CN107703967B

CN107703967B - Control method for controlling track of limited airship

Info

Publication number: CN107703967B
Application number: CN201711000098.0A
Authority: CN
Inventors: 杨跃能; 闫野; 龚秋武; 李超
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2017-10-24
Filing date: 2017-10-24
Publication date: 2020-08-21
Anticipated expiration: 2037-10-24
Also published as: CN107703967A

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 η_d＝[x_d,y_d,z_d,θ_d,ψ_d,φ_d]^T，x_d、y_d、z_d、θ_d、ψ_dAnd phi_dRespectively 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-η_d＝[x-x_d,y-y_d,z-z_d,θ-θ_d,ψ-ψ_d,φ-φ_d]^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 used_exyz and body coordinate system o_bx_by_bz_bDescribing 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 r_G＝[x_G,y_G,z_G]^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:

in the formula

Wherein

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, C_X、C_Y、C_Z、C_l、C_m、C_nIs the aerodynamic coefficient; i is_x、I_y、I_zAre respectively wound around o_bx_b、o_by_b、o_bz_bThe primary inertia of; i is_xy、I_xz、I_yzRespectively about a plane o_bx_by_b、o_bx_bz_b、o_by_bz_bProduct of inertia; t is the magnitude of thrust, μ is the thrust vector and o_bx_bz_bAngle between faces, defined at o_bx_bz_bThe left of the surface is positive, upsilon is the thrust vector at o_bx_bz_bProjection of a surface and_bx_bangle between axes defining projection on o_bx_bPositive below the axis; l_x、l_y、l_zIndicating the distance o of the thrust action point from the origin_bThe 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):

in the formula J^-1(η) is the inverse of J (η).

By differentiating the formula (16), the

In the formula

Formula (19) left multiplication

Can obtain the product

The following equations (3), (19) and (21) can be combined:

in the formula

M_η(η)＝R^TMR (23)

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,

|τ_i|≤τ_i,max(27)

wherein, tau_i,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(k_pe)-γTanh(k_vV) (29)

wherein k is_p≥1，k_v≥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(k_px_e)，tanh(k_py_e)，tanh(k_pz_e)，tanh(k_pθ_e)，tanh(k_pψ_e)，tanh(k_pφ_e)]^T，Tanh(k_pV)＝[tanh(k_pu)，tanh(k_pv)，tanh(k_pw)，tanh(k_pp)，tanh(k_pq)，tanh(k_pr)]^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;

η_d＝[x_d,y_d,z_d,θ_d,ψ_d,φ_d]^Tfor command track, where x_d、y_d、z_d、θ_d、ψ_dAnd phi_dRespectively 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;

o_exyz represents a ground coordinate system;

o_bx_by_bz_brepresenting an airship body coordinate system;

CV is the floating center of the airship;

CG is the center of gravity of the airship;

r_G＝[x_G,y_G,z_G]^Tis the vector from the floating center to the center of gravity;

e＝[x_e,y_e,z_e,θ_e,ψ_e,φ_e]^Tfor track control errors, x_e、y_e、z_e、θ_e、ψ_eAnd phi_eRespectively 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:

η_d＝[5sin(0.02t)m,5cos(0.01t)m,2+sin(0.01t)+cos(0.01t)m,0rad,0rad,0rad]^T，x_d、y_d、z_d、θ_d、ψ_dand phi_dRespectively 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-η_d＝[x-x_d,y-y_d,z-z_d,θ-θ_d,ψ-ψ_d,φ-φ_d]^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:

in the formula

Wherein

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):

in the formula, J^-1(η) is the inverse of J (η),

by differentiating the formula (44), the

In the formula

Formula (47) left multiplication

Can obtain the product

The formula (31), the formula (47) and the formula (49) can be combined to obtain:

in the formula

M_η(η)＝R^TMR (51)

|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

2) Design of track control law

Designing the following control law of limited track

τ＝-N-G-J(η)λTanh(k_pe)-γTanh(k_vV) (57)

Wherein k is_p＝2，k_pλ ═ 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. 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 η_d＝[x_d,y_d,z_d,θ_d,ψ_d,φ_d]^T，x_d、y_d、z_d、θ_d、ψ_dAnd phi_dRespectively 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;

e＝η-η_d＝[x-x_d,y-y_d,z-z_d,θ-θ_d,ψ-ψ_d,φ-φ_d]^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 o_exyz and body coordinate system o_bx_by_bz_bDescribing 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 r_G＝[x_G,y_G,z_G]^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:

in the formula

Wherein

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, C_X、C_Y、C_Z、C_l、C_m、C_nIs the aerodynamic coefficient; i is_x、I_y、I_zAre respectively wound around o_bx_b、o_by_b、o_bz_bThe primary inertia of; i is_xy、I_xz、I_yzRespectively about a plane o_bx_by_b、o_bx_bz_b、o_by_bz_bProduct of inertia; t is the magnitude of thrust, μ is the thrust vector and o_bx_bz_bAngle between faces, defined at o_bx_bz_bThe left of the surface is positive, upsilon is the thrust vector at o_bx_bz_bProjection of a surface and_bx_bangle between axes defining projection on o_bx_bPositive below the axis; l_x、l_y、l_zIndicating the distance o of the thrust action point from the origin_bIs 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):

in the formula J^-1(η) is the inverse of J (η);

by differentiating the formula (16), the

In the formula

Formula (19) left multiplication

Can obtain the product

The following equations (3), (19) and (21) can be combined:

in the formula

M_η(η)＝R^TMR (23)

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;

|τ_i|≤τ_i,max(27)

wherein, tau_i,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;

τ＝-N-G-J(η)λTanh(k_pe)-γTanh(k_vV) (29)

wherein k is_p≥1，k_v≥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(k_px_e)，tanh(k_py_e)，tanh(k_pz_e)，tanh(k_pθ_e)，tanh(k_pψ_e)，tanh(k_pφ_e)]^T，

Tanh(k_pV)＝[tanh(k_pu)，tanh(k_pv)，tanh(k_pw)，tanh(k_pp)，tanh(k_pq)，tanh(k_pr)]^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.