CN112525221B - Advanced numerical prediction correction guidance method based on adaptive control - Google Patents

Advanced numerical prediction correction guidance method based on adaptive control Download PDF

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CN112525221B
CN112525221B CN202011364615.4A CN202011364615A CN112525221B CN 112525221 B CN112525221 B CN 112525221B CN 202011364615 A CN202011364615 A CN 202011364615A CN 112525221 B CN112525221 B CN 112525221B
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孟斌
唐青原
王晓磊
解永春
吴宏鑫
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Beijing Institute of Control Engineering
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Abstract

An advanced numerical prediction correction guidance method based on self-adaptive control comprises (1) establishing a spacecraft reentry guidance dynamics dimensionless equation considering earth rotation; (2) Converting the thermal rate limit, the load limit and the dynamic pressure limit of the aircraft into altitude reference values; (3) Performing differential stratospheric transformation on the longitudinal dynamics state of the aircraft to obtain a model taking the range and the high derivative as states; (4) designing an active disturbance rejection guidance law aiming at the voyage model; (5) designing an active disturbance rejection guidance law aiming at the high derivative model; and (6) designing a guidance law. The method provided by the invention can be used for hypersonic aircrafts, manned airships, deep space exploration entering spacecrafts and pneumatic capturing, and has better universality.

Description

Advanced numerical prediction correction guidance method based on adaptive control
Technical Field
The invention relates to the field of aerospace, in particular to an advanced numerical prediction correction guidance method based on self-adaptive control.
Background
Guidance is one of key technologies for reentry (entry) of a spacecraft, and is also an important research direction in the field of aerospace at home and abroad at present. The on-orbit computer performance is improved, so that the numerical prediction correction guidance method is possible to be applied on the orbit, and the method also becomes a current research hot spot. At present, the numerical prediction correction guidance method adopts a gradient method to calculate guidance variables from position errors in each guidance period. In order to make the guidance variable converge, the dynamics needs to be integrated multiple times in each guidance period, so the required calculation amount is large; when uncertainty exists, convergence of the gradient method is difficult to ensure; tracking a high reference is currently the latest technology for path limitation problems, but requires offline design of feedback coefficients, and lacks adaptability.
Disclosure of Invention
The invention solves the technical problems that: the method overcomes the defects of the prior art, and provides an advanced numerical prediction correction guidance method based on self-adaptive control, which has rapidity, convergence and adaptability, so that the method is an advanced numerical prediction correction guidance method. The method provided by the invention can be used for hypersonic aircrafts, manned airships, deep space exploration entering spacecrafts and pneumatic capturing, and has better universality.
The technical scheme of the invention is as follows: an advanced numerical prediction correction guidance method based on self-adaptive control comprises the following steps:
(1) Establishing a spacecraft reentry guidance dynamics dimensionless equation considering earth rotation;
(2) Converting the thermal rate limit, the load limit and the dynamic pressure limit of the aircraft into altitude reference values;
(3) Performing differential stratospheric transformation on the longitudinal dynamics state of the aircraft to obtain a model taking the range and the high derivative as states;
(4) Designing an active disturbance rejection guidance law aiming at a course model;
(5) Designing an active disturbance rejection guidance law aiming at a high derivative model;
(6) And designing a guidance law.
The equation established in the step (1) is as follows:
Figure BDA0002805063050000021
wherein r represents the earth center distance, θ and φ represent longitude and latitude respectively, V represents the earth relative velocity, γ and ψ represent the flight path angle and heading angle respectively, and s represents the predicted course; sigma represents roll angle, which is the guidance input; omega represents the earth rotation angular velocity; l and D represent aerodynamic lift and drag respectively,
Figure BDA0002805063050000022
Figure BDA0002805063050000023
R 0 represents the earth radius, S ref And m represents the reference area and mass, respectively, of the aircraft, C L And C D Respectively, the lift and drag coefficients, ρ represents the atmospheric density,
Figure BDA0002805063050000024
ρ 0 is at a reference height h 0 Atmospheric density at beta r <0，
h＝r-R 0 (5)
Typical path constraints in atmospheric flight considered in spacecraft reentry include peak heat rates
Figure BDA0002805063050000025
Load a, and dynamic pressure->
Figure BDA0002805063050000026
The expressions are respectively:
peak heat rate:
Figure BDA0002805063050000027
load:
Figure BDA0002805063050000028
dynamic pressure:
Figure BDA0002805063050000029
wherein k is Q Is a known constant;
Figure BDA0002805063050000031
a max and->
Figure BDA0002805063050000032
The heat rate, load and dynamic pressure limits are shown, respectively. The conversion result of the step (2) is as follows:
Figure BDA0002805063050000033
wherein:
sinγ ref ＝max{sinγ,W 1 ,W 2 ,W 3 } (10)
Figure BDA0002805063050000034
Figure BDA0002805063050000035
Figure BDA0002805063050000036
where T represents the guidance period.
The model obtained in the step (3) is as follows:
Figure BDA0002805063050000037
Figure BDA0002805063050000038
wherein,,
y 1 ＝s， (19)
Figure BDA0002805063050000039
the specific process of the step (4) is as follows:
Figure BDA00028050630500000310
Figure BDA00028050630500000311
the range model formula is written as
Figure BDA00028050630500000312
For equation (25), an adaptive guidance law for active disturbance rejection is designed,
Figure BDA00028050630500000313
wherein, the initial value of the differential equation formula (26) is 0; y is 1 =s is obtained by integrating the kinetic formula (1); s is(s) ref For the distance of the current position and the distance of the target position
s ref ＝arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27)
Wherein θ S ,φ S Is the longitude and latitude of the target point,
Figure BDA0002805063050000041
obtained by a second-order tracking differentiator; l (L) 1 ,l 2 ,l 3 ,k d ,k p Is the parameter to be adjusted.
The specific process of the step (5) is as follows:
recording U 2 ＝Lcosγcosσ (28)
Figure BDA0002805063050000042
The high derivative model equation (18) is written as
Figure BDA0002805063050000043
For equation (30), an active-disturbance-rejection adaptive guidance law is designed:
Figure BDA0002805063050000044
wherein, the initial value of the differential equation formula (31) is 0;
Figure BDA0002805063050000045
given by equation (9) of step (2), ->
Figure BDA0002805063050000046
Given by a first order tracking differentiator;
Figure BDA0002805063050000047
Is given by a state measurement and a dynamics equation formula (1); p is p 1 ,p 2 K is the parameter to be adjusted.
The guidance law designed in the step (6) is specifically as follows:
Figure BDA0002805063050000048
compared with the prior art, the invention has the advantages that:
(1) The advanced numerical prediction correction guidance method based on the self-adaptive control provided by the invention only calculates the guidance quantity once in each guidance period, and has rapidity compared with the existing numerical prediction correction guidance method. The existing numerical prediction correction guidance method adopts a gradient method in each guidance period, and the dynamics needs to be integrated for many times in each guidance period, so that the required calculation amount is large.
(2) Compared with the existing numerical prediction correction guidance method, the advanced numerical prediction correction guidance method based on the adaptive control has stronger robustness, convergence and adaptability. In each guidance period, the existing numerical prediction correction guidance method adopts a gradient method, and when uncertainty exists, convergence of the gradient method is difficult to ensure; for the problem of path limitation, the feedback coefficient needs to be designed offline, and the adaptability is lacking. The method provided by the invention adopts the extended state observer to solve the problem of uncertainty and adjusts the feedback coefficient on line, so that the method has stronger robustness, convergence and self-adaptability.
(3) The method provided by the invention can be used for hypersonic aircrafts, manned airships, deep space exploration entering spacecrafts and pneumatic capturing, and has better universality.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
Aiming at the defects of the prior art, the invention provides an advanced numerical prediction correction guidance method based on self-adaptive control, which is realized through steps (1) to (6) as shown in fig. 1.
Step (1) spacecraft reentry guidance dynamics dimensionless equation considering earth rotation
Figure BDA0002805063050000051
Wherein r represents the earth center distance, θ and φ represent longitude and latitude respectively, V represents the earth relative velocity, γ and ψ represent the flight path angle and heading angle respectively, and s represents the predicted course; sigma represents roll angle, which is the guidance input; omega represents the earth rotation angular velocity; l and D represent aerodynamic lift and drag respectively,
Figure BDA0002805063050000052
Figure BDA0002805063050000053
R 0 represents the earth radius, S ref And m respectively represent aircraftReference area and mass, C L And C D Respectively, the lift and drag coefficients, ρ represents the atmospheric density,
Figure BDA0002805063050000061
ρ 0 is at a reference height h 0 Atmospheric density at ρ 0 And h 0 Beta is known to be r <As a result of the fact that 0 is known,
h＝r-R 0 (5)
in general, typical path constraints in atmospheric flight considered in spacecraft reentry include peak heat rates
Figure BDA0002805063050000062
Load a, and dynamic pressure->
Figure BDA0002805063050000063
The expressions are respectively as follows:
peak heat rate:
Figure BDA0002805063050000064
load:
Figure BDA0002805063050000065
dynamic pressure:
Figure BDA0002805063050000066
wherein k is Q Is a known constant;
Figure BDA0002805063050000067
a max and->
Figure BDA0002805063050000068
The heat rate, load and dynamic pressure limits are shown, respectively.
Step (2) converting the thermal rate limits, load limits and dynamic pressure limits of the aircraft into altitude reference values,
Figure BDA0002805063050000069
wherein:
sinγ ref ＝max{sinγ,W 1 ,W 2 ,W 3 } (10)
Figure BDA00028050630500000610
Figure BDA00028050630500000611
Figure BDA00028050630500000612
where T represents the guidance period.
Equation (9) is derived from the following process. And differentiating the limiting formula (6) -formula (8), then introducing a predictive control method, and differentiating by adopting linear interpolation to obtain the relation between the sine sin gamma of the flight path angle and the path constraint. For different path constraints, the following three scenarios are included.
First case: peak heat rate limit equation (6),
Figure BDA00028050630500000613
second case: the load limiting formula (7),
Figure BDA00028050630500000614
third scenario: dynamic pressure limiting formula (8),
Figure BDA0002805063050000071
further, sin gamma is defined according to equation (10) ref . In the sense that, on the one hand, when a certain limit is violated, i.e.
sinγ≤W 1 Or sin gamma is less than or equal to W 2 Or sin gamma is less than or equal to W 3
In the time-course of which the first and second contact surfaces,
sinγ ref ＝W 1 or sin gamma ref ＝W 2 Or sin gamma ref ＝W 3
On the other hand, when either limit is not violated,
sinγ ref ＝sinγ
finally, from equation 1 of the kinetic equation (1), and equation (10), it is apparent that equation (9) can be obtained.
Step (3) performing differential stratospheric transformation on the longitudinal dynamics state of the aircraft to obtain a model taking the range and the altitude derivative as states,
Figure BDA0002805063050000072
Figure BDA0002805063050000073
wherein,,
y 1 ＝s (19)
Figure BDA0002805063050000074
equations (17) and (18) are derived by the following steps. The longitudinal guidance equation without considering the rotation of the earth is
Figure BDA0002805063050000075
Figure BDA0002805063050000076
Figure BDA0002805063050000077
Figure BDA0002805063050000078
Defining y according to formula (19) 1 . For y 1 Obtaining the second derivative
Figure BDA0002805063050000079
Figure BDA0002805063050000081
Substituting the formula (3) and the formula (21) to obtain the formula (17).
Define y according to equation (20) 2 . For y 2 Obtaining the first derivative
Figure BDA0002805063050000082
Substituting the formula (3), the formula (20) and the formula (21) to obtain the formula (18).
Selecting a new state:
z 1 ＝y 1 ＝s
Figure BDA0002805063050000083
Figure BDA0002805063050000084
z 4 ＝r
the transformation is demonstrated to be differential stratospheric as follows. Recording device
x＝[r V γ s] T
z＝[z 1 z 2 z 3 z 4 ] T
The transformation is derived, and is available,
Figure BDA0002805063050000085
the determinant of the matrix to the right of the equal sign in equation (22) is
Figure BDA0002805063050000086
Indicating that the matrix is nonsingular, i.e. the transformation is differential stratospheric.
Therein dynamic state
Figure BDA0002805063050000087
Is neutral and stable.
And (4) designing an active disturbance rejection guidance law aiming at the range model.
For equation (17), record
Figure BDA0002805063050000088
Figure BDA0002805063050000089
Then range model equation (17) can be written as
Figure BDA00028050630500000810
For equation (25), an adaptive guidance law for active disturbance rejection is designed,
Figure BDA0002805063050000091
wherein, the initial value of the differential equation formula (26) is 0; y is 1 =s is obtained by integrating the kinetic equation (1), and therefore, this method is called a numerical prediction correction guidance method; s is(s) ref For the current location distance and the distance of the target location,
s ref ＝arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27)
wherein θ S ,φ S Is the longitude and latitude of the target point.
Figure BDA0002805063050000092
Obtained by a second-order tracking differentiator; l (L) 1 ,l 2 ,l 3 ,k d ,k p The parameters to be adjusted and the adjusting method are described in detail in monograph (Han Jingqing, active disturbance rejection control technique).
And (5) designing an active disturbance rejection guidance law aiming at the high derivative model.
For equation (18), record
U 2 ＝Lcosγcosσ (28)
Figure BDA0002805063050000093
The highly derivative model equation (18) can be written as
Figure BDA0002805063050000094
For equation (30), an active-disturbance-rejection adaptive guidance law is designed:
Figure BDA0002805063050000095
wherein the initial values of the differential equation formula (31) are allSelecting 0;
Figure BDA0002805063050000096
given by equation (9) of step (2), ->
Figure BDA0002805063050000097
Given by a first order tracking differentiator;
Figure BDA0002805063050000098
Is given by a state measurement and a dynamics equation formula (1); p is p 1 ,p 2 K is a parameter to be adjusted, and the adjusting method is described in detail in monograph (Han Jingqing, active disturbance rejection control technique).
Step (6) designing a guidance law,
Figure BDA0002805063050000099
equation (32) is derived by the following method. Equation (32) can be obtained by combining equation (23) and equation (28) and solving the least squares solution.
The invention is not described in detail in the field of technical personnel common knowledge.

Claims (1)

1. An advanced numerical prediction correction guidance method based on self-adaptive control is characterized by comprising the following steps:
(1) Establishing a spacecraft reentry guidance dynamics dimensionless equation considering earth rotation;
(2) Converting the thermal rate limit, the load limit and the dynamic pressure limit of the aircraft into altitude reference values;
(3) Performing differential stratospheric transformation on the longitudinal dynamics state of the aircraft to obtain a model taking the range and the high derivative as states;
(4) Designing an active disturbance rejection guidance law aiming at a course model;
(5) Designing an active disturbance rejection guidance law aiming at a high derivative model;
(6) Designing a guidance law;
the equation established in the step (1) is as follows:
Figure FDA0004037886500000011
Figure FDA0004037886500000012
Figure FDA0004037886500000013
Figure FDA0004037886500000014
Figure FDA0004037886500000015
Figure FDA0004037886500000016
Figure FDA0004037886500000017
wherein r represents the earth center distance, θ and φ represent longitude and latitude respectively, V represents the earth relative velocity, γ and ψ represent the flight path angle and heading angle respectively, and s represents the predicted course; sigma represents roll angle, which is the guidance input; omega represents the earth rotation angular velocity; l and D represent aerodynamic lift and drag respectively,
Figure FDA0004037886500000018
Figure FDA0004037886500000019
R 0 represents the earth radius, S ref And m represents the reference area and mass, respectively, of the aircraft, C L And C D Respectively, the lift and drag coefficients, ρ represents the atmospheric density,
Figure FDA0004037886500000021
ρ 0 is at a reference height h 0 Atmospheric density at beta r ＜0，
h＝r-R 0 (5)
Typical path constraints in atmospheric flight considered in spacecraft reentry include peak heat rates
Figure FDA0004037886500000022
Load a, and dynamic pressure->
Figure FDA0004037886500000023
The expressions are respectively: />
Peak heat rate:
Figure FDA0004037886500000024
load:
Figure FDA0004037886500000025
dynamic pressure:
Figure FDA0004037886500000026
wherein k is Q Is a known constant;
Figure FDA0004037886500000027
a max and->
Figure FDA0004037886500000028
The limits of heat rate, load and dynamic pressure are shown, respectively;
the conversion result of the step (2) is as follows:
Figure FDA0004037886500000029
wherein:
sinγ ref ＝max{sinγ,W 1 ,W 2 ,W 3 } (10)
Figure FDA00040378865000000210
Figure FDA00040378865000000211
Figure FDA00040378865000000212
wherein T represents a guidance period;
the model obtained in the step (3) is as follows:
Figure FDA00040378865000000213
Figure FDA00040378865000000214
wherein,,
y 1 ＝s， (19)
Figure FDA0004037886500000031
the specific process of the step (4) is as follows:
Figure FDA0004037886500000032
Figure FDA0004037886500000033
the range model formula is written as
Figure FDA0004037886500000034
For equation (25), an adaptive guidance law for active disturbance rejection is designed,
Figure FDA0004037886500000035
Figure FDA0004037886500000036
Figure FDA0004037886500000037
Figure FDA0004037886500000038
wherein, the initial value of the differential equation formula (26) is 0; y is 1 =s is obtained by integrating the kinetic formula (1); s is(s) ref For the distance of the current position and the distance of the target position
s ref ＝arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27)
Wherein θ S ,φ S Is the longitude and latitude of the target point,
Figure FDA0004037886500000039
obtained by a second-order tracking differentiator; l (L) 1 ,l 2 ,l 3 ,k d ,k p Is a parameter to be adjusted;
the specific process of the step (5) is as follows:
recording U 2 ＝Lcosγcosσ (28)
Figure FDA00040378865000000310
The high derivative model equation (18) is written as
Figure FDA00040378865000000311
For equation (30), an active-disturbance-rejection adaptive guidance law is designed:
Figure FDA00040378865000000312
Figure FDA00040378865000000313
Figure FDA00040378865000000314
wherein, the initial value of the differential equation formula (31) is 0;
Figure FDA00040378865000000315
given by equation (9) of step (2), ->
Figure FDA00040378865000000316
Given by a first order tracking differentiator;
Figure FDA0004037886500000041
Is given by a state measurement and a dynamics equation formula (1); p is p 1 ,p 2 K is a parameter to be adjusted;
the guidance law designed in the step (6) is specifically as follows:
Figure FDA0004037886500000042
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