CN104570742B - Feedforward PID (proportion, integration and differentiation) control based rapid high-precision relative pointing control method of noncoplanar rendezvous orbit - Google Patents

Abstract

The invention relates to a rapid high-precision relative pointing control method of a noncoplanar rendezvous orbit, in particular to a feedforward PID (proportion, integration and differentiation) control based rapid high-precision relative pointing control method of the noncoplanar rendezvous orbit, and aims to solve the problem that rapid high-precision tracking-pointing control methods related to satellite attitudes under the noncoplanar rendezvous orbit do not exist in the prior art. The feedforward PID control based rapid high-precision relative pointing control method including adopting an Euler angle for attitude description of a spacecraft, creating dynamical and kinematical equations of the spacecraft, and acquiring an precise expected angle theta according to a noise-containing expected angle z by a Kalman filtering algorithm of a spaceborne computer; designing an attitude control law of each axis according to a formula of ; selecting two parallelly-placed single-frame control moment gyroscopes to control a yaw axis, and selecting two flywheels to control a rolling axis and a pitch axis respectively; calculating gyroscopic moment T and flywheel actual output moment uw to complete rapid high-precision relative pointing control of the noncoplanar rendezvous orbit. The feedforward PID control based rapid high-precision relative pointing control method is applicable to rapid high-precision relative pointing control of the noncoplanar rendezvous orbit.

Description

Different-surface cross fast-changing track rapid high-precision relative pointing control method based on feedforward PID control

Technical Field

The invention relates to a rapid high-precision relative pointing control method for a different-surface crossed quick-change track.

Background

With the development of aerospace technology, space technology has been applied in various fields on a large scale, and space is said to exist as a resource on which human beings live and develop. In order to enable the satellite payload to point to a specific target with a certain precision, firstly, an expected attitude of the satellite payload when an apparent axis points to the target needs to be calculated according to the position of the target, and then, the deviation and the relative rotation speed of the satellite from the command attitude are kept within an allowable range under the action of orbital motion and disturbance moment by tracking the expected attitude.

The flexible spacecraft robust backstepping self-adaptive attitude maneuver and active vibration suppression researches the problems of the flexible spacecraft attitude maneuver and active vibration suppression, designs a double-loop robust control method, has strong robustness to parameter uncertainty, increases the damping of a flexible structure, and can realize the high-precision attitude control and vibration suppression of the flexible spacecraft. However, the algorithm is slow to enter steady state, affecting the rapidity of the system.

The application of variable structure control in the attitude rapid maneuver control of the flexible spacecraft emphatically researches the variable structure control law of the flexible spacecraft. The method for setting the variable structure parameters under the fastest maneuver is analyzed, the algorithm has strong robustness and is simple, the algorithm does not depend on model parameters, the dynamic performance is better than PID control, and the rapidity and the precision of the satellite attitude maneuver are improved. However, the algorithm is too dependent on the modeling precision of the satellite attitude dynamics, and the application of the algorithm in practical engineering is limited.

The research on the attitude control method of the satellite with the solar sailboard researches the problems of complex dynamic characteristics of the attitude of the flexible satellite, modeling uncertainty and limited moment output of an actual satellite actuator, and designs an inverse model control law of a non-precise model based on a support vector machine. The control law has good steady-state effect and dynamic quality, effectively reduces the influence of flexible mode vibration on attitude control, and has certain inhibition capability on interference. However, the stability analysis and calculation processes of the algorithm are complex, the application is still relatively few, and documents for combining the support vector machine with the flexible satellite attitude do not appear yet.

At present, the problem of fast and high-precision tracking and pointing of the attitude of a satellite under an out-of-plane cross orbit is hardly researched.

Disclosure of Invention

The invention aims to solve the problem that the existing control method does not have a control method for quickly and accurately tracking and pointing the attitude of a satellite under an out-of-plane crossed orbit.

The method for controlling the rapid high-precision relative pointing of the different-surface crossed fast-changing track based on feedforward PID control comprises the following steps:

step 1: determining a desired pose:

the tracking star and the target star are positioned on the non-coplanar cross orbit, and the tracking star needs to autonomously detect the position of the target; in order to enable a laser transmitter or observation equipment for tracking the star to always point to a target star, an expected attitude needs to be determined firstly, so that the problem of pointing to the target becomes the problem of attitude tracking; because the detection range is limited, laser attack or observation and monitoring can be carried out only when the distance between the tracking satellite and the target satellite is close, when the track included angle of the two satellites is large, only a small section near the track intersection point meets the detection distance requirement, and the expected attitude is changed very fast (embodied by fast change), so that the pointing tracking of the target is required to have higher response speed; the pointing task of the target star is often required to have certain precision, so that higher requirement is provided for the pointing precision;

assuming that a tracking star view axis is coincident with an x axis of a body, enabling the x axis of a desired attitude coordinate system to point to a target star, enabling a y axis to be perpendicular to a plane formed by the x axis and a tracking star geocentric vector and to be opposite to the track angular velocity, and enabling a z axis, the x axis and the y axis to form a right-hand coordinate system as shown in figure 1; the expected attitude coordinate system designed in the way is almost obtained by rotating the centroid orbit coordinate system for a certain angle around the z axis, and the centroid orbit coordinate system is taken as an attitude reference coordinate system, so that the change of the expected attitude is approximately rotated around the z axis;

in the geocentric inertial coordinate system, unit vectors of all coordinate axes of the expected attitude coordinate system are expressed as follows:

wherein r is_tAnd r_cRespectively are position vectors of the tracking star and the target star in the geocentric inertial coordinate system; i. j and k are unit vectors of each coordinate axis of the expected attitude coordinate system;

let x₁、y₁、z₁Is a unit vector, x, of each coordinate axis of the earth's center inertial coordinate system₂、y₂、z₂Is a unit vector of each coordinate axis of a centroid orbit coordinate system, and consists of a unit vector i, j, k of each coordinate axis of an expected attitude coordinate system and a unit vector x of each coordinate axis of a geocentric inertia coordinate system₁，y₁，z₁Obtaining a cosine transformation matrix R of the expected attitude coordinate system relative to the geocentric inertial coordinate system_diUnit vector x of each coordinate axis of the centroid orbital coordinate system₂，y₂，z₂And unit vector x of each coordinate axis of the earth center inertial coordinate system₁，y₁，z₁Solving the cosine transform matrix R of the mass center orbit coordinate system relative to the geocentric inertia coordinate system_oi，

The transformation matrix of the desired pose coordinate system with respect to the centroid orbital coordinate system is

Step 2: the Kalman filtering estimation uses a second derivative of an expected attitude angle in a control law and cannot be directly measured; the measured expected attitude angle hasNoise influence, namely, if the noise is amplified by direct quadratic difference, designing a standard continuous Kalman filter to determine an expected attitude angle and a derivative thereof; the expected attitude angle is an attitude angle obtained by taking the coordinate axis where the i, j and k unit vectors are located as an expected attitude coordinate system, and is theta,to be the first derivative of the desired attitude angle theta,a second derivative of the desired attitude angle θ; take the state vector as

The desired angle z containing noise information is obtained by measurement:

z＝H_zx+v (3)

in the formula H_z＝[1,0,0]V is the high frequency noise that is not estimated;

inputting a desired angle z containing noise into a Kalman filter; in the case of the kalman filter, the filter,

setting estimators of three axes to be in the same form; the equation of state for each axis is:

wherein,w is virtual white noise with variance not zero to reflect the change characteristic of the actual angular acceleration information;

the estimator is

K＝PH_z ^TR^-1(6)

PA^T+AP-PH_z ^TR^-1H_zP+BQB^T＝0 (7)

Is a state estimate for the state variable x;a first derivative of a state estimate for a state variable x; q is a semi-positive definite system noise variance matrix; r is a positive definite measurement noise array; p is a stateA variance matrix of (a);

obtaining an accurate expected angle theta through a Kalman filtering algorithm of an on-board computer according to the expected angle z containing noise;

and step 3: designing an attitude control law of each axis, wherein the attitude control law is specifically represented as a control moment u; has the following form:

where u is the control moment, I is the principal inertia of the shaft, K_pIs a proportional amplification factor, K_iFor integral control coefficient, K_dIs a differential control coefficient; a is_dIs an attitude angle under the body mass center coordinate system,is a_dThe second derivative of (a); e is the Euler attitude angle error;

and 4, step 4: selecting an actuating mechanism, and controlling a yaw axis, namely a z axis, by using two single-frame control moment gyroscopes which are arranged in parallel; two flywheels are used to control the roll axis and the pitch axis, i.e., the x-axis and the y-axis, respectively.

The invention has the following beneficial effects:

1. in practical engineering, the thruster has an upper amplitude limit and is not continuous, and compared with the existing track transfer schemes under some continuous control, the method considers the amplitude limit of the thruster and is more suitable for practical engineering application.

2. Compared with some schemes only considering time optimization or only considering fuel consumption, the invention simultaneously considers the transfer time and the fuel consumption, and can find the time-fuel optimization control scheme under the specific gravity by adjusting the specific gravities of the transfer time and the fuel consumption.

3. Unlike some studies on orbital transfer in an inertial system, the invention studies on orbital transfer in a relative orbital coordinate system, and the starting point and the ending point of orbital transfer in the relative orbital coordinate system are not fixed points in the inertial system, so that the invention has greater practical application value in the problem of relative orbital transfer between spacecrafts.

Drawings

FIG. 1 is a schematic view of a desired pose coordinate system;

FIG. 2 is a schematic diagram of the body and the orbital coordinate system;

FIG. 3 is a schematic view of a control moment gyro mounting configuration;

FIG. 4 is a schematic diagram of a PD controller for the flywheel in a torque mode;

FIG. 5 is a graph of expected attitude versus body attitude change;

FIG. 6 is a graph of a change in attitude angle error;

FIG. 7 is a graph of the variation of angular velocity of a satellite;

FIG. 8 is a graph of CMG versus flywheel output torque;

FIG. 9 is a graph of total control torque variation.

Detailed Description

The first embodiment is as follows:

the method for controlling the rapid high-precision relative pointing of the different-surface crossed fast-changing track based on feedforward PID control comprises the following steps:

step 1: determining a desired pose:

the tracking star and the target star are positioned on the non-coplanar cross orbit, and the tracking star needs to autonomously detect the position of the target; in order to enable a laser transmitter or observation equipment for tracking the star to always point to a target star, an expected attitude needs to be determined firstly, so that the problem of pointing to the target becomes the problem of attitude tracking; because the detection range is limited, laser attack or observation and monitoring can be carried out only when the distance between the tracking satellite and the target satellite is close, when the track included angle of the two satellites is large, only a small section near the track intersection point meets the detection distance requirement, and the expected attitude is changed very fast (embodied by fast change), so that the pointing tracking of the target is required to have higher response speed; the pointing task of the target star is often required to have certain precision, so that higher requirement is provided for the pointing precision;

assuming that a tracking star view axis is coincident with an x axis of a body, enabling the x axis of a desired attitude coordinate system to point to a target star, enabling a y axis to be perpendicular to a plane formed by the x axis and a tracking star geocentric vector and to be opposite to the track angular velocity, and enabling a z axis, the x axis and the y axis to form a right-hand coordinate system as shown in figure 1; the expected attitude coordinate system designed in the way is almost obtained by rotating the centroid orbit coordinate system for a certain angle around the z axis, and the centroid orbit coordinate system is taken as an attitude reference coordinate system, so that the change of the expected attitude is approximately rotated around the z axis;

in the geocentric inertial coordinate system, unit vectors of all coordinate axes of the expected attitude coordinate system are expressed as follows:

wherein r is_tAnd r_cRespectively are position vectors of the tracking star and the target star in the geocentric inertial coordinate system; i. j and k are unit vectors of each coordinate axis of the expected attitude coordinate system;

let x₁、y₁、z₁Is a unit vector, x, of each coordinate axis of the earth's center inertial coordinate system₂、y₂、z₂Is a unit vector of each coordinate axis of a centroid orbit coordinate system, and consists of a unit vector i, j, k of each coordinate axis of an expected attitude coordinate system and a unit vector x of each coordinate axis of a geocentric inertia coordinate system₁，y₁，z₁Obtaining a cosine transformation matrix R of the expected attitude coordinate system relative to the geocentric inertial coordinate system_diUnit vector x of each coordinate axis of the centroid orbital coordinate system₂，y₂，z₂And unit vector x of each coordinate axis of the earth center inertial coordinate system₁，y₁，z₁Solving the cosine transform matrix R of the mass center orbit coordinate system relative to the geocentric inertia coordinate system_oi，

The transformation matrix of the desired pose coordinate system with respect to the centroid orbital coordinate system is

Step 2: the Kalman filtering estimation uses a second derivative of an expected attitude angle in a control law and cannot be directly measured; the measured expected attitude angle has noise influence, and if the noise is amplified by direct second-order difference, a standard continuous Kalman filter is designed to determine the expected attitude angle and the derivative thereof; the desired attitude angle is at the seat where the unit vectors of i, j, k lieThe axis is an attitude angle obtained under an expected attitude coordinate system, the expected attitude angle is set as theta,to be the first derivative of the desired attitude angle theta,a second derivative of the desired attitude angle θ; take the state vector as

The desired angle z containing noise information is obtained by measurement:

z＝H_zx+v (3)

in the formula H_z＝[1,0,0]V is the high frequency noise that is not estimated;

inputting a desired angle z containing noise into a Kalman filter; in the case of the kalman filter, the filter,

setting estimators of three axes to be in the same form; the equation of state for each axis is:

wherein,w is virtual white noise with variance not zero to reflect the change characteristic of the actual angular acceleration information;

the estimator is

K＝PH_z ^TR^-1(6)

PA^T+AP-PH_z ^TR^-1H_zP+BQB^T＝0 (7)

Is a state estimate for the state variable x;a first derivative of a state estimate for a state variable x; q is a semi-positive definite system noise variance matrix; r is a positive definite measurement noise array; p is a stateA variance matrix of (a);

obtaining an accurate expected angle theta through a Kalman filtering algorithm of an on-board computer according to the expected angle z containing noise;

and step 3: designing an attitude control law of each axis, wherein the attitude control law is specifically represented as a control moment u; has the following form:

where u is the control moment, I is the principal inertia of the shaft, K_pIs a proportional amplification factor, K_iFor integral control coefficient, K_dIs a differential control coefficient; a is_dIs an attitude angle under the body mass center coordinate system,is a_dThe second derivative of (a); e is the Euler attitude angle error;

and 4, step 4: selecting an actuating mechanism, and controlling a yaw axis, namely a z axis, by using two single-frame control moment gyroscopes which are arranged in parallel; two flywheels are used to control the roll axis and the pitch axis, i.e., the x-axis and the y-axis, respectively.

The second embodiment is as follows: the implementation process of step 3 in this embodiment is as follows:

the angular velocity omega of the tracking star in the inertial space is equal to the angular velocity omega of the tracking star body coordinate system relative to the attitude reference coordinate system_brAngular velocity ω associated with the attitude reference frame relative to the centroid inertial frame_riTo sum, i.e.

ω＝ω_br+ω_ri(8)

In the inertial directional flight mode

The reference coordinate system is the mass center inertial coordinate system, omega_riIs equal to 0 and has

C_x(·)、C_y(·)、C_z(. The) is the rotation matrix in the transformation process of the coordinate system respectively;

psi is the yaw angle;is a pitch angle;is a roll angle; omega_x、ω_y、ω_zRespectively tracking the components of the angular velocity omega of the star on the x-axis, the y-axis and the z-axis under a centroid inertial coordinate system;

see FIG. 2, Euler angles ψ,The geometrical meaning of (A) is as follows:

psi is yaw angle-Tracking star rolling axis O_bX_b(direction of tracking star velocity) projection on local horizontal plane and orbit coordinate system O_oX_oThe included angle of the axes;

for pitch-tracking star rolling axis O_bX_bThe included angle with the projection of the device on the local horizontal plane;

for roll angle-tracking star pitch axis O_bY_bThe included angle with the projection of the device on the local horizontal plane;

three corners as known in the art

And (3) obtaining an Euler angle attitude kinematic equation:

because the attitude control task is similar to single-axis rotation, a three-axis decoupling design attitude tracking control law is carried out; when the tracking star rotates approximately around the z-axis, the attitude angles of the x-axis and the y-axis are approximately 0, and the orbit angular velocity is also small compared to the tracking star angular velocity, and it can be seen from the equation (10)The angular velocity obtained by the gyro measurement can be directly used for feedback control, and the 3-1-2 rotation sequence Euler angular form is selected to describe and track the star attitude;

the desired attitude angle theta is based on the transformation matrix a_d＝θR_doAttitude angle a converted to body centroid coordinate system_d；Body attitude angle is denoted as a_bThe Euler attitude angle error e ═ a_d-a_b(ii) a When the expected attitude changes rapidly around the z axis, the traditional PID control law cannot meet the requirement of tracking accuracy, so that a feedforward term of an expected Euler angle second derivative (obtained by filtering estimation in step 2) is added to predict the change of angular acceleration and improve the pointing tracking capability;

the attitude control law for each axis has the form:

where u is the control moment, I is the principal inertia of the shaft, K_pIs a proportional amplification factor, K_iFor integral control coefficient, K_dIs a differential control coefficient;

in order to prevent integral saturation, the idea of "integral separation" is adopted, i.e. the integral action is introduced only when the error is small, the integral is started when | e | is smaller than a certain threshold value, and no integral action is taken when | e | is larger than the value; a certain threshold is determined according to the actual euler attitude angle error requirement.

Other steps and parameters are the same as in the first embodiment.

The third concrete implementation mode: the implementation process of step 4 in this embodiment is as follows:

because the expected attitude near the intersection point of the two star non-coplanar orbits is greatly changed, the requirement on the control moment is higher; although the thruster can provide larger torque, the output torque is not continuous and cannot accurately track the command torque, so that the performance of a control system is damaged; in the feedforward PID attitude pointing tracking control, the requirement on the accuracy of the controlled quantity is higher, buffeting is more easily caused by using a thruster as an executing mechanism, and an ideal control effect cannot be achieved;

the invention only has larger torque demand of the yaw axis and has smaller torque demand of other two axes, and the flywheel and the CMG can be combined for use, namely two single-frame control torque gyros which are arranged in parallel are used for controlling the yaw axis, namely the z axis; the two flywheels are used for respectively controlling a rolling shaft and a pitching shaft, namely an x shaft and a y shaft;

a Control moment gyro (CMG for short); the mounting configuration of control moment gyro groups (CMGs) in a tracking star body coordinate system is shown in figure 3, h₁And h₂Two gyro rotor angular momentums; establishing a relative coordinate system for installing the control moment gyroscope in an installation configuration, wherein three axes point to Fx, Fy and Fz respectively; the configuration can only output the moments in the Fx and the Fz directions, and each two-dimensional vector represents the Fx and the Fz directions;

in order to reduce the influence of the coupling moment, the angular momentum of the whole tracking star is made to be zero as much as possible, namely h is made to be zero when the angular velocity of the tracking star body is zero₁And h₂The directions are opposite, and the frame angle of the direction shown in the drawing is defined to be zero;

the yaw axis is controlled by two single-frame control moment gyros arranged in parallel, and the angular momentum h of two gyro rotors is set₁And h₂All have the size of h, and the frame angles of the CMG are respectively₁And₂according to the control moment u designed by the yaw axis control law, the frame angle of the gyroscope is obtained₁And₂then according to₁And₂determining gyro moment T

The total angular momentum of the gyro group in the tracking star system is

The resultant gyro moment T generated by the rotation of each gyro frame can be expressed as

Is the first derivative of H;

except the yaw axis, the rolling axis and the pitching axis adopt flywheels as actuating mechanisms;

the rolling shaft and the pitching shaft are respectively controlled by a flywheel, and the flywheel is used as a simple first-order inertia link to analyze and design the flywheel and the controller as (14) in the working mode of the control moment u designed by the rolling shaft and the pitching shaft control law

In the formula, t_sIs the time constant of the first order inertial system;

the PD controller is adopted for design, and the form is shown in FIG. 4;

actual output torque u of flywheel_w

t_sIs the time constant, k, of a first-order inertial system_pAs integration time constant, k_dIs a differential time constant;

the resultant gyro moment T generated by the rotation of the gyro frame and the actual output moment u of the flywheel_wAnd finishing the rapid high-precision relative pointing control of the different-surface crossed rapid-change track.

Other steps and parameters are the same as in the first or second embodiment.

Examples

Setting the target satellite to be in a 600km sun synchronous orbit, wherein the number of initial orbits is as follows: semi-major axis a of target star orbit₁6978140m, meshEccentricity e of the orbit of the satellite₁0, target star orbit inclination i₁97.7597 °, target star orbit intersection longitude Ω₁0, target star isocenter angular distance omega₁0, true angle f of target star₁-6.2 °; the tracking star is positioned on the homomorphic different-surface orbit and has a certain phase difference with the target, and the number of the initial orbits is as follows: track the star orbit semi-major axis a₂6978140m, tracking satellite orbit eccentricity e₂Track star orbit inclination i ═ 0₂＝i₁+5 °, tracking star orbit elevation point longitude Ω₂0, tracking the angular distance omega of the star near center point₂0, tracking true star near angle f₂＝f₁-0.0821°。

Tracking star inertia matrix

The space disturbance moment added in the simulation is as follows: sunlight pressure moment, gravity gradient moment, geomagnetic moment and pneumatic moment.

Controller design parameters

PID parameter K_p＝1.8I，K_i＝1，K_d1.8I, I is the main inertia of the corresponding axis, the integral threshold value is 0.01 degrees, the filter parameters R is (10/3600/57.3) ^2, Q is (500/5000/100) ^2, the angular momentum h of a single gyro rotor is 30Nms, the upper limit of the angular speed of the gyro frame is 30 degrees/s, and the manipulation law weight coefficient α is e^-10D。

Simulation analysis

The simulation images obtained by the feedforward PID attitude pointing tracking control algorithm are shown in the figures 5-9:

it can be seen from fig. 5 that the yaw angle of the expected attitude is rapidly changed from-80 ° to 80 °, the rolling angle and the pitch angle are almost zero, the assumption of approximate uniaxial rotation is met, and the attitude of the body can well track the change of the expected attitude. It can be seen from fig. 6 that the tracking accuracy is good except for the initial large-deviation adjustment process, and the error near the track intersection increases. From fig. 8 and fig. 8, it can be seen that the control moment is provided by the control moment gyro CMG and the flywheel during the maneuvering process, and the yaw axis moment requirement near the track crossing point is larger and is provided by the control moment gyro CMG.

Claims (3)

1. The method for controlling the rapid high-precision relative pointing of the different-surface cross fast-changing track based on feedforward PID control is characterized by comprising the following steps: the method comprises the following steps:

step 1: determining a desired pose:

assuming that a tracking star view axis is coincident with an x axis of a body, enabling the x axis of a desired attitude coordinate system to point to a target star, enabling a y axis to be perpendicular to a plane formed by the x axis and a tracking star geocentric vector and to be opposite to the track angular velocity, enabling a z axis, the x axis and the y axis to form a right-hand coordinate system, and enabling a centroid track coordinate system to serve as an attitude reference coordinate system, so that the change of the desired attitude is approximately rotated around the z axis;

in the geocentric inertial coordinate system, unit vectors of all coordinate axes of the expected attitude coordinate system are expressed as follows:

$\begin{array}{c}i=\frac{r_t-r_c}{|r_t-r_c|}\\ j=\frac{i\×r_c}{|i\×r_c|}\\ k=i\×j\end{array}---\left(1\right)$

wherein r is_tAnd r_cRespectively are position vectors of the tracking star and the target star in the geocentric inertial coordinate system; i. j and k are unit vectors of each coordinate axis of the expected attitude coordinate system;

let x₁、y₁、z₁Is a unit vector, x, of each coordinate axis of the earth's center inertial coordinate system₂、y₂、z₂Is a unit vector of each coordinate axis of a centroid orbit coordinate system, and consists of a unit vector i, j, k of each coordinate axis of an expected attitude coordinate system and a unit vector x of each coordinate axis of a geocentric inertia coordinate system₁，y₁，z₁Obtaining a cosine transformation matrix R of the expected attitude coordinate system relative to the geocentric inertial coordinate system_diUnit vector x of each coordinate axis of the centroid orbital coordinate system₂，y₂，z₂And unit vector x of each coordinate axis of the earth center inertial coordinate system₁，y₁，z₁Solving the cosine transform matrix R of the mass center orbit coordinate system relative to the geocentric inertia coordinate system_oi，

The transformation matrix of the desired pose coordinate system with respect to the centroid orbital coordinate system is

$R_{do}=R_{di}{R}_{oi}^T---\left(2\right)$

Step 2: designing a standard continuous Kalman filter to determine an expected attitude angle and a derivative thereof; the expected attitude angle is an attitude angle obtained by taking the coordinate axis where the i, j and k unit vectors are located as an expected attitude coordinate system, and is theta,to be the first derivative of the desired attitude angle theta,a second derivative of the desired attitude angle θ; take the state vector as

The desired angle z containing noise information is obtained by measurement:

z＝H_zx+v (3)

in the formula H_z＝[1,0,0]V is the high frequency noise that is not estimated;

inputting a desired angle z containing noise into a Kalman filter; in the case of the kalman filter, the filter,

setting estimators of three axes to be in the same form; the equation of state for each axis is:

$\stackrel{\·}{x}=Ax+Bw---\left(4\right)$

wherein,w is virtual white noise with variance not zero to reflect the change characteristic of the actual angular acceleration information;

the estimator is

$\widehat{\stackrel{\·}{x}}+A\hat{x}+K(z-Hz\hat{x})---\left(5\right)$

K＝PH_z ^TR^-1(6)

PA^T+AP-PH_z ^TR^-1H_zP+BQB^T＝0 (7)

Is a state estimate for the state variable x;a first derivative of a state estimate for a state variable x; q is a semi-positive definite system noise variance matrix; r is a positive definite measurement noise array; p is a stateA variance matrix of (a);

obtaining an accurate expected angle theta through a Kalman filtering algorithm of an on-board computer according to the expected angle z containing noise;

and step 3: designing an attitude control law of each axis, wherein the attitude control law is specifically represented as a control moment u; has the following form:

$u={\stackrel{\·\·}{a}}_{d}I+K_{p}e+K_i\∫edt+K_d\stackrel{\·}{e}---\left(11\right)$

where u is the control moment, I is the principal inertia of the shaft, K_pIs a proportional amplification factor, K_iFor integral control coefficient, K_dIs a differential control coefficient; a is_dIs an attitude angle under the body mass center coordinate system,is a_dThe second derivative of (a); e is the Euler attitude angle error;

and 4, step 4: selecting an actuating mechanism, and controlling a yaw axis, namely a z axis, by using two single-frame control moment gyroscopes which are arranged in parallel; two flywheels are used to control the roll axis and the pitch axis, i.e., the x-axis and the y-axis, respectively.

2. The method for controlling the fast high-precision relative orientation of the different-surface crossed fast-changing orbit based on the feedforward PID control as claimed in claim 1, wherein the implementation process of the step 3 is as follows:

the angular velocity omega of the tracking star in the inertial space is equal to the angular velocity omega of the tracking star body coordinate system relative to the attitude reference coordinate system_brAngular velocity ω associated with the attitude reference frame relative to the centroid inertial frame_riTo sum, i.e.

ω＝ω_br+ω_ri(8)

In the inertial directional flight mode

The reference coordinate system is the mass center inertial coordinate system, omega_riIs equal to 0 and has

C_x(·)、C_y(·)、C_z(. The) is the rotation matrix in the transformation process of the coordinate system respectively;

psi is the yaw angle;is a pitch angle;is a roll angle; omega_x、ω_y、ω_zRespectively tracking the components of the angular velocity omega of the star on the x-axis, the y-axis and the z-axis under a centroid inertial coordinate system;

and (3) obtaining an Euler angle attitude kinematic equation:

because the attitude control task is similar to single-axis rotation, a three-axis decoupling design attitude tracking control law is carried out; when the tracking star rotates approximately around the z-axis, the attitude angles of the x-axis and the y-axis are approximately 0, and the orbit angular velocity is also small compared to the tracking star angular velocity, and it can be seen from the equation (10)The angular velocity obtained by the gyro measurement can be directly used for feedback control, and the 3-1-2 rotation sequence Euler angular form is selected to describe and track the star attitude;

the desired attitude angle theta is based on the transformation matrix a_d＝θR_doAttitude angle a converted to body centroid coordinate system_d；Body attitude angle is denoted as a_bThe Euler attitude angle error e ═ a_d-a_b；

The attitude control law for each axis has the form:

$u={\stackrel{\·\·}{a}}_{d}I+K_{p}e+K_i\∫edt+K_d\stackrel{\·}{e}---\left(11\right)$

where u is the control moment, I is the principal inertia of the shaft, K_pIs a proportional amplification factor, K_iFor integral control coefficient, K_dIs a differential control coefficient;

integration starts when | e | is less than a certain threshold and there is no integration effect when | e | is greater than this value.

3. The method for controlling the fast high-precision relative orientation of the different-surface crossed fast-changing orbit based on the feedforward PID control as claimed in claim 1 or 2, wherein the implementation process of the step 4 is as follows:

controlling a yaw axis, namely a z axis, by using two single-frame control moment gyroscopes which are arranged in parallel; the two flywheels are used for respectively controlling a rolling shaft and a pitching shaft, namely an x shaft and a y shaft;

a control moment gyro, abbreviated as CMG;

the yaw axis is controlled by two single-frame control moment gyros arranged in parallel, and the angular momentum h of two gyro rotors is set₁And h₂All have the size of h, and the frame angles of the CMG are respectively₁And₂according to the control moment u designed by the yaw axis control law, the frame angle of the gyroscope is obtained₁And₂then according to₁And₂determining gyro moment T

The total angular momentum of the gyro group in the tracking star system is

$H=h\left[\begin{array}{c}cos\left({\mathrm{\δ}}_1\right)-cos\left({\mathrm{\δ}}_2\right)\\ -sin\left({\mathrm{\δ}}_1\right)+sin\left({\mathrm{\δ}}_2\right)\end{array}\right]---\left(12\right)$

The resultant gyro moment T generated by the rotation of each gyro frame can be expressed as

$T=-\stackrel{\·}{H}=-h\left[\begin{array}{cc}-{\mathrm{sin\δ}}_1& {\mathrm{sin\δ}}_2\\ -{\mathrm{cos\δ}}_1& {\mathrm{cos\δ}}_2\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\δ}}}_1\\ {\stackrel{\·}{\mathrm{\δ}}}_2\end{array}\right]=-hC\left(\mathrm{\δ}\right)\stackrel{\·}{\mathrm{\δ}}---\left(13\right)$

Is the first derivative of H;

except the yaw axis, the rolling axis and the pitching axis adopt flywheels as actuating mechanisms;

the rolling shaft and the pitching shaft are respectively controlled by a flywheel, and the flywheel is used as a simple first-order inertia link to analyze and design the flywheel and the controller as (14) in the working mode of the control moment u designed by the rolling shaft and the pitching shaft control law

$\frac{1}{t_{s}s+1}---\left(14\right)$

In the formula, t_sIs the time constant of the first order inertial system;

designing by adopting a PD controller;

actual output torque u of flywheel_w

$u_w=(k_p+k_{d}s)\frac{1}{t_{s}s+1}e---\left(15\right)$

t_sIs the time constant, k, of a first-order inertial system_pAs integration time constant, k_dIs a differential time constant;

the resultant gyro moment T generated by the rotation of the gyro frame and the actual output moment u of the flywheel_wAnd finishing the rapid high-precision relative pointing control of the different-surface crossed rapid-change track.