0.2 -0.1 0.1)(rad/s)

(q ₁q ₂q ₃q ₄)=(0.5 0.5 0.5 -0.5)

Assuming that intermittent defect meets-ρ ₀₀=ρ ₀₁=0.5 and-ρ ₁₁=ρ ₁₀=0.8, the parameter designing k of controller ₁=k ₂=k ₃=10, ε=0.001, when there is intermittent defect, parameter becomes make β=2.

Due to fault generation and disappear be all random, therefore do two groups of emulation.Fig. 3 gives at the curve of 0 second time period to the switching function of first in 20 seconds, indicates each moment that fault occurs and disappears.Through inspection, under the failure condition shown in Fig. 3, fault tolerance judgment criterion was all satisfied at 0 second to any time in 20 seconds, Fig. 4 gives corresponding system state track, although can find out and have intermittent defect to occur, but system state (i.e. attitude angular velocity and hypercomplex number) is not taked when any faults-tolerant control to be still bounded at the original controller of maintenance, this demonstrates the validity of fault-tolerant criterion provided by the present invention.Similar, Fig. 5 gives at the curve of 0 second time period to the switching function of second in 20 seconds, curve shown in this curve with Fig. 3 is different, but through inspection, under the failure condition shown in Fig. 5, fault tolerance judgment criterion was also all satisfied at 0 second to any time in 20 seconds, and Fig. 6 gives corresponding system state track, can find out that system state is still bounded when not taking any faults-tolerant control, this indicates the validity of fault-tolerant criterion provided by the present invention equally.

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 (4)

1. an intermittent defect robust parsing method for spacecraft attitude control system, is characterized in that comprising the steps:

(1) the attitude control system mathematical model of spacecraft is set up:

$J\stackrel{.}{\mathrm{\ω}}=-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+\mathrm{\μ}+d$

$\stackrel{.}{q}=\frac{1}{2}(q_4\mathrm{\ω}+{\mathrm{\ω}}^{\×}q)$

${\stackrel{.}{q}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q$

Wherein, represent inertia angular velocity; q ₄scalar, q ₁, q ₂, q ₃, q ₄be expressed as hypercomplex number; J=J ^trepresent positive definite inertial matrix, μ represents that controller exports, i.e. control torque; D represents the uncertain of system and disturbance;

The cross product form of ω is:

${\mathrm{\ω}}^{\×}=\left[\begin{array}{ccc}0& {-\mathrm{\ω}}_3& {\mathrm{\ω}}_2\\ {\mathrm{\ω}}_3& 0& -{\mathrm{\ω}}_1\\ {-\mathrm{\ω}}_2& {\mathrm{\ω}}_1& 0\end{array}\right]$

The equilibrium point of selection posture control system is: ω=q=0, q ₄=1, then have:

$\stackrel{.}{q}=\frac{1}{2}({\tilde{q}}_4+1)\mathrm{\ω}+\frac{1}{2}{\mathrm{\ω}}^{\×}q$

${\stackrel{\stackrel{.}{~}}{q}}_4=-\frac{1}{2}{\mathrm{\ω}}^{T}q$

Wherein, ${\tilde{q}}_4\stackrel{\mathrm{\Δ}}{=}{q}_4-1;$

(2) the controller mathematical model with intermittent defect is set up:

Use μ _σrepresent that the controller with intermittent defect exports, wherein subscript σ (t) is a time dependent switching function, { 0, value in 1}, wherein 0 represents that controller is in normal condition, and 1 represents that controller is in intermittent defect situation, according to the occurrence characteristic of intermittent defect, this switching function Markov chain describes, namely

$P\{\mathrm{\σ}(t+\mathrm{\Δ})=j|\mathrm{\σ}\left(t\right)=i\}=\left\{\begin{array}{cc}{\mathrm{\ρ}}_{\mathrm{ij}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right),& i\≠j\\ 1+{\mathrm{\ρ}}_{\mathrm{ii}}\mathrm{\Δ}+o\left(\mathrm{\Δ}\right)& i=j\end{array}\right.$

Wherein, 0≤ρ _ij≤ 1 represents the rate of transform from pattern i to pattern j, and i ≠ j, ρ _ii=-∑ _{j ≠ i}ρ _ij; Δ >0 is Infinite-dimensional interval transfer time, and ο (Δ) is higher-order shear deformation;

According to attitude control system model, the calm state controller μ of design ₀, this controller is changed to μ in case of a fault ₁;

(3) with the stochastic systems descriptive system operational process with unstable mode:

Attitude control system model is at μ _σeffect under be written as switched system:

dx(t)＝f _σ(t)(x(t))dt

Wherein state f _σobtained by attitude control system model;

Wherein, state convergency factor η is under normal circumstances asked for by the following method ₀with the state emission rate η under failure condition ₁:

Under normal circumstances, a Liapunov conditional function is defined definition:

${\mathrm{LV}}_0\left(x\right)\stackrel{\mathrm{\Δ}}{=}\frac{{\∂V}_0\left(x\right)}{\∂x}{f}_0\left(x\right),$

By selecting suitable k ₁, k ₂, k ₃, have

$\begin{array}{c}{\mathrm{LV}}_0={2\mathrm{\ω}}^T{J}^{-1}(-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+{\mathrm{\μ}}_0)+q^T({\tilde{q}}_4+1)\mathrm{\ω}-{\tilde{q}}_4^T{\mathrm{\ω}}^{T}q+\stackrel{\‾}{d}{V}_0\\ =-{2k}_1{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}({-k}_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0\\ \≤{-\mathrm{\η}}_0{V}_0\end{array}$

Wherein, k ₁>0, k ₂>0, k ₃>0, ε >0 is an arbitrarily small constant, η ₀be greater than 0, show the system that controller can be calmed under normal circumstances, V ₀exponential convergence, for known positive number;

In case of a fault, have

${\mathrm{LV}}_0={2k}_1^f{\mathrm{\ω}}^T\mathrm{\ω}+\frac{{\mathrm{\ω}}^T\mathrm{\ω}}{{\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ}}({-k}_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)+\stackrel{\‾}{d}{V}_0\≤{\mathrm{\η}}_1{V}_0$

Wherein η ₁>0, under showing failure condition, system is no longer stable, function V ₀index is dispersed, $k_2^f>0,$ $k_3^f>0,$ all represent the gain coefficient under fault;

(4) fault tolerance judgment criterion is set up:

Define symbol η ₀and η ₁the state convergency factor of the system that is respectively under normal condition and failure condition and diverging rate, definition Δ t ₁for system work T.T. under normal circumstances in the time period [0, t], Δ t ₂for the work T.T. under system fault conditions in the time period [0, t], $\stackrel{\‾}{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{\right|{\mathrm{\ρ}}_{\mathrm{ii}}\left|\right|i\∈M\left|\right\},$ $\stackrel{\‾}{\mathrm{\λ}}\stackrel{\mathrm{\Δ}}{=}\max \left\{\right|{\mathrm{\ρ}}_{\mathrm{ii}}\left|\right|i,j\∈M\left|\right\};$

The design of fault tolerance judgment criterion is as follows:

In t, make if there is a constant beta >0

$e^{-{\mathrm{\η}}_0{\mathrm{\Δt}}_1+{\mathrm{\η}}_1{\mathrm{\Δt}}_2}\≤{\mathrm{\βe}}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t},$ $\∀t\≥0$

So spacecraft attitude control system is stable under the effect of intermittent defect.

2. the intermittent defect robust parsing method of spacecraft attitude control system as claimed in claim 1, is characterized in that: in described step (1), indeterminate is unknown function d (x) of system state, meets Lipschitz condition, namely for known positive number.

3. the intermittent defect robust parsing method of spacecraft attitude control system as claimed in claim 1, is characterized in that: in described step (2), Controller gain variations is under normal circumstances as follows:

${\mathrm{\μ}}_0={\mathrm{\ω}}^{\×}\mathrm{J\ω}-k_1\mathrm{J\ω}-\frac{1}{2}\mathrm{Jq}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2{q}^{T}q-k_3{\tilde{q}}_4^T{\tilde{q}}_4)$

Wherein, k ₁>0, k ₂>0, k ₃>0, ε >0 is an arbitrarily small constant;

Under failure condition, the circuit performance of controller is abnormal, causes gain amplifier to change, controller μ ₀become

${\mathrm{\μ}}_1={\mathrm{\ω}}^{\×}\mathrm{J\ω}{k}_1^f\mathrm{J\ω}-\frac{1}{2}\mathrm{Jp}+\frac{\mathrm{J\ω}}{2({\mathrm{\ω}}^T\mathrm{\ω}+\mathrm{\ϵ})}(-k_2^f{q}^{T}q-k_3^f{\tilde{q}}_4^T{\tilde{q}}_4)$

Wherein, all represent the gain coefficient under fault, this makes the output of controller depart from normal value.

4. the intermittent defect robust parsing method of spacecraft attitude control system as claimed in claim 1, it is characterized in that: in described step (4), fault tolerance judgment criterion is applicable to any time, namely in any t, if there is a constant beta >0, make

$e^{-{\mathrm{\η}}_0{\mathrm{\Δt}}_1+{\mathrm{\η}}_1{\mathrm{\Δt}}_2}\≤{\mathrm{\βe}}^{(\widetilde{\mathrm{\λ}}-\stackrel{\‾}{\mathrm{\λ}})t},$ $\∀t\≥0$

So spacecraft attitude control system is still stable under the effect of intermittent defect.