CN103213691A - Method of using satellite rolling-axis rapid attitude manoeuvre to unload angular momentum of rolling axis and yawing axis - Google Patents

Abstract

The invention provides a method of using satellite rolling-axis rapid attitude manoeuvre to unload the angular momentum of a rolling axis and a yawing axis, and belongs to the technical field of spacecraft attitude control. The method resolves the problems that at present, an unloading device needs to be additionally installed on a satellite to unload the angular momentum absorbed by momentum exchange actuating mechanisms of the satellite, and therefore manufacturing cost of the satellite is increased, and the size and the weight of the satellite are increased. A body system and an inertial coordinate system of the satellite are defined, and an initial unloading moment is confirmed; and unloading is conducted by means of confirmation of the gravity gradient force moment borne by the satellite, accumulated angular momentum vectors of the gravity gradient force moment inside each orbital period, the angular momentum, needing to be unloaded, of all the momentum exchange actuating mechanisms on the rolling axis, the angular momentum, needing to be unloaded, of all the momentum exchange actuating mechanisms on the yawing axis, the number of turns of unloaded orbits of the satellite, the maneuvering angle in a satellite unloading process, and time used by the satellite rolling-axis maneuvering angle. The method can be widely applied to accumulated angular momentum unloading requirements of the actuating mechanisms.

Description

A kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum

Technical field

The present invention relates to a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum, belong to spacecraft attitude control technology field.

Background technology

Because satellite will be subjected to the influence of space disturbance torque usually in orbit, if disturbance torque is fixed in the direction of inertial space then can be accumulated corresponding moment of momentum in inside satellite, generally this part moment of momentum is that momentum exchange actuating unit by satellite absorbs, it is limited that yet actuating unit absorbs the ability of moment of momentum, therefore when the moment of momentum of the actuating unit accumulation of satellite when saturated, need the moment of momentum that actuating unit accumulates be unloaded.

Satellite utilizes generation moment of face such as magnetic torquer, air jet system to be used for offsetting the moment of momentum that disturbance torque accumulated before usually, but different discharging gears has self intrinsic shortcoming, for example, the unload forces moment ratio that magnetic torquer produces is less, depend on external environment condition simultaneously, and air jet system has the restriction in life-span, is not suitable for long-term use.Except top described shortcoming, the common shortcoming of all discharging gears is need discharging gear be installed additionally on satellite, has not only improved the cost of satellite, has also increased the volume and the weight of satellite simultaneously.

Summary of the invention

The present invention need additionally install discharging gear for the moment of momentum that the momentum exchange actuating unit that solves existing unloading satellite absorbs on satellite, cause the satellite cost to improve, increase the problem of satellite volume and weight, thereby a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum is provided.

A kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum, it comprises the steps:

Step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

Described inertial coordinates system ox _Iy _Iz _I: initially unloading moment barycenter with satellite is initial point, oz _IThe axle in the satellite orbit plane, oz _IDirection needs discharged total angular momentum direction identical with satellite, oy _IAxle is perpendicular to the satellite transit orbit plane, and is opposite with described orbit angular velocity direction, ox _I, oy _IWith oz _IAxle is formed right-handed system;

The body series ox of described satellite _by _bz _bCoordinate origin be the satellite barycenter, each coordinate axle and celestial body are connected, and can guarantee that the satellite moment of inertia matrix of describing at this system of axes is the diagonal matrix form;

Step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Wherein b represents body series, and G represents gravity gradient;

Step 3: with initial unloading moment t ₀Be starting point, calculate gravity gradient torque

The moment of momentum vector h that in each orbit period, accumulates _Circ:

In the formula, k is inertial coordinates system oz _IAxial unit vector; I _zBe satellite yaw axis principal moment of inertia, I _yIt is satellite pitch axis principal moment of inertia;

Step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures

Need discharged moment of momentum with yaw axis

Size;

Step 5: the moment of momentum vector h that obtains according to step 3 _CircNeed discharged moment of momentum with step 4 obtains at the axis of rolling

Need discharged moment of momentum with yaw axis

Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Step 6: estimate the motor-driven angle of the satellite axis of rolling

The used time

In the formula,

Be the motor-driven angle of the satellite axis of rolling

The used time, ω _XmaxBe the maximum angular rate in the satellite axis of rolling mobile process, a _XmaxBe the maximum angular acceleration in the satellite axis of rolling mobile process;

Step 7: the initial unloading moment t that utilizes step 3 to obtain ₀, the step 5 discharged track number of turns n and the power operated angle of satellite uninstall process needs that obtain

With the motor-driven angle of the satellite axis of rolling

The used time

Unload;

Described uninstall process is: at initial unloading moment t ₀The satellite roll angle by 0 fast reserve to

Constantly, the satellite roll angle by Motor-driven arriving

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly the satellite roll angle by

Fast reserve to 0, and finish unloading;

Wherein, symbol T represents satellite orbit period, and the parameter m span is the integer of 0～n-1.

The present invention has realized finishing the work of the angular momentum dumping that the momentum exchange actuating unit of satellite absorbs under the condition that discharging gear additionally is not installed, and have following advantage: the moment that (1) utilization need be carried out discharged actuating unit and provide is carried out motor-driven, and utilize gravity gradient torque that motor-driven back produces that self moment of momentum is unloaded, additionally discharging gear provides cost savings and the space; (2) unloading algorithm simple possible can guarantee discharged precision simultaneously, and the unloading error can guarantee in 1/100 relatively usually; (3) be fit to have the satellite of axis of rolling fast reserve ability, for example the SAR satellite can reasonably distribute the task and the unloading task of satellite, can guarantee to finish unloading in satellite work.

Description of drawings

Fig. 1 is a kind of diagram of circuit that utilizes the method for the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum of the present invention;

Fig. 2 is the symmetry instruction diagram of the initial relatively yaw axis of the specific embodiment one described satellite mobile process;

Fig. 3 is the definition scheme drawing of the specific embodiment one described inertial coordinates system;

Fig. 4 is the specific embodiment one a described satellite unloading initial time scheme drawing;

Fig. 5 is a satellite axis of rolling attitude angle curve in the specific embodiment one described uninstall process, among the figure

Represent the roll angle curve, among the figure

Represent the pitch angle curve, among the figure

Represent the yaw angle curve;

Fig. 6 is an actuating unit moment of momentum change curve in the specific embodiment one described uninstall process, among the figure

Represent axis of rolling moment of momentum change curve, among the figure

Represent pitch axis moment of momentum change curve, among the figure

Represent yaw axis moment of momentum change curve;

Fig. 7 is the local figure of actuating unit moment of momentum after the specific embodiment one described unloading is finished, among the figure

Represent axis of rolling moment of momentum change curve, among the figure

Represent pitch axis moment of momentum change curve, among the figure

Represent yaw axis moment of momentum change curve;

The specific embodiment

The specific embodiment one, this specific embodiment is described in conjunction with Fig. 1-Fig. 7.A kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum, it comprises the steps:

Step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

Described inertial coordinates system ox _Iy _Iz _I: initially unloading moment barycenter with satellite is initial point, oz _IThe axle in the satellite orbit plane, oz _IDirection needs discharged total angular momentum direction identical with satellite, oy _IAxle is perpendicular to the satellite transit orbit plane, and is opposite with described orbit angular velocity direction, ox _I, oy _IWith oz _IAxle is formed right-handed system;

The body series ox of described satellite _by _bz _bCoordinate origin be the satellite barycenter, each coordinate axle and celestial body are connected, and can guarantee that the satellite moment of inertia matrix of describing at this system of axes is the diagonal matrix form;

Step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Wherein b represents body series, and G represents gravity gradient;

Step 3: with initial unloading moment t ₀Be starting point, calculate gravity gradient torque

The moment of momentum vector h that in each orbit period, accumulates _Circ:

In the formula, k is inertial coordinates system oz _IAxial unit vector; I _zBe satellite yaw axis principal moment of inertia, I _yIt is satellite pitch axis principal moment of inertia;

Step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures

Need discharged moment of momentum with yaw axis

Size;

Step 5: the moment of momentum vector h that obtains according to step 3 _CircNeed discharged moment of momentum with step 4 obtains at the axis of rolling

Need discharged moment of momentum with yaw axis

Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Step 6: estimate the motor-driven angle of the satellite axis of rolling

The used time

In the formula,

Be the motor-driven angle of the satellite axis of rolling The used time, ω _XmaxBe the maximum angular rate in the satellite axis of rolling mobile process, a _XmaxBe the maximum angular acceleration in the satellite axis of rolling mobile process;

Step 7: the initial unloading moment t that utilizes step 3 to obtain ₀, the step 5 discharged track number of turns n and the power operated angle of satellite uninstall process needs that obtain

With the motor-driven angle of the satellite axis of rolling

The used time

Unload;

Described uninstall process is: at initial unloading moment t ₀The satellite roll angle by 0 fast reserve to

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly the satellite roll angle by

Fast reserve to 0, and finish unloading;

Wherein, symbol T represents satellite orbit period, and the parameter m span is the integer of 0～n-1.

A kind of unloading strategy of the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum that utilizes of the present invention is: satellite begins to keep the operation of three axis stabilization state, and the moment that calculating satellite executing mechanism needs discharged moment of momentum all to concentrate on yaw axis is designated as t ₀, unload angular momentum h as required _{Un_xz}Size determine that the satellite uninstall process axis of rolling needs power operated angle

With discharged track number of turns n.

Need to guarantee with the selection of n: satellite after unloading n orbit period, the whole completions of discharge of moment of momentum that initial time satellite yaw axis accumulates.t ₀Constantly begin unloading, t ₀Constantly the satellite roll angle by 0 fast reserve to

Constantly, the satellite roll angle by Motor-driven arriving

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly the satellite roll angle by

Unloading is finished in fast reserve to 0.Symbol T represents satellite orbit period, and parameter m is the integer of span at 0～n-1, and detailed process can be seen Fig. 1.

Calculate above in the expression formula in the motor-driven moment,

Item is the symmetry in order to ensure mobile process.Promptly guarantee motor-driven initial time and the finish time satellite in the position of orbital plane about initial yaw axis symmetry.

Be for guarantee to unload the finish time satellite with unload initial time and overlap.Specify and see Fig. 2.

This paper proposes to utilize the fast reserve of the satellite axis of rolling to produce the axial normal value moment of rolling and unloads, can accumulate very big moment of momentum by half motor-driven frequency once of orbit period in an orbit period, this discharging method is relatively to be fit to for the satellite with fast reserve ability.Because the most of the time of satellite transit is not in the state of executing the task, make this discharging method practical more.Utilizing the method for the motor-driven unloading satellite of axis of rolling rolling yaw angle momentum is feasible to present most satellites, for example, SAR satellite in orbit, when being taken pictures, ground need satellite to keep certain angle at the axis of rolling, through accumulating very big moment of momentum after a while, bring very big inconvenience for the design of the control system of satellite, if unloading strategy and the task of SAR reasonably can be planned, not only can eliminate SAR work is the moment of momentum of accumulation, and can save a cover discharging gear.

Detailed step of the present invention is:

Step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

Usually the moment of momentum of actuating unit accumulation is a unmodified in the direction and the size of inertial space at short notice, therefore defines inertial coordinates system ox _Iy _Iz _I: initially unloading moment barycenter with satellite is initial point, oz _IThe axle in the satellite orbit plane, oz _IDirection needs discharged total angular momentum direction identical with satellite, oy _IAxle is perpendicular to the satellite transit orbit plane, and is opposite with described orbit angular velocity direction, ox _I, oy _IWith oz _IAxle is formed right-handed system;

The body series ox of described satellite _by _bz _bCoordinate origin be the satellite barycenter, each coordinate axle and celestial body are connected, and can guarantee that the satellite moment of inertia matrix of describing at this system of axes is the diagonal matrix form;

Described step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

This discharging method need guarantee that the discharged zero hour, all moment of momentums concentrated on yaw axis, and therefore, initial unloading is t constantly ₀Be taken as the moment that the body series of satellite overlaps with inertial coordinates system for the first time, when the satellite yaw axis makes body series yaw axis and oz behind the orbit angular velocity direction rotation α angle _IAxle is for the first time on same straight line the time, and then satellite is initial unloading moment t in the time at the inswept α of orbit plane angle ₀, the formula of embodying is:

t ₀＝α/ω _o

In the formula, ω _OBe the satellite orbit cireular frequency.

Step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Wherein b represents body series, and G represents gravity gradient;

Described step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Process be:

Because the body series of satellite overlaps with principal axis of inertia system of axes, and satellite moves at circular orbit, so gravity gradient torque

Expression formula be:

In the formula, ω _oBe the orbit angular velocity of satellite,

Suffered three gravity gradient torques of expression satellite are at the component of body series, I _x, I _y, I _zRepresent the satellite and the axis of rolling, pitch axis, the pairing principal moments of yaw axis respectively;

θ represents to change roll angle and the pitch angle that preface is described by 3-2-1; Wherein, 3 representatives are around oz _bRotate, 2 representatives are around oy _bAxle rotates, and 1 representative is around ox _bRotate.

Step 3: with initial unloading moment t ₀Be starting point, calculate gravity gradient torque

The moment of momentum vector h that in each orbit period, accumulates _Circ:

In the formula, k is inertial coordinates system oz _IAxial unit vector; I _zBe satellite yaw axis principal moment of inertia, I _yIt is satellite pitch axis principal moment of inertia;

Described step 3: to unload the zero hour is starting point, calculates gravity gradient torque

The moment of momentum vector h that in each orbit period, accumulates _CircProcess be:

Because mobile process about initial yaw axis symmetry, is ignored the influence of the moment that accumulates in the mobile process, the suffered gravity gradient torque of satellite is expressed as in inertial system in the discharged one-period so satellite is from beginning:

In the formula, t is a satellite from beginning unloading institute's elapsed time constantly, and i is inertial coordinates system ox _IThe unit vector of axle, then the moment of momentum that accumulates in an orbit period of satellite can be expressed as:

$h_{\mathrm{circ}}={\∫}_0^{2\mathrm{\π}/{\mathrm{\ω}}_0}{T}_G^b\mathrm{dt}$

Obtain

Carrying out integration obtains

Step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures Need discharged moment of momentum with yaw axis

Size;

Described step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures

Need discharged moment of momentum with yaw axis

The process of size is:

Measure the component of the moment of momentum of each momentum exchange actuating unit, make i momentum exchange actuating unit moment of momentum be at the representation in components of body series at body series

Obtain all momentum exchange actuating units and need discharged moment of momentum at the axis of rolling and yaw axis

Expression formula is:

$h_{\mathrm{un}}^{\mathrm{bx}}=-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{h}_i^b\·x_b^b=-h_c^b\·x_b^b=-h_c^{\mathrm{bx}}$

$h_{\mathrm{un}}^{\mathrm{bz}}=-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{h}_i^b\·z_b^b=-h_c^b\·z_b^b=-h_c^{\mathrm{bz}}$

In the formula,

Be 3 * 1 array, represent the component of i momentum exchange actuating unit moment of momentum at body series,

Represent the component of the summation of all actuating unit moment of momentums at body series,

With Represent the component of all actuating unit moment of momentum summations respectively at the body series axis of rolling and yaw axis,

With

Be respectively the discharged moment of momentum size of the axis of rolling and yaw axis, $x_b^b={\left[\begin{array}{ccc}1& 0& 0\end{array}\right]}^T$ Be the axis of rolling of body series component at body series, $z_b^b={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^T$ Be the yaw axis of body series component at body series; N is the quantity of actuating unit, and i is the integer greater than 0.

Step 5: the moment of momentum vector h that obtains according to step 3 _CircNeed discharged moment of momentum with step 4 obtains at the axis of rolling

Need discharged moment of momentum with yaw axis

Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Described step 5: the moment of momentum vector h that obtains according to step 3 _CircAll momentum exchange actuating units that obtain with step 4 need discharged moment of momentum at the axis of rolling

Need discharged moment of momentum with yaw axis

Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Process be:

Step May Day: determine discharged total angular momentum h _{Un_xy}:

Because the coupled relation of the axis of rolling and yaw axis, the actual discharged moment of momentum of satellite can be expressed as under inertial coordinates system:

$h_{\mathrm{un}\_\mathrm{xz}}=\left\{\begin{array}{cc}\sqrt{{\left(h_{\mathrm{un}}^{\mathrm{bx}}\right)}^2+{\left(h_{\mathrm{un}}^{\mathrm{bz}}\right)}^{2}k}& h_{\mathrm{un}}^{\mathrm{bx}}>0\\ -\sqrt{{\left(h_{\mathrm{un}}^{\mathrm{bx}}\right)}^2+{\left(h_{\mathrm{un}}^{\mathrm{bz}}\right)}^{2}k}& h_{\mathrm{un}}^{\mathrm{bx}}<0\\ h_{\mathrm{un}}^{\mathrm{bz}}k& h_{\mathrm{un}}^{\mathrm{bx}}=0\end{array}\right.$

In the formula, h _{Un_xz}The discharged moment of momentum vectorial sum of expression satellite rolling-yaw axis, h _{Un_xz}Only at oz in inertial system _IAxle is important, h _{Un_xz}At oz _IComponent size can be expressed as:

h _{un_xz}＝h _{un_xz}·k

Step 5 two, determine discharged track number of turns n;

According to the formula mistake! Do not find Reference source.Calculating lock angle momentum that the orbit period accumulated of satellite unloading is:

h _circ(45°)＝6ω ₀(I _z-I _y)k

In the formula, h _Circ(45 °) expression satellite keeps

Move the moment of momentum that the orbit period accumulated;

Because satellite is finished unloading at integer in the orbit period, therefore satellite body tie up to initial unloading constantly with finish the unloading moment and all overlap with inertial coordinates system, therefore the moment of momentum that accumulates in the uninstall process is identical with component at body series at the component of inertial coordinates system, and the power operated number of turns of satellite needs is taken as:

$n=\left\{\begin{array}{cc}\mathrm{mod}\left(\frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\right)+1& \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\&NotElement;N^{*}\\ \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}& \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\&Element;N^{*}\end{array}\right.$

In the formula, mod is a symbol of operation, and the integer part of bracket the inside numerical value, N are got in expression ^*The set of expression positive integer;

Step 5 three: utilize the unloading track number of turns n that has tried to achieve, determine that the initial axis of rolling needs power operated angle

Be moment of momentum and the discharged angular motion value of the satellite h that guarantees that satellite unloading n was accumulated after week _{Un_xz}Identical, therefore should satisfy following relational expression:

Therefore can in the hope of

Expression formula be:

Step 6: estimate the motor-driven angle of the satellite axis of rolling

The used time

In the formula,

Be the motor-driven angle of the satellite axis of rolling

The used time, ω _XmaxBe the maximum angular rate in the satellite axis of rolling mobile process, a _XmaxBe the maximum angular acceleration in the satellite axis of rolling mobile process;

Step 7: the initial unloading moment t that utilizes step 3 to obtain ₀, the step 5 discharged track number of turns n and the power operated angle of satellite uninstall process needs that obtain

With the motor-driven angle of the satellite axis of rolling

The used time Unload;

Described uninstall process is: at initial unloading moment t ₀The satellite roll angle by 0 fast reserve to

Constantly, the satellite roll angle by Motor-driven arriving

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly the satellite roll angle by Fast reserve to 0, and finish unloading;

Wherein, symbol T represents satellite orbit period, and the parameter m span is the integer of 0～n-1.

Specific embodiment: this specific embodiment is described in conjunction with Fig. 4-Fig. 6.

Carrying out the discharged satellite of pitch axis with needs is example, and the reasonableness of designed discharging method is described, detailed process is:

The satellite rotor inertia: $I=\left[\begin{array}{ccc}4000& 0& 0\\ 0& 4000& 0\\ 0& 0& 1000\end{array}\right]\mathrm{kg}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA00003127470900021.png,HDA00003127470900041.png"\; state="\{\{state\}\}">m</figure-callout>}}^2,$ The maximum output torque of axis of rolling actuating unit is 0.4Nm, and the lock angle momentum is 50Nms, and satellite moves on circular orbit, and orbit angular velocity is ω _o=0.00107rad/s, orbit period T=5872s.

Initial parameter: the satellite initial attitude is Φ ₀=[0 0 0] °, the initial angular momentum of actuating unit is h _C0=[32 0 32] Nms.

Calculate h _{Un_xz}=45.25Nms, α=π/4, initial unloading is t constantly ₀=π/4 ω ₀=734s, individual pen accumulation angular momentum h _Circ=-19.26Nm needs discharged number of turns n=3, the power operated angle of satellite

According to the ability of actuating unit, getting the maximum motor-driven cireular frequency of the axis of rolling is ω _Xmax=0.005rad/s.Estimate motor-driven time t (26 °)=139.7s that needs, t (52 °)=229.4.

The unloading strategy unloads according to concrete steps seven described strategies for 734s begins unloading, and concrete outcome is seen Fig. 5 to Fig. 7.

Claims (6)

1. ten thousand methods of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum is characterized in that it comprises the steps:

Step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

Described inertial coordinates system ox _Iy _Iz _I: initially unloading moment barycenter with satellite is initial point, oz _IThe axle in the satellite orbit plane, oz _IDirection needs discharged total angular momentum direction identical with satellite, oy _IAxle is perpendicular to the satellite transit orbit plane, and is opposite with described orbit angular velocity direction, ox _I, oy _IWith oz _IAxle is formed right-handed system;

The body series ox of described satellite _by _bz _bCoordinate origin be the satellite barycenter, each coordinate axle and celestial body are connected, and can guarantee that the satellite moment of inertia matrix of describing at this system of axes is the diagonal matrix form;

Step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Wherein b represents body series, and G represents gravity gradient;

Step 3: with initial unloading moment t ₀Be starting point, calculate gravity gradient torque

The moment of momentum vector h that in each orbit period, accumulates _Circ:

In the formula, k is inertial coordinates system oz _IAxial unit vector; I _zBe satellite yaw axis principal moment of inertia, I _yIt is satellite pitch axis principal moment of inertia;

Step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures

Need discharged moment of momentum with yaw axis

Size;

Step 5: the moment of momentum vector h that obtains according to step 3 _CircNeed discharged moment of momentum with step 4 obtains at the axis of rolling

Need discharged moment of momentum with yaw axis

Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Step 6: estimate the motor-driven angle of the satellite axis of rolling The used time

In the formula,

Be the motor-driven angle of the satellite axis of rolling

The used time, ω _XmaxBe the maximum angular rate in the satellite axis of rolling mobile process, a _XmaxBe the maximum angular acceleration in the satellite axis of rolling mobile process;

Step 7: the initial unloading moment t that utilizes step 3 to obtain ₀, the step 5 discharged track number of turns n and the power operated angle of satellite uninstall process needs that obtain

With the motor-driven angle of the satellite axis of rolling

The used time

Unload;

Described uninstall process is: at initial unloading moment t ₀The satellite roll angle by 0 fast reserve to

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly, the satellite roll angle by

Motor-driven arriving

Constantly the satellite roll angle by

Fast reserve to 0, and finish unloading;

Wherein, symbol T represents satellite orbit period, and the parameter m span is the integer of 0～n-1.

2. a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum according to claim 1 is characterized in that described step 1: the body series ox of definition satellite _by _bz _bWith inertial coordinates system ox _Iy _Iz _IAnd definite initial unloading moment t ₀

Initial unloading is t constantly ₀Be taken as the moment that the body series of satellite overlaps with inertial coordinates system for the first time, when the satellite yaw axis makes body series yaw axis and oz behind the orbit angular velocity direction rotation α angle _IAxle is for the first time on same straight line the time, and then satellite is initial unloading moment t in the time at the inswept α of orbit plane angle ₀, the formula of embodying is:

t ₀＝α/ω _o

In the formula, ω _oBe the satellite orbit cireular frequency.

3. a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum according to claim 2 is characterized in that described step 2: determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia

Process be:

Gravity gradient torque

Expression formula be:

In the formula, ω _oBe the orbit angular velocity of satellite,

Suffered three gravity gradient torques of expression satellite are at the component of body series, I _x, I _y, I _zRepresent the satellite and the axis of rolling, pitch axis, the pairing principal moments of yaw axis respectively;

θ represents to change roll angle and the pitch angle that preface is described by 3-2-1; Wherein, 3 representatives are around oz _bRotate, 2 representatives are around oy _bAxle rotates, and 1 representative is around ox _bRotate.

4. a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum according to claim 3 is characterized in that described step 3: to unload the zero hour is starting point, calculates gravity gradient torque The moment of momentum vector h that in each orbit period, accumulates _CircProcess be:

The suffered gravity gradient torque of satellite is expressed as in inertial system satellite in the discharged one-period from beginning:

In the formula, t is a satellite from beginning unloading institute's elapsed time constantly, and i is inertial coordinates system ox _IThe unit vector of axle, then the moment of momentum that accumulates in an orbit period of satellite is expressed as:

$h_{\mathrm{circ}}={\&Integral;}_0^{2\mathrm{\&pi;}/{\mathrm{\&omega;}}_0}{T}_G^b\mathrm{dt}$

Obtain

Carrying out integration obtains

5. a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum according to claim 4, it is characterized in that described step 4:, determine that all momentum exchange actuating units need discharged moment of momentum at the axis of rolling according to the moment of momentum of the actuating unit that measures

Need discharged moment of momentum with yaw axis

The process of size is:

Measure the component of the moment of momentum of each momentum exchange actuating unit, make i momentum exchange actuating unit moment of momentum be at the representation in components of body series at body series

Obtain all momentum exchange actuating units and need discharged moment of momentum at the axis of rolling and yaw axis

Expression formula is:

$h_{\mathrm{un}}^{\mathrm{bx}}=-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{h}_i^b\&CenterDot;x_b^b=-h_c^b\&CenterDot;x_b^b=-h_c^{\mathrm{bx}}$

$h_{\mathrm{un}}^{\mathrm{bz}}=-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{h}_i^b\&CenterDot;z_b^b=-h_c^b\&CenterDot;z_b^b=-h_c^{\mathrm{bz}}$

In the formula, Be 3 * 1 array, represent the component of i momentum exchange actuating unit moment of momentum at body series,

Represent the component of the summation of all actuating unit moment of momentums at body series,

With

Represent the component of all actuating unit moment of momentum summations respectively at the body series axis of rolling and yaw axis,

With

Be respectively the discharged moment of momentum size of the axis of rolling and yaw axis, $x_b^b={\left[\begin{array}{ccc}1& 0& 0\end{array}\right]}^T$ Be the axis of rolling of body series component at body series, $z_b^b={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^T$ Be the yaw axis of body series component at body series; N is the quantity of actuating unit, and i is the integer greater than 0.

6. a kind of method of utilizing the motor-driven unloading axis of rolling of satellite axis of rolling rapid posture and yaw axis moment of momentum according to claim 1 is characterized in that described step 5: the moment of momentum vector h that obtains according to step 3 _CircAll momentum exchange actuating units that obtain with step 4 need discharged moment of momentum at the axis of rolling

Need discharged moment of momentum with yaw axis Determine the motor-driven angle of satellite discharged track number of turns n and satellite uninstall process

Process be:

Step May Day: determine discharged total angular momentum h _{Un_xy}:

Because the coupled relation of the axis of rolling and yaw axis, the actual discharged moment of momentum of satellite can be expressed as under inertial coordinates system:

$h_{\mathrm{un}\_\mathrm{xz}}=\left\{\begin{array}{cc}\sqrt{{\left(h_{\mathrm{un}}^{\mathrm{bx}}\right)}^2+{\left(h_{\mathrm{un}}^{\mathrm{bz}}\right)}^{2}k}& h_{\mathrm{un}}^{\mathrm{bx}}>0\\ -\sqrt{{\left(h_{\mathrm{un}}^{\mathrm{bx}}\right)}^2+{\left(h_{\mathrm{un}}^{\mathrm{bz}}\right)}^{2}k}& h_{\mathrm{un}}^{\mathrm{bx}}<0\\ h_{\mathrm{un}}^{\mathrm{bz}}k& h_{\mathrm{un}}^{\mathrm{bx}}=0\end{array}\right.$

In the formula, h _{Un_xz}The discharged moment of momentum vectorial sum of expression satellite rolling-yaw axis, h _{Un_xz}Only at oz in inertial system _IAxle is important, h _{Un_xz}At oz _IComponent size can be expressed as:

h _{un_xz}＝h _{un_xz}·k

Step 5 two, determine discharged track number of turns n;

Calculating lock angle momentum that the orbit period accumulated of satellite unloading is:

h _circ(45°)＝6ω ₀(I _z-I _y)k

In the formula, h _Circ(45 °) expression satellite keeps

Move the moment of momentum that the orbit period accumulated;

The moment of momentum that accumulates in the uninstall process is identical with component at body series at the component of inertial coordinates system, and satellite needs the power operated number of turns to be taken as:

$n=\left\{\begin{array}{cc}\mathrm{mod}\left(\frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\right)+1& \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\&NotElement;N^{*}\\ \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}& \frac{\left|h_{\mathrm{un}\_\mathrm{xz}}\right|}{6{\mathrm{\&omega;}}_0(I_z-I_y)}\&Element;N^{*}\end{array}\right.$

In the formula, mod is a symbol of operation, and the integer part of bracket the inside numerical value, N are got in expression ^*The set of expression positive integer;

Step 5 three: utilize the unloading track number of turns n that has tried to achieve, determine that the initial axis of rolling needs power operated angle

Be moment of momentum and the discharged angular motion value of the satellite h that guarantees that satellite unloading n was accumulated after week _{Un_xz}Identical, therefore should satisfy following relational expression:

Therefore can in the hope of Expression formula be:

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