Inertial-airflow coordinate system interaction aircraft airflow disturbance observer design method

Abstract

The application discloses a design method of an air flow disturbance observer of an aircraft inertia-air flow coordinate system interaction, and specific steps include: for a fixed-wing aircraft under air flow disturbance, determining a fixed-wing aircraft coordinate system, calculating a flight path pitch angle, a flight path azimuth angle and a flight path roll angle under an air flow coordinate system according to a conversion relationship between each coordinate system; selecting an inertia system coordinate and air speed, a flight path inclination angle and a flight path inclination angle under an air flow system as system states, and establishing a position loop dynamics model of the fixed-wing aircraft under air flow disturbance; defining equivalent auxiliary variables of air flow disturbance, and performing dynamic analysis on the equivalent auxiliary variables according to the position loop dynamics model; and designing an air flow disturbance observer according to a dynamic analysis result. The application introduces non-deterministic equivalent auxiliary variables, can realize decoupling estimation of air flow disturbance and flight state, and is more suitable for a scene of severe aircraft maneuvering.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic control, in particular to a kind of inertial-airflow coordinate system interaction aircraft airflow interference observer design method. BACKGROUND

[0002] In the process of fixed-wing aircraft maneuvering flight, factors such as gust, turbulence, engine vibration and unpredictable operation will have a negative impact on the performance of the aircraft, especially when the aircraft performs flight tasks in special terrain such as canyons and sea surfaces, if the external disturbance cannot be suppressed in time, it will bring great safety hazards to the entire flight control system. Obviously, the existence of external disturbance not only reduces the flight performance of large maneuvering aircraft, but also couples with the aerodynamic force of the aircraft, making the design of the controller difficult. The current method for handling external disturbance is the most representative interference observer method.

[0003] In the process of designing aircraft interference observer in the prior art, unknown terms caused by airflow disturbance are usually estimated as compound disturbance. However, the external disturbance on the aircraft is coupled with the flight state, especially when the aircraft is maneuvering, the conventional method of handling compound disturbance is not conducive to accurate estimation of airflow disturbance by the aircraft, resulting in a large error in the existing airflow disturbance estimation. SUMMARY

[0004] The purpose of the present application is to provide an inertial-airflow coordinate system interaction aircraft airflow interference observer design method.

[0005] Technical scheme: The inertial-airflow coordinate system interaction aircraft airflow interference observer design method of the present application comprises the following steps:

[0006] S10, for a fixed-wing aircraft under airflow disturbance, determine the fixed-wing aircraft coordinate system, calculate the track pitch angle, track azimuth angle and track roll angle in the airflow coordinate system according to the conversion relationship between each coordinate system;

[0007] S20, select the inertial system coordinate and the airspeed, track inclination angle and track inclination angle in the airflow system as the system state, and establish a position loop dynamics model of the fixed-wing aircraft under airflow disturbance;

[0008] S30, define the equivalent auxiliary variable of airflow disturbance, and perform dynamic analysis on the equivalent auxiliary variable according to the position loop dynamics model;

[0009] S40, design an airflow disturbance observer according to the dynamic analysis result.

[0010] Further, step S10 specifically comprises:

[0011] By defining the state variables in each coordinate system of the fixed-wing aircraft, the transformation matrices between the coordinate systems are obtained as follows:

[0012] Body coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0013]

[0014] Body coordinate system to inertial coordinate system rotation matrix The expression is:

[0015]

[0016] Inertial coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0017]

[0018] In the formula, β a Represents the sideslip angle, α a θ represents the angle of attack. b φ represents the pitch angle. b ψ represents the roll angle. b Indicates the yaw angle;

[0019] According to coordinate system transformation relationships Obtain the pitch angle γ of the flight path p azimuth angle of the flight path χ p and track roll angle μ p .

[0020] Furthermore, step S20 specifically includes:

[0021] Define the state vector of the fixed-wing aircraft as p g =[p x ,p y ,p z ] T Ξ a =[V a ,χ p ,γ p ] T and Ω a =[α a ,β a ,μ p ] T , making w v with w aLet represent the projections of wind speed and wind acceleration onto the inertial coordinate system, respectively. Then, the expression for the position loop dynamics model of the fixed-wing aircraft is:

[0022]

[0023] Where, p x ,p y and p z V represents the location information of the aircraft. a Indicates airspeed; f p (·) and f Ξ (·) represents a known function vector, r Ξ (·) represents a known function matrix, with the following expressions:

[0024]

[0025]

[0026]

[0027] In the formula, F T This indicates engine thrust.

[0028] Furthermore, the wind speed and wind acceleration vector is defined as d w =col{w v ,w a The airflow disturbance of the aircraft is generated by the following external systems:

[0029]

[0030] in, Let l be the state vector of the external system, where l is a positive integer representing the state dimension of the external system. Given a constant matrix, Given a constant matrix, Given a constant matrix, The observability condition is met. Let Δ be an unknown time-varying vector, where t≥0 represents time. w (t) is bounded, i.e., the constant vector δ Δ >0 satisfies the following relationships:

[0031]

[0032] Furthermore, step S30 specifically includes:

[0033] Define the equivalent auxiliary variable for aircraft airflow interference as s w The expression is:

[0034]

[0035] Where, x w For the augmented system state vector, x w =[p x ,p y ,p z V a ,χ p ,γ p ] T , The vector representing a nonlinear function is expressed as:

[0036]

[0037] In the formula, L represents the gain matrix. w and The following relationship exists:

[0038]

[0039] In the formula, r w Let r represent the interference coefficient matrix. w =diag{I3,r Ξ}, where I3 represents a 3×3 identity matrix;

[0040] Based on the external system and position loop dynamics model of the aircraft generating airflow disturbance, the equivalent auxiliary variable s w The dynamic induction can be expressed by the following expression:

[0041]

[0042] in,

[0043] Furthermore, step S40 specifically includes:

[0044] Equivalent auxiliary variable s for airflow disturbance w The expression for the aircraft airflow interference observer is designed as follows:

[0045]

[0046] in, For the observer state, The vector d represents the wind speed and wind acceleration. w The estimate.

[0047] Beneficial effects: Compared with the prior art, the significant advantage of this invention is that, compared with the conventional linear disturbance observer design which estimates the unknowns caused by airflow disturbances as composite disturbances, this invention introduces a special nondeterministic equivalent auxiliary variable s. w It can achieve decoupled estimation of airflow interference and flight status, making it more suitable for scenarios with violent aircraft maneuvers. Attached Figure Description

[0048] Figure 1 Flowchart of the design method for an airflow interference observer for an aircraft with inertial-airflow coordinate system interaction. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0050] like Figure 1 The diagram shows a flowchart of the design method for an aircraft airflow interference observer with inertial-airflow coordinate system interaction as described in this embodiment. The method includes the following steps:

[0051] Step S10: For a fixed-wing aircraft under airflow interference, determine the coordinate system of the fixed-wing aircraft, and calculate the pitch angle, azimuth angle and roll angle of the flight path in the airflow coordinate system according to the transformation relationship between the coordinate systems.

[0052] To describe the dynamics model of the aircraft, we consider an inertial coordinate system. airflow coordinate system Track coordinate system and the body coordinate system To establish the transformation relationships between different coordinate systems, we assume an inertial coordinate system. The origin is the center of mass of the spacecraft, let Indicates the coordinate axis system To the coordinate axis system The transformation matrix of the projection, where i,j∈{g,p,b,a}.

[0053] Specifically, step S10 includes:

[0054] By defining the state variables in each coordinate system of the fixed-wing aircraft, the transformation matrices between the coordinate systems are obtained as follows:

[0055] (1) Body coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0056]

[0057] Where, θ b φ is the pitch angle. b For the roll angle, ψ b For yaw angle, Euler angle θ b ,ψ b ,ψ b It is usually measured by an airborne gyroscope;

[0058] (2) Inertial coordinate system To the track coordinate system Transformation matrix The expression is:

[0059]

[0060] Where, γ p For the pitch angle of the flight path, χ p The azimuth angle of the flight path;

[0061] (3) Track coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0062]

[0063] Where, μ p The roll angle of the flight path;

[0064] (4) Inertial coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0065]

[0066] (5) Body coordinate system To the airflow coordinate system Transformation matrix The expression is:

[0067]

[0068] In the formula, β a Represents the sideslip angle, α a Indicates the angle of attack, which can be obtained from subscripts.

[0069] Based on the above coordinate system transformation relationships Obtain the track angle χ p ,γ p and μ p .

[0070] Step S20: Select the coordinates in the inertial frame and the airspeed, track tilt angle and track tilt angle in the airflow system as the system states, and establish the position loop dynamic model of the fixed-wing aircraft under airflow interference.

[0071] Step S20 specifically includes:

[0072] Define the state vector of the fixed-wing aircraft as p g =[p x ,p y ,p z ] T Ξ a =[V a ,χ p ,γ p ] T and Ω a =[α a ,β a ,μ p ] T , making w v with w a Let represent the projections of wind speed and wind acceleration onto the inertial coordinate system, respectively. Then, the expression for the position loop dynamics model of the fixed-wing aircraft is:

[0073]

[0074] Where, p x ,p y and p z The location information of the aircraft can be obtained through devices such as GPS; V a This represents airspeed, which can be measured by the pitot tube; f p (·) and f Ξ (·) represents a known function vector, r Ξ (·) represents a known function matrix, with the following expressions:

[0075]

[0076]

[0077]

[0078] In one example, to account for the effects of external airflow disturbances in the aircraft motion model, the velocity vector V of the aircraft relative to the inertial coordinate system is defined. g airspeed V a Vector projection V in the inertial coordinate system a→g The projection vector of wind speed onto the inertial coordinate system Based on the relationships between velocity vectors, the following vector trigonometric relationships can be obtained:

[0079] V g =V a→g +w v

[0080] In the inertial coordinate system The above vector trigonometric relationship can be expressed as the following expression:

[0081]

[0082] In the above formula, [V a ,0,0] T airspeed vector V a In the airflow coordinate system The projection vector below. Substitute into the transformation matrix. The specific form in which the aircraft is located can be obtained. Mid-coordinate position p g The kinematic dynamics are as follows:

[0083]

[0084] In the above formula, the first term after the equals sign is f. p (Ξ a The second item is w. v Then we have:

[0085]

[0086] According to Newton's second law, the kinematic equations of the aircraft's center of mass can be written as:

[0087]

[0088] In the formula, F total This represents the vector projection of the net external force acting on the aircraft onto the inertial coordinate system. (The inertial coordinate system is used as the reference point.) If we take a frame of reference as an example, then the kinematic equations of the center of mass can be written as follows:

[0089]

[0090] Among them, F T For engine thrust, and These are the aerodynamic drag, side force, and lift acting on the aircraft, respectively. Simplifying these, we can obtain the pitch angle γ of the flight path. p With track azimuth angle χ p The dynamic differential equation is:

[0091]

[0092] Combining the properties of rotation matrices and The above formula can be derived into the following form:

[0093]

[0094] Therefore, another equation included in the position loop dynamics model can be obtained as follows:

[0095]

[0096] In the above formula, the first term after the equals sign is f. Ξ (Ξ a ,Ω a The second term is r. Ξ (Ξ a )w a Then we have:

[0097]

[0098] In summary, the dynamic relationship of the aircraft's position loop is expressed as follows:

[0099]

[0100] Furthermore, the wind speed and wind acceleration vector is defined as d w =col{w v ,w a The airflow disturbance of the aircraft is generated by the following external systems:

[0101]

[0102] in, Let l be the state vector of the external system, where l is a positive integer representing the state dimension of the external system. Given a constant matrix, Given a constant matrix, Given a constant matrix, The observability condition is met. Let Δ be an unknown time-varying vector, where t represents time and t>0. w (t) is bounded, that is, there exists a constant vector δ. Δ >0 satisfies the following relationship:

[0103]

[0104] Step S30: Define equivalent auxiliary variables for airflow disturbance and perform dynamic analysis on the equivalent auxiliary variables based on the position loop dynamics model.

[0105] Specifically, step S30 includes:

[0106] Define the equivalent auxiliary variable for aircraft airflow interference as sw The expression is:

[0107]

[0108] Where, x w Let x be the system state vector. w =[p x ,p y ,p z V a ,χ p ,γ p ] T , L represents a vector of nonlinear functions. Given that linear systems are more convenient in selecting parameters and analyzing stability, L... w The expression is:

[0109]

[0110] In the formula, L represents the gain matrix. w and The following relationship exists:

[0111]

[0112] In the formula, r w Let r represent the interference coefficient matrix. w =diag{I3,r Ξ}, where I3 represents a 3×3 identity matrix.

[0113] Based on the external system and position loop dynamics model of the aircraft generating airflow disturbance, the equivalent auxiliary variable s w The dynamic induction can be expressed by the following expression:

[0114]

[0115] Where, φ w It can be considered as an auxiliary variable s w The known output in a dynamic context can be written in the following form:

[0116]

[0117] Step S40: Design an airflow interference observer based on the dynamic analysis results.

[0118] Specifically, step S40 includes:

[0119] For the equivalent auxiliary variable s of defining airflow disturbance w The expression for the aircraft airflow interference observer is designed as follows:

[0120]

[0121] in, For the observer state, The vector d represents the wind speed and wind acceleration. w The estimate.

[0122] To further verify the accuracy of the aircraft airflow interference observer proposed in this invention, the interference observer estimation error is defined. Based on the expression for the airflow disturbance observer, the derivative of the estimation error can be obtained as follows:

[0123]

[0124] Specify positive definite matrix The alternative Lyapunov functions are defined as follows:

[0125]

[0126] Using Young's inequality and inequality (15), the derivative of the Lyapunov function satisfies the following inequality based on the derivative of the estimation error:

[0127]

[0128] Where, η w >0 indicates an adjustable parameter;

[0129]

[0130] For any given η e >0, when the parameter P w With η w Choose the following linear matrix inequalities:

[0131]

[0132] The interference observer estimation error satisfies the following inequality:

[0133]

Claims

1. A design method for an aircraft airflow interference observer with inertial-airflow coordinate system interaction, characterized in that, Includes the following steps: S10, for fixed-wing aircraft under airflow interference, determine the coordinate system of the fixed-wing aircraft, and calculate the pitch angle, azimuth angle and roll angle of the flight path in the airflow coordinate system according to the transformation relationship between the coordinate systems; S20. By selecting coordinates in the inertial frame and airspeed, track tilt angle and track tilt angle in the airflow system as the system states, a position loop dynamic model of a fixed-wing aircraft under airflow interference is established. S30 defines the equivalent auxiliary variables of airflow disturbance, and performs dynamic analysis on the equivalent auxiliary variables based on the position loop dynamics model; S40, an airflow interference observer is designed based on dynamic analysis results; Step S30 specifically includes: Define the equivalent auxiliary variable for aircraft airflow interference as s w The expression is: In the formula, x w For the augmented system state vector, x w =[p x ,p y ,p z V a ,χ p ,γ p ] T , The vector representing a nonlinear function is expressed as: In the formula, L represents the gain matrix. w and The following relationship exists: In the formula, r w Let r represent the interference coefficient matrix. w =diag{I3,r Ξ }, where I3 represents a 3×3 identity matrix; Based on the external system and position loop dynamics model of the aircraft generating airflow disturbance, the equivalent auxiliary variable s w The dynamic induction can be expressed by the following expression: In the formula, Given a constant matrix, Given a constant matrix, f p with f Ξ Given a function vector: V a F represents airspeed. T Indicates engine thrust, β a Represents the sideslip angle, α a θ represents the angle of attack. b φ represents the pitch angle. b ψ represents the roll angle. b Indicates the yaw angle; γ p For the pitch angle of the flight path, χ p For the azimuth angle of the flight path, μ p The roll angle of the track. and These are the aerodynamic drag, side force, and lift acting on the aircraft, respectively.

2. The design method for an aircraft airflow interference observer according to claim 1, characterized in that, Step S10 specifically includes: By defining the state variables in each coordinate system of the fixed-wing aircraft, the transformation matrices between the coordinate systems are obtained as follows: Body coordinate system To the airflow coordinate system Transformation matrix The expression is: Body coordinate system to inertial coordinate system rotation matrix The expression is: Inertial coordinate system To the airflow coordinate system Transformation matrix The expression is: In the formula, β a Represents the sideslip angle, α a θ represents the angle of attack. b φ represents the pitch angle. b ψ represents the roll angle. b Indicates the yaw angle; Furthermore, based on the coordinate system transformation relationship Obtain the pitch angle γ of the flight path p azimuth angle of the flight path χ p and track roll angle μ p .

3. The design method for an aircraft airflow interference observer according to claim 2, characterized in that, Step S20 specifically includes: Define the state vector of the fixed-wing aircraft as p g =[p x ,p y ,p z ] T Ξ a =[V a ,χ p ,γ p ] T and Ω a =[α a ,β a ,μ p ] T , making w v with w a Let represent the projections of wind speed and wind acceleration onto the inertial coordinate system, respectively. Then, the expression for the position loop dynamics model of the fixed-wing aircraft is: Where, p x p y and p z V represents the coordinates of the aircraft in the inertial frame. a Indicates airspeed; f p (·) and f Ξ (·) represents a known function vector, r Ξ (·) represents a known function matrix, expressed as follows: In the formula, F T This indicates engine thrust.

4. The design method for an aircraft airflow interference observer according to claim 3, characterized in that, The wind speed and wind acceleration vector is defined as d w =col{w v ,w a The airflow disturbance of the aircraft is generated by the following external systems: In the formula, Let l be the state vector of the external system, where l is a positive integer representing the state dimension of the external system. Given a constant matrix, Given a constant matrix, Given a constant matrix, The observability condition is met. Let Δ be an unknown time-varying vector, where t≥0 represents time. w (t) is bounded, that is, there exists a constant vector δ. Δ >0 satisfies the following relationship:

5. The design method for an aircraft airflow interference observer according to claim 4, characterized in that, Step S40 specifically includes: Equivalent auxiliary variable s for airflow disturbance w The expression for the aircraft airflow interference observer is designed as follows: in, For the observer state, The vector d represents the wind speed and wind acceleration. w The estimate.

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