CN103213691B - Method of using satellite rolling-axis rapid attitude manoeuvre to unload angular momentum of rolling axis and yawing axis - Google Patents

Abstract

A method for unloading the angular momentum of the rolling axis and yaw axis by using the rapid attitude maneuver of the satellite rolling axis, which belongs to the technical field of aerospace attitude control, and solves the problem that the angular momentum absorbed by the momentum exchange actuator of the existing unloading satellite needs to be additionally installed and unloaded on the satellite device, causing the cost of satellites to increase, and increasing the volume and weight of satellites. Define the satellite's own system and inertial coordinate system and determine the initial unloading time; by determining the gravity gradient moment on the satellite, the angular momentum vector accumulated by the gravity gradient moment in each orbital period, and all momentum exchange actuators that need to be unloaded on the rolling axis The angular momentum and the angular momentum of the yaw axis that need to be unloaded, the orbital number of satellite unloading, the maneuvering angle of the satellite unloading process, and the time it takes for the maneuvering angle of the satellite rolling axis to unload. The invention can be widely applied to the unloading requirement of the accumulated angular momentum of the actuator.

Description

A method of unloading roll axis and yaw axis angular momentum using satellite roll axis rapid attitude maneuver

technical field

The invention relates to a method for unloading the angular momentum of a rolling axis and a yaw axis by using a satellite rolling axis to perform rapid attitude maneuvering, and belongs to the technical field of spacecraft attitude control.

Background technique

Since the orbiting satellite is usually affected by the space disturbance torque, if the direction of the disturbance torque is fixed in the inertial space, the corresponding angular momentum will be accumulated inside the satellite. Usually, this part of the angular momentum is carried out by the momentum exchange actuator of the satellite. However, the ability of the actuator to absorb angular momentum is limited, so when the angular momentum accumulated by the actuator of the satellite is close to saturation, it is necessary to unload the accumulated angular momentum of the actuator.

Satellites usually use magnetic torque devices, jet devices, etc. to generate external torque to offset the angular momentum accumulated by the previous disturbance torque, but different unloading devices have their own inherent disadvantages. For example, the unloading torque generated by the magnetic torque device is relatively small, while relying on In the external environment, and the jet device has a life limit, it is not suitable for long-term use. In addition to the disadvantages mentioned above, the common disadvantage of all unloading devices is that an additional unloading device needs to be installed on the satellite, which not only increases the cost of the satellite, but also increases the volume and weight of the satellite.

Contents of the invention

In order to solve the angular momentum absorbed by the momentum exchange actuator of the existing unloading satellite, an additional unloading device needs to be installed on the satellite, resulting in an increase in the cost of the satellite, increasing the volume and weight of the satellite, thereby providing a fast attitude maneuver using the satellite rolling axis A method for unloading the angular momentum of the roll and yaw axes.

A method for unloading the angular momentum of the rolling axis and the yaw axis by utilizing the rapid attitude maneuver of the satellite rolling axis, comprising the following steps:

Step 1: Define the satellite's own system ox _b y _b z _b and the inertial coordinate system ox _I y _I z _I and determine the initial unloading time t ₀ ;

The inertial coordinate system ox _I y _I z _I : take the center of mass at the initial unloading moment of the satellite as the origin, the oz _I axis is in the satellite orbit plane, the oz _I direction is the same as the total angular momentum direction that the satellite needs to unload, and the oy _I axis is perpendicular to the satellite The plane of the running orbit is opposite to the direction of the orbital angular velocity, and the ox _I , oy _I and oz _I axes form a right-handed coordinate system;

The origin of the coordinate system ox _by y _b z _b of the satellite's own system is the center of mass of the satellite, and each coordinate axis is fixedly connected to the star, and can ensure that the satellite moment of inertia matrix described in the coordinate system is in the form of a diagonal matrix;

Step 2: Determine the gravity gradient moment experienced by the satellite according to the moment of inertia of the satellite Where b represents the system, G represents the gravity gradient;

Step 3: Taking the initial unloading time t ₀ as the starting point, calculate the gravity gradient moment The angular momentum vector h _circ accumulated during each orbital period:

In the formula, k is the unit vector in the direction of _{the I} axis of the inertial coordinate system oz; I _z is the main moment of inertia of the satellite yaw axis, and I _y is the main moment of inertia of the satellite pitch axis;

Step 4: According to the measured angular momentum of the actuator, determine the angular momentum that all momentum exchange actuators need to unload on the rolling axis The angular momentum that needs to be unloaded with the yaw axis size;

Step 5: According to the angular momentum vector h _circ obtained in step 3 and the angular momentum to be unloaded on the rolling axis obtained in step 4 The angular momentum that needs to be unloaded with the yaw axis Determining the orbital number n of satellite unloading and the maneuvering angle during satellite unloading

Step 6: Estimate the satellite roll axis maneuver angle The time spent

In the formula, is the maneuvering angle of the satellite roll axis The time used, ω _xmax is the maximum angular velocity during the maneuvering process of the satellite rolling axis, and a _xmax is the maximum angular acceleration during the maneuvering process of the satellite rolling axis;

Step 7: Use the initial unloading time t ₀ obtained in step 3, the orbital number n of unloading obtained in step 5, and the maneuvering angle during the satellite unloading process and satellite roll axis maneuver angle The time spent Uninstall;

The unloading process is as follows: at the initial unloading time t ₀ the satellite roll angle quickly maneuvers from 0 to exist time, the satellite roll angle is given by maneuver to exist time, the satellite roll angle is given by maneuver to exist The time satellite roll angle is given by Quickly maneuver to 0 and complete unloading;

Wherein, the symbol T represents the orbit period of the satellite, and the value of the parameter m is an integer ranging from 0 to n-1.

The invention realizes the unloading of the angular momentum absorbed by the momentum exchange actuator of the satellite without installing an additional unloading device, and has the following advantages: (1) maneuvering by using the torque provided by the actuator that needs to be unloaded, and Use the gravity gradient moment generated after maneuvering to unload its own angular momentum, without additional unloading device, saving cost and space; (2) The unloading algorithm is simple and feasible, and at the same time can ensure the accuracy of unloading, usually the relative unloading error will be guaranteed at 1/ Within 100; (3) It is suitable for satellites with fast maneuverability of the rolling axis, such as SAR satellites, which can reasonably allocate satellite tasks and unloading tasks, and can ensure that the unloading is completed while the satellite is working.

Description of drawings

Fig. 1 is a flow chart of a method for unloading the angular momentum of the rolling axis and the yaw axis using the rapid attitude maneuver of the satellite rolling axis according to the present invention;

Fig. 2 is an explanatory diagram of the symmetry of the satellite maneuvering process relative to the initial yaw axis in Embodiment 1;

Fig. 3 is a schematic diagram of the definition of the inertial coordinate system described in Embodiment 1;

Fig. 4 is a schematic diagram of the initial moment of satellite unloading described in Embodiment 1;

Fig. 5 is the satellite rolling axis attitude angle curve in the unloading process described in the specific embodiment one, in the figure Represents the rolling angle curve, in the figure Represents the pitch angle curve, in the figure table yaw angle curve;

Fig. 6 is the angular momentum change curve of the actuator during the unloading process described in the first embodiment, in the figure Represents the angular momentum change curve of the rolling axis, in the figure Represents the angular momentum change curve of the pitch axis, in the figure Represents the angular momentum change curve of the yaw axis;

Fig. 7 is a partial diagram of the angular momentum of the actuator after the unloading of the specific embodiment 1 is completed, in which Represents the angular momentum change curve of the rolling axis, in the figure Represents the angular momentum change curve of the pitch axis, in the figure Represents the angular momentum change curve of the yaw axis;

Detailed ways

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 1. This specific implementation will be described with reference to FIGS. 1-7 . A method for unloading the angular momentum of the rolling axis and the yaw axis by utilizing the rapid attitude maneuver of the satellite rolling axis, comprising the following steps:

Step 1: Define the satellite's own system ox _b y _b z _b and the inertial coordinate system ox _I y _I z _I and determine the initial unloading time t ₀ ;

The inertial coordinate system ox _I y _I z _I : take the center of mass at the initial unloading moment of the satellite as the origin, the oz _I axis is in the satellite orbit plane, the oz _I direction is the same as the total angular momentum direction that the satellite needs to unload, and the oy _I axis is perpendicular to the satellite The plane of the running orbit is opposite to the direction of the orbital angular velocity, and the ox _I , oy _I and oz _I axes form a right-handed coordinate system;

The origin of the coordinate system ox _by y _b z _b of the satellite's own system is the center of mass of the satellite, and each coordinate axis is fixedly connected to the star, and can ensure that the satellite moment of inertia matrix described in the coordinate system is in the form of a diagonal matrix;

Step 2: Determine the gravity gradient moment experienced by the satellite according to the moment of inertia of the satellite Where _b represents the system, G represents the gravity gradient;

Step 3: Taking the initial unloading time t ₀ as the starting point, calculate the gravity gradient moment The angular momentum vector h _circ accumulated during each orbital period:

In the formula, k is the unit vector in the direction of _{the I} axis of the inertial coordinate system oz; I _z is the main moment of inertia of the satellite yaw axis, and I _y is the main moment of inertia of the satellite pitch axis;

Step 4: According to the measured angular momentum of the actuator, determine the angular momentum that all momentum exchange actuators need to unload on the rolling axis The angular momentum that needs to be unloaded with the yaw axis size;

Step 5: According to the angular momentum vector h _circ obtained in step 3 and the angular momentum to be unloaded on the rolling axis obtained in step 4 The angular momentum that needs to be unloaded with the yaw axis Determining the orbital number n of satellite unloading and the maneuvering angle during satellite unloading

Step 6: Estimate the satellite roll axis maneuver angle The time spent

In the formula, Satellite Roll Axis Maneuvering Angle The time used, ω _xmax is the maximum angular velocity during the maneuvering process of the satellite rolling axis, and a _xmax is the maximum angular acceleration during the maneuvering process of the satellite rolling axis;

Step 7: Use the initial unloading time t ₀ obtained in step 3, the orbital number n of unloading obtained in step 5, and the maneuvering angle during the satellite unloading process and satellite roll axis maneuver angle The time spent Uninstall;

The unloading process is as follows: at the initial unloading time t ₀ the satellite roll angle quickly maneuvers from 0 to exist time, the satellite roll angle is given by maneuver to exist time, the satellite roll angle is given by maneuver to exist The time satellite roll angle is given by Quickly maneuver to 0 and complete unloading;

Wherein, the symbol T represents the orbit period of the satellite, and the value of the parameter m is an integer ranging from 0 to n-1.

In the present invention, an unloading strategy for unloading the angular momentum of the rolling axis and the yaw axis by using the rapid attitude maneuver of the satellite rolling axis is as follows: the satellite starts to operate in a stable three-axis state, and the calculation of the angular momentum that needs to be unloaded by the satellite actuator is all concentrated on the yaw axis Time is recorded as t ₀ , according to the size of the required unloading angular momentum h _{un_xz} , determine the angle that the satellite roll axis needs to maneuver during the unloading process and the number of unloaded orbital turns n. The choice of n needs to ensure that after the satellite is unloaded for n orbital periods, all the angular momentum accumulated by the yaw axis of the satellite at the initial moment is completely unloaded. The unloading starts at time t ₀ , _and the satellite roll angle rapidly maneuvers from 0 to exist time, the satellite roll angle is given by maneuver to exist time, the satellite roll angle is given by maneuver to exist The time satellite roll angle is given by Quickly maneuver to 0 to complete unloading. The symbol T represents the satellite orbit period, and the parameter m is an integer ranging from 0 to n-1. The specific process can be seen in Figure 1.

In the above expression for computing the moment of motion, The term is to ensure the symmetry of the maneuvering process. That is to ensure that the position of the satellite on the orbital plane at the initial moment and the end moment of the maneuver is symmetrical about the initial yaw axis. The item is to ensure that the satellite at the end of unloading coincides with the initial time of unloading. See Figure 2 for details.

This paper proposes to use the rapid maneuvering of the satellite rolling axis to generate a constant moment in the direction of the rolling axis for unloading. The frequency of maneuvering once in half an orbital period can accumulate a large angular momentum in one orbital period. This unloading method is suitable for satellites with fast maneuvering capabilities. Satellites are more suitable. This offloading method is more practical since the satellite spends most of its time in the off-duty state. The method of unloading satellite rolling yaw angular momentum by using the roll axis maneuver is feasible for most satellites at present. Large angular momentum brings great inconvenience to the design of the satellite control system. If the unloading strategy and SAR tasks can be reasonably planned, not only can the accumulated angular momentum of SAR work be eliminated, but also a set of unloading can be saved. device.

Detailed steps of the present invention are:

Step 1: Define the satellite's own system ox _b y _b z _b and the inertial coordinate system ox _I y _I z _I and determine the initial unloading time t ₀ ;

Usually, the direction and size of the angular momentum accumulated by the actuator in the inertial space is constant in a short period of time, so the inertial coordinate system ox _I y _I z _I is defined: the center of mass at the initial unloading moment of the satellite is the origin, and the oz _I axis is in the orbit of the satellite In the plane, the direction of oz _I is the same as the direction of the total angular momentum that the satellite needs to unload, the axis oy _I is perpendicular to the orbital plane of the satellite, and is opposite to the direction of the orbital angular velocity, and the axes ox _I , oy _I and oz _I form a right-handed coordinate system;

The origin of the coordinate system ox _by y _b z _b of the satellite's own system is the center of mass of the satellite, and each coordinate axis is fixedly connected to the star, and can ensure that the satellite moment of inertia matrix described in the coordinate system is in the form of a diagonal matrix;

The first step: define the body system ox _by y _b z _b of the satellite and the inertial coordinate system ox _I y _I z _I and determine the initial unloading time t ₀ ;

This unloading method needs to ensure that all angular momentum is concentrated on the yaw axis at the beginning of unloading. Therefore, the initial unloading time t ₀ is taken as the moment when the satellite’s own system coincides with the inertial coordinate system for the first time. When the satellite’s yaw axis along the orbital angular velocity After the direction is rotated by α angle so that the yaw axis of the system and the oz _I axis are on the same straight line for the first time, the time when the satellite sweeps the α angle in the orbital plane is the initial unloading time t ₀ , and the specific expression is:

t ₀ =α/ω _o

In the formula, ω _o is the orbital angular velocity of the satellite.

Step 2: Determine the gravity gradient moment experienced by the satellite according to the moment of inertia of the satellite Where _b represents the system, G represents the gravity gradient;

The second step: determine the gravity gradient moment suffered by the satellite according to the moment of inertia of the satellite The process is:

Since the body system of the satellite coincides with the coordinate system of the principal axis of inertia, and the satellite is in a circular orbit, the gravity gradient moment The expression is:

where ω _o is the orbital angular velocity of the satellite, Indicates the component of the three-axis gravity gradient moment on the satellite in the system, and I _x , I _y , and I _z represent the main inertia corresponding to the satellite and the roll axis, pitch axis, and yaw axis, respectively; θ represents the roll angle and pitch angle described in the order of 3-2-1 rotation; among them, 3 represents rotation around oz _b , 2 represents rotation around oy _b axis, and 1 represents rotation around ox _b .

Step 3: Taking the initial unloading time t ₀ as the starting point, calculate the gravity gradient moment The angular momentum vector h _circ accumulated during each orbital period:

In the formula, k is the unit vector in the direction of _{the I} axis of the inertial coordinate system oz; I _z is the main moment of inertia of the satellite yaw axis, and I _y is the main moment of inertia of the satellite pitch axis;

The third step: taking the unloading start moment as the starting point, calculate the gravity gradient moment The process of accumulating angular momentum vector h _circ in each orbital period is:

Since the maneuvering process is symmetric about the initial yaw axis, and the influence of the accumulated moment during the maneuvering process is ignored, the gravity gradient moment experienced by the satellite in a cycle from the beginning of the unloading of the satellite is expressed in the inertial system as:

In the formula, t is the elapsed time from the moment when the satellite starts unloading, and i is the unit vector of the ox _I axis of the inertial coordinate system, then the angular momentum accumulated by the satellite in one orbital period can be expressed as:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; circle</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

get

Integrate to get

Step 4: According to the measured angular momentum of the actuator, determine the angular momentum that all momentum exchange actuators need to unload on the rolling axis The angular momentum that needs to be unloaded with the yaw axis size;

The fourth step: according to the measured angular momentum of the actuator, determine the angular momentum that all momentum exchange actuators need to unload on the rolling axis The angular momentum that needs to be unloaded with the yaw axis The size process is:

Measure the component of the angular momentum of each momentum exchange actuator in the system, so that the component of the angular momentum of the ith momentum exchange actuator in the system is expressed as Get the angular momentum that all momentum exchange actuators need to unload on the roll and yaw axes The expression is:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}$

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bz</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; bz</span>}}$

In the formula, is a 3×1 array, representing the component of the angular momentum of the ith momentum exchange actuator in the system, Indicates the component of the sum of angular momentum of all actuators in this system, and represent the components of the sum of angular momentum of all actuators on the roll axis and yaw axis of the system, respectively, and are the angular momentum unloaded by the rolling axis and the yaw axis, respectively, $x_b^b={\left[\begin{array}{ccc}1& 0& 0\end{array}\right]}^T$ is the component of the rolling axis of the system in the system, $z_b^b={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^T$ is the component of the yaw axis of the system in the system; N is the number of actuators, and i is an integer greater than 0.

Step 5: According to the angular momentum vector h _circ obtained in step 3 and the angular momentum to be unloaded on the rolling axis obtained in step 4 The angular momentum that needs to be unloaded with the yaw axis Determining the orbital number n of satellite unloading and the maneuvering angle during satellite unloading

Step 5: According to the angular momentum vector h _circ obtained in step 3 and all the momentum obtained in step 4, exchange the angular momentum that the actuator needs to unload on the rolling axis The angular momentum that needs to be unloaded with the yaw axis Determining the orbital number n of satellite unloading and the maneuvering angle during satellite unloading The process is:

Step 51: Determine the unloaded total angular momentum h _{un_xy} :

Due to the coupling relationship between the rolling axis and the yaw axis, the angular momentum of the actual unloading of the satellite can be expressed in the inertial coordinate system as:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; xz</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bz</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; k</span>}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bz</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bz</span>}}\mathrm{<span\; class="notranslate">\; k</span>}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}}^{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.$

In the formula, h _{un_xz} represents the angular momentum vector sum of satellite roll-yaw axis unloading, h _{un_xz} only has a component on the oz _I axis of the inertial system, and the size of the h _{un_xz} component on oz _I can be expressed as:

h _{un_xz} = h _{un_xz} k

Step five two, determine the orbital number n of unloading;

Calculate the maximum angular momentum accumulated by the satellite unloading for one orbital period as:

h _circ (45°)＝6ω ₀ (I _z -I _y )k

In the formula, h _circ (45°) means that the satellite keeps The angular momentum accumulated during one orbital period;

Since the satellite completes unloading in an integer orbital period, the satellite body system coincides with the inertial coordinate system at the initial unloading time and the completion time of unloading, so the angular momentum accumulated during the unloading process has the same component in the inertial coordinate system as in the body system , the number of turns the satellite needs to maneuver is taken as:

$\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; mod</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; xz</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; xz</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&NotElement;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}^{<span\; class="notranslate">\; *</span>}\\ \frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; xz</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}& \frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; un</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; xz</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}^{<span\; class="notranslate">\; *</span>}\end{array}\right.$

In the formula, mod is an operation symbol, which means to take the integer part of the value in the brackets, and N ^* means a set of positive integers;

Step 53: Use the calculated number of unloading track turns n to determine the initial maneuvering angle of the rolling axis

In order to ensure that the accumulated angular momentum after n weeks of satellite unloading is the same as the angular momentum h _{un_xz} of satellite unloading, the following relationship should be satisfied:

Therefore it can be obtained The expression is:

Step 6: Estimate the satellite roll axis maneuver angle The time spent

In the formula, is the maneuvering angle of the satellite roll axis The time used, ω _xmax is the maximum angular velocity during the maneuvering process of the satellite rolling axis, and a _xmax is the maximum angular acceleration during the maneuvering process of the satellite rolling axis;

Step 7: Use the initial unloading time t ₀ obtained in step 3, the orbital number n of unloading obtained in step 5, and the maneuvering angle during the satellite unloading process and satellite roll axis maneuver angle The time spent Uninstall;

The unloading process is as follows: at the initial unloading time t ₀ the satellite roll angle quickly maneuvers from 0 to exist time, the satellite roll angle is given by maneuver to exist time, the satellite roll angle is given by maneuver to exist The time satellite roll angle is given by Quickly maneuver to 0 and complete unloading;

Wherein, the symbol T represents the orbit period of the satellite, and the value of the parameter m is an integer ranging from 0 to n-1.

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

Taking the satellite that needs to unload the pitch axis as an example, the rationality of the designed unloading method is illustrated. The specific process is as follows:

Satellite moment of inertia: $I=\left[\begin{array}{ccc}4000& 0& 0\\ 0& 4000& 0\\ 0& 0& 1000\end{array}\right]\mathrm{kg}\&Center\; Dot;m^2,$ The maximum output torque of the rolling axis actuator is 0.4Nm, the maximum angular momentum is 50Nms, the satellite runs in a circular orbit, the orbital angular velocity is ω _o =0.00107rad/s, and the orbital period T=5872s.

Initial parameters: the initial attitude of the satellite is Φ ₀ =[0 0 0]°, the initial angular momentum of the actuator is h _c0 =[-32 0 32]Nms.

Calculate h _{un_xz} = 45.25Nms, α = π/4, initial unloading time t ₀ = π/4ω ₀ = 734s, single-turn accumulated angular momentum h _circ = -19.26Nm, number of turns to be unloaded n = 3, satellite maneuver Angle According to the capability of the actuator, take the maximum maneuvering angular velocity of the rolling shaft as ω _xmax =0.005rad/s. Estimated maneuvering time t(26°)=139.7s, t(52°)=229.4.

The uninstallation strategy starts at 734s, and the uninstallation is performed according to the strategy described in the specific step 7. The specific results are shown in Figures 5 to 7.

Claims (6)

1. utilize satellite axis of rolling rapid attitude maneuver to unload a method for the axis of rolling and yaw axis moment of momentum, it is characterized in that it comprises the steps:

Step one: the body series ox of definition satellite _by _bz _bwith inertial coordinates system ox _iy _iz _iand determine initially to unload moment t ₀;

Described inertial coordinates system ox _iy _iz _i: initially unload moment barycenter for initial point with satellite, oz _iaxle in satellite orbit plane, oz _idirection and satellite need the total angular momentum direction that unloads identical, oy _iaxle is perpendicular to satellite transit orbit plane, contrary with described orbit angular velocity direction, ox _i, oy _iwith oz _iaxle composition right-handed system;

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

Step 2: determine the gravity gradient torque suffered by satellite according to satellite rotor inertia wherein _brepresent body series, G represents gravity gradient;

Step 3: initially to unload moment t ₀for starting point, calculate gravity gradient torque the angular-momentum vector h accumulated within each orbit period _circ:

In formula, k is inertial coordinates system oz _iaxial unit vector; I _zsatellite yaw axis principal moment of inertia, I _yit is satellite pitch axis principal moment of inertia;

Step 4: according to the moment of momentum measuring the actuating unit obtained, determines that all momentum exchange actuating units need the moment of momentum of unloading at the axis of rolling the moment of momentum that unloads is needed with yaw axis size;

Step 5: the angular-momentum vector h obtained according to step 3 _circwhat obtain with step 4 needs at the axis of rolling moment of momentum that unloads the moment of momentum that unloads is needed with yaw axis determine the motor-driven angle of the track number of turns n that satellite unloads and satellite uninstall process

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

In formula, for the motor-driven angle of the satellite axis of rolling time used, for the maximum angular rate in satellite axis of rolling mobile process, a _xmaxfor the maximum angular acceleration in satellite axis of rolling mobile process;

Step 7: the initial unloading moment t utilizing step 3 to obtain ₀, the track number of turns n of unloading that obtains of step 5 and satellite uninstall process need motor-driven angle angle motor-driven with the satellite axis of rolling time used unload;

Described uninstall process is: at initial unloading moment t ₀satellite roll angle by 0 fast reserve to ? moment, satellite roll angle by motor-drivenly to arrive ? moment, satellite roll angle by motor-drivenly to arrive ? moment satellite roll angle by fast reserve to 0, and completes unloading;

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

2. a kind of method utilizing satellite axis of rolling rapid attitude maneuver to unload the axis of rolling and yaw axis moment of momentum according to claim 1, is characterized in that described step one: the body series ox of definition satellite _by _bz _bwith inertial coordinates system ox _iy _iz _iand determine initially to unload moment t ₀;

Initial unloading moment t ₀in the moment that the body series first time being taken as satellite overlaps with inertial coordinates system, after satellite yaw axis rotates α angle along orbit angular velocity direction, make body series yaw axis and oz _iaxle first time on the same line time, then satellite is initial unloading moment t in the time at the inswept α angle of orbit plane ₀, expression is:

t ₀＝α/ω _o

In formula, ω _ofor satellite orbit cireular frequency.

3. a kind of method utilizing satellite axis of rolling rapid attitude maneuver to unload the axis of rolling and yaw axis moment of momentum according to claim 2, is characterized in that described step 2: determine the gravity gradient torque suffered by satellite according to satellite rotor inertia process be:

Gravity gradient torque expression formula be:

In formula, ω _ofor the orbit angular velocity of satellite, represent that suffered by satellite, three axle gravity gradient torques are at the component of body series, I _x, I _y, I _zrepresent satellite and the axis of rolling, pitch axis, principal moments corresponding to yaw axis respectively; θ represents the roll angle and the pitch angle that turn sequence description 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 utilizing satellite axis of rolling rapid attitude maneuver to unload the axis of rolling and yaw axis moment of momentum according to claim 3, is characterized in that described step 3: to unload start time for starting point, calculates gravity gradient torque the angular-momentum vector h accumulated within each orbit period _circprocess be:

Satellite from unloading one-period in gravity gradient torque suffered by satellite be expressed as in inertial system:

In formula, t is for satellite is from starting to unload institute's elapsed time the moment, and i is inertial coordinates system ox _ithe unit vector of axle, then the moment of momentum that satellite accumulates within an orbit period is expressed as:

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

Obtain

Carry out integration to obtain

5. a kind of method utilizing satellite axis of rolling rapid attitude maneuver to unload the axis of rolling and yaw axis moment of momentum according to claim 4, it is characterized in that described step 4: according to the moment of momentum measuring the actuating unit obtained, determine that all momentum exchange actuating units need the moment of momentum of unloading at the axis of rolling the moment of momentum that unloads is needed with yaw axis the process of size is:

Measure the component of moment of momentum at body series of each momentum exchange actuating unit, make i-th momentum exchange actuating unit moment of momentum at the representation in components of body series be obtain the moment of momentum that all momentum exchange actuating units need at the axis of rolling and yaw axis to unload 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 formula, be the array of 3 × 1, represent the component of i-th momentum exchange actuating unit moment of momentum at body series, represent the component of summation at body series of all actuating unit moment of momentums, with represent the component of all actuating unit moment of momentum summations at the body series axis of rolling and yaw axis respectively, with be respectively the moment of momentum size that the axis of rolling and yaw axis unload, $x_b^b={\left[\begin{array}{ccc}1& 0& 0\end{array}\right]}^T$ For the axis of rolling of body series is at the component of body series, $z_b^b={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^T$ For the yaw axis of body series is at the component of body series; N is the quantity of actuating unit, i be greater than 0 integer.

6. a kind of method utilizing satellite axis of rolling rapid attitude maneuver to unload the axis of rolling and yaw axis moment of momentum according to claim 1, is characterized in that described step 5: the angular-momentum vector h obtained according to step 3 _circthe all momentum exchange actuating units obtained with step 4 need the moment of momentum unloaded at the axis of rolling the moment of momentum that unloads is needed with yaw axis determine the motor-driven angle of the track number of turns n that satellite unloads and satellite uninstall process process be:

Step May Day: determine the total angular momentum h unloaded _{un_xy}:

Due to the coupled relation of the axis of rolling and yaw axis, the moment of momentum of the actual unloading 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 formula, h _{un_xz}represent the angular-momentum vector of satellite rollings-yaw axis unloading and, h _{un_xz}only at the 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 unload track number of turns n;

Calculate satellite to unload the lock angle momentum that an orbit period accumulates and be:

h _circ(45°)＝6ω ₀(I _z-I _y)k

In formula, h _circ(45 °) represent that satellite keeps run the moment of momentum that an orbit period accumulates;

The component of the moment of momentum accumulated in uninstall process at inertial coordinates system is identical with the component at body series, and satellite needs the motor-driven 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 formula, mod is a symbol of operation, represents the integer part of getting numerical value inside bracket, N ^*represent Positive Integer Set;

Step 5 three: utilize the unloading track number of turns n tried to achieve, determine that the initial axis of rolling needs motor-driven angle

For the angular motion value h that the moment of momentum that accumulates after ensureing satellite unloading n week and satellite unload _{un_xz}identical, therefore should meet following relational expression:

Therefore can be in the hope of expression formula be: