CN104090489B - A kind of flexible agile satellite attitude maneuvers rolling optimization control method - Google Patents

Abstract

A kind of flexible agile satellite attitude maneuvers rolling optimization control method, relate to satellite maneuver control method, solve existing when carrying out fast reserve for Flexible Satellite Attitude, there is strong nonlinearity, the feature easily vibrated by multiple constraint and flexible appendage, and then cause being difficult to meet the problems such as demand for control, establish and comprise Satellite Attitude Dynamics, kinesiology and the non-linear state space equation of flexible appendage vibration, for carrying out the Accurate Prediction of attitude of satellite Future Information.Establish satellite attitude rapid maneuver and the weighted optimization index of suppression flexible appendage vibration, nonlinear model predictive control method is utilized to carry out the design of desired control rule, based on input forming technology, the expectation moment of planning is formed, use the manipulation rule of robust pseudoinverse technique design CMG group, with the desired control moment after input forming for input, cook up the frame corners speed of each CMG, it is achieved the attitude of satellite Large Angle Rapid Maneuvering of suppression flexible appendage vibration controls.

Description

A kind of flexible agile satellite attitude maneuvers rolling optimization control method

Technical field

The present invention relates to a kind of satellite gravity anomaly technical field, be specifically related to a kind of satellite maneuver control method, The Large Angle Rapid Maneuvering being particularly well-suited to have the flexible appendage attitude of satellite controls process.

Background technology

Along with the fast development of space mission planning, in the attitude of satellite is had the short time, carry out the quick machine of wide-angle Dynamic ability need increases day by day, i.e. needs satellite to have the agility of attitude.Compared with conventional satellite, this have quick machine The satellite of kinetic force can be significantly greatly increased the scope of earth observation, increases the call duration time with earth station, and is the spirit of multiple space Skilful imaging pattern provides safeguard.

In order to realize the fast reserve of the attitude of satellite, on the one hand it is to use novel high-torque attitude of satellite actuator, On the other hand it is to use advanced satellite maneuver control method.Control-moment gyro is by changing the angular momentum direction of rotor And produce control moment, from the point of view of counteraction flyback, output control moment is amplified, but how to be designed to evade The rule algorithm of handling of singularity becomes a difficult point of CMG application.It addition, the attitude of satellite is when carrying out Large Angle Rapid Maneuvering, The dynamics of satellite shows strong nonlinearity, and control method based on inearized model is difficult to meet demand for control, with Time, the actuator torque output capability of satellite attitude control system is limited, and output torque amplitude and increment etc. are the most constrained, this Also the design for controller brings difficulty.Additionally, due to the complication day by day of satellite structure layout, the flexibility of satellite structure is moved State becomes increasingly conspicuous, especially as solar array and the flexibility of large-scale antenna.The attitude of satellite, when carrying out fast reserve, easily causes The vibration of flexible appendage, cause the attitude of satellite in mobile process or motor-driven complete after can not quickly stablize, it is impossible to quickly Reach imaging demand, limit the application of quick satellite.

In sum, Flexible Satellite Attitude Large Angle Rapid Maneuvering based on CMG controls technology and becomes quick satellite in-orbit One key technology of application, also the design for satellite attitude control system becomes complexity especially.

Summary of the invention

The present invention solves existing when carrying out fast reserve for Flexible Satellite Attitude, have strong nonlinearity, by multiple about The feature that bundle and flexible appendage easily vibrate, and then cause being difficult to meet the problems such as demand for control, it is provided that a kind of flexible agility is defended Star attitude maneuver rolling optimization control method.

A kind of flexible agile satellite attitude maneuvers rolling optimization control method, the method is realized by following steps:

Step one, selection inertial coodinate system are reference frame, set up the tool with pyramid configuration CMG group as actuator There are Satellite Attitude Dynamics and the kinematical equation of flexible appendage；On the basis of the modal coordinate system of flexible appendage, set up flexibility The kinetics equation of accessory vibration, by defining new state variable, obtains based on three equations set up and is used for predicting satellite The non-linear state space equation of attitude Future Information；

After step 2, the non-linear state space equation setting up step one carry out discretization, measure according to current time The attitude of satellite quaternary number obtained and attitude angular velocity information, set up the prediction output equation of attitude of satellite information, it is achieved in advance Survey the attitude of satellite in time domain and the prediction of angular velocity information；

Step 3, the attitude of satellite information prediction output equation obtained according to step 2, utilize mission planning attitude maneuver The expectation quaternary number of guidance law output, expectation angular velocity information, foundation takes into account the motor-driven rapidity of the attitude of satellite and flexible appendage shakes The Optimal Control Problem of dynamic rejection, through solving this Optimal Control Problem, it is thus achieved that desired non-linear mould predictive Maneuver autopilot moment；According to the kinetics equation of the flexible appendage vibration that step one is set up, use input forming technology, to described Expect that non-linear mould predictive maneuver autopilot moment forms design；

Step 4, using the maneuver autopilot moment after form finding design as input, use robust to violate method, set up and ask for gold The Optimal Control Problem of word tower configuration CMG group's frame corners speed, by solving the frame corners speed obtaining pyramid configuration CMG group Handle rule, according to the angular momentum of pyramid configuration CMG group in the decomposition of the attitude of satellite three axle, it is thus achieved that drive the attitude of satellite motor-driven Actual control moment；

Step 5, employing Discrete Control Technique, in each sampling instant repetition step 2 to step 4, pass through progressive updating Attitude of satellite information, it is achieved the rolling optimization control that Flexible Satellite Attitude is motor-driven.

Beneficial effects of the present invention: the present invention is by by nonlinear model predictive control method, input forming technology and control The methods such as the manipulation rule of moment gyro processed mutually merge, and propose one and realize attitude of satellite Large Angle Rapid Maneuvering and effectively suppress The control method of flexible appendage vibration.

One, establish comprise Satellite Attitude Dynamics, kinesiology and flexible appendage vibration non-linear state space equation, For carrying out the Accurate Prediction of attitude of satellite Future Information.

Two, under considering pyramid configuration CMG group's torque output capability constraints, satellite attitude rapid maneuver is established And the weighted optimization index of suppression flexible appendage vibration, utilize nonlinear model predictive control method to carry out setting of desired control rule Meter, has taken into account the rejection of attitude of satellite mobility and accessory vibration.

Three, based on input forming technology, the expectation moment of planning is formed so that complete the motor-driven mesh of the attitude of satellite In the case of mark, eliminate the vibrational energy that flexible appendage is remaining.

Four, robust pseudoinverse technique is used to devise the manipulation rule of pyramid configuration CMG group, with the desired control after input forming Moment is input, cooks up the frame corners speed of each CMG, it is achieved the attitude of satellite wide-angle of suppression flexible appendage vibration is quick Maneuver autopilot.

Accompanying drawing explanation

Fig. 1 is quick Satellite Attitude in a kind of flexible agile satellite attitude maneuvers rolling optimization control method of the present invention State mobile process schematic diagram；

Fig. 2 is input forming skill in a kind of flexible agile satellite attitude maneuvers rolling optimization control method of the present invention The schematic diagram of art；

Fig. 3 is pyramid configuration in a kind of flexible agile satellite attitude maneuvers rolling optimization control method of the present invention In CMG group each CMG mounting means and with the graph of a relation of satellite body coordinate system；

In Fig. 4, a to f is to use a kind of flexible agile satellite attitude maneuvers rolling optimization control method of the present invention Simulated effect figure.

Detailed description of the invention

Detailed description of the invention one, combine Fig. 1 to Fig. 4 present embodiment is described, a kind of flexible agile satellite attitude maneuvers rolling Dynamic optimal control method, the method is realized by following steps:

Step A: selected reference frame, sets up the flexible appendage that has with pyramid configuration CMG group as actuator Satellite Attitude Dynamics and kinematical equation, and set up the kinetics equation that the flexible appendage under modal coordinate system vibrates；Pass through Define new state variable, set up the non-linear state space equation for predicting attitude of satellite Future Information；

Step B: the attitude of satellite information recorded according to current time, by the non-linear state space side after discretization Journey, is predicted the attitude of satellite information in prediction time domain, sets up the prediction output equation of the attitude of satellite；

Step C: in view of the bandwidth feature of four Gimbal servo mechanisms and the control ability of pyramid configuration CMG group, will Its Filters with Magnitude Constraints being converted into output control moment and increment restriction condition.Foundation comprises attitude of satellite mobility and suppression is scratched Property accessory vibration Optimal Control Problem, and optimize desired control moment to be designed under actuator capacity consistency considering, Obtain maneuver autopilot moment based on Nonlinear Model Predictive Control；

Step D: according to flexible appendage vibration equation, utilizes input forming technology, it is achieved the one-tenth of planning expectation control moment Shape, ensure flexible satellite attitude target desirably carry out motor-driven in the case of, suppression flexible appendage residual oscillation.

Step E: according to the construction features of pyramid configuration CMG group, ask for its angular momentum at satellite three axle, pseudo-with robust Inverse method sets up the optimizing index asking for CMG frame corners speed, by choosing rational controller parameter, designs pyramid configuration The manipulation rule of CMG group, and then drive the attitude of satellite to carry out motor-driven.

Step F: according to Discrete Control Technique principle, in each sampling instant repetition step B to step E, by the most more New attitude of satellite information, it is achieved the rolling optimization control that Flexible Satellite Attitude is motor-driven.

Detailed description of the invention two, combining Fig. 1 to Fig. 4 present embodiment is described, present embodiment is detailed description of the invention one The embodiment of described a kind of flexible agile satellite attitude maneuvers rolling optimization control method, its detailed process is:

One, with inertial coodinate system as reference frame, scratching with pyramid configuration CMG group having as actuator of foundation The Satellite Attitude Dynamics of property adnexa is:

$J\stackrel{\·}{w}+{\mathrm{\δ}}^T\stackrel{\·\·}{\mathrm{\η}}+\[w\×\]Jw+\[w\×\]{\mathrm{\δ}}^T\stackrel{\·}{\mathrm{\η}}=-{\stackrel{\·}{H}}_{CMG}-\[w\×\]H_{CMG}+T_d$

In formula, J is the moment of inertia matrix of satellite, and w is celestial body three-axis attitude angular velocity, and δ is flexible appendage and celestial body Coupled Rigid-flexible matrix, η is flexible appendage displacement under modal coordinate system, H_CMGThree shaft angles for pyramid configuration CMG group move Amount, T_dFor spatial interference moment.The control moment of definition CMG group is $T=-{\stackrel{\·}{H}}_{CMG}-\[w\×\]H_{CMG},$ Wherein [w ×] is defined as:

$\[w\×\]=\left[\begin{array}{ccc}0& -w_z& w_y\\ w_z& 0& -w_x\\ -w_y& w_x& 0\end{array}\right]$

Describe the kinematical equation of the attitude of satellite with Eulerian angles univocal in engineering, define θ_x,θ_y,θ_zIt is respectively xyz Turn the roll angle under sequence, the angle of pitch and yaw angle.And then satellite three-axis attitude angular velocity w can be expressed as:

$\left[\begin{array}{c}{w}_x\\ w_y\\ w_z\end{array}\right]=A_z{A}_y{A}_x\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_x\\ 0\\ 0\end{array}\right]+A_z{A}_y\left[\begin{array}{c}0\\ {\stackrel{\·}{\mathrm{\θ}}}_y\\ 0\end{array}\right]+A_z\left[\begin{array}{c}0\\ 0\\ {\stackrel{\·}{\mathrm{\θ}}}_z\end{array}\right]=\left[\begin{array}{ccc}{\mathrm{cos\θ}}_z{\mathrm{cos\θ}}_y& {\mathrm{sin\θ}}_z& 0\\ -{\mathrm{sin\θ}}_z{\mathrm{cos\θ}}_y& {\mathrm{cos\θ}}_z& 0\\ {\mathrm{sin\θ}}_y& 0& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_x\\ {\stackrel{\·}{\mathrm{\θ}}}_y\\ {\stackrel{\·}{\mathrm{\θ}}}_z\end{array}\right]$

In formula, A_x,A_y,A_zRepresent corresponding spin matrix.Arrangement has:

$\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_x\\ {\stackrel{\·}{\mathrm{\θ}}}_y\\ {\stackrel{\·}{\mathrm{\θ}}}_z\end{array}\right]=\frac{1}{{\mathrm{cos\θ}}_y}\left[\begin{array}{ccc}{\mathrm{cos\θ}}_z& -{\mathrm{sin\θ}}_z& 0\\ {\mathrm{cos\θ}}_y{\sin }_z& {\mathrm{cos\θ}}_y{\mathrm{cos\θ}}_z& 0\\ -{\mathrm{cos\θ}}_z{\mathrm{sin\θ}}_y& {\mathrm{sin\θ}}_z{\mathrm{sin\θ}}_y& {\mathrm{cos\θ}}_y\end{array}\right]\left[\begin{array}{c}{w}_x\\ w_y\\ w_z\end{array}\right]$

The attitude of satellite stable operation or carry out the axis of rolling motor-driven time, pitch axis and yaw axis attitude angle and angular velocity are In a small amount, therefore have ${\left[\begin{array}{ccc}{\stackrel{\·}{\mathrm{\θ}}}_x& {\stackrel{\·}{\mathrm{\θ}}}_y& {\stackrel{\·}{\mathrm{\θ}}}_z\end{array}\right]}^T\≈{\left[\begin{array}{ccc}{w}_x& w_y& w_z\end{array}\right]}^T,$ Assume the satellite three-axis attitude angular velocity obtained by gyro to measure Information can be directly used for design of control law.

Under modal coordinate system, the kinetics equation of flexible appendage vibration is:

$\stackrel{\·\·}{\mathrm{\η}}+2{\mathrm{\ζ}}_f{w}_f\stackrel{\·}{\mathrm{\η}}+w_f^2\mathrm{\η}+\mathrm{\δ}\stackrel{\·}{w}=0$

In formula, ζ_fFor the damping ratio matrix of flexible appendage mode, w_fFrequency of vibration matrix for flexible appendage mode.

Merge the kinetics equation of the attitude of satellite, kinematical equation and the vibration equation of flexible appendage, and define new shape State variable x=[θ η w w_η]^T, ignore the impact of spatial interference moment, arrange and obtain following formula:

$\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& I& 0& 0\\ 0& 0& J& {\mathrm{\δ}}^T\\ 0& 0& \mathrm{\δ}& I\end{array}\right]\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ \stackrel{\·}{\mathrm{\η}}\\ \stackrel{\·}{w}\\ {\stackrel{\·}{w}}_{\mathrm{\η}}\end{array}\right]+\left[\begin{array}{cccc}0& 0& -I& 0\\ 0& 0& 0& -I\\ 0& 0& \[w\×\]J& \[w\×\]{\mathrm{\δ}}^T\\ 0& w_f^2& 0& 2{\mathrm{\ζ}}_f{w}_f\end{array}\right]\left[\begin{array}{c}\mathrm{\θ}\\ \mathrm{\η}\\ w\\ w_{\mathrm{\η}}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ I\\ 0\end{array}\right]T$

And then have a state space equation:

$\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ \stackrel{\·}{\mathrm{\η}}\\ \stackrel{\·}{w}\\ {\stackrel{\·}{w}}_{\mathrm{\η}}\end{array}\right]=-{\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& I& 0& 0\\ 0& 0& J& {\mathrm{\δ}}^T\\ 0& 0& \mathrm{\δ}& I\end{array}\right]}^{-1}\left[\begin{array}{cccc}0& 0& -I& 0\\ 0& 0& 0& -I\\ 0& 0& \[w\×\]J& \[w\×\]{\mathrm{\δ}}^T\\ 0& w_f^2& 0& 2{\mathrm{\ζ}}_f{w}_f\end{array}\right]\left[\begin{array}{c}\mathrm{\θ}\\ \mathrm{\η}\\ w\\ w_{\mathrm{\η}}\end{array}\right]+{\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& I& 0& 0\\ 0& 0& J& {\mathrm{\δ}}^T\\ 0& 0& \mathrm{\δ}& I\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ I\\ 0\end{array}\right]T$

Equation that describes satellite three-axis attitude and angular velocity, the vibration displacement of flexible appendage and the strong nonlinearity of angular velocity Coupled relation.The information such as the attitude of satellite recorded according to current time sensor and accessory vibration displacement, the available equation is carried out The prediction of the information such as the attitude of satellite in following a period of time.

Two, current information x (k) of the attitude of satellite etc. recorded according to sensor, the nonlinear state utilizing discretization is empty Between equation:

X (k+1)=f (x (k), u (k))

By iterative computation, following N can be asked for_pAttitude of satellite information in prediction time domain:

$\begin{array}{c}\stackrel{\‾}{x}(k+1)=f\left(x\right(k),u(k\left)\right)\\ \stackrel{\‾}{x}(k+2)=f\left(\stackrel{\‾}{x}\right(k+1),u(k+1\left)\right)\\ .\\ .\\ .\\ \stackrel{\‾}{x}(k+N_p)=f\left(\stackrel{\‾}{x}\right(k+N_p-1),u(k+N_p-1\left)\right)\end{array}$

In formula,Represent the status information of prediction.From above N_pSystem mode in step prediction time domain understands, it was predicted that after Free variable to be designed be N_pControlled quentity controlled variable in time step u (k), u (k+1) ... u (k+N_p-1) }, i.e. CMG group's is to be designed Control moment.When prediction time domain N_pBeyond controlling time domain N_uTime, it is assumed that control moment input is at interval [N_u,N_p] keep constant, i.e. Have:

u(k+N_u-1)=u (k+N_u)=...=u (k+N_p-1)

Now the prediction output equation of the attitude of satellite is:

$\begin{array}{c}\stackrel{\‾}{x}(k+1)=f\left(x\right(k),u(k\left)\right)\\ \stackrel{\‾}{x}(k+2)=f\left(\stackrel{\‾}{x}\right(k+1),u(k+1\left)\right)\\ .\\ .\\ .\\ \stackrel{\‾}{x}(k+N_u)=f\left(\stackrel{\‾}{x}\right(k+N_u-1),u(k+N_u-1\left)\right)\\ .\\ .\\ .\\ \stackrel{\‾}{x}(k+N_p)=f\left(\stackrel{\‾}{x}\right(k+N_p-1),u(k+N_u-1\left)\right)\end{array}$

Three, Fig. 3 is combined, in figure,Represent body coordinate system three axial vector of satellite.Represent four The mounting coordinate system vector of individual CMG).Under normal circumstances, four rotors of pyramid configuration CMG group are all with constant rotating speed rotation Turn, i.e. the angular momentum of rotor is fixing, is carried out the control of output torque by the frame corners speed controlling each CMG.Consider To bandwidth characteristic and the control ability of Gimbal servo system, which limit frame corners velocity amplitude and the acceleration capacity of each CMG, And then the torque output capability of pyramid configuration CMG group is proposed constraint, this constraint can use the control moment of CMG group to export The form of amplitude limit and increment amplitude limit describes, then have:

|T_i|≤T_max, i={x, y, z} control moment output constraint

|ΔT_i|≤ΔT_max, i={x, y, z} control moment output increment retrains

Four, in view of the motor-driven of the attitude of satellite and tracking performance, CMG group exports energy and the flexible appendage of control moment Vibrational energy etc., set up following object function J (x (k), U_k):

$\begin{array}{c}J\left(x\right(k),U_k)\\ =\underset{i=1}{\overset{N_p}{\Σ}}\left|\right|{\stackrel{\‾}{x}}_{\mathrm{\θ},w}(k+i)-r(k+i)|{|}_Q^2+\underset{i=0}{\overset{N_u-1}{\Σ}}|\left|\stackrel{\‾}{u}(k+i)\right|{|}_R^2+\underset{i=1}{\overset{N_p}{\Σ}}\left|\right|{\stackrel{\‾}{x}}_{\mathrm{\η},w_{\mathrm{\η}}}(k+i)|{|}_P^2\end{array}$

In formula,Represent the satellite rigid-body attitude output of prediction,Represent that the satellite of prediction is scratched Property adnexa attitude output.The integrality of systemCan be calculated by following mathematical model:

$\left\{\begin{array}{c}\stackrel{\‾}{x}(i+1)=f\left(\stackrel{\‾}{x}\right(i),\stackrel{\‾}{u}(i\left)\right),k\≤i\≤k+N_p\\ \stackrel{\‾}{x}\left(k\right)=x\left(k\right)\end{array}\right.$

In superincumbent optimization problem, symbol N_p,N_uIt is expressed as predicting time domain and controlling time domain, and has N_u≤N_p。r () is the output of desired satellite gravity anomaly, i.e. reference input, it is obtained by satellite mobile mission planning.(Q, R, P) is Tracking error weighting matrix, control moment weighting matrix and flexible appendage vibration weighting matrix.X (k) is current time Satellite Attitude The initial value of state, namely the following dynamic starting point of the attitude of satellite of prediction.PREDICTIVE CONTROL for system inputs, and i.e. treats excellent The control moment changed, is defined as:

$\stackrel{\‾}{u}(k+i)={\stackrel{\‾}{u}}_i,i=0,1,\mathrm{...},N_u-1,$

In formula,It is the most independent optimized variable, is designated as:

$U_k={\left[\begin{array}{cccc}{\stackrel{\‾}{u}}_0& {\stackrel{\‾}{u}}_1& \mathrm{...}& {\stackrel{\‾}{u}}_{N_u-1}\end{array}\right]}^T$

The optimal solution assuming the constrained optimization problems of satellite gravity anomaly is:

$U_k^{*}={\left[\begin{array}{cccc}{\stackrel{\‾}{u}}_0^{*}& {\stackrel{\‾}{u}}_1^{*}& \mathrm{...}& {\stackrel{\‾}{u}}_{N_u-1}^{*}\end{array}\right]}^T$

According to PREDICTIVE CONTROL principle, first element of optimal solution, i.e. the optimal control torque of current time will act on Satellite attitude control system, the current controlled quentity controlled variable of definition current time is:

$u\left(k\right)={\stackrel{\‾}{u}}_0^{*}.$

Five, for the desired control moment planned by nonlinear model predictive control method, although it considers when design The factor of suppression flexible appendage vibration, but still can evoke the vibration of adnexa to a certain extent.For decay adnexa further Vibration, carries out input forming process by the desired control moment of planning, and the design of input forming device is as follows:

(1) relatively big due to the single order vibration effect of flexible appendage mode, shaking of flexible appendage under considering first-order modal Dynamic equation is rewritten as:

$\stackrel{\·\·}{\mathrm{\η}}+2{\mathrm{\ζ}}_f{w}_f\stackrel{\·}{\mathrm{\η}}+w_f^2\mathrm{\η}=-{\mathrm{\δJ}}^{-1}T$

By moment is regarded as a series of pulses under zero initial condition, and then the response analysis to system can obtain:

$\underset{j=1}{\overset{n}{\Σ}}{\mathrm{bA}}_j\frac{w_f}{\sqrt{1-{\mathrm{\ζ}}_f^2}}{e}^{-{\mathrm{\ζ}}_j{w}_f(t_n-t_j)}\sin \left(t_j{w}_f\sqrt{1-{\mathrm{\ζ}}_f^2}\right)=0$

$\underset{j=1}{\overset{n}{\Σ}}{\mathrm{bA}}_j\frac{w_f}{\sqrt{1-{\mathrm{\ζ}}_f^2}}{e}^{-{\mathrm{\ζ}}_f{w}_f(t_n-t_j)}\cos \left(t_j{w}_f\sqrt{1-{\mathrm{\ζ}}_f^2}\right)=0$

In formula, A_jIt is the amplitude of jth pulse torque, t_jIt is the action time of jth pulse torque, wherein b=-δ J^-1, And haveAmplitude and the A of n the pulse torque acted on satellite can be obtained by solving above formula_j With t action time_j, and ensure that the residual oscillation of system spare is 0 after the n-th Pulse Width Control moment effect.

(2) according to input forming technology, according to the principle shown in Fig. 2, the kinetics equation that flexible appendage vibrates is utilized, can Obtain a series of impulse function, and then composition input forming device.By desired non-linear mould predictive maneuver autopilot moment with defeated Enter former and carry out convolution, the desired control moment after shaping can be obtained.Desired control moment after this input forming can Ensure at t_nFlexible appendage after moment does not has the vibration of remnants, and ensure that flexible satellite attitude target desirably Carry out motor-driven.

Six, according to the installation form of the pyramid configuration CMG group shown in Fig. 3, the total angular momentum of pyramid configuration CMG group exists Satellite body coordinate system is represented by:

$h=\underset{i=1}{\overset{4}{\Σ}}{h}_i\left({\mathrm{\δ}}_i\right)=h_0\[\left(\begin{array}{c}-{\mathrm{cos\βsin\δ}}_1\\ {\mathrm{cos\δ}}_1\\ {\mathrm{sin\βsin\δ}}_1\end{array}\right)+\left(\begin{array}{c}-{\mathrm{cos\δ}}_2\\ -{\mathrm{cos\βsin\δ}}_2\\ {\mathrm{sin\βsin\δ}}_2\end{array}\right)+\left(\begin{array}{c}{\mathrm{cos\βsin\δ}}_3\\ -{\mathrm{cos\δ}}_3\\ {\mathrm{sin\βsin\δ}}_3\end{array}\right)+\left(\begin{array}{c}{\mathrm{cos\δ}}_4\\ {\mathrm{cos\βsin\δ}}_4\\ {\mathrm{sin\βsin\δ}}_4\end{array}\right)\]$

For above pyramid configuration CMG group, when the frame corners taking SGCMG is respectively following parameter:

δ=[-0.5 π, π, 0.5 π, 0]^T, δ=[0 ,-0.5 π, π, 0.5 π]^T, δ=[0.5 π, 0.5 π, 0.5 π, 0.5 π]^T

Correspondingly, pyramid configuration CMG group respectively at satellite x, y, z tri-axle output maximum angular momentum, be respectively as follows:

h_{x max}=2h (1+cos β), h_{y max}=2h (1+cos β), h_{z max}=4hsin β

If it is desire to satellite three axle has identical maximum angular momentum ability, above formula the inclination angle that can calculate SGCMG is β =53.1 degree.

The manipulation rule effect of SGCMG is that the desired control moment gone out by control law module planning is converted into pyramid configuration The movement instruction of each SGCMG in CMG group, the frame corners speed movement instruction of the most each SGCMG.For making pyramid configuration CMG group energy enough exports control moment stable, smooth, and the manipulation rule designing good SGCMG is particularly important.Simultaneously as it is golden There is singular problem in word tower configuration CMG group so that the manipulation rule design of SGCMG is increasingly complex.

Robust pseudoinverse is handled rule and can be reached to depart from unusual mesh by producing, when unusual state, the deviation moment allowed 's.Robust pseudoinverse handles the design of rule can be by minimizing following optimizing index:

$J={(A\stackrel{\·}{\mathrm{\δ}}-\mathrm{\τ})}^{T}P(A\stackrel{\·}{\mathrm{\δ}}-\mathrm{\τ})+\stackrel{\·}{{\mathrm{\δ}}^T}Q\stackrel{\·}{\mathrm{\δ}},$

In formula, P, Q are normal value matrix to be designed, and τ is the desired control moment cooked up.Matrix A is Jacobi square Battle array, it may be assumed that

By above optimization problem, it may be determined that going out frame corners velocity variations rule is:

$\stackrel{\·}{\mathrm{\δ}}=A^{+}\stackrel{\·}{h}=\frac{1}{h_0}{\mathrm{WA}}^T{({\mathrm{AWA}}^T+V)}^{-1}\stackrel{\·}{h}$

In order to avoid SGCMG framework is locked, improve robust pseudoinverse and handle the rule avoidance to singularity, need reasonably design Matrix P, Q.Use following method design matrix P, Q:

$V\≡P^{-1}=\mathrm{\λ}\left(\begin{array}{ccc}1& {\mathrm{\ϵ}}_3& {\mathrm{\ϵ}}_2\\ {\mathrm{\ϵ}}_3& 1& {\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2& {\mathrm{\ϵ}}_1& 1\end{array}\right)>0$

$W\≡Q^{-1}=\left(\begin{array}{cccc}{W}_1& \mathrm{\λ}& \mathrm{\λ}& \mathrm{\λ}\\ \mathrm{\λ}& W_2& \mathrm{\λ}& \mathrm{\λ}\\ \mathrm{\λ}& \mathrm{\λ}& W_3& \mathrm{\λ}\\ \mathrm{\λ}& \mathrm{\λ}& \mathrm{\λ}& W_4\end{array}\right)>0$

In formula, ε_iIt is chosen for the function of mechanical periodicity near null value, is taken as ε_i=ε₀sin(ωt+φ_i), parameter lambda₀,μ,ε₀, φ_iFor design ratio undetermined, it is typically based on the motor-driven situation of the attitude of satellite and is adjusted.Choosing of matrix W need to be according to Satellite Attitude State maneuver model and given choose with reference to control moment feature.

Seven, at current sample time, according to design procedure two to six, the pyramid each frame of configuration CMG group can be calculated The angular velocity of frame, and then produce the actual moment driving the attitude of satellite motor-driven.In next sampling instant, implement step in line interation Rapid two to six, the motor-driven rolling optimization of Flexible Satellite Attitude can be realized and control.

In this embodiment as a example by certain type moonlet, its moment of inertia matrix is as follows:

$I=\left(\begin{array}{ccc}103.9& -1.85& -0.2\\ -1.85& 106.38& -1.55\\ -0.2& -1.55& 146.82\end{array}\right)(Kg\·m2)$

Here, suppose that the initial attitude Eulerian angles of satellite are [25 °, 0 °, 0 °], targeted attitude Eulerian angles be [-25 °, 0 °, 0 °], initial and targeted attitude angular velocity is [0 °/s, 0 °/s, 0 °/s].The flexible windsurfing fundamental frequency considered is 2.23Hz, Damping is 0.032, and Coupled Rigid-flexible coefficient matrix is [0.00041,3.833,0].SGCMG maximum frame corners speed is 3rad/s, The specified angular momentum of rotor is 5Nms.The control moment of the pyramid configuration CMG group considered is constrained to [-6Nm, 6Nm], and its increment is about Bundle is [-0.4Nm, 0.4Nm].Motor-driven for the satellite axis of rolling single shaft considered, the robust pseudoinverse of design handles rule parameter successively It is chosen for:

$\mathrm{\μ}=10,{\mathrm{\λ}}_0=0.01,{\mathrm{\ϵ}}_0=0.01,{\mathrm{\φ}}_0=\[0,\frac{\mathrm{\π}}{2},\mathrm{\π},\frac{3\mathrm{\π}}{2}\],W=diag\{1,2,3,4\}.$

Perturbation employing typical case's expression-form:

$\left\{\begin{array}{c}{M}_{dx}={10}^{-5}(3{\mathrm{cos\ω}}_{0}t+1)\\ M_{dy}={10}^{-5}(1.5{\mathrm{sin\ω}}_{0}t+3{\mathrm{cos\ω}}_{0}t)\\ M_{dz}={10}^{-5}(3{\mathrm{sin\ω}}_{0}t+1)\end{array}\right.$

Present embodiment, in order to the robustness of the method for the invention is described, only considers that the principal moments matrix of satellite three axle enters Row design, and the impact of spatial interference moment is not considered when control method designs.Fig. 4 gives the attitude of satellite and attitude angle speed The change curve of degree, control moment and increment change curve and the frame corners speed of pyramid configuration CMG group and frame corners Change curve.Find out from simulation result, reasonably control parameter by choosing and handle rule parameter, it is possible to achieve the attitude of satellite Fast reserve, and in mobile process, the vibration of bigger flexible windsurfing will not be evoked.Satellite axis of rolling attitude can be about In 20s motor-driven 50 °, and motor-driven complete after there is higher attitude stability.Control moment and increment change song is exported from CMG group Line is it can be seen that met its constraint all the time by CMG group's output torque of maneuver autopilot rule planning, and the moment in mobile process increases Measure less, be difficult to evoke the vibration of flexible windsurfing.The inventive method is utilized to only account for satellite three when designing maneuver autopilot rule Axle principal moments matrix, and do not consider the impact that spatial interference moment is brought, but in terms of simulation result, the control method of design can Complete satellite attitude rapid maneuver and the control target of suppression flexible windsurfing vibration, show certain robustness.

Claims (1)

1. a flexible agile satellite attitude maneuvers rolling optimization control method, is characterized in that, the method is realized by following steps:

Step one, selection inertial coodinate system are reference frame, set up and scratch with pyramid configuration CMG group having as actuator The Satellite Attitude Dynamics of property adnexa and kinematical equation；On the basis of the modal coordinate system of flexible appendage, set up flexible appendage The kinetics equation of vibration, by defining new state variable, obtains based on three equations set up and is used for predicting the attitude of satellite The non-linear state space equation of Future Information；

Detailed process is: the attitude of satellite power with flexible appendage with pyramid configuration CMG group as actuator of foundation Equation is:

$J\stackrel{\·}{w}+{\mathrm{\δ}}^T\stackrel{\·\·}{\mathrm{\η}}+\[w\×\]Jw+\[w\×\]{\mathrm{\δ}}^T\stackrel{\·}{\mathrm{\η}}=-{\stackrel{\·}{H}}_{CMG}-\[w\×\]H_{CMG}+T_d$

In formula, J is the moment of inertia matrix of satellite, and w is celestial body three-axis attitude angular velocity, and what δ was flexible appendage with celestial body is hard and soft Coupling matrix, η is flexible appendage displacement under modal coordinate system, H_CMGFor the three shaft angle momentum of pyramid configuration CMG group, T_d For spatial interference moment；

The control moment of definition CMG groupWherein [w ×] is defined as:

$\[w\×\]=\left[\begin{array}{ccc}0& -w_z& w_y\\ w_z& 0& -w_x\\ -w_y& w_x& 0\end{array}\right]$

In formula, w_x, w_yAnd w_zIt is respectively axis of rolling attitude angular velocity, pitch axis attitude angular velocity and yaw axis attitude angular velocity；

Under modal coordinate system, the kinetics equation of flexible appendage vibration is:

$\stackrel{\·\·}{\mathrm{\η}}+2{\mathrm{\ζ}}_f{w}_f\stackrel{\·}{\mathrm{\η}}+w_f^2\mathrm{\η}+\mathrm{\δ}\stackrel{\·}{w}=0$

In formula, ζ_fFor the damping ratio matrix of flexible appendage mode, w_fFrequency of vibration matrix for flexible appendage mode；

Merge the kinetics equation of the attitude of satellite, kinematical equation and the kinetics equation of flexible appendage vibration, and define new State variable x=[θ η w w_η]^T, it is thus achieved that non-linear state space equation:

$\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ \stackrel{\·}{\mathrm{\η}}\\ \stackrel{\·}{w}\\ {\stackrel{\·}{w}}_{\mathrm{\η}}\end{array}\right]=-{\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& I& 0& 0\\ 0& 0& J& {\mathrm{\δ}}^T\\ 0& 0& \mathrm{\δ}& I\end{array}\right]}^{-1}\left[\begin{array}{cccc}0& 0& -I& 0\\ 0& 0& 0& -I\\ 0& 0& \[w\×\]J& \[w\×\]{\mathrm{\δ}}^T\\ 0& w_f^2& 0& 2{\mathrm{\ζ}}_f{w}_f\end{array}\right]\left[\begin{array}{c}\mathrm{\θ}\\ \mathrm{\η}\\ w\\ w_{\mathrm{\η}}\end{array}\right]+{\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& I& 0& 0\\ 0& 0& J& {\mathrm{\δ}}^T\\ 0& 0& \mathrm{\δ}& I\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ I\\ 0\end{array}\right]T$

In formula, θ represents attitude of satellite angle, w_ηFor flexible appendage displacement under modal coordinate system；I is unit matrix；

After step 2, the non-linear state space equation setting up step one carry out discretization, measure according to current time and obtain Attitude of satellite quaternary number and attitude angular velocity information, set up the prediction output equation of attitude of satellite information, it is achieved to prediction time The attitude of satellite in territory and the prediction of angular velocity information；

Step 3, the attitude of satellite information prediction output equation obtained according to step 2, utilize mission planning attitude maneuver to guide The expectation quaternary number of rule output and expectation angular velocity information, foundation takes into account the motor-driven rapidity of the attitude of satellite and flexible appendage vibration presses down The Optimal Control Problem of performance processed, through solving this Optimal Control Problem, it is thus achieved that desired non-linear mould predictive is motor-driven Control moment；According to the kinetics equation of the flexible appendage vibration that step one is set up, use input forming technology, to described expectation Non-linear mould predictive maneuver autopilot moment；

Step 4, using described maneuver autopilot moment as input, use robust to violate method, set up and ask for pyramid configuration The Optimal Control Problem of CMG group's frame corners speed, by solving Optimal Control Problem, it is thus achieved that the frame of pyramid configuration CMG group Frame angular velocity handles rule, according to the angular momentum of pyramid configuration CMG group in the decomposition of the attitude of satellite three axle, it is thus achieved that drive Satellite Attitude The actual control moment that state is motor-driven；

Step 5, employing Discrete Control Technique, in each sampling instant repetition step 2 to step 4, by progressive updating satellite Attitude information, it is achieved the rolling optimization control that Flexible Satellite Attitude is motor-driven.