CN115657480A - Optimal sliding mode guidance law construction method based on observer compensation - Google Patents

Optimal sliding mode guidance law construction method based on observer compensation Download PDF

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CN115657480A
CN115657480A CN202211313208.XA CN202211313208A CN115657480A CN 115657480 A CN115657480 A CN 115657480A CN 202211313208 A CN202211313208 A CN 202211313208A CN 115657480 A CN115657480 A CN 115657480A
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aircraft
guidance law
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王玥
李瀚宇
刘劲涛
侯婷婷
李响
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Beijing Institute of Technology BIT
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Abstract

The invention discloses an optimal sliding mode guidance law construction method based on observer compensation, relates to the technical field of aircraft guidance, has strong anti-interference capability and good guidance effect, and can perform optimal guidance under angle and precision constraints aiming at an aircraft-target relative motion model in a three-dimensional space. The technical scheme of the invention comprises the following steps: step 1: establishing an aircraft-target relative motion model in a three-dimensional space; step 2: correcting the deviation of the optimal guidance law caused by error interference through the sliding mode variable structure guidance law; and step 3: and constructing an extended state observer to observe the target maneuver and accurately compensate the guidance law.

Description

Optimal sliding mode guidance law construction method based on observer compensation
Technical Field
The invention relates to the technical field of aircraft guidance, in particular to an optimal sliding mode guidance law construction method based on observer compensation.
Background
When facing a target hitting task in a complex environment, the aircraft needs to adopt a proper terminal guidance law to improve the guidance precision. According to the task scene and the requirement, the terminal guidance law with reasonable precision and strong anti-interference capability is designed.
Aiming at high-speed aircrafts such as reentry aircrafts and boosted gliding aircrafts, the aircrafts are generally required to attack targets vertically and enter into and convert the targets into the design problem of terminal guidance law with angle constraint, and currently, related theoretical methods are many and comprise proportion guidance law with bias terms, optimal guidance law and the like.
In an ideal state, the optimal guidance law can be used for obtaining the optimal guidance method with the optimal hit precision and the minimum energy consumption, but uncertain interference which cannot be completely eliminated exists in the guidance process, target maneuvering can also influence the guidance result, and the optimal guidance law can possibly generate larger guidance errors. At present, an improvement method aiming at the optimal guidance law is usually to add a sliding mode variable structure term for correction, but most theoretical methods are researched based on aircraft motion in a two-dimensional plane and are not expanded into a three-dimensional space.
Therefore, a guidance law optimization construction method aiming at the relative motion of the three-dimensional space vehicle target is lacked at present.
Disclosure of Invention
In view of the above, the invention provides an optimal sliding mode guidance law construction method based on observer compensation, which has strong anti-interference capability and good guidance effect and can perform optimal guidance under angle and precision constraints for an aircraft-target relative motion model in a three-dimensional space.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
step 1: establishing an aircraft-target relative motion model in a three-dimensional space;
and 2, step: correcting the deviation of the optimal guidance law caused by error interference through the sliding mode variable structure guidance law;
and 3, step 3: and constructing an extended state observer to observe the target maneuver and accurately compensate the guidance law.
As a preferred embodiment of the present invention, step 1 specifically comprises:
the established aircraft-target relative motion model in the three-dimensional space specifically comprises the following steps:
Figure BDA0003907897990000021
in which the aircraft-target relative movement in three-dimensional space is decomposed into a dive plane x s Oy s And a turning plane x s Oz s Motion in two-dimensional planes; the elevation angle of the aircraft in the plane of dive is lambda D ', the reference line OT' turns counterclockwise onto the aircraft-target line, λ D The 'is negative, and the' is negative,
Figure BDA0003907897990000022
is λ D The second derivative of the' is the derivative,
Figure BDA0003907897990000023
is λ D The first derivative of'; the azimuth angle of the sight line of the aircraft in the turning plane is lambda T ，
Figure BDA0003907897990000024
Is λ T The second derivative of (a) is,
Figure BDA0003907897990000025
is λ T The first derivative of (a); r mt Is the aircraft-to-target distance,
Figure BDA0003907897990000026
is R mt The first derivative of (a); v. of 1 In the form of a vector of the speed of the aircraft,
Figure BDA0003907897990000027
is v is 1 The first derivative of (a); v. of 2 Is the velocity vector of the target and is,
Figure BDA0003907897990000028
is v is 2 The first derivative of (a); aircraft velocity vector
Figure BDA0003907897990000029
The component in the plane of dive is
Figure BDA00039078979900000210
Velocity vector
Figure BDA00039078979900000211
Has a high and low angle of gamma D Azimuthal angle of gamma T ；
As a preferred embodiment of the present invention, step 2 specifically includes:
will be provided with
Figure BDA00039078979900000212
Is introduced into the aircraft-target relative motion model
Figure BDA00039078979900000213
Respectively deriving in a diving plane and a turning plane to obtain a guidance law instruction:
Figure BDA00039078979900000214
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00039078979900000215
for the in-plane control commands of nose-down,
Figure BDA00039078979900000216
for control instructions in the plane of the turn, ∈ 1 、ε 2 Gain, k, of the switching term in the plane of dive and in the plane of turn 1 And k 2 Respectively are the approaching law coefficients of a diving plane and a turning plane;
Figure BDA0003907897990000031
λ Topt is λ T The optimal trajectory of (a); lambda Dopt Is λ D The optimal trajectory of.
As a preferred embodiment of the present invention, step 3 specifically comprises:
respectively constructing extended state observers in a diving plane and a turning plane according to the aircraft-target relative motion model;
wherein the detector for the expanded state of the turning plane is:
Figure BDA0003907897990000032
wherein e is 1 An estimated error of the dilated state detector for the turning plane; z is a radical of 1T 、z 2T Output of the extended state detector for the plane of the turn, z 2T Is an estimate of the uncertainty therein,
Figure BDA0003907897990000033
is z 1T 、z 2T The first derivative of (a); beta is a beta 1T 、β 2T The gain of the detector for the expanded state of the turning plane; a is a T ,δ T Parameters of the expansion state detector of the turning plane; fun (e) 1 ,a T ,δ T ) To relate to e 1 ,a T ,δ T A non-linear function of (d);
wherein the dive plane's expansion state detector is:
Figure BDA0003907897990000034
wherein e is 2 An estimated error of the extended state detector for the dive plane; z is a radical of 1D 、z 2D Output of the extended state detector for the plane of dive, z 2D Is an estimate of the uncertainty term therein,
Figure BDA0003907897990000035
is z 1D 、z 2D The first derivative of (a); beta is a beta 1D 、β 2D The gain of the detector for the extended state of the dive plane; a is D ,δ D Parameters of the extended state detector for the dive plane; fun (e) 1 ,a D ,δ D ) To relate to e 1 ,a D ,δ D A non-linear function of (a);
and (3) accurately compensating the guidance law based on the constructed extended state observer to obtain an optimal sliding mode guidance law control instruction based on ESO:
Figure BDA0003907897990000036
it e 1 And e 2 Estimation errors of extended state observers in the plane of dive and turn, respectively, z 2D For the output of a nose-down in-plane extended state observer, z 2T Is the output of the extended state observer in the turning plane.
Has the advantages that:
the invention provides an optimal sliding mode guidance law based on an extended state observer for a slow-speed moving target, which is characterized in that the optimal sliding mode guidance law is designed on the basis of the optimal guidance law by establishing an aircraft-target relative motion model in a three-dimensional space, the extended state observer is constructed to observe the movement of the target, and the guidance law is accurately compensated. The method has strong anti-interference capability and good guidance effect, and can realize optimal guidance under angle and precision constraints aiming at maneuvering targets.
Drawings
FIG. 1 is a diagram of the spatial relationship of an aircraft to a target;
fig. 2 is a structural diagram of an optimal guidance law based on observer compensation.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides an optimal sliding mode guidance law construction method based on an extended state observer and aiming at a slow moving target, which comprises the following steps:
step 1: and establishing an aircraft-target relative motion model in the three-dimensional space. Establishing a relative motion model of the aircraft and the marine maneuvering target, and decomposing the aircraft-target relative motion in the three-dimensional space into a diving plane x for simplifying the research s Oy s And a turning plane x s Oz s Motion in two-dimensional planes. Aircraft and target in a plane x of dive s Oy s The relative motion relationship is shown in figure 1.
In FIG. 1, λ D 'is the view angle of the aircraft in the plane of dive, and the reference line OT' turns to the aircraft-target connecting line along the counterclockwise direction, lambda D ' is negative. Aircraft velocity vector
Figure BDA0003907897990000041
The component in the plane of dive is
Figure BDA0003907897990000042
Figure BDA0003907897990000043
Has an azimuth angle of gamma D In the figure gamma D <0，
Figure BDA0003907897990000044
Angle eta with respect to the aircraft-target line D Eta in the figure D >0. Velocity vector of target
Figure BDA0003907897990000045
Component in the plane of dive
Figure BDA0003907897990000046
At an angle-lambda to the aircraft-target line D ', the geometrical relationship in the figure can be known
η D ＝γ D -λ D ′ (1)
Figure BDA0003907897990000051
The simultaneous derivation of the time for both the left and right sides of the second equation in equation (2) can be obtained
Figure BDA0003907897990000052
The equation in the formula (2) can be found as cos η D And sin eta D Is substituted into the formula (3) to obtain
Figure BDA0003907897990000053
Approximately regarding the motion in the plane of the aircraft diving within the time delta t as uniform-speed circular motion
Figure BDA0003907897990000054
It can be simplified to:
Figure BDA0003907897990000055
in the same way, in the plane of turning
η T ＝γ T -λ T (6)
Figure BDA0003907897990000056
Suppose that the included angles between the aircraft velocity vector and the target velocity vector and the plane of dive are small angles v T And v D All can be approximated as v 1 ，v M And v N Is approximately v 2 Then the aircraft-target relative motion equation is
Figure BDA0003907897990000057
In which the aircraft-target relative movement in three-dimensional space is decomposed into a dive plane x s Oy s And a turning plane x s Oz s Motion in two-dimensional planes; the elevation angle of the aircraft in the plane of dive is lambda D ', the reference line OT' turns anticlockwise on the aircraft-target line, λ D The 'is negative, and the' is negative,
Figure BDA0003907897990000058
is λ D The second derivative of the' is the derivative,
Figure BDA0003907897990000059
is λ D The first derivative of'; the azimuth angle of the sight of the aircraft in the turning plane is lambda T ，
Figure BDA00039078979900000510
Is λ T The second derivative of (a) is,
Figure BDA00039078979900000511
is λ T The first derivative of (a); r mt Is the aircraft-to-target distance,
Figure BDA00039078979900000512
is R mt The first derivative of (a); v. of 1 In the form of a vector of the speed of the aircraft,
Figure BDA00039078979900000513
is v is 1 The first derivative of (a); v. of 2 Is a vector of the velocity of the target,
Figure BDA00039078979900000514
is v 2 The first derivative of (a); aircraft velocity vector
Figure BDA00039078979900000515
The component in the plane of dive is
Figure BDA00039078979900000516
Velocity vector
Figure BDA00039078979900000517
Has a high and low angle of gamma D Azimuthal angle of gamma T ；。
The aircraft-target distance R can be known according to the relative position relation of the aircraft and the target mt Comprises the following steps:
Figure BDA0003907897990000061
wherein (X) t 、Y t 、Z t ) Is the coordinate of the target, (X) m 、Y m 、Z m ) As coordinates of the aircraft
Angle of view λ in plane of dive D ' is
Figure BDA0003907897990000062
High and low angle of sight lambda D Is composed of
Figure BDA0003907897990000063
Azimuth lambda of line of sight T
Figure BDA0003907897990000064
Angle of line of sight lambda D ' and line of sight azimuth λ T The rate of change of the line-of-sight angle derived from the time t is
Figure BDA0003907897990000065
Figure BDA0003907897990000066
Step 2: and correcting the deviation of the optimal guidance law caused by error interference through the sliding mode variable structure guidance law.
Will be provided with
Figure BDA0003907897990000067
The model of the relative motion between the aircraft and the target established in the step 1 is substituted to obtain
Figure BDA0003907897990000068
FIG. 2 is a block diagram of an optimal sliding mode guidance law based on observation period compensation. And respectively deriving guidance law instructions in a plane of diving and a plane of turning.
The derivation process in the plane of dive is as follows:
since the aircraft terminal guidance phase has a greater velocity, it is assumed that
Figure BDA0003907897990000069
And order
Figure BDA00039078979900000610
Figure BDA00039078979900000611
Can obtain
Figure BDA00039078979900000612
By u opt And x opt To represent the control signals and optimal trajectories of the optimal guidance law, then
Figure BDA0003907897990000071
Let x e ＝x-x opt ，u e ＝u-u opt Then, then
Figure BDA0003907897990000072
The form of the selection of the approximation law is
Figure BDA0003907897990000073
In the formula: ε -switching term gain, ε >0; k is the approach law coefficient, and k is greater than 0.
Taking the Lyapunov function
Figure BDA0003907897990000074
The derivation is carried out on the above formula
Figure BDA0003907897990000075
During flight of the aircraft, T g >0, satisfy
Figure BDA0003907897990000076
The Lyapunov function is strictly negative, and the system is asymptotically stable. By adopting the approach law, as the aircraft gradually approaches the target, T g The rho is gradually reduced, the speed approaching the sliding mode is accelerated, and the condition that the speed is increased can be ensured
Figure BDA0003907897990000077
The divergence is avoided, and the hit precision is improved.
For S = x e Derived from both sides
Figure BDA0003907897990000078
Then
Figure BDA0003907897990000079
X is to be e ＝x-x opt Can be brought into the above formula
Figure BDA00039078979900000710
Because the switching function exists in the formula, the function value jumps in a short time, the control quantity of the system needs a certain time to reach the required quantity and shakes, the sign function is replaced by the saturation function sat (x), and the quasi-sliding mode control is realized, wherein the expression is as follows:
Figure BDA0003907897990000081
wherein delta is a boundary layer, the outside of the boundary layer is standard sliding mode control, and the inside of the boundary layer is continuous state feedback control. To obtain finally
Figure BDA0003907897990000082
Order to
Figure BDA0003907897990000083
Derivation method in same plane of dive can obtain guidance equation in turning plane
Figure BDA0003907897990000084
Then the
Figure BDA0003907897990000085
Therefore, the control instruction of the optimal sliding mode guidance law is deduced to be as follows:
Figure BDA0003907897990000086
wherein epsilon 1 、ε 2 Gain, k, of the switching term in the plane of dive and in the plane of turn 1 And k 2 Respectively are the approaching law coefficients of a diving plane and a turning plane;
Figure BDA0003907897990000087
λ Topt is λ T The optimal trajectory of (a); lambda [ alpha ] Dopt Is λ D ' is determined.
And 3, step 3: and constructing an extended state observer to observe the target maneuver and accurately compensate the guidance law.
Wherein the detector for the expanded state of the turning plane is:
Figure BDA0003907897990000088
wherein e is 1 An estimation error of the dilated state detector for the turning plane; z is a radical of 1T 、z 2T Output of the extended state detector for the plane of the turn, z 2T Is an estimate of the uncertainty therein,
Figure BDA0003907897990000089
is z 1T 、z 2T The first derivative of (a); beta is a 1T 、β 2T The gain of the detector for the expanded state of the turning plane; a is T ,δ T Parameters of the expansion state detector of the turning plane; fun (e) 1 ,a T ,δ T ) To relate to e 1 ,a T ,δ T A non-linear function of (a);
wherein the dive plane's expansion state detector is:
Figure BDA0003907897990000091
wherein e is 2 An estimated error of the extended state detector for the dive plane; z is a radical of 1D 、z 2D Output of the extended state detector for the plane of dive, z 2D Is an estimate of the uncertainty therein,
Figure BDA0003907897990000092
is z 1D 、z 2D The first derivative of (a); beta is a 1D 、β 2D The gain of the extended state detector for the nose down plane; a is D ,δ D Parameters of the extended state detector for the dive plane; fun (e) 1 ,a D ,δ D ) To relate to e 1 ,a D ,δ D A non-linear function of (a);
the nonlinear function fun (. Cndot.) is defined as
Figure BDA0003907897990000093
Figure BDA0003907897990000094
e takes the value of e 1 、e 2 (ii) a a takes the value of a D 、a T (ii) a The value of delta being delta D 、δ T 。
Adjusting parameter beta 1T 、β 2T 、β 1D 、β 2D A, δ causing the observer to converge, thereby estimating the value of the disturbance;
Figure BDA0003907897990000095
wherein z is 1 Value of z 1D 、z 1T ；z 2 Value of z 2D 、z 2T (ii) a d (t) is an uncertain item, d (t) is taken as d D (t)、d T (t) are uncertainties of the dive plane and the turn plane, respectively, and satisfy
Figure BDA0003907897990000096
L is a constant greater than 0, control input
Figure BDA0003907897990000097
It is possible to measure the amount of,
Figure BDA0003907897990000098
is defined as an absolute continuous function in the time domain t is more than or equal to 0; t → T where T is the upper limit value of the time domain.
And (3) accurately compensating the guidance law based on the constructed extended state observer to obtain an optimal sliding mode guidance law control instruction based on ESO:
Figure BDA0003907897990000099
wherein e 1 And e 2 Estimation errors of extended state observers in the plane of dive and turn, respectively, z 2D For the output of the extended state observer in the plane of dive, z 2T Is the output of the extended state observer in the turning plane.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. An optimal sliding mode guidance law construction method based on observer compensation is characterized by comprising the following steps:
step 1: establishing an aircraft-target relative motion model in a three-dimensional space;
step 2: correcting the deviation of the optimal guidance law caused by error interference through the sliding mode variable structure guidance law;
and 3, step 3: and constructing an extended state observer to observe the target maneuver and accurately compensate the guidance law.
2. The optimal sliding-mode guidance law method based on observer compensation according to claim 1, wherein the step 1 specifically comprises:
the established aircraft-target relative motion model in the three-dimensional space specifically comprises the following steps:
Figure FDA0003907897980000011
in which the aircraft-target relative motion in three-dimensional space is decomposed into a dive plane x s Oy s And a turning plane x s Oz s Motion in two-dimensional planes; aircraft in a bowThe elevation angle of the line of sight in the plane of attack is lambda D ′，
Figure FDA0003907897980000012
Is λ D The second derivative of the' is the sum of,
Figure FDA0003907897980000013
is λ D The first derivative of'; the azimuth angle of the sight line of the aircraft in the turning plane is lambda T ，
Figure FDA0003907897980000014
Is λ T The second derivative of (a) is,
Figure FDA0003907897980000015
is λ T The first derivative of (a); r is mt Is the aircraft-to-target distance,
Figure FDA0003907897980000016
is R mt The first derivative of (a); v. of 1 In the form of a vector of the speed of the aircraft,
Figure FDA0003907897980000017
is v is 1 The first derivative of (a); v. of 2 Is the velocity vector of the target and is,
Figure FDA0003907897980000018
is v is 2 The first derivative of (a); aircraft velocity vector
Figure FDA0003907897980000019
The component in the plane of dive is
Figure FDA00039078979800000110
Velocity vector
Figure FDA00039078979800000111
Has a high and low angle of gamma D Azimuth angle of gamma T ；
Figure FDA00039078979800000112
Is gamma D The first derivative of (a) is,
Figure FDA00039078979800000113
is gamma T The first derivative of (a).
3. The optimal sliding-mode guidance law method based on observer compensation according to claim 2, wherein the step 2 specifically comprises:
will be provided with
Figure FDA00039078979800000114
Is introduced into the aircraft-target relative motion model
Figure FDA00039078979800000115
Respectively deriving in a diving plane and a turning plane to obtain a guidance law instruction:
Figure FDA0003907897980000021
wherein the content of the first and second substances,
Figure FDA0003907897980000022
for in-plane control commands for nose-down,
Figure FDA0003907897980000023
for control instructions in the plane of the turn, ∈ 1 、ε 2 Gain of switching term, k, in the plane of dive and in the plane of turn, respectively 1 And k 2 Respectively are the approaching law coefficients of a diving plane and a turning plane;
Figure FDA0003907897980000024
λ Topt is λ T The optimal trajectory of (a); lambda Dopt Is a λ D ' is the optimal trajectory; sat () is a saturation function.
4. The optimal sliding-mode guidance law method based on observer compensation according to claim 3, wherein the step 3 specifically comprises:
respectively constructing extended state observers in a diving plane and a turning plane according to the aircraft-target relative motion model;
wherein the detector for the expanded state of the turning plane is:
Figure FDA0003907897980000025
wherein e is 1 An estimated error of the dilated state detector for the turning plane; z is a radical of formula 1T 、z 2T Output of the extended state detector for the plane of the turn, z 2T Is an estimate of the uncertainty therein,
Figure FDA0003907897980000026
is z 1T 、z 2T The first derivative of (a); beta is a beta 1T 、β 2T The gain of the detector for the expanded state of the turning plane; a is T ,δ T Parameters of the expansion state detector of the turning plane; fun (e) 1 ,a T ,δ T ) Is in relation to e 1 ,a T ,δ T A non-linear function of (d);
wherein the dive plane's expansion state detector is:
Figure FDA0003907897980000027
wherein e is 2 An estimated error of the extended state detector for the dive plane; z is a radical of 1D 、z 2D Output of the extended state detector for the plane of dive, z 2D For estimation of uncertainty thereinThe value is evaluated and the value is calculated,
Figure FDA0003907897980000028
is z 1D 、z 2D The first derivative of (a); beta is a beta 1D 、β 2D The gain of the detector for the extended state of the dive plane; a is a D ,δ D Parameters of the detector for the extended state of the dive plane; fun (e) 1 ,a D ,δ D ) Is in relation to e 1 ,a D ,δ D A non-linear function of (a);
and (3) accurately compensating the guidance law based on the constructed extended state observer to obtain the control instruction of the optimal sliding mode guidance law based on the extended state detector, wherein the control instruction comprises the following steps:
Figure FDA0003907897980000031
wherein e 1 And e 2 The estimated error of the extended state observer in the plane of dive and turn, z 2D For the output of a nose-down in-plane extended state observer, z 2T Is the output of the extended state observer in the turning plane.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117348402A (en) * 2023-10-26 2024-01-05 北京航空航天大学 Hypersonic aircraft three-dimensional guidance method based on interference utilization technology

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117348402A (en) * 2023-10-26 2024-01-05 北京航空航天大学 Hypersonic aircraft three-dimensional guidance method based on interference utilization technology

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