CN110737279B - Longitudinal swing amplitude control method for air-drop hanger of unmanned helicopter - Google Patents

Longitudinal swing amplitude control method for air-drop hanger of unmanned helicopter Download PDF

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CN110737279B
CN110737279B CN201911028975.4A CN201911028975A CN110737279B CN 110737279 B CN110737279 B CN 110737279B CN 201911028975 A CN201911028975 A CN 201911028975A CN 110737279 B CN110737279 B CN 110737279B
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unmanned helicopter
air
mass
drop
height
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CN110737279A (en
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王薇
孙梦超
钱瑞
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Beihang University
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models

Abstract

The invention discloses a longitudinal swing amplitude control method for an air-drop hanger of an unmanned helicopter, which comprises self-adaptive estimation of unknown parameters before and after air-drop and a control method for the swing amplitude of the unmanned helicopter after air-drop hanger based on a BLF (binary noise filter) method. By the technical scheme, accurate control of the swing amplitude in the height direction can be realized under the condition that the mass of the helicopter suddenly changes after air-drop, the safety of the air-drop operation of the unmanned helicopter is improved, the possibility is provided for the air-drop of the unmanned helicopter in low altitude and complex environment, and a feasible control scheme is provided for other control system application scenes with parameter sudden changes. The invention realizes accurate quantitative control on the swing amplitude in the stabilizing process, and has the advantages of accurate parameter estimation and better control on the longitudinal swing amplitude.

Description

Longitudinal swing amplitude control method for air-drop hanger of unmanned helicopter
Technical Field
The invention belongs to the technical field of automatic control of unmanned planes, and particularly relates to a longitudinal swing amplitude control method for an air-drop hanger of an unmanned helicopter.
Background
Helicopters have been the focus of research because of their ability to take off and land vertically, and carry heavy cargo. Helicopter hangar systems have attracted attention since the 60's of the 20 th century because of their successful use in the vietnam war. The application scene of the helicopter is wider due to the additional hanging transportation mode, and the helicopter hanging is applied to aspects such as rescue, monitoring, aerial geophysical prospecting, war material conveying and the like.
When the helicopter carries out an air-drop hanging task, particularly, when the air-drop is used for hanging a load with larger mass relative to the helicopter, the helicopter inevitably swings in the height direction due to the sudden change of the mass. However, when the helicopter performs the airdrop task at low altitude, especially when the airdrop task is performed under a relatively complex terrain condition such as a mountain or a forest, the safety of the helicopter is seriously affected by the excessive longitudinal swing amplitude of the helicopter after the airdrop. In addition, when the helicopter hanging system executes the tasks of taking off, landing and the like, the problem of sudden change of mass also exists.
The traditional control method can only stabilize the helicopter to a height as soon as possible after air drop, but the longitudinal swing is difficult to avoid in the process of controlling the stability of the helicopter, and the swing amplitude is difficult to accurately and quantitatively control. Therefore, designing a proper control strategy and quantitatively controlling the longitudinal swing amplitude of the helicopter hanging system when the quality mutation problem exists is a very important subject.
At present, the research on helicopter fixed height control at home and abroad is not few, but only the fixed height control of a helicopter body is researched, and the research on the problem of mass mutation of a model of helicopter air-drop suspension, particularly the problem of air-drop suspension, is less.
Disclosure of Invention
The invention aims to solve the problem of accurate control of the swing amplitude in the height direction after the air-drop of a helicopter, the traditional control method only enables the helicopter to be stabilized to a height as soon as possible after the air-drop, however, the longitudinal swing in the process of controlling the stability of the helicopter is difficult to avoid, and the accurate and quantitative control of the swing amplitude in the process of stabilizing the helicopter is difficult to realize.
The invention provides a longitudinal swing amplitude control method for an unmanned helicopter aerial drop hanger, which is characterized in that a Barrier Lyapunov Function is adopted to quantitatively control the swing amplitude, so that guarantee is provided for the unmanned helicopter to safely execute an aerial drop task, and the specific technical scheme of the invention is as follows:
a longitudinal swing amplitude control method for an unmanned helicopter aerial drop hanger is characterized by comprising the following steps:
s1: establishing a 6-degree-of-freedom nonlinear system model of the unmanned helicopter system, and further considering an unmanned helicopter air-drop hanging system with a quality mutation problem to obtain a height subsystem model of the unmanned helicopter air-drop hanging system;
a6-degree-of-freedom unmanned helicopter system model established by a Newton-Euler equation:
Figure BDA0002249544260000021
Figure BDA0002249544260000022
Figure BDA0002249544260000023
Figure BDA0002249544260000024
wherein the content of the first and second substances,
Figure BDA0002249544260000025
is the position coordinate of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA0002249544260000026
is the derivative of the coordinates of the position of the center of mass of the unmanned helicopter,
Figure BDA0002249544260000027
the speed of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA0002249544260000028
is the derivative of the velocity of the center of mass of the unmanned helicopter; m is the mass of the unmanned helicopter;
Figure BDA0002249544260000029
g is the acceleration of gravity;
Figure BDA00022495442600000210
for the attitude of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA00022495442600000211
the pitch angle is the attitude of the unmanned helicopter, theta is the roll angle of the attitude of the unmanned helicopter, and psi is the yaw angle of the attitude of the unmanned helicopter; rt(gamma) is a rotation matrix transformed from a body coordinate system to a ground coordinate system, is a 3 x 3 matrix related to the attitude gamma of the unmanned helicopter,
Figure BDA00022495442600000212
is RtThe derivative of (gamma) is determined,
Figure BDA00022495442600000213
a rotation matrix transformed from a body coordinate system to a ground coordinate system;
Figure BDA00022495442600000214
is the angular velocity in the coordinate system of the body,
Figure BDA00022495442600000215
is the derivative of ω, representing angular acceleration; s (-) is a skew-symmetric matrix,
Figure BDA00022495442600000216
j is a rotational inertia matrix, IxxIs the moment of inertia about the x-axis in the coordinate system of the body, IyyIs the moment of inertia about the y-axis in the coordinate system of the body, IzzIs the moment of inertia about the z-axis in the coordinate system of the body, IxzIs the product of inertia about the x-axis and z-axis in the body coordinate system, Q is the control moment,
the simplified height subsystem is:
Figure BDA0002249544260000031
wherein, PzIs the height of the center of mass of the unmanned helicopter,
Figure BDA0002249544260000032
is the derivative of the height of the center of mass, V, of the unmanned helicopterzIs the longitudinal speed of the unmanned helicopter,
Figure BDA0002249544260000033
the derivative of the longitudinal speed of the unmanned helicopter represents the acceleration in the height direction; m isiThe mass of the unmanned helicopter hanging system is the mass of the unmanned helicopter hanging system, sudden change can occur before and after air drop hanging, and i is 1 and 2, wherein i is 1 and represents the mass of the unmanned helicopter hanging system before air drop, and i is 2 and represents the mass of the unmanned helicopter hanging system after air drop; t ismThe lift force generated by the main rotor of the unmanned helicopter;
s2: designing a self-adaptive height control algorithm of the hanging system of the unmanned helicopter, designing a self-adaptive law, estimating the hanging quality of the unmanned helicopter unknown before and after air drop, and controlling the height tracking of the unmanned helicopter; designing a height swing amplitude control method after the unmanned helicopter is air-dropped and hung based on a Barrier Lyapunov Function method, introducing parameters of an upper bound of the swing amplitude of the unmanned helicopter, realizing the pre-definition of the upper bound of the swing amplitude, and integrating the upper bound of the swing amplitude into an adaptive control law;
the unmanned helicopter hanging system is designed to carry out air drop in an air hovering scene, only the longitudinal characteristic of the unmanned helicopter hanging system is considered, and the pitch angle and the roll angle of the unmanned helicopter are both close to 0, so cos phi cos theta is approximately equal to 1;
the self-adaptive control law of the unmanned helicopter is designed by adopting a self-adaptive backstepping method:
s21: height error
Figure BDA0002249544260000034
And velocity error in the vertical direction
Figure BDA0002249544260000035
Comprises the following steps:
Figure BDA0002249544260000036
wherein, VzdRepresenting virtual control signals, zrFor a set height reference signal the height of the sensor,
to pair
Figure BDA0002249544260000037
And (3) obtaining a height tracking error system by derivation:
Figure BDA0002249544260000038
Figure BDA0002249544260000039
for a derivative of the set altitude reference signal, representing the desired altitude direction velocity,
designing virtual control quantities
Figure BDA00022495442600000310
k1Is a positive constant, and the virtual control is brought into the height error system to obtain
Figure BDA00022495442600000311
S22: computing
Figure BDA00022495442600000312
Derivative of (2)
Figure BDA00022495442600000313
Obtaining a vertical direction tracking error dynamic system equation:
Figure BDA0002249544260000041
defining two estimation errors as
Figure BDA0002249544260000042
Figure BDA0002249544260000043
Figure BDA0002249544260000044
Mass m of suspension system of unmanned helicopteriRespectively estimating the mass m of the suspension system of the unmanned helicopter before air drop by an adaptive updating law1And the mass m of the suspension system of the unmanned helicopter after air drop2，
Figure BDA0002249544260000045
Is an estimation error, and the airdrop time is recorded as t1＞0，
Figure BDA0002249544260000046
And 0 < b0≤bi≤bmax1,2, wherein b isiThe values of b before and after the air drop are shown, i-1 represents the value of b before the air drop, i-2 represents the value of b after the air drop, and b0Is b isiUnder (2) isBoundary, bmaxIs b isiThe control law is as follows:
Figure BDA0002249544260000047
wherein, the parameter k is designed based on the BLF methodzIs an upper bound limiting the amplitude of the height swing, is a positive constant, k2For the designed control coefficient, a positive constant,
Figure BDA0002249544260000048
for the virtual control signal VzdThe adaptive law of the parameters is:
Figure BDA0002249544260000049
wherein r, l0Is a constant that is positive in number,
Figure BDA00022495442600000410
for mass m of suspension system of unmanned helicopteriThe update law of the estimate of (2).
The invention has the beneficial effects that:
1. the problem of accurate control of the swing amplitude in the height direction after the air-drop of the helicopter is solved, the safety of the air-drop operation of the unmanned helicopter is improved, and the possibility of air-drop of the unmanned helicopter in low altitude and complex environments is provided.
2. The method provides a feasible control method solution for the application scene of the control system with parameter mutation, such as the autonomous take-off and landing process of helicopters with hanging loads, quadrotors and the like with system quality mutation, and ensures the control precision.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a block diagram of the flow of the method for controlling the longitudinal oscillation amplitude of an unmanned helicopter air drop hanger of the present invention;
FIG. 2 is a schematic aerial delivery view;
FIG. 3(a) is a control input for the airborne suspension of the helicopter of the present invention;
FIG. 3(b) is a control input for a PD control method using the same control parameters as the embodiment of the invention;
FIG. 4(a) is a graph showing the effect of height tracking of an aerial delivery hanger of a helicopter of the present invention;
FIG. 4(b) is a graph showing the effect of height tracking in a PD control method using the same control parameters as in the embodiment of the present invention;
fig. 5 is an estimation of an unknown parameter (quality) of a handover.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
According to the technical scheme, firstly, a 6-degree-of-freedom nonlinear system model of an unmanned helicopter system is established, and an unmanned helicopter air-drop hanging system with the quality mutation problem is further considered to obtain a height subsystem model of the unmanned helicopter air-drop hanging system; secondly, designing a self-adaptive height control algorithm of the unmanned helicopter hanging system, designing a self-adaptive law, estimating unknown hanging quality of the helicopter before and after air drop, and controlling height tracking of the unmanned helicopter; based on a Barrier Lyapunov Function (BLF) method, a height swing amplitude control method after the unmanned helicopter is airdropped and hung is designed, parameters of an upper bound of the swing amplitude of the unmanned helicopter are introduced, the upper bound of the swing amplitude is predefined, and the upper bound of the swing amplitude is integrated into an adaptive control law. Specifically, the longitudinal swing amplitude control method for the air-drop hanger of the unmanned helicopter is characterized by comprising the following steps of:
s1: establishing a 6-degree-of-freedom nonlinear system model of the unmanned helicopter system, and further considering an unmanned helicopter air-drop hanging system with a quality mutation problem to obtain a height subsystem model of the unmanned helicopter air-drop hanging system;
a6-degree-of-freedom unmanned helicopter system model established by a Newton-Euler equation:
Figure BDA0002249544260000051
Figure BDA0002249544260000052
Figure BDA0002249544260000061
Figure BDA0002249544260000062
wherein the content of the first and second substances,
Figure BDA0002249544260000063
is the position coordinate of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA0002249544260000064
is the derivative of the coordinates of the position of the center of mass of the unmanned helicopter,
Figure BDA0002249544260000065
the speed of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA0002249544260000066
is the derivative of the velocity of the center of mass of the unmanned helicopter; m is the mass of the unmanned helicopter;
Figure BDA0002249544260000067
g is the acceleration of gravity;
Figure BDA0002249544260000068
for the attitude of the unmanned helicopter in the terrestrial coordinate system,
Figure BDA0002249544260000069
the pitch angle is the attitude of the unmanned helicopter, theta is the roll angle of the attitude of the unmanned helicopter, and psi is the yaw angle of the attitude of the unmanned helicopter; rt(gamma) is a rotation matrix transformed from a body coordinate system to a ground coordinate system, is a 3 x 3 matrix related to the attitude gamma of the unmanned helicopter,
Figure BDA00022495442600000610
is RtThe derivative of (gamma) is determined,
Figure BDA00022495442600000611
a rotation matrix transformed from a body coordinate system to a ground coordinate system;
Figure BDA00022495442600000612
is the angular velocity in the coordinate system of the body,
Figure BDA00022495442600000613
is the derivative of ω, representing angular acceleration; s (·) is an oblique symmetric matrix, S (ω) J ω ═ ω × J ω;
Figure BDA00022495442600000614
j is a rotational inertia matrix, IxxIs the moment of inertia about the x-axis in the coordinate system of the body, IyyIs the moment of inertia about the y-axis in the coordinate system of the body, IzzIs the moment of inertia about the z-axis in the coordinate system of the body, IxzIs the product of inertia about the x-axis and z-axis in the body coordinate system, Q is the control moment,
the simplified height subsystem is:
Figure BDA00022495442600000615
wherein, PzIs the height of the center of mass of the unmanned helicopter,
Figure BDA00022495442600000616
is the derivative of the height of the center of mass, V, of the unmanned helicopterzIs the longitudinal speed of the unmanned helicopter,
Figure BDA00022495442600000617
the derivative of the longitudinal speed of the unmanned helicopter represents the acceleration in the height direction; m isiThe mass of the unmanned helicopter hanging system is the mass of the unmanned helicopter hanging system, sudden change can occur before and after air drop hanging, and i is 1 and 2, wherein i is 1 and represents the mass of the unmanned helicopter hanging system before air drop, and i is 2 and represents the mass of the unmanned helicopter hanging system after air drop; t ismThe lift force generated by the main rotor of the unmanned helicopter;
s2: designing a self-adaptive height control algorithm of the unmanned helicopter hanging system, designing a self-adaptive law, estimating unknown helicopter hanging quality before and after air drop, and controlling the height tracking of the unmanned helicopter; designing a height swing amplitude control method after the unmanned helicopter is air-dropped and hung based on a Barrier Lyapunov Function method, introducing parameters of an upper bound of the swing amplitude of the unmanned helicopter, realizing the pre-definition of the upper bound of the swing amplitude, and integrating the upper bound of the swing amplitude into an adaptive control law;
the method is characterized in that a helicopter hanging system is designed to carry out air drop in an air suspension scene, because the air drop in an unmanned helicopter suspension scene is considered, and only the longitudinal characteristic of the unmanned helicopter hanging system is considered, the pitch angle and the roll angle of the helicopter are both close to 0, so cos phi cos theta is approximately equal to 1;
the self-adaptive control law of the unmanned helicopter is designed by adopting a self-adaptive backstepping method:
s21: height error
Figure BDA0002249544260000071
And velocity error in the vertical direction
Figure BDA0002249544260000072
Comprises the following steps:
Figure BDA0002249544260000073
wherein, VzdRepresenting virtual control signals, zrFor a set height reference signal the height of the sensor,
to pair
Figure BDA0002249544260000074
And (3) obtaining a height tracking error system by derivation:
Figure BDA0002249544260000075
Figure BDA0002249544260000076
for a derivative of the set altitude reference signal, representing the desired altitude direction velocity,
designing virtual control quantities
Figure BDA0002249544260000077
k1Is a positive constant, and the virtual control is brought into the height error system to obtain
Figure BDA0002249544260000078
S22: computing
Figure BDA0002249544260000079
Derivative of (2)
Figure BDA00022495442600000710
Obtaining a vertical direction tracking error dynamic system equation:
Figure BDA00022495442600000711
because the quality of the unmanned helicopter model is unknown, a parameter self-adaptive law needs to be designed to estimate unknown parameters; the quality of the whole system can be changed before and after the suspension air-drop, so that the system is a switching system with unknown parameters changing; in addition, the quality of the system can be considered as a constant value in both stages before and after the air drop.
Defining two estimation errors as
Figure BDA00022495442600000712
Figure BDA00022495442600000713
Figure BDA00022495442600000714
Mass m of suspension system of unmanned helicopteriThe self-adaptive updating law respectively estimates the quality of the suspension system of the unmanned helicopter before and after air drop,
Figure BDA00022495442600000715
Figure BDA00022495442600000716
is an estimation error, and the airdrop time is recorded as t1＞0，
Figure BDA00022495442600000717
And 0 < b0≤bi≤bmax1,2, wherein b isiThe values of b before and after the air drop are shown, i-1 represents the value of b before the air drop, i-2 represents the value of b after the air drop, and b0Is b isiLower boundary of (b)maxIs b isiThe control law is as follows:
Figure BDA0002249544260000081
wherein, the parameter k is designed based on the BLF methodzIs an upper bound limiting the amplitude of the height swing, is a positive constant, k2For the designed control coefficient, a positive constant,
Figure BDA0002249544260000082
for the virtual control signal VzdThe adaptive law of the parameters is:
Figure BDA0002249544260000083
wherein r, l0Is a constant that is positive in number,
Figure BDA0002249544260000084
for mass m of suspension system of unmanned helicopteriThe update law of the estimate of (2).
The parameters limiting the amplitude of the longitudinal oscillations of the unmanned helicopter, designed on the basis of the Barrier Lyapunov Function method, have been integrated in the above steps into the control law of the design, where the stability of the system is analyzed,
selected Lyapunov function
Figure BDA0002249544260000085
i is 1,2, wherein L1Is a Lyapunov function before air-drop,
Figure BDA0002249544260000086
Estimated error of mass of suspension system for unmanned helicopter before head-off, L2Is a Lyapunov function after air-drop,
Figure BDA0002249544260000087
For the estimation error of the mass of the hanging system of the unmanned helicopter after the head is empty,
for an arbitrary positive number a, if the initial value s (0) of the state quantity s satisfies | s (0) | < a, then
Figure BDA0002249544260000088
This is true for all | s | < a,
to LiThe derivation yields:
Figure BDA0002249544260000089
wherein a ═min{2k1,2k2,l0}，
Figure BDA00022495442600000810
Satisfies L for two Lyapunov functionsi≤μLj+ Delta, wherein,
Figure BDA0002249544260000091
Figure BDA0002249544260000092
λm＝|mi-mj|；
in summary, the following conclusions are drawn:
1) all signals in a closed loop system are bounded;
2) if the initial value of the height error is satisfied
Figure BDA0002249544260000093
Then for an arbitrarily small positive constant τ > 0, when
Figure BDA0002249544260000094
The output height error of the system will be strict
Figure BDA0002249544260000095
Within the range;
3) if the dwell time T of the switching signal*Satisfy the requirement of
Figure BDA0002249544260000096
E (0, a), then the steady state tracking error of the system will be satisfied
Figure BDA0002249544260000097
Where ∈ (0, a).
For the convenience of understanding the above technical aspects of the present invention, the following detailed description will be given of the above technical aspects of the present invention by way of specific examples.
Example 1
And (3) simulating the established unmanned helicopter model and the designed adaptive controller by using MATLAB software. The selected hanging mass of the unmanned helicopter air drop accounts for 10% of the total mass of the helicopter hanging system, and the specific simulation parameters are shown in table 1:
table 1 simulation parameters
Figure BDA0002249544260000098
In order to compare the control effects, the simulation of the control scheme and the PD control designed by the present invention is performed using the same control coefficients, and the simulation results are shown in fig. 3 to 5. Fig. 3(a), (b) are control input comparisons, fig. 4(a), (b) are height tracking error comparisons, the left side is the control scheme of the present invention, and the right side is the PD control scheme. Fig. 5 is an estimation of unknown parameters for handover. As can be seen from the simulation result graph, the desired bounded error tracking effect can be achieved and all signals in the closed loop system are bounded.
As can be seen from the simulation result, the adaptive control method based on the BLF method can well control the output boundary, the adaptive law can accurately estimate the parameters, and the adaptive controller designed by the invention is effective.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. A first feature being "under", beneath and "under" a second feature includes the first feature being directly under and obliquely under the second feature, or simply means that the first feature is at a lesser elevation than the second feature.
In the present invention, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. The term "plurality" means two or more unless expressly limited otherwise.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. 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 (1)

1. A longitudinal swing amplitude control method for an unmanned helicopter aerial drop hanger is characterized by comprising the following steps:
s1: establishing a 6-degree-of-freedom nonlinear system model of the unmanned helicopter system, and further considering an unmanned helicopter air-drop hanging system with a quality mutation problem to obtain a height subsystem model of the unmanned helicopter air-drop hanging system;
a6-degree-of-freedom unmanned helicopter system model established by a Newton-Euler equation:
Figure FDA0002710147320000011
Figure FDA0002710147320000012
Figure FDA0002710147320000013
Figure FDA0002710147320000014
wherein the content of the first and second substances,
Figure FDA0002710147320000015
is the position coordinate of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure FDA0002710147320000016
is the derivative of the coordinates of the position of the center of mass of the unmanned helicopter,
Figure FDA0002710147320000017
the speed of the mass center of the unmanned helicopter in the terrestrial coordinate system,
Figure FDA0002710147320000018
is the derivative of the velocity of the center of mass of the unmanned helicopter; m is the mass of the unmanned helicopter;
Figure FDA0002710147320000019
g is the acceleration of gravity;
Figure FDA00027101473200000110
the attitude of the unmanned helicopter in the terrestrial coordinate system is defined, phi is the pitch angle of the attitude of the unmanned helicopter, theta is the roll angle of the attitude of the unmanned helicopter, and psi is the yaw angle of the attitude of the unmanned helicopter; rt(gamma) is a rotation matrix transformed from a body coordinate system to a ground coordinate system, is a 3 x 3 matrix related to the attitude gamma of the unmanned helicopter,
Figure FDA00027101473200000111
is RtThe derivative of (gamma) is determined,
Figure FDA00027101473200000112
a rotation matrix transformed from a body coordinate system to a ground coordinate system;
Figure FDA00027101473200000113
is the angular velocity in the coordinate system of the body,
Figure FDA00027101473200000114
is the derivative of ω, representing angular acceleration; s (·) is an oblique symmetric matrix, S (ω) J ω ═ ω × J ω;
Figure FDA00027101473200000115
j is a rotational inertia matrix, IxxIs the moment of inertia about the x-axis in the coordinate system of the body, IyyIs the moment of inertia about the y-axis in the coordinate system of the body, IzzIs the moment of inertia about the z-axis in the coordinate system of the body, IxzIs the product of inertia about the x-axis and z-axis in the body coordinate system, Q is the control moment,
the simplified height subsystem is:
Figure FDA0002710147320000021
wherein, PzIs the height of the center of mass of the unmanned helicopter,
Figure FDA0002710147320000022
is the derivative of the height of the center of mass, V, of the unmanned helicopterzIs the longitudinal speed of the unmanned helicopter,
Figure FDA0002710147320000023
the derivative of the longitudinal speed of the unmanned helicopter represents the acceleration in the height direction; m isiThe mass of the unmanned helicopter hanging system is the mass of the unmanned helicopter hanging system, sudden change can occur before and after air drop hanging, and i is 1 and 2, wherein i is 1 and represents the mass of the unmanned helicopter hanging system before air drop, and i is 2 and represents the mass of the unmanned helicopter hanging system after air drop; t ismThe lift force generated by the main rotor of the unmanned helicopter;
s2: designing a self-adaptive height control algorithm of the hanging system of the unmanned helicopter, designing a self-adaptive law, estimating the hanging quality of the unmanned helicopter unknown before and after air drop, and controlling the height tracking of the unmanned helicopter; designing a height swing amplitude control method after the unmanned helicopter is air-dropped and hung based on a Barrier Lyapunov Function method, introducing parameters of an upper bound of the swing amplitude of the unmanned helicopter, realizing the pre-definition of the upper bound of the swing amplitude, and integrating the upper bound of the swing amplitude into an adaptive control law; the unmanned helicopter hanging system is designed to carry out air drop in an air hovering scene, only the longitudinal characteristic of the unmanned helicopter hanging system is considered, and the pitch angle and the roll angle of the unmanned helicopter are both close to 0, so cos phi cos theta is approximately equal to 1;
the self-adaptive control law of the unmanned helicopter is designed by adopting a self-adaptive backstepping method:
s21: height error
Figure FDA0002710147320000024
And velocity error in the vertical direction
Figure FDA0002710147320000025
Comprises the following steps:
Figure FDA0002710147320000026
wherein, VzdRepresenting virtual control signals, zrFor a set height reference signal the height of the sensor,
to pair
Figure FDA0002710147320000027
And (3) obtaining a height tracking error system by derivation:
Figure FDA0002710147320000028
for a derivative of the set altitude reference signal, representing the desired altitude direction velocity,
designing virtual control quantities
Figure FDA0002710147320000029
k1Is a positive constant, and the virtual control is brought into the height error system to obtain
Figure FDA00027101473200000210
S22: computing
Figure FDA00027101473200000211
Derivative of (2)
Figure FDA00027101473200000212
Obtaining a vertical direction tracking error dynamic system equation:
Figure FDA00027101473200000213
defining two estimation errors as
Figure FDA00027101473200000214
Mass m of suspension system of unmanned helicopteriRespectively estimating the mass m of the suspension system of the unmanned helicopter before air drop by an adaptive updating law1And the mass m of the suspension system of the unmanned helicopter after air drop2，
Figure FDA0002710147320000031
Is an estimation error, and the airdrop time is recorded as t1＞0，
Figure FDA0002710147320000032
And 0 < b0≤bi≤bmax1,2, wherein b isiThe values of b before and after the air drop are shown, i-1 represents the value of b before the air drop, i-2 represents the value of b after the air drop, and b0Is b isiLower boundary of (b)maxIs b isiThe control law is as follows:
Figure FDA0002710147320000033
wherein, the parameter k is designed based on the BLF methodzIs an upper bound limiting the amplitude of the height swing, is a positive constant, k2For the designed control coefficient, a positive constant,
Figure FDA0002710147320000034
for the virtual control signal VzdThe adaptive law of the parameters is:
Figure FDA0002710147320000035
wherein r, l0Is a constant that is positive in number,
Figure FDA0002710147320000036
for mass m of suspension system of unmanned helicopteriThe update law of the estimate of (2).
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