CN104483973A - Low-orbit flexible satellite attitude tracking control method based on sliding-mode observer - Google Patents

Abstract

The invention discloses a low-orbit flexible satellite attitude tracking control method based on a sliding-mode observer, relates to a low-orbit flexible satellite attitude tracking control method based on a sliding-mode observer, and aims at solving the problems that an existing low-orbit flexible satellite is low in satellite attitude tracking control accuracy due to relatively large aerodynamic interference torque and vibration of flexile components. The low-orbit flexible satellite attitude tracking control method based on the sliding-mode observer comprises the following steps: building a geocentric inertial coordinate system and a satellite body coordinate system; building a state space expression, and determining an upper bound of an interference signal received by the observer; solving a gain matrix of the observer, a matching matrix of the observer and a Lyapunov equation matrix variable; observing to obtain an estimated mode vibration velocity value of the sliding-mode observer and an estimated mode vibration state value of the sliding-mode observer; rewriting a kinetic equation of a flexible satellite attitude into an error attitude tracking control model; determining a sliding-mode term gain of the control law, and carrying out tracking control on the error attitude tracking model by adopting the siding-mode control law according to measured satellite attitude quaternion, attitude angular velocity information and estimated mode quantity value. The low-orbit flexible satellite attitude tracking control method is applied to satellite attitude tracking control.

Description

Based on the low rail Flexible Satellite Attitude tracking and controlling method of sliding mode observer

Technical field

The present invention relates to a kind of low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer.

Background technology

Along with the development of satellite gravity anomaly technology, more and more higher to the requirement of Satellite Attitude Control, be particularly the satellite of load with optical camera, load over the ground pointing accuracy requirement is high.For this kind of satellite, in order to improve the precision of optical imagery, low rail is often selected to run, low orbit satellite is for middle high rail satellite, the impact of the aerodynamic moment be subject to is larger, and suffered aerodynamic moment changes with the change of the attitude of satellite, large on the impact of Satellite Attitude Control, therefore, must consider that aerodynamic interference moment affects when designing high-precision satellite attitude control method.In addition, the vibration of the flexible parts such as the solar array that satellite carries, large-scale antenna, imaging load, also can reduce the precision of satellite gravity anomaly.Impact for flexible part adopts observer to observe modal vibration information usually, and to flexible vibration real-Time Compensation in attitude control method.In a word, in order to improve Satellite Attitude Control, during design satellite gravity anomaly algorithm, suitable method must be adopted to compensate the impact of pneumatic disturbance torque and flexible part.

Summary of the invention

The object of the invention is to solve the low problem of attitude of satellite tracing control precision that existing low rail flexible satellite causes because larger aerodynamic interference moment and self flexible part vibrate, and propose a kind of low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer.

Based on a low rail Flexible Satellite Attitude tracking and controlling method for sliding mode observer, described low rail Flexible Satellite Attitude tracking and controlling method is realized by following steps:

Step one: set up geocentric inertial coordinate system OX _iy _iz _iwith satellite body coordinate system OX _by _bz _b;

Step 2: definition modal vibration state thus be state-space expression by Flexible Satellite Attitude kinetics equation; In formula, represent modal vibration speed, δ represents Coupled Rigid-flexible matrix, ω _bIrepresent current pose angular velocity;

Step 3, excite the relational expression of flexible vibration according to satellite transit orbital environment character and angular velocity, determine the undesired signal that observer is subject to the upper bound, and observer sliding formwork item gain ρ meet: ρ>=sup||d||; In formula, the observational error value of inter-modal vibrational state amount ψ ' and the observational error value of described inter-modal vibrational state amount ψ ' numerical value be less than or equal to the magnitude of modal vibration speed;

Step 4, theoretical according to sliding mode observer, and comprehensive Lyapunov stablizes the constraint with matching condition, solves LMI: $\left\{\begin{array}{c}P(A-\mathrm{GH})+{(A-\mathrm{GH})}^{T}P<0\\ \left(\begin{array}{cc}-I& \mathrm{PB}-H^T{F}^T\\ B^{T}P-\mathrm{FH}& 0\end{array}\right)<0\end{array}\right.$ : observer gain matrix G, observer coupling matrix F and Lyapunov equation matrix variables P;

Step 5, employing sliding mode observer: $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=A\hat{x}+\mathrm{Bu}+B\hat{f}-G(\hat{y}-y)+\mathrm{\&upsi;}\\ \hat{y}=H\hat{x}\end{array}\right.$ Observation obtains the real-time information of modal vibration displacement η and modal vibration state ψ, and then obtains synovial membrane observer estimation modal vibration acceleration magnitude modal vibration state magnitude is estimated with synovial membrane observer

Step 6, definition error attitude quaternion Q _ewith error attitude angular velocity ω _e, Flexible Satellite Attitude kinetics equation is rewritten into error Attitude tracking control model: $J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_e+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\mathrm{\&psi;}+{\mathrm{\&delta;}}^T{\mathrm{C\&delta;\&omega;}}_{\mathrm{bI}}-{\mathrm{\&delta;}}^T\mathrm{C\&psi;}-{\mathrm{\&delta;}}^T\mathrm{K\&eta;}=u+T_d,$ In formula, Q _bIrepresent current pose hypercomplex number, and q ₀represent current pose hypercomplex number Q _bIscalar component, q represent current pose hypercomplex number Q _bIvector section, Q _dIfor targeted attitude hypercomplex number, ω _dIfor targeted attitude angular velocity, obtain error attitude quaternion and error attitude angular velocity wherein, q _e0for described error attitude quaternion Q _escalar component, q _efor described error attitude quaternion Q _evector section;

Step 7, according to satellite orbit Airflow Environment characteristic and observer error state value determine the sliding formwork item gain k=diag (k of control law ₁k ₂k ₃), and wherein represent the observed reading of modal vibration displacement η and the difference of true value, represent the observed reading of inter-modal vibrational state amount ψ ' and the difference of true value, represent the numerical value of corresponding vector section absolute value i-th;

Step 8, obtain according to measuring the attitude of satellite hypercomplex number, attitude angular velocity information and the step 5 that obtain the mode value that described sliding mode observer estimates to obtain with the sliding formwork control law of following form is adopted to realize the high precision tracking control of the attitude of satellite to the error Attitude Tracking model that step 6 obtains:

$\begin{array}{c}u=\frac{\mathrm{\&lambda;}}{2}{J}_m(\left(q_e^T{\mathrm{\&omega;}}_e\right)q_e-q_{e0}(q_{e0}I+{q_e}^{\&times;}){\mathrm{\&omega;}}_e)+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&delta;}}^T{\mathrm{C\&delta;\&omega;}}_{\mathrm{bI}}\\ +{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}C\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}K\widehat{\mathrm{\&eta;}}-k{J}_m\mathrm{sat}\left(s\right)\end{array};$ In formula, sliding-mode surface s=λ q _e0q _e+ ω _e, λ is positive constant and sliding formwork item meets $\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}\mathrm{sign}\left(s_i\right)& \left|s_i\right|>\mathrm{\&alpha;}\\ s_i/\mathrm{\&alpha;}& \left|s_i\right|\&le;\mathrm{\&alpha;}\end{array}\right.,$ α represents sliding formwork control law boundary layer thickness.

Beneficial effect of the present invention is:

Present invention achieves the Attitude tracking control of low orbit satellite under larger pneumatic disturbance torque and flexible part vibration effect, and can under larger pneumatic disturbing effect, by increasing the coefficient value of observer sliding formwork item, in conjunction with sliding mode observer real-time monitored modal information, the robustness making observer resist disturbing effect improves 50-60%;

The sliding formwork control law adopted can observe the real-time information of mode amount η, ψ, and then the sliding formwork control law real-Time Compensation satellite flexible part passing through to adopt is on the impact of subjective posture, and the precision of Attitude Tracking is improve 30-40% by more existing attitude control method;

And according to the mode value measured the attitude of satellite hypercomplex number, attitude angular velocity information and the sliding mode observer that obtain and estimate to obtain, tracing control is carried out to the error Attitude Tracking model obtained, thus overcome the problem that general sliding formwork controls error attitude quaternion to be stabilized to, really achieve the equivalence of error pose stabilization control and Attitude tracking control, stability contorting and both tracing control are synchronously carried out, simplifies control method and control effects of refining.

Accompanying drawing explanation

Fig. 1 is the result curve figure of the error attitude quaternion that emulation embodiment 1 relates to;

Fig. 2 is the result curve figure of the error attitude angular velocity that emulation embodiment 1 relates to;

Fig. 3 is the result curve figure that satellite that emulation embodiment 1 relates to is subject to aerodynamic interference moment;

Fig. 4 is the result curve figure of satellite flexible part vibration to celestial body coupling torque that emulation embodiment 1 relates to;

Fig. 5 to Fig. 7 is the result curve figure of first three rank modal vibration displacement of satellite η that emulation embodiment 1 relates to;

Fig. 8 value Figure 10 is the result curve figure of the corresponding observational error value of satellite first three rank modal vibration displacement η that emulation embodiment 1 relates to;

Figure 11 to Figure 13 is the result curve figure of first three rank inter-modal vibrational state amount of satellite that emulation embodiment 1 relates to;

Figure 14 to Figure 16 is the result curve figure of the corresponding observational error value of first three rank inter-modal vibrational state amount of satellite that emulation embodiment 1 relates to;

Embodiment

Embodiment one:

The low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer of present embodiment, described low rail Flexible Satellite Attitude tracking and controlling method is realized by following steps:

Step one: set up geocentric inertial coordinate system OX _iy _iz _iwith satellite body coordinate system OX _by _bz _b;

Step 2: definition modal vibration state thus be state-space expression by Flexible Satellite Attitude kinetics equation; In formula, represent modal vibration speed, δ represents Coupled Rigid-flexible matrix, ω ^bIrepresent current pose angular velocity;

Step 3, excite the relational expression of flexible vibration according to satellite transit orbital environment character and angular velocity, determine the undesired signal that observer is subject to the upper bound, and observer sliding formwork item gain ρ meet: ρ>=sup||d||; In formula, the observational error value of inter-modal vibrational state amount ψ ' and the observational error value of described inter-modal vibrational state amount ψ ' numerical value be less than or equal to the magnitude of modal vibration speed;

Step 4, theoretical according to sliding mode observer, and comprehensive Lyapunov stablizes the constraint with matching condition, solves LMI: $\left\{\begin{array}{c}P(A-\mathrm{GH})+{(A-\mathrm{GH})}^{T}P<0\\ \left(\begin{array}{cc}-I& \mathrm{PB}-H^T{F}^T\\ B^{T}P-\mathrm{FH}& 0\end{array}\right)<0\end{array}\right.$ : observer gain matrix G, observer coupling matrix F and Lyapunov equation matrix variables P;

Step 5, employing sliding mode observer: $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=A\hat{x}+\mathrm{Bu}+B\hat{f}-G(\hat{y}-y)+\mathrm{\&upsi;}\\ \hat{y}=H\hat{x}\end{array}\right.$ Observation obtains the real-time information of modal vibration displacement η and modal vibration state ψ, and then obtains synovial membrane observer estimation modal vibration acceleration magnitude modal vibration state magnitude is estimated with synovial membrane observer

Step 6, definition error attitude quaternion Q _ewith error attitude angular velocity ω _e, Flexible Satellite Attitude kinetics equation is rewritten into error Attitude tracking control model:

$J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_e+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\mathrm{\&psi;}+{\mathrm{\&delta;}}^T{\mathrm{C\&delta;\&omega;}}_{\mathrm{bI}}-{\mathrm{\&delta;}}^T\mathrm{C\&psi;}-{\mathrm{\&delta;}}^T\mathrm{K\&eta;}=u+T_d,$ In formula, Q _bIrepresent current pose hypercomplex number, and q ₀represent current pose hypercomplex number Q _bIscalar component, q represent current pose hypercomplex number Q _bIvector section, Q _dIfor targeted attitude hypercomplex number, ω _dIfor targeted attitude angular velocity, obtain error attitude quaternion and error attitude angular velocity wherein, q _e0for described error attitude quaternion Q _escalar component, q _efor described error attitude quaternion Q _evector section;

Step 7, according to satellite orbit Airflow Environment characteristic and observer error state value determine the sliding formwork item gain k=diag (k of control law ₁k ₂k ₃), and wherein represent the observed reading of modal vibration displacement η and the difference of true value, represent the observed reading of inter-modal vibrational state amount ψ ' and the difference of true value, represent the numerical value of corresponding vector section absolute value i-th;

Step 8, obtain according to measuring the attitude of satellite hypercomplex number, attitude angular velocity information and the step 5 that obtain the mode value that described sliding mode observer estimates to obtain with the sliding formwork control law of following form is adopted to realize the high precision tracking control of the attitude of satellite to the error Attitude Tracking model that step 6 obtains: $\begin{array}{c}u=\frac{\mathrm{\&lambda;}}{2}{J}_m(\left(q_e^T{\mathrm{\&omega;}}_e\right)q_e-q_{e0}(q_{e0}I+{q_e}^{\&times;}){\mathrm{\&omega;}}_e)+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&delta;}}^T{\mathrm{C\&delta;\&omega;}}_{\mathrm{bI}}\\ +{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}C\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}K\widehat{\mathrm{\&eta;}}-k{J}_m\mathrm{sat}\left(s\right)\end{array};$ In formula, sliding-mode surface s=λ q _e0q _e+ ω _e, λ is positive constant and sliding formwork item meets $\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}\mathrm{sign}\left(s_i\right)& \left|s_i\right|>\mathrm{\&alpha;}\\ s_i/\mathrm{\&alpha;}& \left|s_i\right|\&le;\mathrm{\&alpha;}\end{array}\right.,$ α represents sliding formwork control law boundary layer thickness.

Embodiment two:

With embodiment one unlike, the low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer of present embodiment, geocentric inertial coordinate system OX described in step one _iy _iz _i, the true origin of described geocentric inertial coordinate system is earth centroid, OZ _iaxle points to the north, OX along earth rotation direction of principal axis _iaxle points to direction in the first point of Aries, OY _iaxle and OX _iaxle and OZ _iaxle forms right hand rectangular coordinate system;

Satellite body coordinate system OX described in step one _by _bz _b, the true origin of described satellite body coordinate system is centroid of satellite, OX _baxle, OY _baxle and OZ _baxle and celestial body are connected, and make the OX of coordinate axis _baxle, OY _baxle and OZ _baxle overlaps with the satellite principal axis of inertia.

Embodiment three:

With embodiment one or two unlike, the low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer of present embodiment, is rewritten as state-space expression by Flexible Satellite Attitude kinetics equation described in step 2: $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{Ax}+\mathrm{Bu}+\mathrm{Bf}+{\mathrm{BT}}_d\\ y=\mathrm{Hx}\end{array}\right.;$ In formula,

X is system state amount and x=(η ^tψ ^tω _bI ^t) ^t,

η represents modal vibration displacement,

A represent system matrix and $A=\left(\begin{array}{ccc}0& I& -\mathrm{\&delta;}\\ -K& -C& \mathrm{C\&delta;}\\ J_m^{-1}{\mathrm{\&delta;}}^{T}K& J_m^{-1}{\mathrm{\&delta;}}^{T}C& -J_m^{-1}{\mathrm{\&delta;}}^T\mathrm{C\&delta;}\end{array}\right),$

B represent control inputs matrix and $B=\left(\begin{array}{c}0\\ 0\\ J_m^{-1}\end{array}\right),$

C represents the damping matrix of modal vibration,

K represents the stiffness matrix of modal vibration,

Y represents system measurements output valve,

H represents measurement output matrix, because observer only needs attitude angular velocity information and Observable to obtain modal vibration amount, for ease of observer statement, then and H=(0 0 I ₃),

U represents control signal,

F represents nonlinear terms and f=-ω _bI× J _mω _bI-ω _bI× δ ^tψ, wherein, ω _bIrepresent current pose angular velocity,

J _m=J-δ ^tδ represents satellite rigid element moment of inertia, and J represents the overall moment of inertia of satellite, and δ represents Coupled Rigid-flexible matrix, δ ^trepresent the transposed matrix of Coupled Rigid-flexible matrix delta,

T _drepresent aerodynamic interference moment.

By the state-space expression that Flexible Satellite Attitude kinetics equation is rewritten, it is a kind of attitude dynamics model being convenient to state.

Embodiment four:

With embodiment three unlike, the low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer of present embodiment, obtain synovial membrane observer described in step 5 and estimate that the detailed process of mode value is: the observer gain matrix G that the sliding formwork item gain ρ that the state-space expression described with modal vibration damping, step 2 according to modal vibration frequency, Zi Kong topworks real-time control signal u, step 3 are determined tries to achieve with step 4, observer mate matrix F and Lyapunov equation matrix variables P, employing sliding mode observer: $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=A\hat{x}+\mathrm{Bu}+B\hat{f}-G(\hat{y}-y)+\mathrm{\&upsi;}\\ \hat{y}=H\hat{x}\end{array}\right.$ Observation obtains the real-time information of modal vibration displacement η and modal vibration state ψ, namely obtains estimating mode value with in formula, the estimated value of control system quantity of state $\hat{x}={\left(\begin{array}{ccc}{\widehat{\mathrm{\&eta;}}}^T& {\widehat{\mathrm{\&psi;}}}^T& {{\widehat{\mathrm{\&omega;}}}_{\mathrm{bI}}}^T\end{array}\right)}^T,$ The estimated value of nonlinear terms f $\hat{f}=-{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}-{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widehat{\mathrm{\&psi;}},$ The observational error of system measurements output valve y the sliding formwork item of observer $\mathrm{\&upsi;}=\left\{\begin{array}{cc}-\mathrm{\&rho;}{P}^{-1}\frac{H^T{F}^T{\mathrm{Fe}}_y}{\left|\right|{\mathrm{Fe}}_y\left|\right|}& \left|\right|{\mathrm{Fe}}_y\left|\right|\&GreaterEqual;\mathrm{\&epsiv;}\\ -\mathrm{\&rho;}{P}^{-1}\frac{H^T{F}^T{\mathrm{Fe}}_y}{\mathrm{\&epsiv;}}& \left|\right|{\mathrm{Fe}}_y\left|\right|<\mathrm{\&epsiv;}\end{array}\right.,$ ρ is the gain of sliding formwork item, simultaneously Fe _yrepresent sliding-mode surface, ε is the boundary layer thickness of observer sliding-mode surface, and described boundary layer thickness ε requires to regulate according to control accuracy, and its value is close with control accuracy.

Embodiment 1:

For low orbit flexible satellite, verify the rationality of the low rail Flexible Satellite Attitude tracking and controlling method based on sliding mode observer of the present invention's design and validity, detailed process is:

The overall moment of inertia of satellite: $J=\left(\begin{array}{ccc}12.5& 0& 0\\ 0& 96.5& 0\\ 0& 0& 96.5\end{array}\right)\mathrm{kg}\&CenterDot;m^2,$

Targeted attitude angular velocity: ${\mathrm{\&omega;}}_{\mathrm{dI}}=\left(\begin{array}{c}0\\ 0.3\sin \left(0.1t\right)\\ 0.2\cos \left(0.1t\right)\end{array}\right)\mathrm{rad}/s,$

Coupled Rigid-flexible matrix: $\mathrm{\&delta;}=\left(\begin{array}{ccc}1.0167& 0.1811& -0.1847\\ 0.0373& 3.4012& 3.4017\\ -0.0351& 3.4024& -3.4021\end{array}\right),$

Flexible part modal vibration frequency and modal vibration damping are:

ω _fl＝(0.768 1.504 2.843) ^T，ζ _fl＝(0.01 0.01 0.01) ^T，

Aerodynamic parameter has resistance coefficient to be C _d=2.4, ρ=2.789 × 10 ^-10kg/m ³,

Sliding formwork control law boundary layer thickness α=1 × 10 ^-4, observer sliding formwork boundary layer thickness ε=1 × 10 ^-3, sliding formwork control law parameter: λ=3, k=diag (0.025 0.024 0.02), control cycle gets 0.02s,

Sliding mode observer sliding formwork parameter ρ=1, coupling matrix F is: $\left(\begin{array}{ccc}0.1864& 0.0005& 0.0001\\ 0.0005& 0.0294& -0.0002\\ 0.0002& -0.0002& 0.0294\end{array}\right),$

Initial parameter:

ω _bo0＝(0.1 0.1 0.1) ^T°/s A _bo0＝(0.1° 0.1° 0.1°) ^T

ω _bI0＝ω _bo0+C _bo0ω ₀A _bI0＝(-30° 10° 20°) ^T，

Obtain the simulation result figure of Fig. 1 to Figure 16, show the inventive method can realize satellite be subject to larger pneumatic disturbance torque and flexible coupling torque affect under Attitude Tracking result, and the sliding mode observer adopted can realize the observation to flexible mode vibration displacement and speed under large disturbed condition.

Claims (4)

1. based on a low rail Flexible Satellite Attitude tracking and controlling method for sliding mode observer, it is characterized in that: described low rail Flexible Satellite Attitude tracking and controlling method is realized by following steps:

Step one: set up geocentric inertial coordinate system OX _iy _iz _iwith satellite body coordinate system OX _by _bz _b;

Step 2: definition modal vibration state thus be state-space expression by Flexible Satellite Attitude kinetics equation; In formula, represent modal vibration speed, δ represents Coupled Rigid-flexible matrix, ω _bIrepresent current pose angular velocity;

Step 3, excite the relational expression of flexible vibration according to satellite transit orbital environment character and angular velocity, determine the undesired signal that observer is subject to the upper bound, and observer sliding formwork item gain ρ meet: ρ>=sup||d||; In formula, the observational error value of inter-modal vibrational state amount ψ ' and the observational error value of described inter-modal vibrational state amount ψ ' numerical value be less than or equal to the magnitude of modal vibration speed;

Step 4, theoretical according to sliding mode observer, and comprehensive Lyapunov stablizes the constraint with matching condition, solves LMI: $\left\{\begin{array}{c}P(A-\mathrm{GH})+{(A-\mathrm{GH})}^{T}P<0\\ \left(\begin{array}{cc}-I& \mathrm{PB}-H^T{F}^T\\ B^{T}P-\mathrm{FH}& 0\end{array}\right)<0\end{array}\right.$ : observer gain matrix G, observer coupling matrix F and Lyapunov equation matrix variables P;

Step 5, employing sliding mode observer: $\left\{\begin{array}{c}\stackrel{\stackrel{\&CenterDot;}{^}}{x}=A\hat{x}+\mathrm{Bu}+B\hat{f}-G(\hat{y}-y)+u\\ \hat{y}=H\hat{x}\end{array}\right.$ Observation obtains the real-time information of modal vibration displacement η and modal vibration state ψ, and then obtains synovial membrane observer estimation modal vibration acceleration magnitude modal vibration state magnitude is estimated with synovial membrane observer

Step 6, definition error attitude quaternion Q _ewith error attitude angular velocity ω _e, Flexible Satellite Attitude kinetics equation is rewritten into error Attitude tracking control model:

$J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_e+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\mathrm{\&psi;}+{\mathrm{\&delta;}}^T\mathrm{C\&delta;}{\mathrm{\&omega;}}_{\mathrm{bI}}-{\mathrm{\&delta;}}^T\mathrm{C\&psi;}-{\mathrm{\&delta;}}^T\mathrm{K\&eta;}=u+T_d,$ In formula, Q _bIrepresent current pose hypercomplex number, and q ₀represent current pose hypercomplex number Q _bIscalar component, q represent current pose hypercomplex number Q _bIvector section, Q _dIfor targeted attitude hypercomplex number, ω _dIfor targeted attitude angular velocity, obtain error attitude quaternion and error attitude angular velocity wherein, q _e0for described error attitude quaternion Q _escalar component, q _efor described error attitude quaternion Q _evector section;

Step 7, according to satellite orbit Airflow Environment characteristic and observer error state value determine the sliding formwork item gain k=diag (k of control law ₁k ₂k ₃), and $k_i>|J_m^{-1}(T_d+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widetilde{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}C\widetilde{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}K\widetilde{\mathrm{\&eta;}}){|}_i,$ Wherein represent the observed reading of modal vibration displacement η and the difference of true value, ψ represents the observed reading of inter-modal vibrational state amount ψ and the difference of true value, $|J_m^{-1}(T_d+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widetilde{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}C\widetilde{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}K\widetilde{\mathrm{\&eta;}}){|}_i$ Represent the numerical value of corresponding vector section absolute value i-th;

Step 8, obtain according to measuring the attitude of satellite hypercomplex number, attitude angular velocity information and the step 5 that obtain the mode value that described sliding mode observer estimates to obtain with the sliding formwork control law of following form is adopted to realize the high precision tracking control of the attitude of satellite to the error Attitude Tracking model that step 6 obtains: $\begin{array}{c}u=\frac{\mathrm{\&lambda;}}{2}{J}_m(\left(q_e^T{\mathrm{\&omega;}}_e\right)q_e-q_{e0}(q_{e0}I+{q_e}^{\&times;}){\mathrm{\&omega;}}_e)+J_m{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_{\mathrm{dI}}^b+{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}+{\mathrm{\&delta;}}^T\mathrm{C\&delta;}{\mathrm{\&omega;}}_{\mathrm{bI}}\\ +{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}C\widehat{\mathrm{\&psi;}}-{\mathrm{\&delta;}}^{T}K\widehat{\mathrm{\&eta;}}-k{J}_m\mathrm{sat}\left(s\right)\end{array};$ In formula, sliding-mode surface s=λ q _e0q _e+ ω _e, λ is positive constant and sliding formwork item meets $\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}\mathrm{sign}\left(s_i\right)& \left|s_i\right|>\mathrm{\&alpha;}\\ s_i/\mathrm{\&alpha;}& \left|s_i\right|\&le;\mathrm{\&alpha;}\end{array}\right.,$ α represents sliding formwork control law boundary layer thickness.

2., according to claim 1 based on the low rail Flexible Satellite Attitude tracking and controlling method of sliding mode observer, it is characterized in that: geocentric inertial coordinate system OX described in step one _iy _iz _i, the true origin of described geocentric inertial coordinate system is earth centroid, OZ _iaxle points to the north, OX along earth rotation direction of principal axis _iaxle points to direction in the first point of Aries, OY _iaxle and OX _iaxle and OZ _iaxle forms right hand rectangular coordinate system;

Satellite body coordinate system OX described in step one _by _bz _b, the true origin of described satellite body coordinate system is centroid of satellite, OX _baxle, OY _baxle and OZ _baxle and celestial body are connected, and make the OX of coordinate axis _baxle, OY _baxle and OZ _baxle overlaps with the satellite principal axis of inertia.

3. according to claim 1 or 2 based on the low rail Flexible Satellite Attitude tracking and controlling method of sliding mode observer, it is characterized in that: described in step 2, Flexible Satellite Attitude kinetics equation is rewritten as state-space expression:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{Ax}+\mathrm{Bu}+\mathrm{Bf}+{\mathrm{BT}}_d\\ y=\mathrm{Hx}\end{array}\right.;$ In formula,

X is system state amount and x=(η ^tψ ^tω _bI ^t) ^t,

η represents modal vibration displacement,

A represent system matrix and $A=\left(\begin{array}{ccc}0& I& -\mathrm{\&delta;}\\ -K& -C& \mathrm{C\&delta;}\\ J_m^{-1}{\mathrm{\&delta;}}^{T}K& J_m^{-1}{\mathrm{\&delta;}}^{T}C& {-J}_m^{-1}{\mathrm{\&delta;}}^T\mathrm{C\&delta;}\end{array}\right),$

B represent control inputs matrix and $B=\left(\begin{array}{c}0\\ 0\\ J_m^{-1}\end{array}\right),$

C represents the damping matrix of modal vibration,

K represents the stiffness matrix of modal vibration,

Y represents that state space system measures output valve,

H represents that measurement exports square H=(0 0 I ₃),

U represents control signal,

F represents nonlinear terms and f=-ω _bI× J _mω _bI-ω _bI× δ ^tψ, wherein, ω _bIrepresent current pose angular velocity,

J _m=J-δ ^tδ represents satellite rigid element moment of inertia, and J represents the overall moment of inertia of satellite, and δ represents Coupled Rigid-flexible matrix, δ ^trepresent the transposed matrix of Coupled Rigid-flexible matrix delta,

T _drepresent aerodynamic interference moment.

4. according to claim 3 based on the low rail Flexible Satellite Attitude tracking and controlling method of sliding mode observer, it is characterized in that: obtain synovial membrane observer described in step 5 and estimate that the detailed process of mode value is: the observer gain matrix G that the sliding formwork item gain ρ that the state-space expression described with modal vibration damping, step 2 according to modal vibration frequency, Zi Kong topworks real-time control signal u, step 3 are determined tries to achieve with step 4, observer mate matrix F and Lyapunov equation matrix variables P, employing sliding mode observer: $\left\{\begin{array}{c}\stackrel{\stackrel{\&CenterDot;}{^}}{x}=A\hat{x}+\mathrm{Bu}+B\hat{f}-G(\hat{y}-y)+u\\ \hat{y}=H\hat{x}\end{array}\right.$ Observation obtains the real-time information of modal vibration displacement η and modal vibration state ψ, namely obtains estimating mode value with in formula, the estimated value of control system quantity of state $\hat{x}={\left(\begin{array}{ccc}{\widehat{\mathrm{\&eta;}}}^T& {\widehat{\mathrm{\&psi;}}}^T& {{\widehat{\mathrm{\&omega;}}}_{\mathrm{bI}}}^T\end{array}\right)}^T,$ The estimated value of nonlinear terms f $\hat{f}={-\mathrm{\&omega;}}_{\mathrm{bI}}\&times;J_m{\mathrm{\&omega;}}_{\mathrm{bI}}-{\mathrm{\&omega;}}_{\mathrm{bI}}\&times;{\mathrm{\&delta;}}^T\widehat{\mathrm{\&psi;}},$ The observational error of system measurements output valve y $e_y=\hat{y}-y,$ The sliding formwork item of observer $v=\left\{\begin{array}{cc}-\mathrm{\&rho;}{P}^{-1}\frac{H^T{F}^T{\mathrm{Fe}}_y}{\left|\right|{\mathrm{Fe}}_y\left|\right|}& \left|\right|{\mathrm{Fe}}_y\left|\right|\&GreaterEqual;\mathrm{\&epsiv;}\\ -\mathrm{\&rho;}{P}^{-1}\frac{H^T{F}^T{\mathrm{Fe}}_y}{\mathrm{\&epsiv;}}& \left|\right|{\mathrm{Fe}}_y\left|\right|<\mathrm{\&epsiv;}\end{array}\right.,$ ρ is the gain of sliding formwork item, simultaneously Fe _yrepresent sliding-mode surface, ε is the boundary layer thickness of observer sliding-mode surface.