CN105068425A - State feedback robustnon-fragile control method applicable for determination of agile satellite postures - Google Patents

Abstract

The invention provides a state feedback robust non-fragile control method applicable for determination of agile satellite postures. The objective is to solve problems of high fragility and restrains on control input of a current controller. The control method comprises following steps of 1:obtaining a satellite posture system state equation according to a satellite posture kinetic equation based on the model parameter uncertainty Delta A, external disturbance torque w(t), controller gain perturbation and gyroscopic drift d(t); 2: obtaining a state feedback controller gain matrix K according to the satellite posture kinetic equation; 3) obtaining a theoretical control input torque [mu](t) according to the state feedback controller gain matrix K; and 4) judging whether the theoretical control input torque is smaller than the upper limit of the actual control input torque so as to determine postures of satellite in the time tk. The control method is applicable for satellite field.

Description

A kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining

Technical field

The present invention relates to the Robust State-Feedback non-fragiie control method that the attitude of satellite is determined.

Background technology

The design of quick satellite attitude control system is very complicated, and its control accuracy and control efficiency play a part very crucial for the aerial mission of satellite.Owing to usually there is a lot of disturbing factor in quick satellite operation environment, as model parameter uncertainty, gyroscopic drift, external interference moment, controller gain perturbations etc., these factors can affect the serviceability of satellite, therefore need to design high performance controller.In the controls, robustness mainly refers to that resisting external disturbance makes self to keep the ability of stability comparatively strong, and fragility causes due to controller self perturbation, changes more responsive to inherent parameters.When designing the robust non-fragile controller of attitude of satellite system, the problem of can not ignore run into is that the control inputs of system is limited, causes that the fragility of existing controller is high and control inputs is limited.

Summary of the invention

The object of the invention is the problem that fragility is high and control inputs is limited in order to solve existing controller, and propose a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining.

Above-mentioned goal of the invention is achieved through the following technical solutions:

Step one, according to Dynamical Attitude Equations, when model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), obtain attitude of satellite system state equation;

Step 2, according to attitude of satellite system state equation, obtain state feedback controller gain matrix K;

Step 3, given satellite initial attitude x (0), according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks.

Invention effect

Adopt a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining of the present invention, satellite considers model parameter uncertainty in gesture stability process, gyroscopic drift, external interference moment, the impact of controller gain perturbations factor, these uncertain factors are taken into account Satellite Attitude Control System state equation, according to the known coefficient matrix in system state equation, propose three LMIs, convex optimization problem under utilizing the mincx function in LMI tool box to solve LMI constraint, and then obtain the gain matrix of Robust State-Feedback non-fragile controller, thus the problem that the fragility solving controller is high, additional saturated process is carried out to theoretical control inputs moment, solve the problem that control inputs is limited.When considering that model parameter uncertainty, gyroscopic drift, external interference moment and the gain of controller addition type are perturbed at the same time, the control inputs moment that the attitude angle of satellite, attitude angular velocity and topworks provide can be obtained, as shown in figs 2-4.Can find out, designed robust non-fragile controller can make satellite closed cycle attitude control system reach steady state (SS) in 15s, and under this controller action, the control inputs moment maximal value of satellite is no more than 0.25Nm.Non-fragiie control is not also mentioned in this in satellite gravity anomaly field; The control inputs moment upper limit of Fig. 5 has exceeded the control inputs moment upper limit of 0.25Nm, Fig. 4 not more than 0.25Nm.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that Robust State-Feedback non-fragile controller controls;

Fig. 2 is the attitude angle of satellite under the effect of Robust State-Feedback non-fragile controller, wherein, solid line represents the roll angle of satellite, dotted line represents the angle of pitch of satellite, phase line represents the crab angle of satellite, and θ is the angle of pitch of satellite, and ψ is the crab angle of satellite, for the roll angle of satellite, rad is radian;

Fig. 3 is the attitude angular velocity of satellite under the effect of Robust State-Feedback non-fragile controller, wherein, solid line represents the rate of roll of satellite, dotted line represents the rate of pitch of satellite, phase line represents the yaw rate of satellite, and rad/s is radian per second;

Fig. 4 is the working control input torque of satellite under the effect of Robust State-Feedback non-fragile controller, wherein, solid line represents the working control input torque of satellite around the axis of rolling, dotted line represents the working control input torque of satellite around pitch axis, phase line represents the working control input torque of satellite around yaw axis, u _xfor satellite is around the working control input torque of the axis of rolling, u _yfor satellite is around the working control input torque of pitch axis, u _zfor satellite is around the working control input torque of yaw axis, Nm is ox rice;

Fig. 5 is the theoretical control inputs moment of satellite under the effect of Robust State-Feedback non-fragile controller, wherein, solid line represents the theoretical control inputs moment of satellite around the axis of rolling, dotted line represents the theoretical control inputs moment of satellite around pitch axis, phase line represents the theoretical control inputs moment of satellite around yaw axis.

Embodiment

Embodiment one: composition graphs 1 illustrates present embodiment, a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining, it is characterized in that, be a kind ofly applicable to that Robust State-Feedback non-fragiie control method that the quick attitude of satellite determines specifically carries out according to the following steps:

Step one, according to Dynamical Attitude Equations, when model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), obtain attitude of satellite system state equation;

Step 2, according to attitude of satellite system state equation, obtain state feedback controller gain matrix K;

Step 3, given satellite initial attitude x (0), according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks.

Embodiment two: present embodiment and embodiment one unlike: according to Dynamical Attitude Equations in described step one, when model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), obtain attitude of satellite system state equation, detailed process is:

Dynamical Attitude Equations is:

$I_x\left\{\begin{array}{c}{I}_x{\stackrel{\·}{\mathrm{\ω}}}_x+(I_z-I_y){\mathrm{\ω}}_y{\mathrm{\ω}}_z=T_{cx}+T_{gx}+T_{dx}\\ I_y{\stackrel{\·}{\mathrm{\ω}}}_y+(I_x-I_z){\mathrm{\ω}}_z{\mathrm{\ω}}_x=T_{cy}+T_{g\mathrm{\ν}}+T_{dy}\\ I_z{\stackrel{\·}{\mathrm{\ω}}}_z+(I_y-I_x){\mathrm{\ω}}_x{\mathrm{\ω}}_y=T_{cz}+T_{gz}+T_{dz}\end{array}\right.---\left(1\right)$

In formula, I _xfor satellite orbit coordinate system x-axis moment of inertia, I _yfor satellite orbit coordinate system y-axis moment of inertia, I _zfor satellite orbit coordinate system z-axis moment of inertia, ω _xfor satellite orbit coordinate system x-axis measuring satellite angular velocities, ω _yfor satellite orbit coordinate system y-axis measuring satellite angular velocities, ω _zfor satellite orbit coordinate system z-axis measuring satellite angular velocities, T _cxfor the control inputs moment of satellite orbit coordinate system x-axis, T _cyfor the control inputs moment of satellite orbit coordinate system y-axis, T _czfor the control inputs moment of satellite orbit coordinate system z-axis, T _gxfor satellite orbit coordinate system x-axis gravity gradient torque, T _gyfor satellite orbit coordinate system y-axis gravity gradient torque, T _gzfor satellite orbit coordinate system z-axis gravity gradient torque, T _dxfor satellite orbit coordinate system x-axis external interference moment, T _dyfor satellite orbit coordinate system y-axis external interference moment, T _dzfor satellite orbit coordinate system z-axis external interference moment, for the first order derivative of satellite orbit coordinate system x-axis angular velocity, for the first order derivative of satellite orbit coordinate system y-axis angular velocity, for the first order derivative of satellite orbit coordinate system z-axis angular velocity;

Wherein,

In formula, ω ₀for orbit angular velocity, for roll angle, θ is the angle of pitch;

Be located under attitude angle is less than the angle of 10 °, measuring satellite angular velocities is:

In formula, for first order derivative, ψ is crab angle, for the first order derivative of θ, for the first order derivative of ψ;

Adopt zyx rotating manner, obtaining attitude dynamic equations is:

In formula, for second derivative, for the second derivative of θ, for the second derivative of ψ;

When model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), definition status variable is utilize the surveying instrument such as star sensor and gyroscope to record output variable to be by above-mentioned attitude dynamic equations linearization, draw attitude of satellite system state equation:

$\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=(A+\mathrm{\Δ}A)x\left(t\right)+B_{1}u\left(t\right)+B_{2}w\left(t\right)\\ y\left(t\right)=C_{1}x\left(t\right)+D_{1}d\left(t\right)+D_2\\ z\left(t\right)=C_{2}x\left(t\right)\end{array}---\left(5\right)$

In formula, u (t) is theoretical control inputs moment, and w (t) is external interference moment, and z (t) is control output variable, for the first order derivative of t state variable, the output variable that y (t) is t, the state variable that x (t) is t, B ₁for control inputs matrix of coefficients, B ₂for external interference matrix of coefficients, C ₁for coefficient of regime matrix in output can be surveyed, C ₂for controlling coefficient of regime matrix in output, D ₁for Gyro drift coefficient matrix, D ₂for surveying constant value matrix in output, A is model coefficient matrix, and Δ A is model parameter uncertainty, and its form is

ΔA＝M ₁F ₁(t)N ₁

(6)

F ₁(t) ^TF ₁(t)≤I

In formula, M ₁for determining the known constant real matrix of Δ A line number, N ₁for determining the known constant real matrix of Δ A columns, F ₁t (), for determining that Δ A changes the unknown matrix of speed, I is unit diagonal matrix, and T is matrix transpose symbol;

Definition gyroscopic drift is constant value drift:

$A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ A_{41}& 0& 0& 0& 0& -{\mathrm{\ω}}_0{I}_x^{-1}(I_y-I_x-I_z)\\ 0& A_{52}& 0& 0& 0& 0\\ 0& 0& A_{63}& {\mathrm{\ω}}_0{I}_z^{-1}(I_y-I_x-I_z)& 0& 0\end{array}\right]$

$A_{41}=-4{\mathrm{\ω}}_0^2{I}_x^{-1}(I_y-I_z)$

$A_{52}=-3{\mathrm{\ω}}_0^2{I}_y^{-1}(I_x-I_z)$

$A_{63}=-{\mathrm{\ω}}_0^2{I}_z^{-1}(I_y-I_x)$

$B_1=B_2=D_1={\left[\begin{array}{cc}{0}_{3\×3}& diag(I_x^{-1},I_y^{-1},I_z^{-1})\end{array}\right]}^T$

u(t)＝[T _cxT _cyT _cz] ^T

w(t)＝[T _dxT _dyT _dz] ^T

D ₂＝[0 _1×4-ω ₀0] ^T

$C_1=\left[\begin{array}{cc}{I}_{3\×3}& 0_{3\×3}\\ B& I_{3\×3}\end{array}\right]$

$B=\left[\begin{array}{cc}0& -{\mathrm{\ω}}_0\\ {\mathrm{\ω}}_0& 0_{2\×2}\end{array}\right]$

C ₂＝[I _6×6]

In formula, T is matrix transpose symbol, I _{3 × 3}be the diagonal unit battle array of 3 × 3, I _{6 × 6}be the diagonal unit battle array of 6 × 6,0 _{1 × 4}be the null matrix of 1 × 4,0 _{3 × 3}be the null matrix of 3 × 3, B is the constant real matrix determined by orbit angular velocity, 0 _{2 × 2}be the null matrix of 2 × 2,0 is the null matrix of 1 × 1, for by I _xinverse, I _yinverse and I _zthe inverse diagonal matrix formed.

Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: according to attitude of satellite system state equation in described step 2, obtain state feedback controller gain matrix K; Detailed process is:

Design point feedback robust non-fragile controller is:

u(t)＝(K+ΔK)x(t)(7)

In formula, u (t) for theoretical control inputs moment, K be standard controller gain matrix, Δ K is controller gain perturbations,

And meet: ${\mathrm{\ΔK\ΔK}}^T\≤{\mathrm{\η}}_0^{2}I$

In formula, I is unit diagonal matrix, η ₀for given constant, because the gain perturbation of Robust State-Feedback non-fragile controller (7) to controller has certain robustness, be called as non-fragile controller,

Only consider the addition type perturbation situation of controller gain herein, have:

ΔK＝M ₂F ₂(t)N ₂

(8)

F ₂(t) ^TF ₂(t)≤I

In formula, M ₂for determining the known constant real matrix of Δ K line number, N ₂for determining the known constant real matrix of Δ K columns, F ₂(t) for determining that Δ K changes the unknown matrix of speed,

For given ξ ₁>0, ξ ₂>0 and γ >0, consider that the attitude dynamic equations of uncertain factor is Quadratic Stability under the Robust State-Feedback non-fragile controller effect of design, z (t) meets H _∞performance constraints, and control inputs u (t) is limited, if there is symmetric positive definite matrix X and matrix W, LMI (9), (10), (11) is set up:

$\left[\begin{array}{ccccccc}AX+B_{1}W+{\mathrm{XA}}^T+W^T{B}_1^T& M_1& {\mathrm{XN}}_1^T& B_1{M}_2& {\mathrm{XN}}_2^T& {\mathrm{XC}}_2^T& B_2\\ M_1^T& -{\mathrm{\&xi;}}_1^{-1}I& 0& 0& 0& 0& 0\\ N_{1}X& 0& -{\mathrm{\&xi;}}_{1}I& 0& 0& 0& 0\\ {\left(B_1{M}_2\right)}^T& 0& 0& -{\mathrm{\&xi;}}_2^{-1}I& 0& 0& 0\\ N_{2}X& 0& 0& 0& -{\mathrm{\&xi;}}_{2}I& 0& 0\\ C_{2}X& 0& 0& 0& 0& -I& 0\\ B_2^T& 0& 0& 0& 0& 0& -{\mathrm{\&gamma;}}^{2}I\end{array}\right]<0---\left(9\right)$

$\left[\begin{array}{cc}-{\mathrm{\&gamma;}}_{0}I& x{\left(0\right)}^T\\ x\left(0\right)& -X\end{array}\right]<0---\left(10\right)$

$\left[\begin{array}{ccc}-X& W^T& X^T\\ W& -{\mathrm{\&lambda;}}_0{\mathrm{\&gamma;}}_0^{-1}I+{\mathrm{\&epsiv;}}^{-1}{\mathrm{\&eta;}}_0^{2}I& 0\\ X& 0& -{\mathrm{\&epsiv;}}^{-1}I\end{array}\right]<0---\left(11\right)$

In formula, X is symmetric positive definite matrix, and W is general matrix, M ₁for the constant real matrix of known dimension, N ₁for the constant real matrix of known dimension, M ₂for the constant real matrix of known dimension, N ₂for the constant real matrix of known dimension, ξ ₁for known normal number, ξ ₂for known normal number, I is diagonal unit battle array, and γ is known normal number, γ ₀for known normal number, x (0) is satellite initial attitude, λ ₀for ensureing the optimized variable of input-bound, ε is known normal number, for known normal number;

According to attitude of satellite system state equation, utilize the mincx function in LMI tool box, minimize λ ₀solve the convex optimization optimum solution under LMI (9), (10), (11) constraint, and each known matrix in LMI is determined by the matrix of coefficients in attitude of satellite system state equation, thus obtain state feedback controller gain matrix: K=WX ^-1.

Other step and parameter identical with embodiment one or two.

Embodiment four: present embodiment and embodiment one, two or three are unlike given satellite initial attitude x (0) in described step 3, according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks; Detailed process is:

Given satellite initial attitude x (0), substitutes into Robust State-Feedback non-fragile controller (7) by state feedback controller gain matrix K, obtains theoretical control inputs moment u (t);

Judge whether theoretical control inputs moment u (t) obtained by state feedback controller gain matrix K is less than the working control input torque upper limit, and the working control input torque upper limit is determined by topworks;

If theoretical control inputs moment is less than or equal to working control input torque sat (u) upper limit, then preserve previous moment, i.e. t _k-1the control inputs moment in moment, substitutes into Satellite Attitude Control System state equation (5), determines that satellite is at t _kthe attitude in moment;

If theoretical control inputs moment is greater than the working control input torque upper limit, then saturated process is carried out to theoretical control inputs moment u (t), obtain t _k-1working control input torque sat (u) in moment, substitutes into Satellite Attitude Control System state equation (5), determines that satellite is at t _kthe attitude in moment;

Wherein, saturated process is carried out to theoretical control inputs moment u (t), obtain t _k-1the process of working control input torque sat (u) in moment is:

Working control input torque is sat (u), and its form is

sat(u)＝[sat(u _x)sat(u _y)sat(u _z)] ^T(12)

In formula, sat (u _x) be the working control input torque on x-axis component, sat (u _y) be the working control input torque on y-axis component, sat (u _z) be the working control input torque on z-axis component, T is matrix transpose symbol;

Detailed process is:

$sat\left(u_i\right)=\left\{\begin{array}{cc}{u}_{mi}& u_i>u_{mi}\\ u_i& -u_{mi}\&le;u_i\&le;u_{mi}\\ -u_{mi}& u_i<-u_{mi}\end{array}\right.---\left(13\right)$

Wherein, u _mithe working control input torque upper limit that (i=x, y, z) can provide for topworks, m represents upper limit symbol, sat (u _i) be working control input torque on the i-th axle component.

Wherein, topworks is counteraction flyback or control-moment gyro, is the topworks of satellite attitude control system;

Other step and parameter and embodiment one, two or three identical.

Embodiment five: present embodiment and embodiment one, two, three or four unlike: the working control input torque upper limit in described step 3 is when selecting counteraction flyback to be topworks, and the scope of its actual control inputs moment upper limit is generally 0 ~ 1Nm.

Other step and parameter and embodiment one, two, three or four identical.

Embodiment six: present embodiment and embodiment one, two, three or four unlike: the working control input torque upper limit in described step 3 is when selecting control-moment gyro to be topworks, and the scope of its actual control inputs moment upper limit is 0 ~ 50Nm.

Other step and parameter and embodiment one, two, three or four identical.

Embodiment 1:

A kind ofly be applicable to that Robust State-Feedback non-fragiie control method that the quick attitude of satellite determines specifically carries out according to the following steps:

Step one, according to Dynamical Attitude Equations, when uncertain factors such as model parameter uncertainty Δ A, external interference moment w (t) and gyroscopic drifts d (t), obtain attitude of satellite system state equation;

Step 2, according to attitude of satellite system state equation, obtain state feedback controller gain matrix K;

Step 3, given satellite initial attitude x (0), according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks;

If satellite moment of inertia I _x=20kgm ², I _y=18kgm ², I _z=15kgm ², be highly 300km in orbit,

Original state

x(0)＝[0.08rad,0.06rad,-0.06rad,0.01rad/s,0.01rad/s,0.01rad/s]，

External interference moment:

$w\left(t\right)=\left[\begin{array}{c}5cos\left({\mathrm{\&omega;}}_{0}t\right)\\ 5\cos ({\mathrm{\&omega;}}_{0}t+\mathrm{\&pi;}/4)\\ 5\cos ({\mathrm{\&omega;}}_{0}t+\mathrm{\&pi;}/3)\end{array}\right]\&times;{10}^{-4}Nm$

Wherein, ω ₀for the orbit angular velocity of satellite.

M ₁＝[0.81.11.31.51.61.8] ^T,N ₁＝[-0.1-0.2-0.3-0.4-0.21]

M ₂＝[111] ^T,N ₂＝[0.10.10.10.10.10.1],F ₂(t)＝sin(100ω ₀t+π/4),

ξ ₁＝0.025,ξ ₂＝0.022,γ＝0.1,ε＝0.001,η ₀＝0.1,F ₁(t)＝sin(100ω ₀t)

Control moment upper limit value is u _mx=u _my=u _mz=0.25Nm.

Thus it is as follows to obtain simulation result:

The gain utilizing LMI tool box can obtain the lower Robust State-Feedback non-fragile controller of addition type gain perturbation is:

$K=\left[\begin{array}{cccccc}-21.3156& -13.8040& -67.5413& -49.3180& -11.3360& 24.2525\\ 6.8685& -40.5112& -105.5648& -19.3245& -46.8950& 13.7111\\ 14.3558& -8.5390& -127.3973& 1.4976& -14.4843& -99.5766\end{array}\right]$

As shown in Figure 5, as shown in Figure 4, as shown in Figure 2, attitude angular velocity as shown in Figure 3 at corresponding attitude of satellite angle for the working control input torque obtained after carrying out saturated process for the theoretical control inputs moment obtained.

The control inputs moment upper limit of Fig. 5 has exceeded the control inputs moment upper limit of 0.25Nm, Fig. 4 not more than 0.25Nm.

Claims (6)

1. be applicable to the Robust State-Feedback non-fragiie control method that the quick attitude of satellite is determined, it is characterized in that, be a kind ofly applicable to that Robust State-Feedback non-fragiie control method that the quick attitude of satellite determines specifically carries out according to the following steps:

Step one, according to Dynamical Attitude Equations, when model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), obtain attitude of satellite system state equation;

Step 2, according to attitude of satellite system state equation, obtain state feedback controller gain matrix K;

Step 3, given satellite initial attitude x (0), according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks.

2. a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining according to claim 1, it is characterized in that, according to Dynamical Attitude Equations in described step one, when model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), obtain attitude of satellite system state equation, detailed process is:

Dynamical Attitude Equations is:

$I_x\left\{\begin{array}{c}{I}_x{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_x+(I_z-I_y){\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z=T_{cx}+T_{gx}+T_{dx}\\ I_y{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_y+(I_x-I_z){\mathrm{\&omega;}}_z{\mathrm{\&omega;}}_x=T_{cy}+T_{g\mathrm{\&nu;}}+T_{dy}\\ I_z{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z+(I_y-I_x){\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y=T_{cz}+T_{gz}+T_{dz}\end{array}\right.---\left(1\right)$

In formula, I _xfor satellite orbit coordinate system x-axis moment of inertia, I _yfor satellite orbit coordinate system y-axis moment of inertia, I _zfor satellite orbit coordinate system z-axis moment of inertia, ω _xfor satellite orbit coordinate system x-axis measuring satellite angular velocities, ω _yfor satellite orbit coordinate system y-axis measuring satellite angular velocities, ω _zfor satellite orbit coordinate system z-axis measuring satellite angular velocities, T _cxfor the control inputs moment of satellite orbit coordinate system x-axis, T _cyfor the control inputs moment of satellite orbit coordinate system y-axis, T _czfor the control inputs moment of satellite orbit coordinate system z-axis, T _gxfor satellite orbit coordinate system x-axis gravity gradient torque, T _gyfor satellite orbit coordinate system y-axis gravity gradient torque, T _gzfor satellite orbit coordinate system z-axis gravity gradient torque, T _dxfor satellite orbit coordinate system x-axis external interference moment, T _dyfor satellite orbit coordinate system y-axis external interference moment, T _dzfor satellite orbit coordinate system z-axis external interference moment, for the first order derivative of satellite orbit coordinate system x-axis angular velocity, for the first order derivative of satellite orbit coordinate system y-axis angular velocity, for the first order derivative of satellite orbit coordinate system z-axis angular velocity;

Wherein,

In formula, ω ₀for orbit angular velocity, for roll angle, θ is the angle of pitch;

Be located under attitude angle is less than the angle of 10 °, measuring satellite angular velocities is:

In formula, for first order derivative, ψ is crab angle, for the first order derivative of θ, for the first order derivative of ψ;

Adopt zyx rotating manner, obtaining attitude dynamic equations is:

In formula, for second derivative, for the second derivative of θ, for the second derivative of ψ;

When model parameter uncertainty Δ A, external interference moment w (t), controller gain perturbations and gyroscopic drift d (t), definition status variable is utilize star sensor and gyroscope survey instrument to record output variable to be by above-mentioned attitude dynamic equations linearization, draw attitude of satellite system state equation:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=(A+\mathrm{\&Delta;}A)x\left(t\right)+B_{1}u\left(t\right)+B_{2}w\left(t\right)\\ y\left(t\right)=C_{1}x\left(t\right)+D_{1}d\left(t\right)+D_2\\ z\left(t\right)=C_{2}x\left(t\right)\end{array}\right.---\left(5\right)$

In formula, u (t) is theoretical control inputs moment, and w (t) is external interference moment, and z (t) is control output variable, for the first order derivative of t state variable, the output variable that y (t) is t, the state variable that x (t) is t, B ₁for control inputs matrix of coefficients, B ₂for external interference matrix of coefficients, C ₁for coefficient of regime matrix in output can be surveyed, C ₂for controlling coefficient of regime matrix in output, D ₁for Gyro drift coefficient matrix, D ₂for surveying constant value matrix in output, A is model coefficient matrix, and Δ A is model parameter uncertainty, and its form is

ΔA＝M ₁F ₁(t)N ₁

(6)

F ₁(t) ^TF ₁(t)≤I

In formula, M ₁for determining the known constant real matrix of Δ A line number, N ₁for determining the known constant real matrix of Δ A columns, F ₁t (), for determining the unknown matrix that Δ A changes, I is unit diagonal matrix, T is matrix transpose symbol;

Definition gyroscopic drift is constant value drift:

$A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ A_{41}& 0& 0& 0& 0& -{\mathrm{\&omega;}}_0{I}_x^{-1}(I_y-I_x-I_z)\\ 0& A_{52}& 0& 0& 0& 0\\ 0& 0& A_{63}& {\mathrm{\&omega;}}_0{I}_z^{-1}(I_y-I_x-I_z)& 0& 0\end{array}\right]$

$A_{41}=-4{\mathrm{\&omega;}}_0^2{I}_x^{-1}(I_y-I_z)$

$A_{52}=-3{\mathrm{\&omega;}}_0^2{I}_y^{-1}(I_x-I_z)$

$A_{63}=-{\mathrm{\&omega;}}_0^2{I}_z^{-1}(I_y-I_x)$

$B_1=B_2=D_1={\left[\begin{array}{cc}{\mathrm{\&theta;}}_{3\&times;3}& diag(I_x^{-1},I_y^{-1},I_z^{-1})\end{array}\right]}^T$

u(t)＝[T _cxT _cyT _cz] ^T

w(t)＝[T _dxT _dyT _dz] ^T

D ₂＝[0 _1×4-ω ₀0] ^T

$C_1=\left[\begin{array}{cc}{I}_{3\&times;3}& 0_{3\&times;3}\\ B& I_{3\&times;3}\end{array}\right]$

$B=\left[\begin{array}{cc}0& -{\mathrm{\&omega;}}_0\\ {\mathrm{\&omega;}}_0& 0_{2\&times;2}\end{array}\right]$

C ₂＝[I _6×6]

In formula, T is matrix transpose symbol, I _{3 × 3}be the diagonal unit battle array of 3 × 3, I _{6 × 6}be the diagonal unit battle array of 6 × 6,0 _{1 × 4}be the null matrix of 1 × 4,0 _{3 × 3}be the null matrix of 3 × 3, B is the constant real matrix determined by orbit angular velocity, 0 _{2 × 2}be the null matrix of 2 × 2,0 is the null matrix of 1 × 1, for by I _xinverse, I _yinverse and I _zthe inverse diagonal matrix formed.

3. a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining according to claim 2, is characterized in that, according to attitude of satellite system state equation in described step 2, obtains state feedback controller gain matrix K; Detailed process is:

Design point feedback robust non-fragile controller is:

u(t)＝(K+ΔK)x(t)(7)

In formula, u (t) for theoretical control inputs moment, K be standard controller gain matrix, Δ K is controller gain perturbations,

And meet: ${\mathrm{\&Delta;K\&Delta;K}}^T\&le;{\mathrm{\&eta;}}_0^{2}I$

In formula, I is unit diagonal matrix, η ₀for given constant;

The addition type perturbation situation of Robust State-Feedback non-fragile controller gain is:

ΔK＝M ₂F ₂(t)N ₂

(8)

F ₂(t) ^TF ₂(t)≤I

In formula, M ₂for determining the known constant real matrix of Δ K line number, N ₂for determining the known constant real matrix of Δ K columns, F ₂t () is for determining the unknown matrix that Δ K changes;

Given ξ ₁>0, ξ ₂>0 and γ >0, if there is symmetric positive definite matrix X and matrix W, then makes LMI (9), (10), (11) set up:

$\left[\begin{array}{ccccccc}AX+B_{1}W+{\mathrm{XA}}^T+W^T{B}_1^T& M_1& {\mathrm{XN}}_1^T& B_1{M}_2& {\mathrm{XN}}_2^T& {\mathrm{XC}}_2^T& B_2\\ M_1^T& -{\mathrm{\&xi;}}_1^{-1}I& 0& 0& 0& 0& 0\\ N_{1}X& 0& -{\mathrm{\&xi;}}_{1}I& 0& 0& 0& 0\\ {\left(B_1{M}_2\right)}^T& 0& 0& -{\mathrm{\&xi;}}_2^{-1}I& 0& 0& 0\\ N_{2}X& 0& 0& 0& -{\mathrm{\&xi;}}_{2}I& 0& 0\\ C_{2}X& 0& 0& 0& 0& -I& 0\\ B_2^T& 0& 0& 0& 0& 0& -{\mathrm{\&gamma;}}^{2}I\end{array}\right]<0---\left(9\right)$

$\left[\begin{array}{cc}-{\mathrm{\&gamma;}}_{0}I& x{\left(0\right)}^T\\ x\left(0\right)& -X\end{array}\right]<0---\left(10\right)$

$\left[\begin{array}{ccc}-X& W^T& X^T\\ W& -{\mathrm{\&lambda;}}_0{\mathrm{\&gamma;}}_0^{-1}I+{\mathrm{\&epsiv;}}^{-1}{\mathrm{\&eta;}}_0^{2}I& 0\\ X& 0& -{\mathrm{\&epsiv;}}^{-1}I\end{array}\right]<0---\left(11\right)$

In formula, X is symmetric positive definite matrix, and W is general matrix, M ₁for the constant real matrix of known dimension, N ₁for the constant real matrix of known dimension, M ₂for the constant real matrix of known dimension, N ₂for the constant real matrix of known dimension, ξ ₁for known normal number, ξ ₂for known normal number, I is diagonal unit battle array, and γ is known normal number, γ ₀for known normal number, x (0) is satellite initial attitude, λ ₀for ensureing the optimized variable of input-bound, ε is known normal number, for known normal number;

According to attitude of satellite system state equation, utilize the mincx function in LMI tool box, minimize λ ₀, solve the convex optimization optimum solution under LMI (9), (10), (11) constraint, thus obtain state feedback controller gain matrix: K=WX ^-1.

4. a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining according to claim 3, it is characterized in that, given satellite initial attitude x (0) in described step 3, according to state feedback controller gain matrix K, obtain theoretical control inputs moment u (t); Judge whether theoretical control inputs moment is less than the working control input torque upper limit, and then determine that satellite is at t _kthe attitude in moment, the working control input torque upper limit is determined by topworks; Detailed process is:

Given satellite initial attitude x (0), substitutes into Robust State-Feedback non-fragile controller (7) by state feedback controller gain matrix K, obtains theoretical control inputs moment u (t);

Judge whether theoretical control inputs moment u (t) obtained by state feedback controller gain matrix K is less than the working control input torque upper limit, and the working control input torque upper limit is determined by topworks;

If theoretical control inputs moment is less than or equal to working control input torque sat (u) upper limit, then preserve previous moment, i.e. t _k-1the control inputs moment in moment, substitutes into Satellite Attitude Control System state equation, determines that satellite is at t _kthe attitude in moment;

If theoretical control inputs moment is greater than the working control input torque upper limit, then saturated process is carried out to theoretical control inputs moment u (t), obtain t _k-1working control input torque sat (u) in moment, substitutes into Satellite Attitude Control System state equation, determines that satellite is at t _kthe attitude in moment;

Wherein, saturated process is carried out to theoretical control inputs moment u (t), obtain t _k-1the process of working control input torque sat (u) in moment is:

Working control input torque is sat (u), and its form is

sat(u)＝[sat(u _x)sat(u _y)sat(u _z)] ^T(12)

In formula, sat (u _x) be the working control input torque on x-axis component, sat (u _y) be the working control input torque on y-axis component, sat (u _z) be the working control input torque on z-axis component, T is matrix transpose symbol;

Detailed process is:

$sat\left(u_i\right)=\left\{\begin{array}{cc}{u}_{mi}& u_i>u_{mi}\\ u_i& -u_{mi}\&le;u_i\&le;u_{mi}\\ -u_{mi}& u_i<-u_{mi}\end{array}\right.---\left(13\right)$

Wherein, u _mithe working control input torque upper limit that (i=x, y, z) can provide for topworks, m represents upper limit symbol, sat (u _i) be working control input torque on the i-th axle component.

5. a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining according to claim 4, it is characterized in that, the working control input torque upper limit in described step 3 is when selecting counteraction flyback to be topworks, and the scope of its actual control inputs moment upper limit is 0 ~ 1Nm.

6. a kind of Robust State-Feedback non-fragiie control method being applicable to the quick attitude of satellite and determining according to claim 4, it is characterized in that, the working control input torque upper limit in described step 3 is when selecting control-moment gyro to be topworks, and the scope of its actual control inputs moment upper limit is 0 ~ 50Nm.