CN108445895B - Robust control method for position control of tilting type three-rotor unmanned aerial vehicle - Google Patents

Robust control method for position control of tilting type three-rotor unmanned aerial vehicle Download PDF

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CN108445895B
CN108445895B CN201810113891.XA CN201810113891A CN108445895B CN 108445895 B CN108445895 B CN 108445895B CN 201810113891 A CN201810113891 A CN 201810113891A CN 108445895 B CN108445895 B CN 108445895B
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aerial vehicle
unmanned aerial
rotor unmanned
tilting
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CN108445895A (en
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鲜斌
金鑫
张旭
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Tianjin 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
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Abstract

The invention relates to nonlinear control of a position of a tilting type three-rotor unmanned aerial vehicle, and designs a controller of a position subsystem and an attitude subsystem of the tilting type three-rotor unmanned aerial vehicle aiming at the problem of an inner and outer ring control strategy of the tilting type three-rotor unmanned aerial vehicle, so that the robust control method for the position control of the tilting type three-rotor unmanned aerial vehicle comprises the following steps: 1) establishing a coordinate system related to the tilting three-rotor unmanned aerial vehicle: 2) establishing a dynamic model of the position and the posture of the tilt rotor unmanned aerial vehicle: 3) design non-linear controller a) position subsystem controller design b) attitude subsystem controller design. The invention is mainly applied to the nonlinear control occasion of the position of the three-rotor unmanned aerial vehicle.

Description

Robust control method for position control of tilting type three-rotor unmanned aerial vehicle
Technical Field
The invention relates to a nonlinear control design of a position of a tilting type three-rotor unmanned aerial vehicle, in particular to a robust control method for the position control of the tilting type three-rotor unmanned aerial vehicle.
Background
Three rotor unmanned vehicles of formula of verting have fused the two advantage of many rotors helicopter and the formula of verting aircraft, are keeping many rotors helicopter VTOL, on the basis of the characteristics of the operation of being convenient for, have increased the steering wheel at the tail vane, have improved power unit, therefore also possess the formula of verting aircraft maneuverability reinforce, advantage such as payload is big possesses certain research potentiality and research value.
As one of the multi-rotor unmanned aerial vehicle, the tilting type three-rotor unmanned aerial vehicle has the characteristics of static instability, underactuation, strong coupling, nonlinear mathematical model and the like. Static instability requires that a control strategy designed for a multi-rotor unmanned aerial vehicle must be a real-time control law; the under-actuated characteristic shows that the multi-rotor unmanned aerial vehicle is difficult to realize the independent control of six degrees of freedom, and the coupling of related degrees of freedom is required; the strong coupling and the nonlinearity of the mathematical model require that the designed controller has good robustness, and meanwhile, the control difficulty of the type of the aircraft is increased due to various uncertain factors in the flight process of the unmanned aerial vehicle.
Researchers at the university of France' S Gongbene technology establish a dynamic model of the attitude and position of a tilting three-rotor unmanned aerial vehicle under the condition of neglecting the lateral force generated by a tail rudder, and design an attitude and position controller of the unmanned aerial vehicle by combining a saturation function and a proportional differential controller, wherein the position Control precision is within 0.1m, the Control precision of a roll angle and a pitch angle is within 2, and the Control precision of a yaw angle is within 5 (journal: Control Engineering Practice; author: Salazar-Cruz S, Lozano R,
Figure BDA0001570087290000011
J, published month and year: 2009; the article title: stabilization and nonlinear control for a novel triotor mini-aircraft, page number: 886-: IEEE Transactions on Aerospace&Electronic Systems; the authors: Salazar-Cruz S, Kendoul F, Lozano R, published New year month: 2008; the article title: real-time stabilization of a small thread-rotor aircraft, page number: 783-794).
The researcher of national defense science and technology university combines together three rotor unmanned aerial vehicle structures of formula of verting and fixed wing aircraft, keeps the tail vane motor fixed, installs the steering wheel under the motor of front side to install the wing additional in unmanned aerial vehicle fuselage both sides, obtained a comparatively nimble wing section structure. The configuration effectively improves the endurance time of the unmanned aerial vehicle, enhances the maneuvering performance of the unmanned aerial vehicle, and makes the analysis and the control of the unmanned aerial vehicle dynamic model more complex. Researchers mainly study the dynamic model of the unmanned aerial vehicle and verify the dynamic model on a suspension type experiment platform. A PI-PD dual-ring controller is designed on The basis of The prior art, The stabilization of The speed and The posture of The unmanned aerial vehicle is realized, and The numerical simulation verification is carried out (The Conference: The 35th Chinese Control Conference (CCC); The authors: Chen A, Zhang D, Zhang J; The publication year: 2016; The article title: A new structural configuration of The top unmanned aerial vehicle temporal modification; The page number: 2120-.
The steering wheel is all installed to mining schools such as national paris in France below the brushless direct current motor of each axle of three rotor unmanned aerial vehicle, and the inclination of its every motor rotation axis can independently be adjusted, therefore this kind of three rotor unmanned aerial vehicle has possessed stronger maneuverability. Researchers analyze the stress condition of the unmanned aerial vehicle, deduce a dynamic model of the attitude and the position, on the basis, a control scheme based on flatness is designed aiming at the problem of trajectory tracking of the three-rotor unmanned aerial vehicle, and the circular Trajectory tracking flight experiment is completed, the diameter of the reference Trajectory is about 2.0m, and the control precision is within 0.2m (Conference: the International Conference on Unmanned air Systems; authors: service E, D 'Andrea-Novel B, Mounder H; published month: 2015; article title: group control of a hybrid tracker; page number: 945. 950) (Conference: International Conference on Methods and MODS in Automation and Robotics; authors: service E, D' Andrea-Novel B, Mounder H; published month: 2015; article title: Trajectory UAV packaging with suspension load; and du: 517. 522).
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a controller for a position subsystem and an attitude subsystem of a tilting three-rotor unmanned aerial vehicle aiming at the problem of an inner and outer ring control strategy of the tilting three-rotor unmanned aerial vehicle, and therefore, the robust control method for the position control of the tilting three-rotor unmanned aerial vehicle comprises the following steps:
1) establishing a coordinate system related to the tilting three-rotor unmanned aerial vehicle:
defining two coordinate systems, namely an inertial coordinate system { I } and a body coordinate system { B }, which both meet the right-hand rule, wherein the origin of the inertial coordinate system { I } is located on the ground, the origin of the body coordinate system { B } is located in the mass center of the three-rotor unmanned aerial vehicle, { E }x Ey EzAnd { B }x By BzRespectively representing three main shafts corresponding to an inertial coordinate system (I) and a body coordinate system (B);
2) establishing a dynamic model of the position and the posture of the tilt rotor unmanned aerial vehicle:
the position model is represented as:
Figure BDA0001570087290000021
wherein x, y and z respectively represent coordinate values of the centroid position of the tilting three-rotor unmanned aerial vehicle in an inertial coordinate system { I }, and FzTo representThe unmanned plane is in an inertial coordinate system { I }, EzThe lift force in the axial direction, m represents the mass of the unmanned aerial vehicle, phi, theta and psi respectively represent the attitude information of the unmanned aerial vehicle, namely the roll angle, the pitch angle and the yaw angle, g represents the gravity acceleration, d represents the disturbance acceleration introduced by a tail rudder of the tilting three-rotor unmanned aerial vehicle, and H (e)η,ηd) Express three rotor unmanned aerial vehicle ectonexine coupling parts of tilting, v expresses three rotor unmanned aerial vehicle's of tilting controller, expresses as:
Figure BDA0001570087290000022
in the above formula, phid、θd、ψdRespectively obtaining the target roll angle, the target pitch angle and the target yaw angle of the unmanned aerial vehicle obtained by resolving through a position controller;
the attitude dynamics model of the tilting three-rotor unmanned aerial vehicle is expressed as follows:
Figure BDA0001570087290000031
where M (η) is an inertia matrix, abbreviated as M,
Figure BDA0001570087290000032
a matrix of coriolis forces and centripetal forces, which may be referred to as C,
Figure BDA0001570087290000033
the kinetic moment of each channel of the unmanned aerial vehicle is eta (t) [ [ phi ] theta ] psi]TThe attitude of the drone is represented and,
Figure BDA0001570087290000034
psi represents an angular velocity conversion matrix from a body coordinate system { B } to an inertial coordinate system { I } for a disturbance moment vector received by the unmanned aerial vehicle in the body coordinate system { B };
3) designing a non-linear controller
a) Position subsystem controller design
When designing the outer loop control ware, the three rotor unmanned aerial vehicle kinetic model that vert that adopts is as shown as follows:
Figure BDA0001570087290000035
the outer loop error is denoted as EηAnd designing an error system filter gamma, and constructing a disturbance observer as shown in the following formula:
Figure BDA0001570087290000036
defining the intermediate variable δ ═ s-z and substituting into the formula above to obtain:
Figure BDA0001570087290000037
wherein the content of the first and second substances,
Figure BDA0001570087290000038
as an observed value of disturbance d of a formula system, a reasonable assumption is made, and when the lateral force disturbance d and a derivative thereof are bounded, a condition d is less than or equal to | M1|，
Figure BDA0001570087290000039
Estimating disturbances
Figure BDA00015700872900000310
The first derivative with respect to time of (a) is designed as:
Figure BDA00015700872900000311
in the above formula
Figure BDA00015700872900000312
Are diagonal parameter matrixes, and simultaneously, a position loop controller v is designed as follows:
Figure BDA00015700872900000313
wherein
Figure BDA00015700872900000314
Is a positive angle parameter matrix;
b) attitude subsystem controller design
Utilize three rotor unmanned aerial vehicle attitude dynamics models of tilting type that following formula shows:
Figure BDA00015700872900000315
where M (η) is an inertia matrix, abbreviated as M,
Figure BDA00015700872900000316
an attitude angle tracking error is defined for the Coriolis force and centripetal force matrix, denoted C
Figure BDA00015700872900000317
And filtering error
Figure BDA00015700872900000318
Represented by the formula:
eη＝η-ηd,
Figure BDA00015700872900000319
wherein etad＝[φd θd ψd]TRepresenting a target pose of the drone,
Figure BDA00015700872900000320
is a positive diagonal normal coefficient matrix. The first derivative with respect to time is taken for r η to obtain the following equation:
Figure BDA0001570087290000041
wherein N is defined as an intermediate variable expressed as
Figure BDA0001570087290000042
Deducing an intermediate variable N, so that
Figure BDA0001570087290000043
Then there are:
Figure BDA0001570087290000044
simultaneous definition of
Figure BDA0001570087290000045
Definition sη＝[eη rη]TTherefore, the attitude control power moment tau of the tilting type three-rotor unmanned aerial vehicle can be designed as follows:
τ＝(ΨT)-1(-Krrη-Γ1sign(rη)-Γ2||sη||sign(rη))
wherein
Figure BDA0001570087290000046
And
Figure BDA0001570087290000047
are positive diagonal parameter matrixes and can be adjusted by self.
The invention has the characteristics and beneficial effects that:
aiming at the position control of the tilting type three-rotor unmanned aerial vehicle, the position-attitude double-loop kinetic model of the unmanned aerial vehicle is established, and a position controller and an attitude controller based on the unmanned aerial vehicle are designed on the basis, so that the position control of the tilting type three-rotor unmanned aerial vehicle can be effectively realized, better control stability is kept, and certain robustness is achieved.
Description of the drawings:
fig. 1 is a schematic diagram of the present invention employing a tilt-type three-rotor drone;
FIG. 2 is a schematic diagram of a coordinate system employed in the present invention;
FIG. 3 is a block diagram of a dual-ring controller designed by the present invention;
fig. 4 is a schematic diagram of a curve of a rectangular trajectory tracking flight process of the unmanned aerial vehicle after the control scheme is adopted.
a is an attitude error curve of the unmanned aerial vehicle in the rectangular track tracking flight process after the control scheme is adopted;
b, adopting the control scheme to track the actual position curve of the flight process by the rectangular track of the unmanned aerial vehicle;
c, adopting the control scheme to obtain a position error curve of the rectangular track tracking flight process of the unmanned aerial vehicle;
d is a position three-dimensional schematic diagram of the rectangular track tracking flight process of the unmanned aerial vehicle after the control scheme is adopted.
Detailed Description
The invention aims to solve the technical problem that a nonlinear controller which has better robustness and can ensure the stability of a position-attitude closed-loop coupling closed-loop system is designed for a tilting type three-rotor unmanned aerial vehicle with a tail rudder inclination angle capable of being independently controlled.
The technical scheme adopted by the invention is as follows: the method comprises the following steps of establishing a position-attitude double-loop dynamic model of the tilting three-rotor unmanned aerial vehicle, and designing a corresponding nonlinear controller, wherein the method comprises the following steps:
the following definitions are first accomplished: two coordinate systems are defined, an inertial coordinate system { I } and a body coordinate system { B } as shown in FIG. 2. The origin of the inertial coordinate system { I } is located on the ground, and the origin of the body coordinate system { B } is located in the center of mass of the three-rotor unmanned aerial vehicle, and both meet the right-hand rule. Defining the attitude angle of the tilting three-rotor unmanned plane in an inertial coordinate system as eta ═ phi theta psi]TWherein phi, theta and psi respectively represent the roll angle, yaw angle and pitch angle of the unmanned aerial vehicle. In an inertial coordinate system { I }, a position vector of the tilting three-rotor unmanned aerial vehicle is represented as epsilon ═ x y z]TWherein x, y, z respectively represent { E } of the three-rotor unmanned aerial vehicle under an inertial coordinate system { I }x Ey EzCoordinate values on the axis. In the inertial coordinateIn the system { I }, the target attitude of the tilting type three-rotor unmanned aerial vehicle is defined as etad＝[φd θd ψd]TWherein phid、θd、ψdRespectively representing target roll angle, pitch angle, yaw angle, epsilond＝[xd yd zd]TIs defined as the target position of the drone, where xd、yd、zdRespectively representing the target position of the unmanned aerial vehicle. The target position and attitude and its derivative with respect to time are bounded. Under the body coordinate system { B }, three rotor unmanned aerial vehicle of tilting, the angular velocity of each gesture passageway of this unmanned aerial vehicle expresses as
Figure BDA0001570087290000051
The second pair of tilting type three-rotor unmanned aerial vehicle is subjected to stress analysis, and a position dynamic model of the three-rotor unmanned aerial vehicle with a downward tilting rotation inertial coordinate system (I) is established
Figure BDA0001570087290000052
Wherein R istRepresenting a rotation matrix transformed from the bulk coordinate system { B } to the inertial coordinate system { I },
Figure BDA0001570087290000053
for under body coordinate system { B }, the power that three rotor unmanned aerial vehicle rotors of formula of verting and steering wheel produced shows as:
Figure BDA0001570087290000054
the equations of dynamics for this drone can therefore be written as:
Figure BDA0001570087290000055
therefore, the tilting type three-rotor unmanned plane position ring dynamic model can be written as follows:
Figure BDA0001570087290000056
in the normal flight process of the tilting three-rotor unmanned aerial vehicle, the lateral force under a body coordinate system (B)
Figure BDA0001570087290000057
The lift force of the tail rudder is represented as ByProjection on axis, denoted f3sin α, normally overriding this force at drone B when controlling the position of a tilt-type tri-rotor droneyAcceleration of direction due to both the magnitude of the force and the total lift FzCompared to a smaller value. Because the model can contain FyIs treated as a bounded perturbation
Figure BDA0001570087290000061
Therefore, the position dynamics model of the unmanned aerial vehicle can be rewritten into the following model:
Figure BDA0001570087290000062
wherein
Figure BDA0001570087290000063
Indicating lateral force F from tail rudderyThe unknown bounded perturbation introduced into the system can be expressed as:
Figure BDA0001570087290000064
virtual control input that simultaneously defines a dynamic system position loop
Figure BDA0001570087290000065
It is expressed as:
Figure BDA0001570087290000066
wherein Fz、φd、θd、ψdRespectively represent byThe target vertical lift force, the target roll angle and the target pitch angle obtained by the position outer ring controller and the target yaw angle of the system can be solved to obtain Fz、φd、θdAs follows:
Figure BDA0001570087290000067
Figure BDA0001570087290000068
Figure BDA0001570087290000069
closed loop system position error system is defined herein
Figure BDA00015700872900000610
And attitude error system
Figure BDA00015700872900000611
As shown in the following formula:
Figure BDA00015700872900000612
Figure BDA00015700872900000613
wherein
Figure BDA00015700872900000614
Defined as the difference between the reference position trajectory and the actual position of the drone, written Eη＝ε-εd，
Figure BDA00015700872900000615
Is defined as the difference between the attitude reference trajectory of the unmanned aerial vehicle and the actual attitude angle, and is written as eη＝η-ηdThus, the following formula can be obtained:
φ＝eφ+φd
θ＝eθ+θd
ψ＝eψ+ψd.
from the trigonometric function sum and difference formula, the kinetic model of the position subsystem can be rewritten as:
Figure BDA0001570087290000071
wherein
Figure BDA0001570087290000072
Representing the coupling terms of the inner and outer rings of a rotor unmanned aerial vehicle system, which can be written as H (e)η,ηd)＝[Hx(eη,ηd)Hy(eη,ηd)Hz(eη,ηd)]T. The position dynamics model of a tilt-type tri-rotor drone can therefore be expressed as:
Figure BDA0001570087290000073
thirdly, establishing an attitude dynamics model of the tilting three-rotor unmanned aerial vehicle,
Figure BDA0001570087290000074
represents the moment of inertia matrix, j, of the three-rotor unmanned aerial vehicle1、j2、j3The rotational inertia of the unmanned aerial vehicle in the rolling channel, the pitching channel and the yawing channel is respectively expressed as:
Figure BDA0001570087290000075
Ψ (η) is an angular velocity transformation matrix, whose expression is:
Figure BDA0001570087290000076
a dynamic model which takes the power moment of the unmanned aerial vehicle as control input is established by using an integral moment analysis method for the tilting type three-rotor unmanned aerial vehicle:
Figure BDA0001570087290000077
wherein M (η) represents an inertia matrix, which is defined as M (η) ═ ΨTJ Ψ is a positive definite symmetric matrix,
Figure BDA0001570087290000078
representing a matrix of Coriolis force and centripetal force, the definition of which
Figure BDA0001570087290000079
τd＝[τdφτdθτdψ]TRepresenting unknown external disturbance torques on the roll, pitch, yaw channels of the three-rotor drone. As shown in FIG. 1 with l1、l2、l3Come to show each rotor to the arm of force of this unmanned aerial vehicle barycenter, c shows the counter-torque coefficient, three rotor unmanned aerial vehicle's of formula of verting each gesture passageway dynamic moment this moment
Figure BDA00015700872900000710
Can be expressed as:
Figure BDA00015700872900000711
after the dynamic model of the position posture is established, the design idea for the inner and outer ring control strategies of the tilting three-rotor unmanned aerial vehicle is shown in fig. 3 and respectively:
1. designing a control law for a position ring of the tilting type three-rotor unmanned aerial vehicle to make the position error x of the unmanned aerial vehicle converge to 0;
2. designing a control law for an attitude ring of the tilting type three-rotor unmanned aerial vehicle to make an attitude error xi of the unmanned aerial vehicle converge to 0;
the fourth is accomplished the nonlinear control ware design to three rotor unmanned aerial vehicle positions of tilting and gesture respectively, when design position ring control ware, the three rotor unmanned aerial vehicle kinetic model of tilting that adopt as shown in the following formula:
Figure BDA0001570087290000081
the outer loop error may be denoted as EηAnd an error system filter gamma is designed. Here, a disturbance observer can be constructed as follows:
Figure BDA0001570087290000082
defining the intermediate variable δ -s-z and substituting into the above formula, one can obtain:
Figure BDA0001570087290000083
wherein
Figure BDA0001570087290000084
As an observed value of disturbance d of a formula system, a reasonable assumption is made, and when the lateral force disturbance d and a derivative thereof are bounded, a condition d is less than or equal to | M1|，
Figure BDA0001570087290000085
The disturbance can be estimated
Figure BDA0001570087290000086
The first derivative with respect to time of (a) is designed as:
Figure BDA0001570087290000087
in the above formula
Figure BDA0001570087290000088
Are diagonal parameter matrixes, and simultaneously, a position loop controller v is designed as follows:
Figure BDA0001570087290000089
wherein
Figure BDA00015700872900000810
Is a positive angle parameter matrix.
On the basis, the design of the attitude controller of the unmanned aerial vehicle is changed, and the tracking error of the attitude angle is defined
Figure BDA00015700872900000811
And filtering error
Figure BDA00015700872900000812
Represented by the formula:
eη＝η-ηd,
Figure BDA00015700872900000813
wherein etad＝[φd θd ψd]TRepresenting a target pose of the drone,
Figure BDA00015700872900000814
is a positive diagonal normal coefficient matrix. To rηThe first derivative with respect to time is found as follows:
Figure BDA00015700872900000815
wherein N is defined as an intermediate variable expressed as
Figure BDA00015700872900000816
Deducing an intermediate variable N, so that
Figure BDA00015700872900000817
Then there are:
Figure BDA00015700872900000818
simultaneous definition of
Figure BDA0001570087290000091
Definition sη＝[eη rη]TTherefore, the attitude control power moment tau of the tilting type three-rotor unmanned aerial vehicle can be designed as follows:
τ＝(ΨT)-1(-Krrη-Γ1sign(rη)-Γ2||sη||sign(rη)).
wherein Kr、Γ1And gamma2Are positive diagonal parameter matrixes and can be adjusted by self.
The nonlinear controller for the position control of the tilting three-rotor unmanned aerial vehicle is designed.
The following describes the establishment of the dynamic model and the design of the nonlinear controller and the adaptive law in combination with the real derivation and the attached drawings.
The invention comprehensively aims at the problem of flight position control of the tilting three-rotor unmanned aerial vehicle, and establishes a position-attitude dynamic model of the tilting three-rotor unmanned aerial vehicle due to the under-actuated characteristic of the unmanned aerial vehicle, and designs a nonlinear controller respectively aiming at the position control and the attitude control of the tilting three-rotor unmanned aerial vehicle on the basis, thereby realizing the position control of the unmanned aerial vehicle under an inertial coordinate system { I }.
The invention designs a position nonlinear controller of a tilting type three-rotor unmanned aerial vehicle, which comprises the following steps:
1) establishing a coordinate system related to the tilting three-rotor unmanned aerial vehicle:
in order to facilitate the design of the nonlinear controller and the adaptive law, the present invention defines a coordinate system as shown in fig. 2.
In order to facilitate the design of the nonlinear controller and the adaptive law, two coordinate systems are defined as an inertial coordinate system { I } and a body coordinate system { B } which meet the right-hand rule, the origin of the inertial coordinate system { I } is located on the ground, and the body is located on the groundThe origin of coordinate system { B } is located at the center of mass of the triple rotor drone, { Ex Ey EzAnd { B }x By BzRespectively representing three main shafts corresponding to an inertial coordinate system (I) and a body coordinate system (B);
2) establishing a position-posture double-ring system dynamic model of the tilting three-rotor unmanned aerial vehicle:
after carrying out the atress analysis, establish three rotor unmanned aerial vehicle's of formula of verting position dynamics model:
Figure BDA0001570087290000092
a dynamic model which takes the power moment of the unmanned aerial vehicle as control input is established by using an integral moment analysis method for the tilting type three-rotor unmanned aerial vehicle:
Figure BDA0001570087290000093
3) designing a non-linear controller for the position-attitude of the unmanned aerial vehicle
When the position and attitude dynamics model is adopted, the position nonlinear disturbance observer, the controller and the attitude nonlinear controller of the tilting three-rotor unmanned aerial vehicle are respectively designed, and the control structure block diagram is shown in fig. 3.
The position controller v is designed to:
Figure BDA0001570087290000094
the external disturbance observer is designed as follows:
Figure BDA0001570087290000095
in addition to three rotor unmanned aerial vehicle's of formula of verting gesture dynamics model, design nonlinear controller does:
τ＝(ΨT)-1(-Krrη-Γ1sign(rη)-Γ2||sη||sign(rη)).
the variables in the above equations are defined above.
The controller is designed to converge the asymptotic closed loop dynamics system to 0.
Specific examples are given below:
first, introduction of semi-physical simulation platform
The semi-physical simulation platform of the tilting three-rotor unmanned aerial vehicle built by a subject group is used for verifying the effects of the nonlinear controller and the self-adaptation law designed in the text. The platform adopts a PC/104 embedded computer as a processor, an xPC system based on a MATLABRTW tool box is used as a semi-physical simulation environment, an independently designed circuit board and an inertia measurement sensor are adopted to obtain the attitude angle of the tilting type three-rotor unmanned aerial vehicle and the angular acceleration of each corresponding channel through a filtering link, and virtual position information is calculated by combining the dynamic model and the attitude information of the unmanned aerial vehicle. The measurement precision of the pitch angle and the roll angle of the experimental platform is about 1.0, and the measurement precision of the yaw angle is about 2.0 degrees. The experiment platform system controls the frequency to be 500 Hz.
Second, flight experiment results
To verify the effectiveness and realizability of the nonlinear control algorithm proposed herein, matrix trajectory tracking flight experiments of the tilting triple-rotor drone were performed for about 90 seconds on the semi-physical experimental platform described above.
As can be seen from fig. 4a to 4d, the control accuracy of the roll angle, the pitch angle and the yaw angle of the unmanned aerial vehicle after the experiment is started is within 3.0 degrees; in the inertial frame { I }, Ex、EyPosition tracking error in direction within 1.0m, EzThe directional height error is in the range of 0.1 m.

Claims (1)

1. A robust control method for position control of a tilting type three-rotor unmanned aerial vehicle comprises the following steps:
1) establishing a coordinate system related to the tilting three-rotor unmanned aerial vehicle:
define the following two coordinate systemsAn inertial coordinate system { I } and a body coordinate system { B } which both meet the right-hand rule, wherein the origin of the inertial coordinate system { I } is located on the ground, the origin of the body coordinate system { B } is located in the center of mass of the three-rotor unmanned aerial vehicle, { E }x Ey EzAnd { B }xBy BzRespectively representing three main shafts corresponding to an inertial coordinate system (I) and a body coordinate system (B);
2) establishing a dynamic model of the position and the posture of the tilting three-rotor unmanned aerial vehicle:
the position model is represented as:
Figure FDA0002806288640000011
wherein x, y and z respectively represent coordinate values of the centroid position of the tilting three-rotor unmanned aerial vehicle in an inertial coordinate system { I }, and FzRepresenting the unmanned plane in an inertial coordinate system { I }, EzThe lift force in the axial direction, m represents the mass of the unmanned aerial vehicle, phi, theta and psi respectively represent the attitude information of the unmanned aerial vehicle, namely the roll angle, the pitch angle and the yaw angle, g represents the gravity acceleration, d represents the disturbance acceleration introduced by a tail rudder of the tilting three-rotor unmanned aerial vehicle, and H (e)η,ηd) Express three rotor unmanned aerial vehicle ectonexine coupling parts of tilting, v expresses three rotor unmanned aerial vehicle's of tilting virtual controller, expresses as:
Figure FDA0002806288640000012
in the above formula, phid、θd、ψdRespectively obtaining the target roll angle, the target pitch angle and the target yaw angle of the unmanned aerial vehicle obtained by resolving through a position controller;
the attitude dynamics model of the tilting three-rotor unmanned aerial vehicle is expressed as follows:
Figure FDA0002806288640000013
where M (η) is an inertia matrix which can be abbreviated as
Figure FDA0002806288640000014
Is a matrix of Coriolis force and centripetal force, which can be abbreviated as
Figure FDA0002806288640000015
Figure FDA0002806288640000016
The kinetic moment of each channel of the unmanned aerial vehicle is eta (t) [ [ phi ] theta ] psi]TThe attitude of the drone is represented and,
Figure FDA0002806288640000017
psi represents an angular velocity conversion matrix from a body coordinate system { B } to an inertial coordinate system { I } for a disturbance moment vector received by the unmanned aerial vehicle in the body coordinate system { B };
3) designing a non-linear controller
a) Position subsystem controller design
When designing the outer loop control ware, the three rotor unmanned aerial vehicle kinetic model that vert that adopts is as shown as follows:
Figure FDA0002806288640000018
define the outer-loop error as EηAnd designing an error system filter gamma, and obtaining by the following formula:
Figure FDA0002806288640000019
wherein, define disturbance observer z, write:
Figure FDA0002806288640000021
wherein, the intermediate variable δ ═ γ -z is defined and substituted into the formula above to obtain:
Figure FDA0002806288640000022
wherein the content of the first and second substances,
Figure FDA0002806288640000023
as an observed value of disturbance d of a formula system, a reasonable assumption is made, and if the disturbance d of the lateral force and a derivative thereof are bounded, the condition that the d is less than or equal to | M1|，
Figure FDA0002806288640000024
Wherein the disturbance is estimated
Figure FDA0002806288640000025
The first derivative with respect to time of (a) is designed as:
Figure FDA0002806288640000026
in the above formula
Figure FDA0002806288640000027
Are all diagonal parameter matrices, while the virtual controller v is numerically designed as:
Figure FDA0002806288640000028
wherein the content of the first and second substances,
Figure FDA0002806288640000029
is a positive angle parameter matrix;
b) attitude subsystem controller design
Utilize three rotor unmanned aerial vehicle attitude dynamics models of tilting type that following formula shows:
Figure FDA00028062886400000210
where M (η) is an inertia matrix which can be abbreviated as
Figure FDA00028062886400000211
An attitude angle tracking error is defined for the Coriolis force and centripetal force matrix, denoted C
Figure FDA00028062886400000212
And filtering error
Figure FDA00028062886400000213
Represented by the formula:
Figure FDA00028062886400000214
wherein etad＝[φd θd ψd]TRepresenting a target pose of the drone,
Figure FDA00028062886400000215
is a matrix of normal diagonal normal coefficients, for rηThe first derivative with respect to time is found as follows:
Figure FDA00028062886400000216
where N is defined as an intermediate variable, expressed as:
Figure FDA00028062886400000217
deducing an intermediate variable N, so that
Figure FDA00028062886400000218
Then there are:
Figure FDA00028062886400000219
simultaneous definition of
Figure FDA0002806288640000031
Definition sη＝[eη rη]TTherefore, the attitude control power moment tau of the tilting type three-rotor unmanned aerial vehicle is designed as follows:
τ＝(ΨT)-1(-Krrη-Γ1sign(rη)-Γ2||sη||sign(rη)),
wherein
Figure FDA0002806288640000032
And
Figure FDA0002806288640000033
all are positive diagonal parameter matrixes and are adjusted by self.
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