CN111178589A - Iterative guidance method and system based on gray prediction - Google Patents

Iterative guidance method and system based on gray prediction Download PDF

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CN111178589A
CN111178589A CN201911248613.6A CN201911248613A CN111178589A CN 111178589 A CN111178589 A CN 111178589A CN 201911248613 A CN201911248613 A CN 201911248613A CN 111178589 A CN111178589 A CN 111178589A
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张蓉
何信华
连彦泽
刘朝阳
刘莞尔
钱航
崔鑫
王仙勇
李世鹏
马利
赵雷
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China Academy of Launch Vehicle Technology CALT
Beijing Institute of Astronautical Systems Engineering
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Beijing Institute of Astronautical Systems Engineering
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Abstract

The invention discloses an iterative guidance method and system based on gray prediction, wherein the method comprises the following steps: for known engine thrust vector
Figure DDA0002308388480000011
Sampling to obtain a sampling sequence: performing primary accumulation on the sampling sequence to obtain a primary accumulation sequence: performing sequence reduction on the sampling sequence according to the primary accumulation sequence; determining a whitening equation set: solving by a least square method to obtain parameter values in the whitening equation set; predicting to obtain an engine thrust vector at the next moment according to the solved parameter value; and predicting to obtain a speed vector and a position vector at the next moment according to the predicted engine thrust vector at the next moment. The invention fully utilizes the existing information, predicts the required thrust vector direction of the engine on line in real time, can simplify the calculation process of iterative guidance, and is easy to realize。

Description

Iterative guidance method and system based on gray prediction
Technical Field
The invention belongs to the technical field of guidance, and particularly relates to an iterative guidance method and system based on gray prediction.
Background
With the continuous development of the related technology in the aerospace field, the requirement on the launch task of the launch vehicle is higher and higher, the guidance precision is an important index, and the traditional perturbation guidance cannot meet the requirements at the present stage.
Disclosure of Invention
The technical problem of the invention is solved: the iterative guidance method and the iterative guidance system based on gray prediction overcome the defects of the prior art, fully utilize the existing information, predict the required thrust vector direction of the engine on line in real time, simplify the calculation process of iterative guidance and are easy to realize.
In order to solve the technical problem, the invention discloses an iterative guidance method based on gray prediction, which comprises the following steps:
for known engine thrust vector
Figure BDA0002308388460000011
Sampling to obtain a sampling sequence:
Figure BDA0002308388460000012
wherein n represents the length of the sampling sequence, n is 1, 2, 3, T, and T represents the iteration period;
performing primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure BDA0002308388460000013
sequence reduction according to formula (1) and formula (2) gives:
Figure BDA0002308388460000014
wherein k is more than or equal to 1 and less than or equal to n;
obtaining a whitening equation set according to the formula (3):
Figure BDA0002308388460000021
wherein, a represents a development coefficient, and b represents a gray effect amount;
solving by a least square method to obtain values of a and b;
according to the values of a and b obtained by solving, the engine thrust vector at the next moment is predicted and obtained by combining the formula (3)
Figure BDA0002308388460000022
The predicted engine thrust vector at the next moment
Figure BDA0002308388460000023
Substituting the speed and position solution formula (5) to predict the speed vector at the next moment
Figure BDA0002308388460000024
And position vector
Figure BDA0002308388460000025
Figure BDA0002308388460000026
Wherein the content of the first and second substances,
Figure BDA0002308388460000027
ω represents the angular velocity of the earth motion.
In the iterative guidance method based on gray prediction, the values of a and b are obtained by solving through a least square method, and the iterative guidance method comprises the following steps:
a and b satisfy:
Figure BDA0002308388460000028
wherein:
Figure BDA0002308388460000029
Figure BDA00023083884600000210
Figure BDA00023083884600000211
equations (7) to (9) are substituted for equation (6), and the values of a and b are obtained by solving.
In the iterative guidance method based on gray prediction, the engine thrust vector at the next moment is predicted according to the values of a and b obtained by solving and combining the formula (3)
Figure BDA0002308388460000031
The method comprises the following steps:
solving the differential equation yields:
Figure BDA0002308388460000032
will be provided with
Figure BDA0002308388460000033
As an initial value for solving the differential equation (10), formula (10) is substituted for formula (3) to obtain formula (11):
Figure BDA0002308388460000034
wherein j represents the j prediction, and the values of j are n +1, n +2 and … …;
substituting the values of a and b obtained by solving into an equation (11), and obtaining the thrust vector of the engine at the next moment by solving
Figure BDA0002308388460000035
In the above iterative guidance method based on gray prediction, equation (5) is determined by the following steps:
determining a mass center motion equation outside the atmosphere of the active section of the rocket:
Figure BDA0002308388460000036
wherein:
Figure BDA0002308388460000037
wherein, W represents the apparent acceleration,
Figure BDA0002308388460000038
which represents the gravitational force of the earth,
Figure BDA0002308388460000039
the velocity vector is represented by a vector of velocities,
Figure BDA00023083884600000310
the position vector is represented by a vector of positions,
Figure BDA00023083884600000311
representing the nozzle swing angle in the pitching direction of the engine, and psi representing the nozzle swing angle in the yawing direction of the engine;
set the terminal radius as
Figure BDA00023083884600000312
An initial radial of
Figure BDA00023083884600000313
Then the mean radial
Figure BDA00023083884600000314
Comprises the following steps:
Figure BDA00023083884600000315
the centroid radial size of any point of the active segment can be expressed as:
r＝rc+Δr····(14)
wherein Δ r represents a high-order term;
will accelerate the gravitational force
Figure BDA0002308388460000041
In that
Figure BDA0002308388460000042
Unfolding and omitting high-level items to obtain an average gravitational acceleration as follows:
Figure BDA0002308388460000043
and (3) carrying the simplified gravitation item into formula (12), and obtaining a simplified motion equation as follows:
Figure BDA0002308388460000044
equation (16) is written as an expression of the equation of state:
Figure BDA0002308388460000045
discretization of formula (17) yields formula (5).
In the above iterative guidance method based on gray prediction, the method further includes:
determining a velocity vector at a next time
Figure BDA0002308388460000046
And position vector
Figure BDA0002308388460000047
Whether a terminal condition is satisfied;
if yes, ending; if not, returning iteration until the predicted speed vector and the predicted position vector meet the terminal condition.
In the above iterative guidance method based on gray prediction,
when in use
Figure BDA0002308388460000048
Or
Figure BDA0002308388460000049
Determining that the predicted speed vector and the predicted position vector meet the terminal condition;
wherein the content of the first and second substances,
Figure BDA00023083884600000410
a vector representing the desired speed of shutdown is shown,
Figure BDA00023083884600000411
indicating a desired shutdown position vector.
In the above iterative guidance method based on gray prediction, the method further includes:
if the predicted speed vector and the predicted position vector do not meet the terminal condition after iteration for p times, then the pair
Figure BDA00023083884600000412
Correcting the initial value by small step length of 0.01 times until the requirement is met;
wherein pT > TThreshold value，TThreshold valueIndicating setting an iteration threshold time.
The invention also discloses an iterative guidance system based on gray prediction, which comprises the following components:
using modules for thrust vectoring of known engines
Figure BDA00023083884600000413
Sampling to obtain a sampling sequence:
Figure BDA0002308388460000051
wherein n represents the length of the sampling sequence, n is 1, 2, 3, T, and T represents the iteration period;
the accumulation module is used for carrying out primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure BDA0002308388460000052
a sequence reduction module for performing sequence reduction according to formula (1) and formula (2) to obtain:
Figure BDA0002308388460000053
wherein k is more than or equal to 1 and less than or equal to n;
a whitening equation set determination module for obtaining a whitening equation set according to equation (3):
Figure BDA0002308388460000054
wherein, a represents a development coefficient, and b represents a gray effect amount;
the parameter solving module is used for solving by a least square method to obtain values of a and b;
a thrust vector predicting module for predicting the engine thrust vector at the next moment according to the values of a and b obtained by solving and the combination formula (3)
Figure BDA0002308388460000055
A speed position prediction module for predicting the engine thrust vector at the next moment
Figure BDA0002308388460000056
Substituting the speed and position solution formula (5) to predict the speed vector at the next moment
Figure BDA0002308388460000057
And position vector
Figure BDA0002308388460000058
Figure BDA0002308388460000059
Wherein the content of the first and second substances,
Figure BDA00023083884600000510
ω represents the angular velocity of the earth motion.
The invention has the following advantages:
the invention discloses an iterative guidance method and an iterative guidance system based on gray prediction, which adopt a gray prediction theory to predict the future change trend of an obtained engine thrust vector direction data by mining the relationship between the obtained engine thrust vector direction data, so that the terminal constraint condition can be quickly achieved, the calculation process of iterative guidance is simplified, the iterative guidance is easy to realize, and an optimization scheme is provided for iterative guidance.
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FIG. 1 is a flowchart illustrating steps of an iterative guidance method based on gray prediction according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Example 1
As shown in fig. 1, in this embodiment, the iterative guidance method based on gray prediction includes:
step 101, for known engine thrust vector
Figure BDA0002308388460000061
Sampling to obtain a sampling sequence:
Figure BDA0002308388460000062
where n denotes the length of the sample sequence, n ═ 1, 2, 3, ·, T, and T denotes the iteration period.
Step 102, performing primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure BDA0002308388460000063
step 103, performing sequence reduction according to formula (1) and formula (2) to obtain:
Figure BDA0002308388460000064
wherein k is more than or equal to 1 and less than or equal to n.
And 104, obtaining a whitening equation set according to the formula (3):
Figure BDA0002308388460000065
wherein a represents a coefficient of progression and b represents an amount of action of gray.
And step 105, solving the values of a and b by a least square method.
And step 106, predicting and obtaining the engine thrust vector at the next moment according to the values of a and b obtained by solving and the combination formula (3)
Figure BDA0002308388460000066
Step 107, the predicted engine thrust vector at the next moment is used
Figure BDA0002308388460000067
Substituting the speed and position solution formula (5) to predict the speed vector at the next moment
Figure BDA0002308388460000071
And position vector
Figure BDA0002308388460000072
Figure BDA0002308388460000073
Wherein the content of the first and second substances,
Figure BDA0002308388460000074
ω represents the angular velocity of the earth motion.
In a preferred embodiment of the present invention, the solving process for a and b is as follows:
a and b satisfy:
Figure BDA0002308388460000075
wherein:
Figure BDA0002308388460000076
Figure BDA0002308388460000077
Figure BDA0002308388460000078
equations (7) to (9) are substituted for equation (6), and the values of a and b are obtained by solving.
In a preferred embodiment of the present invention, the engine thrust vector at the next time is predicted according to the solved values of a and b, in combination with equation (3)
Figure BDA0002308388460000079
The method specifically comprises the following steps:
solving the differential equation yields:
Figure BDA00023083884600000710
will be provided with
Figure BDA00023083884600000711
As an initial value for solving the differential equation (10), formula (10) is substituted for formula (3) to obtain formula (11):
Figure BDA00023083884600000712
wherein j represents the j prediction, and the values of j are n +1, n +2 and … ….
Substituting the values of a and b obtained by solving into an equation (11), and obtaining the thrust vector of the engine at the next moment by solving
Figure BDA0002308388460000081
In a preferred embodiment of the present invention, formula (5) can be determined by:
determining a mass center motion equation outside the atmosphere of the active section of the rocket:
Figure BDA0002308388460000082
wherein:
Figure BDA0002308388460000083
wherein, W represents the apparent acceleration,
Figure BDA0002308388460000084
which represents the gravitational force of the earth,
Figure BDA0002308388460000085
the velocity vector is represented by a vector of velocities,
Figure BDA0002308388460000086
the position vector is represented by a vector of positions,
Figure BDA0002308388460000087
representing the nozzle yaw angle in the engine pitch direction and psi representing the nozzle yaw angle in the engine yaw direction.
In equation (12), the engine thrust direction is the control variable, the starting condition is given by the navigation system, and the terminal condition is determined according to the specific task. Because the gravity item has serious nonlinearity and is not beneficial to development in the process of solving iterative guidance, the gravity item needs to be simplified.
Set the terminal radius as
Figure BDA0002308388460000088
An initial radial of
Figure BDA0002308388460000089
Then the mean radial
Figure BDA00023083884600000810
Comprises the following steps:
Figure BDA00023083884600000811
the centroid radial size of any point of the active segment can be expressed as:
r＝rc+Δr····(14)
where Δ r represents a high-order term.
Will accelerate the gravitational force
Figure BDA00023083884600000812
In that
Figure BDA00023083884600000813
Unfolding and omitting high-level items to obtain an average gravitational acceleration as follows:
Figure BDA00023083884600000814
and (3) carrying the simplified gravitation item into formula (12), and obtaining a simplified motion equation as follows:
Figure BDA00023083884600000815
in equation (16), the average gravity is used to replace the true gravity, which brings a certain error term, but since the iterative guidance method will eliminate the accumulated error of the previous cycle in each iteration cycle, the final iteration result will not cause large deviation.
Equation (16) is written as an expression of the equation of state:
Figure BDA0002308388460000091
discretization of formula (17) yields formula (5).
As can be seen from the formula (5), the speed and the position at the next moment can be predicted only by knowing the value of the thrust vector of the engine and combining the current speed and position, and the ideal predicted value can be obtained by sufficiently taking the value of the thrust vector of the engine.
In a preferred embodiment of the present invention, the iterative guidance method based on gray prediction may further include: determining a velocity vector at a next time
Figure BDA0002308388460000092
And position vector
Figure BDA0002308388460000093
Whether a terminal condition is satisfied; if yes, ending; if not, returning iteration until the predicted speed vector and the predicted position vector meet the terminal condition.
Preferably, when
Figure BDA0002308388460000094
Or
Figure BDA0002308388460000095
And then, determining that the predicted speed vector and the predicted position vector meet the terminal condition. Wherein the content of the first and second substances,
Figure BDA0002308388460000096
a vector representing the desired speed of shutdown is shown,
Figure BDA0002308388460000097
indicating a desired shutdown position vector.
Preferably, if the predicted speed vector and the predicted position vector do not satisfy the terminal condition after p iterations, the pair
Figure BDA0002308388460000098
The initial value is corrected in small steps of 0.01 times until the requirement is met. Wherein pT > TThreshold value，TThreshold valueIndicating setting an iteration threshold time.
Example 2
On the basis of the above embodiment, the present invention also discloses an iterative guidance system based on gray prediction, which includes:
using modules for thrust vectoring of known engines
Figure BDA0002308388460000099
Sampling to obtain a sampling sequence:
Figure BDA00023083884600000910
the accumulation module is used for carrying out primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure BDA0002308388460000101
a sequence reduction module for performing sequence reduction according to formula (1) and formula (2) to obtain:
Figure BDA0002308388460000102
a whitening equation set determination module for obtaining a whitening equation set according to equation (3):
Figure BDA0002308388460000103
and the parameter solving module is used for solving by a least square method to obtain the values of a and b.
A thrust vector predicting module for predicting the engine thrust vector at the next moment according to the values of a and b obtained by solving and the combination formula (3)
Figure BDA0002308388460000104
A speed position prediction module for predicting the engine thrust vector at the next moment
Figure BDA0002308388460000105
Substituting the speed and position solution formula (5) to predict the speed vector at the next moment
Figure BDA0002308388460000106
And position vector
Figure BDA0002308388460000107
Figure BDA0002308388460000108
For the system embodiment, since it corresponds to the method embodiment, the description is relatively simple, and for the relevant points, refer to the description of the method embodiment section.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (8)

1. An iterative guidance method based on gray prediction is characterized by comprising the following steps:
for known engine thrust vector
Figure FDA0002308388450000011
Sampling to obtain a sampling sequence:
Figure FDA0002308388450000012
wherein n represents the length of the sampling sequence, n is 1, 2, 3, …, T, and T represents the iteration period;
performing primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure FDA0002308388450000013
sequence reduction according to formula (1) and formula (2) gives:
Figure FDA0002308388450000014
wherein k is more than or equal to 1 and less than or equal to n;
obtaining a whitening equation set according to the formula (3):
Figure FDA0002308388450000015
wherein, a represents a development coefficient, and b represents a gray effect amount;
solving by a least square method to obtain values of a and b;
according to a and obtained by solvingb value, in conjunction with equation (3), the engine thrust vector at the next time is predicted
Figure FDA0002308388450000016
The predicted engine thrust vector at the next moment
Figure FDA0002308388450000017
Substituting the speed and position solution formula (5) to predict the speed vector at the next moment
Figure FDA0002308388450000018
And position vector
Figure FDA0002308388450000019
Figure FDA00023083884500000110
Wherein the content of the first and second substances,
Figure FDA00023083884500000111
ω represents the angular velocity of the earth motion.
2. The iterative guidance method based on gray prediction of claim 1, wherein the values of a and b are solved by a least squares method, comprising:
a and b satisfy:
Figure FDA0002308388450000021
wherein:
Figure FDA0002308388450000022
Figure FDA0002308388450000023
Figure FDA0002308388450000024
equations (7) to (9) are substituted for equation (6), and the values of a and b are obtained by solving.
3. Iterative guidance method based on grey prediction according to claim 2, characterized in that the engine thrust vector at the next moment is predicted according to the values of a and b obtained by solving, in combination with equation (3)
Figure FDA0002308388450000025
The method comprises the following steps:
solving the differential equation yields:
Figure FDA0002308388450000026
will be provided with
Figure FDA0002308388450000027
As an initial value for solving the differential equation (10), formula (10) is substituted for formula (3) to obtain formula (11):
Figure FDA0002308388450000028
wherein j represents the j prediction, and the values of j are n +1, n +2 and … …;
substituting the values of a and b obtained by solving into an equation (11), and obtaining the thrust vector of the engine at the next moment by solving
Figure FDA0002308388450000029
4. The iterative guidance method based on gray prediction of claim 1, wherein equation (5) is determined by:
determining a mass center motion equation outside the atmosphere of the active section of the rocket:
Figure FDA0002308388450000031
wherein:
Figure FDA0002308388450000032
wherein, W represents the apparent acceleration,
Figure FDA0002308388450000033
which represents the gravitational force of the earth,
Figure FDA0002308388450000034
the velocity vector is represented by a vector of velocities,
Figure FDA0002308388450000035
the position vector is represented by a vector of positions,
Figure FDA0002308388450000036
representing the nozzle swing angle in the pitching direction of the engine, and psi representing the nozzle swing angle in the yawing direction of the engine;
set the terminal radius as
Figure FDA0002308388450000037
An initial radial of
Figure FDA0002308388450000038
Then the mean radial
Figure FDA0002308388450000039
Comprises the following steps:
Figure FDA00023083884500000310
the centroid radial size of any point of the active segment can be expressed as:
r＝rc+Δr…·(14)
wherein Δ r represents a high-order term;
will accelerate the gravitational force
Figure FDA00023083884500000311
In that
Figure FDA00023083884500000312
Unfolding and omitting high-level items to obtain an average gravitational acceleration as follows:
Figure FDA00023083884500000313
and (3) carrying the simplified gravitation item into formula (12), and obtaining a simplified motion equation as follows:
Figure FDA00023083884500000314
equation (16) is written as an expression of the equation of state:
Figure FDA00023083884500000315
discretization of formula (17) yields formula (5).
5. The iterative guidance method based on gray prediction of claim 1, further comprising:
determining a velocity vector at a next time
Figure FDA0002308388450000041
And position vector
Figure FDA0002308388450000042
Whether a terminal condition is satisfied;
if yes, ending; if not, returning iteration until the predicted speed vector and the predicted position vector meet the terminal condition.
6. The iterative guidance method based on gray prediction of claim 5,
when in use
Figure FDA0002308388450000043
Or
Figure FDA0002308388450000044
Determining that the predicted speed vector and the predicted position vector meet the terminal condition;
wherein the content of the first and second substances,
Figure FDA0002308388450000045
a vector representing the desired speed of shutdown is shown,
Figure FDA0002308388450000046
indicating a desired shutdown position vector.
7. The iterative guidance method based on gray prediction of claim 5, further comprising:
if the predicted speed vector and the predicted position vector do not meet the terminal condition after iteration for p times, then the pair
Figure FDA0002308388450000047
Correcting the initial value by small step length of 0.01 times until the requirement is met;
wherein pT > TThreshold value，TThreshold valueIndicating setting an iteration threshold time.
8. An iterative guidance system based on gray prediction, comprising:
using modules for thrust vectoring of known engines
Figure FDA0002308388450000048
Sampling to obtain a sampling sequence:
Figure FDA0002308388450000049
wherein n represents the length of the sampling sequence, n is 1, 2, 3, …, T, and T represents the iteration period;
the accumulation module is used for carrying out primary accumulation on the sampling sequence to obtain a primary accumulation sequence:
Figure FDA00023083884500000410
a sequence reduction module for performing sequence reduction according to formula (1) and formula (2) to obtain:
Figure FDA00023083884500000411
wherein k is more than or equal to 1 and less than or equal to n;
a whitening equation set determination module for obtaining a whitening equation set according to equation (3):
Figure FDA0002308388450000051
wherein, a represents a development coefficient, and b represents a gray effect amount;
the parameter solving module is used for solving by a least square method to obtain values of a and b;
a thrust vector predicting module for predicting the engine thrust vector at the next moment according to the values of a and b obtained by solving and the combination formula (3)
Figure FDA0002308388450000052
A speed position prediction module for predicting the engine thrust vector at the next moment
Figure FDA0002308388450000053
Substituting the speed and position solving formula (5) to predict the next timeVelocity vector of the moment
Figure FDA0002308388450000054
And position vector
Figure FDA0002308388450000055
Figure FDA0002308388450000056
Wherein the content of the first and second substances,
Figure FDA0002308388450000057
ω represents the angular velocity of the earth motion.
CN201911248613.6A 2019-12-09 2019-12-09 Iterative guidance method and system based on gray prediction Pending CN111178589A (en)

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