CN107703967B - Control method for controlling track of limited airship - Google Patents

Control method for controlling track of limited airship Download PDF

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CN107703967B
CN107703967B CN201711000098.0A CN201711000098A CN107703967B CN 107703967 B CN107703967 B CN 107703967B CN 201711000098 A CN201711000098 A CN 201711000098A CN 107703967 B CN107703967 B CN 107703967B
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CN107703967A (en
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杨跃能
闫野
龚秋武
李超
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National University of Defense Technology
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Abstract

The invention provides a control method of the flight path of a limited airship aiming at the problem of flight path tracking of the airship, and the method establishes a mathematical model of the space motion of the limited airship; the model is used as a controlled object, airship control limitation is considered, and a track control law is designed by adopting a hyperbolic tangent function. The closed-loop system controlled by the method can stably track the command track, has good control precision, and provides an effective scheme for realizing the track control project of the control-limited airship.

Description

Control method for controlling track of limited airship
Technical Field
The invention relates to an airship control method, provides a control method for controlling three-dimensional track tracking of a limited airship, and belongs to the technical field of automatic control.
Background
The airship is a floating aircraft which depends on gas (such as helium) lighter than air to provide static buoyancy for levitation and depends on a flight control system to realize low-speed maneuvering and fixed-point residence, has the advantages of long air-remaining time, low energy consumption, high efficiency-cost ratio and the like, is widely applied to the fields of environmental monitoring, homeland surveying and mapping, earth observation, reconnaissance monitoring and the like, has important application value and wide application prospect, and is a research hotspot in the field of aviation at present.
The track tracking means that the airship gradually tends to and stably tracks the command track under a given ground coordinate system from any given initial state. The space motion of the airship has the characteristics of nonlinearity, channel coupling, uncertainty, easiness in external disturbance and the like, so that the track control becomes one of key technologies of the airship flight control. Aiming at the problem of track tracking of the airship, a plurality of researchers provide methods such as PID control, feedback control, sliding mode control, backstepping control and the like, and provide a technical scheme for reference for the track control of the airship. However, the control laws are designed on the assumption that the airship has sufficient control capability, and the problem of flight path control of the airship under the condition of limited control is not considered.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a control method for controlling the track of a limited airship, and a control engineer can realize three-dimensional track tracking control for controlling the limited airship according to the method. According to the method, firstly, the error amount is calculated according to the given instruction track and the given actual track, and then the control law of the control limited track is designed by utilizing the characteristics of the hyperbolic tangent function. In practical application, the flight path of the airship is measured by a navigation system, and the control quantity calculated by the method is transmitted to an executing mechanism, so that the flight path control function can be realized.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for controlling the track of a restricted airship comprises the following steps:
the method comprises the following steps: giving an instruction track;
given a commanded trajectory as generalized coordinates ηd＝[xd,yd,zd,θd,ψd,φd]T，xd、yd、zd、θd、ψdAnd phidRespectively an instruction x coordinate, an instruction y coordinate, an instruction z coordinate, an instruction pitch angle, an instruction yaw angle and an instruction roll angle, and superscript T represents the transpose of a vector or a matrix.
Step two: calculating an error e between the instruction track and the actual track;
e＝η-ηd＝[x-xd,y-yd,z-zd,θ-θd,ψ-ψd,φ-φd]T(1)
η＝[x,y,z,θ,ψ,φ]Tfor the actual track, x, y, z, theta, psi, phi are the x, y, z, pitch, yaw and roll coordinates, respectively, of the actual track.
Step three: and (3) controlling the limited track control law design: and constructing a hyperbolic tangent function, designing a control-limited track control law, and calculating a track control quantity tau.
1) Mathematical model for establishing airship space motion
For convenience of description, the coordinate system and motion parameters of the airship space motion are defined as follows. As shown in fig. 2, a ground coordinate system o is usedexyz and body coordinate system obxbybzbDescribing the space motion of the airship, wherein CV is a floating center, CG is a gravity center, and a vector from the floating center to the gravity center is rG＝[xG,yG,zG]T. And (3) defining motion parameters: position P ═ x, y, z]TX, y, z are displacements in the axial, lateral and vertical directions, respectively; attitude angle Ω [ θ, ψ, φ ]]TTheta, psi and phi are respectively a pitch angle, a yaw angle and a roll angle; velocity v ═ u, v, w]TU, v and w are the speeds in the axial direction, the lateral direction and the vertical direction in the body coordinate system respectively; angular velocity ω ═ p, q, r]TP, q, r are roll, pitch, and yaw angular velocities, respectively, let generalized coordinates η [ [ x, y, z, θ, ψ, φ]TGeneralized velocity is V ═ u, V, w, p, q, r]T。
The mathematical model of the airship's spatial motion is described as follows:
Figure BDA0001443159600000021
Figure BDA0001443159600000022
in the formula
Figure BDA0001443159600000023
Figure BDA0001443159600000024
Figure BDA0001443159600000025
Figure BDA0001443159600000031
Figure BDA0001443159600000032
Figure BDA0001443159600000033
Wherein
Figure BDA0001443159600000034
Figure BDA0001443159600000035
Figure BDA0001443159600000036
Figure BDA0001443159600000037
Figure BDA0001443159600000038
Figure BDA0001443159600000039
Wherein m is the airship mass, m11、m22、m33For additional mass, I11、I22、I33Additional inertia, Λ airship volume, Q dynamic pressure, α attack angle, β sideslip angle, CX、CY、CZ、Cl、Cm、CnIs the aerodynamic coefficient; i isx、Iy、IzAre respectively wound around obxb、obyb、obzbThe primary inertia of; i isxy、Ixz、IyzRespectively about a plane obxbyb、obxbzb、obybzbProduct of inertia; t is the magnitude of thrust, μ is the thrust vector and obxbzbAngle between faces, defined at obxbzbThe left of the surface is positive, upsilon is the thrust vector at obxbzbProjection of a surface andbxbangle between axes defining projection on obxbPositive below the axis; lx、ly、lzIndicating the distance o of the thrust action point from the originbThe distance of (c).
The expression (3) is an expression relating to the generalized velocity V, and it is necessary to convert it into an expression relating to the generalized coordinate η.
From formula (2):
Figure BDA0001443159600000041
in the formula J-1(η) is the inverse of J (η).
Figure BDA0001443159600000042
Figure BDA0001443159600000043
By differentiating the formula (16), the
Figure BDA0001443159600000044
In the formula
Figure BDA0001443159600000045
Formula (19) left multiplication
Figure BDA0001443159600000046
Can obtain the product
Figure BDA0001443159600000047
The following equations (3), (19) and (21) can be combined:
Figure BDA0001443159600000048
in the formula
Mη(η)＝RTMR (23)
Figure BDA0001443159600000049
Figure BDA00014431596000000410
Figure BDA00014431596000000411
Wherein τ ═ τ [ τ ]1,τ2,τ3,τ4,τ5,τ6]TFor the flight path control quantity, τ, of an airship1For axial control of force, tau2For lateral control of force, tau3For controlling force, tau, in a vertical direction4Controlling torque, tau, for rolling5Pitching control moment, tau6The yaw control moment.
The control amount for controlling the restricted airship satisfies the following inequality,
|τi|≤τi,max(27)
wherein, taui,maxFor a predefined upper threshold value of the ith control variable, i is 1,2,3,4,5, 6.
2) And (4) designing a control limited track control law by taking the mathematical model described by the formula (22) as a controlled object.
The following control laws are designed according to the track tracking error and the generalized speed:
τ＝-N-G-J(η)λTanh(kpe)-γTanh(kvV) (29)
wherein k isp≥1，kv≥1，λ＝diag(λ1,λ2,λ3,λ4,λ5,λ6)，γ＝diag(γ1,γ2,γ3,γ4,γ5,γ6)，γ1,γ2,γ3,γ4,γ5,γ6，λ1,λ2,λ3,λ4,λ5,λ6Are all preset control parameters; tanh (k)pe)＝[tanh(kpxe)，tanh(kpye)，tanh(kpze)，tanh(kpθe)，tanh(kpψe)，tanh(kpφe)]T，Tanh(kpV)＝[tanh(kpu)，tanh(kpv)，tanh(kpw)，tanh(kpp)，tanh(kpq)，tanh(kpr)]TTanh (-) represents a hyperbolic tangent function, and diag (-) represents a diagonal matrix. V ═ u, V, w, p, q, r]TThe speed of the airship is shown, wherein u, v and w are the speeds in the axial direction, the lateral direction and the vertical direction in a body coordinate system respectively, and p, q and r are the rolling angular speed, the pitching angular speed and the yaw angular speed respectively.
The beneficial technical effects of the invention are as follows:
compared with the prior art, the invention has the advantages that: the method is suitable for controlling the track of the limited airship and solves the problem of the track control of the airship under the condition of insufficient control capacity. In the application process, a control engineer can give any command track according to an actual airship and transmit the control quantity obtained by the method to an executing mechanism to realize the track control function.
In the prior art, the track control law designed by the applicant before is designed on the assumption that the airship can output enough control force and control torque, and the problem that the airship control capacity is limited in actual engineering is not considered. The problem that the control capability of the airship is limited is considered, and the control limitation is shown as a formula (27).
The tanh function is a type of tanh function whose value range is (-1,1), i.e., the tanh function is bounded. This boundedness is consistent with the control limitation described by equation (27), and therefore, the hyperbolic tangent function is used to design the trajectory control law. The method breaks through the assumed condition that the airship has sufficient enough control capacity, and can solve the problem of flight path control of the airship under the condition of limited control.
Drawings
FIG. 1 is a flow chart of the steps of the airship flight path control method of the invention
FIG. 2 illustrates the airship coordinate system and the definition of motion parameters according to the present invention
FIG. 3 shows the result of the airship track control according to the present invention
FIG. 4 shows the flight path control error of the airship according to the present invention
FIG. 5 shows the flight path control of the airship according to the invention
The symbols in the figures are as follows:
η＝[x,y,z,θ,ψ,φ]Tthe method comprises the following steps of (1) taking an airship track, wherein x, y, z, theta, psi and phi are an x coordinate, a y coordinate, a z coordinate, a pitch angle, a yaw angle and a roll angle of the actual track respectively;
ηd＝[xd,yd,zd,θd,ψd,φd]Tfor command track, where xd、yd、zd、θd、ψdAnd phidRespectively an instruction x coordinate, an instruction y coordinate, an instruction z coordinate, an instruction pitch angle, an instruction yaw angle and an instruction roll angle;
V＝[u,v,w,p,q,r]Tthe speed of the airship is shown, wherein u, v and w are body coordinate systems respectivelyThe velocities in the medial axial, lateral and vertical directions, p, q, r are roll, pitch and yaw angular velocities, respectively;
oexyz represents a ground coordinate system;
obxbybzbrepresenting an airship body coordinate system;
CV is the floating center of the airship;
CG is the center of gravity of the airship;
rG＝[xG,yG,zG]Tis the vector from the floating center to the center of gravity;
e＝[xe,ye,ze,θe,ψe,φe]Tfor track control errors, xe、ye、ze、θe、ψeAnd phieRespectively an x coordinate error, a y coordinate error, a z coordinate error, a pitch angle error, a yaw angle error and a roll angle error of track control;
τ＝[τ1,τ2,τ3,τ4,τ5,τ6]Tfor the flight path control quantity, τ, of an airship1For axial control of force, tau2For lateral control of force, tau3For controlling force, tau, in a vertical direction4Controlling torque, tau, for rolling5Pitching control moment, tau6The yaw control moment.
Detailed Description
In order to make the technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method for controlling the track of the limited airship, provided by the application, is applied to a specific embodiment and comprises the following steps:
the method comprises the following specific steps:
the method comprises the following steps: given command track
The given command track is:
ηd＝[5sin(0.02t)m,5cos(0.01t)m,2+sin(0.01t)+cos(0.01t)m,0rad,0rad,0rad]T，xd、yd、zd、θd、ψdand phidRespectively an instruction x coordinate, an instruction y coordinate, an instruction z coordinate, an instruction pitch angle, an instruction yaw angle and an instruction roll angle;
step two: error amount calculation
Calculating the error amount between the instruction track and the actual track:
e＝η-ηd＝[x-xd,y-yd,z-zd,θ-θd,ψ-ψd,φ-φd]T，
wherein η is [ x, y, z, theta, psi, phi ═ phi]TThe x, y, z, theta, psi and phi are respectively the x coordinate, y coordinate, z coordinate, pitch angle, yaw angle and roll angle of the actual track and are continuous variation values.
The initial track is:
η0＝[-2m,-2m,2m,0.001rad,0.001rad,0.001rad]T。
initial speed:
V0＝[2m/s,0.5m/s,0.2m/s,0rad/s,0rad/s,0rad/s]T
step three: designing a track control law:
1) mathematical model for establishing airship space motion
The mathematical model of the airship's spatial motion may be represented as:
Figure BDA0001443159600000071
Figure BDA0001443159600000072
in the formula
Figure BDA0001443159600000073
Figure BDA0001443159600000074
Figure BDA0001443159600000075
Figure BDA0001443159600000076
Figure BDA0001443159600000081
Figure BDA0001443159600000082
Wherein
Figure BDA0001443159600000083
Figure BDA0001443159600000084
Figure BDA0001443159600000085
Figure BDA0001443159600000086
Figure BDA0001443159600000087
Figure BDA0001443159600000088
Wherein m is the airship mass, m11、m22、m33For additional mass, I11、I22、I33Additional inertia, Λ airship volume, Q dynamic pressure, α attack angle, β sideslip angle, CX、CY、CZ、Cl、Cm、CnIs the aerodynamic coefficient; i isx、Iy、IzAre respectively wound around obxb、obyb、obzbThe primary inertia of; i isxy、Ixz、IyzRespectively about a plane obxbyb、obxbzb、obybzbProduct of inertia; t is the magnitude of thrust, μ is the thrust vector and obxbzbAngle between faces, defined at obxbzbThe left of the surface is positive, upsilon is the thrust vector at obxbzbProjection of a surface andbxbangle between axes defining projection on obxbPositive below the axis; lx、ly、lzIndicating the distance o of the thrust action point from the originbThe distance of (c).
The expression (31) is an expression relating to the generalized velocity V, and it is necessary to convert this into an expression relating to the generalized coordinate η.
From formula (30):
Figure BDA0001443159600000089
in the formula, J-1(η) is the inverse of J (η),
Figure BDA0001443159600000091
Figure BDA0001443159600000092
by differentiating the formula (44), the
Figure BDA0001443159600000093
In the formula
Figure BDA0001443159600000094
Formula (47) left multiplication
Figure BDA0001443159600000095
Can obtain the product
Figure BDA0001443159600000096
The formula (31), the formula (47) and the formula (49) can be combined to obtain:
Figure BDA0001443159600000097
in the formula
Mη(η)＝RTMR (51)
Figure BDA0001443159600000098
Figure BDA0001443159600000099
Figure BDA00014431596000000911
The control amount for controlling the restricted airship satisfies the following inequality,
|τ1|≤0.8N,|τ2|≤0.8N,|τ3|≤0.8N (55)
|τ4|≤0.4N·m,|τ5|≤0.4N·m,|τ6|≤0.4N·m (56)
the airship parameters in this example are shown in table 2.
TABLE 2 airship parameters
Figure BDA00014431596000000910
Figure BDA0001443159600000101
2) Design of track control law
Designing the following control law of limited track
τ＝-N-G-J(η)λTanh(kpe)-γTanh(kvV) (57)
Wherein k isp＝2，kpλ ═ diag (1.5,1.5,1.5, 1.5), γ ═ diag (3,3,3,3,3,3), tanh (·) denotes a hyperbolic tangent function, diag (·) denotes a diagonal matrix.
The three-dimensional track tracking results of the airship in the embodiment are shown in the figures 3-5. Fig. 3 shows the result of the airship trajectory control, which can be obtained from fig. 3: the airship can accurately track the command track, and the effectiveness of the track control method provided by the invention is verified; fig. 4 shows the track control error, which can be derived from fig. 4: the flight path control error can be asymptotically converged to zero, and the control precision is good. Fig. 5 shows a change curve of the track control quantity with time, and the airship can meet the requirement of track tracking under the condition of limited control, which can be obtained from fig. 5.
In summary, although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.

Claims (1)

1. A method for controlling the track of a restricted airship is characterized by comprising the following steps:
the method comprises the following steps: giving an instruction track;
where the given commanded path is a generalized coordinate ηd＝[xd,yd,zd,θd,ψd,φd]T，xd、yd、zd、θd、ψdAnd phidRespectively are an instruction x coordinate, an instruction y coordinate, an instruction z coordinate, an instruction pitch angle and an instructionYaw angle and command roll angle, superscript T representing the transpose of a vector or matrix;
step two: calculating an error e between the instruction track and the actual track;
e＝η-ηd＝[x-xd,y-yd,z-zd,θ-θd,ψ-ψd,φ-φd]T(1)
η＝[x,y,z,θ,ψ,φ]Tthe actual flight path is defined as x, y, z, theta, psi and phi, and the x, y, z, pitch angle, yaw angle and roll angle of the actual flight path are respectively defined as x, y, z, theta, psi and phi;
step three: and (3) controlling the limited track control law design: constructing a hyperbolic tangent function, designing a control-limited track control law, and calculating a track control quantity tau, wherein the method comprises the following steps:
1) establishing a mathematical model of the space motion of the airship;
using a ground coordinate system oexyz and body coordinate system obxbybzbDescribing the space motion of the airship, wherein CV is a floating center, CG is a gravity center, and a vector from the floating center to the gravity center is rG＝[xG,yG,zG]T(ii) a And (3) defining motion parameters: position P ═ x, y, z]TX, y, z are displacements in the axial, lateral and vertical directions, respectively; attitude angle Ω [ θ, ψ, φ ]]TTheta, psi and phi are respectively a pitch angle, a yaw angle and a roll angle; velocity v ═ u, v, w]TU, v and w are the speeds in the axial direction, the lateral direction and the vertical direction in the body coordinate system respectively; angular velocity ω ═ p, q, r]TP, q, r are roll, pitch, and yaw angular velocities, respectively, and generalized coordinates η are [ x, y, z, θ, ψ, φ]TGeneralized velocity is V ═ u, V, w, p, q, r]T；
The mathematical model of the airship's spatial motion is described as follows:
Figure FDA0002567588530000011
Figure FDA0002567588530000012
in the formula
Figure FDA0002567588530000013
Figure FDA0002567588530000014
Figure FDA0002567588530000021
Figure FDA0002567588530000022
Figure FDA0002567588530000023
Figure FDA0002567588530000024
Wherein
Figure FDA0002567588530000025
Figure FDA0002567588530000026
Figure FDA0002567588530000027
Figure FDA0002567588530000028
Figure FDA0002567588530000029
Figure FDA00025675885300000210
Wherein m is the airship mass, m11、m22、m33For additional mass, I11、I22、I33Additional inertia, Λ airship volume, Q dynamic pressure, α attack angle, β sideslip angle, CX、CY、CZ、Cl、Cm、CnIs the aerodynamic coefficient; i isx、Iy、IzAre respectively wound around obxb、obyb、obzbThe primary inertia of; i isxy、Ixz、IyzRespectively about a plane obxbyb、obxbzb、obybzbProduct of inertia; t is the magnitude of thrust, μ is the thrust vector and obxbzbAngle between faces, defined at obxbzbThe left of the surface is positive, upsilon is the thrust vector at obxbzbProjection of a surface andbxbangle between axes defining projection on obxbPositive below the axis; lx、ly、lzIndicating the distance o of the thrust action point from the originbIs a distance of
Equation (3) is an expression regarding the generalized velocity V, which is converted into an expression regarding the generalized coordinate η below;
from formula (2):
Figure FDA0002567588530000031
in the formula J-1(η) is the inverse of J (η);
Figure FDA0002567588530000032
Figure FDA0002567588530000033
by differentiating the formula (16), the
Figure FDA0002567588530000034
In the formula
Figure FDA0002567588530000035
Formula (19) left multiplication
Figure FDA0002567588530000036
Can obtain the product
Figure FDA0002567588530000037
The following equations (3), (19) and (21) can be combined:
Figure FDA0002567588530000038
in the formula
Mη(η)＝RTMR (23)
Figure FDA0002567588530000039
Figure FDA00025675885300000310
Figure FDA0002567588530000041
Wherein τ ═ τ [ τ ]1,τ2,τ3,τ4,τ5,τ6]TIs an airshipFlight path control quantity, tau1For axial control of force, tau2For lateral control of force, tau3For controlling force, tau, in a vertical direction4Controlling torque, tau, for rolling5Pitching control moment, tau6Controlling moment for yaw;
the control amount for controlling the restricted airship satisfies the following inequality,
|τi|≤τi,max(27)
wherein, taui,maxAn upper threshold value for a predefined ith control variable, i being 1,2,3,4,5, 6;
2) designing a control law of a controlled limited track by using the mathematical model described by the formula (22) as a controlled object;
the following control laws are designed according to the track tracking error and the generalized speed:
τ＝-N-G-J(η)λTanh(kpe)-γTanh(kvV) (29)
wherein k isp≥1，kv≥1，λ＝diag(λ1,λ2,λ3,λ4,λ5,λ6)，γ＝diag(γ1,γ2,γ3,γ4,γ5,γ6)，γ1,γ2,γ3,γ4,γ5,γ6，λ1,λ2,λ3,λ4,λ5,λ6Are all preset control parameters;
Tanh(kpe)＝[tanh(kpxe)，tanh(kpye)，tanh(kpze)，tanh(kpθe)，tanh(kpψe)，tanh(kpφe)]T，
Tanh(kpV)＝[tanh(kpu)，tanh(kpv)，tanh(kpw)，tanh(kpp)，tanh(kpq)，tanh(kpr)]Ttan h (·) denotes a hyperbolic tangent function, and diag (·) denotes a diagonal matrix; v ═ u, V, w, p, q, r]TThe speed of the airship is shown, wherein u, v and w are respectively the axial direction, the lateral direction and the vertical direction in a body coordinate systemP, q, r are roll, pitch and yaw angular velocities, respectively.
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