Universal aircraft digital simulation model design method

Abstract

The invention discloses a general aircraft digital simulation model design method, and belongs to the field of aircraft simulation design. Firstly, acquiring a conversion relation of four common coordinate systems describing the movement of the aircraft, establishing a six-degree-of-freedom movement mathematical model of the aircraft by utilizing a Newton second law and a moment of momentum theorem, and obtaining a kinematics equation set according to a projection relation between an attitude angle and an angular rate and a relation between a velocity component and the position of the aircraft; then, the complex dynamic equation set is decoupled into longitudinal motion and transverse heading motion; according to a small disturbance model, respectively linearly simplifying the longitudinal motion and the transverse course motion into a standard state space equation form; and finally, establishing a digital simulation model of the general aircraft by using the standard state space equation, and loading the model to an aircraft simulation system to realize task-level simulation. According to the method, the actual movement of the aircraft is considered, the modeling process is simplified, and the simulation precision requirement is met.

Description

Technical Field

[0001] The invention belongs to the field of simulation design of aircraft cluster verification platforms, and specifically relates to a general aircraft digital simulation model design method. Background Art

[0002] With the rapid development of artificial intelligence, sensing and communication technologies, aircraft swarms have attracted widespread attention due to their high fault tolerance and ability to effectively respond to diverse tasks. However, the development of swarm technology faces problems such as multiple disciplines involved, long verification time and high experimental costs.

[0003] Therefore, building a simulation system for intelligent aircraft is of great significance to the formation control, target allocation, and mission decision-making algorithms of aircraft clusters, and even to strategic testing, verification, and deduction.

[0004] However, the actual motion of an aircraft is complex, involving the interaction and control of modules such as the seeker, autopilot, servo, and sensor, and there are many factors to consider during the flight process, such as ground curvature and changes in the mass of the aircraft. Therefore, designing an aircraft motion simulation model that fully fits the actual situation is large and cumbersome, and takes up a lot of resources. The simplified three-degree-of-freedom motion model is relatively simple, but it cannot meet the simulation accuracy requirements. Summary of the invention

[0005] In view of the above problems, the present invention proposes a universal aircraft digital simulation model design method, which is based on the six-degree-of-freedom motion mathematical model of the aircraft. From an engineering perspective, the small disturbance model is linearly simplified to achieve the control of the aircraft motion. It not only takes into account the actual movement of the aircraft but also simplifies the modeling process, thereby meeting the simulation accuracy requirements.

[0006] The general aircraft digital simulation model design method comprises the following steps:

[0007] Step 1: Establish four common coordinate systems to describe the motion of the aircraft: ground coordinate system, body coordinate system, velocity coordinate system and track coordinate system;

[0008] Assume the ground coordinate system is O g X g Y g Z g , where the origin O g is the take-off point of the aircraft, O g X g The axis passes through the origin O g In the horizontal plane, pointing to the target is positive; O g Y g Axis passes through origin O g , perpendicular to the ground, with upward being positive; O g Z gAxis passes through origin O g , and O g X g Axis, O g Y g The axis is in right-hand relationship, and the four fingers are from O g X g Axis points to O g Y g Axis, the direction of the thumb is O g Z g The positive direction of the axis.

[0009] Assume the body coordinate system is OX b Y b Z b , where the origin O is the center of mass of the aircraft, OX b The axis points in the direction of the bullet; OZ b The axis is perpendicular to OX in the symmetry plane of the aircraft b Axis, pointing downward; OY b Axis and OX b Axis, OZ b The axis is in right-hand relationship, and the four fingers are from OZ b Axis points to OX b Axis, the direction of the thumb is OY b The positive direction of the axis.

[0010] Assume the velocity coordinate system is OX w Y w Z w , where the origin O is the center of mass of the aircraft, OX w Axis points to the direction of flight speed; OZ w The axis is perpendicular to OX in the symmetry plane of the aircraft w Axis, pointing downward; OY w Axis and OX w Axis, OZ w The axis is in right-hand relationship, and the four fingers are from OZ w Axis points to OX w Axis, the direction of the thumb is OY w The positive direction of the axis.

[0011] Assume the track coordinate system is OX k Y k Z k , where the origin O is the center of mass of the aircraft, OX k Axis points to the direction of flight speed; OZ k The axis is in the vertical plane containing the velocity vector and is perpendicular to OX k Axis, pointing downward; OY k Axis and OX k Axis, OZ k The axis is in right-hand relationship, and the four fingers are from OZk Axis points to OX k Axis, the direction of the thumb is OY k The positive direction of the axis.

[0012] Step 2: Obtain the transformation relationship and transformation matrix between coordinate systems, including:

[0013] 1) Relationship between the ground coordinate system and the body coordinate system: The ground coordinate system is rotated three times around the axis in different directions to obtain the body coordinate system.

[0014] The rotation angle is defined as follows:

[0015] The yaw angle ψ is the longitudinal axis OX of the aircraft b Projection on the horizontal plane and ground coordinate system OX g The angle between them is positive in the clockwise direction from due north, and the range is [O°, 360°];

[0016] The pitch angle θ is the longitudinal axis OX of the aircraft b With ground plane O g X g Y g The angle is positive when the nose is raised, and the range is [-90°, 90°];

[0017] Roll angle φ is the vertical axis OZ of the machine body b With OX b The included angle between the plumb planes is positive when the right side drops, and the range is [-90°, 90°];

[0018] Rotate the yaw angle ψ clockwise around the vertical axis of the ground system according to the right-hand principle, rotate the pitch angle θ counterclockwise around the horizontal axis of the transition system according to the right-hand principle, and rotate the roll angle φ counterclockwise around the longitudinal axis of the aircraft system according to the right-hand principle. The rotation matrix is:

[0019]

[0020] Among them, S ψθφ is the rotation matrix from the ground coordinate system to the body coordinate system, and a vector is expressed in ground coordinates as In the body coordinate system, it is expressed as Then there is the following relationship:

[0021] P b =S ψθφ P g

[0022] 2) Relationship between body coordinate system and velocity coordinate system:

[0023] The body coordinate system first revolves around its horizontal axis OY bRotate the attack angle α clockwise to get the transition system, the transformation matrix is ​​L(α), and then rotate around the transition system vertical axis OZ w The axis rotates clockwise by a sideslip angle β to obtain a velocity coordinate system, and the transformation matrix is ​​L(β). αβ Represents the rotation matrix from the body coordinate system to the velocity coordinate system:

[0024] Let a vector be expressed in the body coordinate system as In velocity coordinates it is expressed as Then there is the following relationship:

[0025] P w =S αβ P b

[0026] 3) Relationship between track coordinate system and ground coordinate system:

[0027] The ground coordinate system first revolves around the vertical axis OZ g Rotate a track azimuth angle χ, the transformation matrix is ​​L(χ), get the transition system, and then rotate around the horizontal axis OY of the transition system k Rotate the track by an inclination angle γ to obtain the track coordinate system, and the transformation matrix is ​​L(γ). χγ Represents the rotation matrix from the ground coordinate system to the track coordinate system:

[0028]

[0029] Let a vector be expressed in the ground coordinate system as In track coordinates it is expressed as Then there is the following relationship:

[0030] P k =S χγ P g

[0031] Step 3: Using Newton's second law and the momentum theorem, establish a mathematical model of the aircraft's six-degree-of-freedom motion, and obtain a group of kinematic equations based on the projection relationship between the attitude angle and the angular velocity and the relationship between the velocity component and the aircraft's position;

[0032] Specifically include:

[0033] The equation of motion for the center of mass is:

[0034]

[0035] Angular motion equations:

[0036]

[0037] M x , M y , Mz are the components of the moment of the total external force on the center of mass of the aircraft on each axis of the body coordinate system, M x Denotes the rolling moment, M y is the pitching moment, M z Represents the yaw moment.

[0038] Attitude motion equation:

[0039]

[0040] Navigation equation:

[0041]

[0042] in, Represents the component of the aircraft's velocity in the ground coordinate system, V k It represents the speed of the aircraft in the track coordinate system, S χγ T It is the rotation matrix from the track coordinate system to the ground coordinate system.

[0043] m represents the mass of the aircraft; u, w, v represent the components of the velocity vector of the aircraft in the ground coordinate system in the body coordinate system; p, q, r represent the components of the angular velocity of the body relative to the ground coordinate system in the body coordinate system; T represents thrust, D represents drag, L represents lift; Y represents side force; I represents side force. x Indicates the aircraft's OX b Moment of inertia about the shaft, I y Indicates the aircraft's OY to the aircraft body b Moment of inertia about the shaft, I z Indicates the aircraft's position on the aircraft's OZ b Moment of inertia about the shaft, I xz Indicates the aircraft's axis OX b With OZ b moment of inertia.

[0044] Step 4: Divide the dynamic equation group into longitudinal motion and lateral heading motion with the smallest relative coupling;

[0045] Longitudinal motion includes 1 rotation and 2 translations. When only considering longitudinal motion, β=φ≡0, p=r≡0, so the variable is [uwqθ]. The following equations are obtained:

[0046]

[0047] The lateral motion includes two rotations and one translation. When only the lateral motion is considered, α=θ≡0, q=0, so the variable is [vpr φ]. The following equations are obtained:

[0048]

[0049] Step 5: Linearly simplify the longitudinal motion according to the small disturbance model and simplify it into the standard state space equation form;

[0050] Let the state variable be x = [u, w, q, θ], and the control variable be u = [δ e , δ T ]. Among them, δ e represents the elevator deflection angle, δ T represents the throttle lever deflection angle. The longitudinal motion equations are simplified into the following form:

[0051]

[0052] By using the linear simplification of the small disturbance model and considering only two state variables, the angle of attack disturbance α and the pitch rate disturbance q, from the perspective of flight control engineering application, the speed change is u≈O, and the following formula is obtained:

[0053]

[0054] Among them, V m0 Indicates the flight speed of the aircraft, Z α , M α , is the large derivative in longitudinal motion, and the calculation formula is as follows:

[0055]

[0056] Where Q represents dynamic pressure, S represents wing area, d represents average aerodynamic chord length, I y represents the moment of inertia about the Y axis, C zα is the pitching force coefficient caused by the angle of attack, is the pitching force coefficient caused by elevator deflection, C mα is the pitching moment coefficient caused by the angle of attack, is the pitching moment coefficient caused by elevator deflection;

[0057] Step 6: Simplify the lateral motion linearly according to the small disturbance model and simplify it into the standard state space equation form;

[0058] Let the state variable be x = [v, p, r, φ], and the control variable be u = [δ r , δ a ]. Among them, δ r represents the rudder deflection angle, δ a Represents the aileron deflection angle. Similarly, using the small disturbance model linearization and taking the disturbance of the sideslip angle as a state variable, the following formula is obtained:

[0059]

[0060] Among them, Y β , N β , L β , L p , L r , N p , N r , is the large derivative in the lateral heading motion, and the calculation formula is as follows:

[0061] in, is the side force coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the rolling angular rate, is the rolling moment coefficient caused by the yaw rate, is the yaw moment coefficient caused by the sideslip angle, is the yaw moment coefficient caused by the roll angular rate, is the yaw moment coefficient caused by the yaw rate, is the side force coefficient caused by rudder deflection, is the side force coefficient caused by aileron deflection, is the rolling moment coefficient caused by rudder deflection, is the rolling moment coefficient caused by aileron deflection, is the yaw moment coefficient caused by rudder deflection, is the yaw moment coefficient caused by aileron deflection.

[0062] Step 7: Use the lateral and longitudinal motions in the form of standard state-space equations to build a digital simulation model of a general aircraft, and load the model into the aircraft simulation system to achieve mission-level simulation.

[0063] The advantages of the present invention are:

[0064] 1) A general aircraft digital simulation model design method, compared with the prior art that uses different coordinate systems to cause huge differences in subsequent research results, is difficult to convert between each other, and brings unnecessary trouble to the research. The present invention uniformly uses the European and American coordinate system to model missile and aircraft models, provides convenience for weapon simulation systems, and expands the wide application of the system.

[0065] 2) A general aircraft digital simulation model design method is proposed. Aiming at the simplicity and accuracy requirements of the simulation system, from an engineering perspective, the traditional six-degree-of-freedom nonlinear time-varying flight dynamics equations are decoupled into longitudinal and lateral motions. The small disturbance model is linearly simplified and the factors with small influence are ignored. The simplified longitudinal and lateral small disturbance state equations expressed by large aerodynamic derivatives are obtained, which ultimately realizes the control of general aircraft motion and meets the simulation accuracy requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 A flowchart of a method for designing a general aircraft digital simulation model according to the present invention;

[0067] Figure 2 A schematic diagram of the European and American coordinate system used in the present invention;

[0068] Figure 3 A schematic diagram of the ground coordinate system used in the present invention;

[0069] Figure 4 This is a schematic diagram of the body coordinate system used in the present invention;

[0070] Figure 5 A schematic diagram of the velocity coordinate system used in the present invention;

[0071] Figure 6 A schematic diagram of the track coordinate system used in the present invention;

[0072] Figure 7 It is a schematic diagram of the forces and moments acting on the aircraft according to the present invention;

[0073] Figure 8 A schematic diagram of the pitch rate error of a certain aircraft longitudinal control simulation system of the present invention;

[0074] Fig. 9 A schematic diagram of the yaw rate error of a certain aircraft lateral heading control simulation system of the present invention;

[0075] Fig.10 A schematic diagram of the roll angular rate error of a certain aircraft lateral heading control simulation system of the present invention; DETAILED DESCRIPTION

[0076] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only partial embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0077] The invention discloses a general aircraft digital simulation model design method. Based on the aircraft six-degree-of-freedom motion mathematical model, the six-degree-of-freedom motion mathematical model is decoupled into longitudinal and lateral heading motion from an engineering perspective. The small disturbance model is linearly simplified to obtain longitudinal and lateral heading small disturbance state equations represented by aerodynamic derivatives. Some aerodynamic derivatives with negligible effects are then removed to simplify the equations, thereby finally realizing the control of general aircraft motion.

[0078] The general aircraft digital simulation model design method is as follows: Figure 1 As shown, it includes the following steps:

[0079] Step 1: Establish four common coordinate systems to describe the motion of the aircraft: ground coordinate system, body coordinate system, velocity coordinate system and track coordinate system;

[0080] The Soviet coordinate system and the European and American coordinate system are two right-handed rectangular coordinate systems commonly used in the study of aircraft guidance and control problems. Missiles are generally modeled using the Soviet coordinate system, while aircraft are generally modeled using the European and American coordinate system. Figure 2 The difference in the coordinate systems used by the two results in very different subsequent conclusions, which brings inconvenience to the general aircraft digital simulation.

[0081] like Figure 3 As shown, let the ground coordinate system be O g X g Y g Z g , where the origin O g is the take-off point of the aircraft, O g X g The axis passes through the origin O g In the horizontal plane, pointing to the target is positive; O g Y g Axis passes through origin O g , perpendicular to the ground, with upward being positive; O g Z g Axis passes through origin O g , and O g X g Axis, O g Y g The axis is in right-hand relationship, and the four fingers are from O g X g Axis points to O g Y g Axis, the direction of the thumb is O g Z g The positive direction of the axis.

[0082] like Figure 4 As shown, let the body coordinate system be OX b Y b Z b, where the origin O is the center of mass of the aircraft, OX b The axis points in the direction of the bullet; OZ b The axis is perpendicular to OX in the symmetry plane of the aircraft b Axis, pointing downward; OY b Axis and OX b Axis, OZ b The axis is in right-hand relationship, and the four fingers are from OZ b Axis points to OX b Axis, the direction of the thumb is OY b The positive direction of the axis.

[0083] like Figure 5 As shown, let the velocity coordinate system be OX w Y w Z w , where the origin O is the center of mass of the aircraft, OX w Axis points to the direction of flight speed; OZ w The axis is perpendicular to OX in the symmetry plane of the aircraft w Axis, pointing downward; OY w Axis and OX w Axis, OZ w The axis is in right-hand relationship, and the four fingers are from OZ w Axis points to OX w Axis, the direction of the thumb is OY w The positive direction of the axis.

[0084] like Figure 6 As shown, let the track coordinate system be OX k Y k Z k , where the origin O is the center of mass of the aircraft, OX k Axis points to the direction of flight speed; OZ k The axis is in the vertical plane containing the velocity vector and is perpendicular to OX k Axis, pointing downward; OY k Axis and OX k Axis, OZ k The axis is in right-hand relationship, and the four fingers are from OZ k Axis points to OX k Axis, the direction of the thumb is OY k The positive direction of the axis.

[0085] Step 2: Obtain the transformation relationship and transformation matrix between coordinate systems, including:

[0086] 1) Relationship between the ground coordinate system and the body coordinate system: The ground coordinate system is rotated three times around the axis in different directions to obtain the body coordinate system.

[0087] The rotation angle is defined as follows:

[0088] The yaw angle ψ is the longitudinal axis OX of the aircraft b Projection on the horizontal plane and ground coordinate system OX g The angle between them is positive in the clockwise direction from due north, and the range is [O°, 360°];

[0089] The pitch angle θ is the longitudinal axis OX of the aircraft b With ground plane O g X g Y g The angle is positive when the nose is raised, and the range is [-90°, 90°];

[0090] Roll angle φ is the vertical axis OZ of the machine body b With OX b The included angle between the plumb planes is positive when the right side drops, and the range is [-90°, 90°];

[0091] The first rotation: Rotate the yaw angle ψ clockwise around the ground axis according to the right-hand rule. The transformation matrix is:

[0092]

[0093] Second rotation: Rotate the pitch angle θ counterclockwise around the horizontal axis of the transition system according to the right-hand rule. The transformation matrix is:

[0094]

[0095] The third rotation: rotate the roll angle φ counterclockwise around the longitudinal axis of the machine system according to the right-hand principle. The transformation matrix is:

[0096]

[0097] The total rotation matrix is

[0098]

[0099] Among them, S ψθφ is the rotation matrix from the ground coordinate system to the body coordinate system, S ψθφ T is the rotation matrix from the body coordinate system to the ground coordinate system. Let a vector be expressed in ground coordinates as In the body coordinate system, it is expressed as Then there is the following relationship:

[0100] P b =S ψθφ P g (5)

[0101] P g =S ψθφ T P b (6)

[0102] 2) Relationship between body coordinate system and velocity coordinate system:

[0103] The body coordinate system first revolves around its horizontal axis OY b Rotate the attack angle α clockwise (from right to left) to get the transition system, the transformation matrix is ​​L(α), and then rotate around the vertical axis OZ of the transition system w The axis rotates clockwise (from top to bottom) by a sideslip angle β to obtain a velocity coordinate system with a transformation matrix of L(β). αβ Represents the rotation matrix from the body coordinate system to the velocity coordinate system, S αβ T It is the rotation matrix from the velocity coordinate system to the body coordinate system.

[0104]

[0105] Let a vector be expressed in the body coordinate system as In velocity coordinates it is expressed as Then there is the following relationship:

[0106] P w =S αβ P b (8)

[0107] P b =S αβ T P w (9)

[0108] 3) Relationship between track coordinate system and ground coordinate system:

[0109] The ground coordinate system first revolves around the vertical axis OZ g Rotate a track azimuth X, the transformation matrix is ​​L(X), get the transition system, and then rotate around the horizontal axis OY of the transition system k Rotate the track by an inclination angle γ to obtain the track coordinate system, and the transformation matrix is ​​L(γ). χγ Represents the rotation matrix from the ground coordinate system to the track coordinate system, S χγ T It is the rotation matrix from the track coordinate system to the ground coordinate system.

[0110]

[0111] Let a vector be expressed in the ground coordinate system as In track coordinates it is expressed as Then there is the following relationship:

[0112] P k =S χγ P g (11)

[0113] P g =S χγ T P k (12)

[0114] Step 3: Using Newton's second law and the momentum theorem, establish a mathematical model of the aircraft's six-degree-of-freedom motion, and obtain a group of kinematic equations based on the projection relationship between the attitude angle and the angular velocity, and the relationship between the velocity component and the aircraft's position;

[0115] First, analyze the forces and moments acting on the aircraft, such as Figure 7 As shown, G represents gravity. The force balance equations are established according to Newton's second law. Since the body coordinate system is a non-inertial system, the traditional Newton's second law is corrected using the vector differential formula so that it can also be used in a non-inertial system:

[0116]

[0117] All forces are decomposed into the body coordinate system for analysis, and the coordinate transformation matrix is ​​used to obtain equation (15), where F x , F y , F z It represents the components of the resultant force acting on the missile in the three axes of the body coordinate system.

[0118]

[0119] Similarly, according to the momentum moment theorem and vector differential formula, the torque balance equations are established in the body coordinate system.

[0120]

[0121] in, is the resultant force acting on the missile, is the resultant torque acting on the missile, represents the velocity of the missile relative to the ground coordinate system, represents the missile's momentum relative to the ground coordinate system, It represents the total angular velocity vector of the body coordinate system relative to the ground coordinate system. Assuming the basic unit vectors of the body system are i, j, k, then In the machine system, it can be vectorized into According to the above inferences, we get:

[0122] 1. Dynamic equation of mass center motion in the body coordinate system:

[0123]

[0124] 2. Dynamic equation of rotation around the center of mass in the body coordinate system:

[0125]

[0126] m represents the mass of the aircraft; p, q, r are the components of the angular velocity of the aircraft relative to the ground coordinate system in the aircraft coordinate system; u, w, v are the components of the flight velocity of the aircraft relative to the ground coordinate system in the aircraft coordinate system; M x ,M y ,M z are the components of the moment of the total external force on the center of mass of the aircraft on each axis of the body coordinate system, M x Denotes the rolling moment, M y is the pitching moment, M z represents the yaw moment. T represents the thrust of the engine, D represents the drag, and L represents the lift;

[0127] Y represents the lateral force;

[0128] I x Indicates the aircraft's OX b Moment of inertia about the shaft, I y Indicates the aircraft's OY to the aircraft body b Moment of inertia about the shaft, I z Indicates the aircraft's position on the aircraft's OZ b Moment of inertia about the shaft, I xz Indicates the aircraft's axis OX b With OZ b moment of inertia.

[0129] According to the projection relationship between attitude angle and angular velocity and the relationship between velocity component and aircraft position, the kinematic equations are obtained:

[0130] 3. Posture motion equation:

[0131]

[0132] 4. Navigation equation:

[0133]

[0134] in, Represents the component of the aircraft's velocity in the ground coordinate system, V k Indicates the speed of the aircraft in the track coordinate system.

[0135] Step 4: Divide the dynamic equation group into longitudinal motion and lateral heading motion with the smallest relative coupling;

[0136] It can be seen from the established mathematical model of missile motion that 9 state variables are needed to describe the flight state of the missile, among which the yaw angle is not affected by the force, and the remaining variables are coupled with each other, which is troublesome to handle, so they are decoupled into two groups of motion: longitudinal motion and lateral heading motion.

[0137] Longitudinal motion includes 1 rotation and 2 translations, resulting in the following set of equations. When only considering longitudinal motion, β=φ≡0, p=r≡0, so the variables are [uwq θ].

[0138]

[0139] The lateral motion includes two rotations and one translation, resulting in the following set of equations. When only the lateral motion is considered, α=θ≡0, q=0, so the variable is [vpr φ].

[0140]

[0141] Step 5: Linearly simplify the longitudinal motion according to the small disturbance model and simplify it into the standard state space equation form in order to directly utilize the results of LQG control theory;

[0142] Let the state variable be x = [u, w, q, θ], and the control variable be u = [δ e ,δ T ]. Among them, δ e represents the elevator deflection angle, δ T Represents the throttle stick deflection angle. Simplify the above equations into the following form:

[0143]

[0144] After linearization with the small disturbance model, the longitudinal small disturbance equation is obtained:

[0145]

[0146] But in many cases, for the convenience of observation, the disturbance of the angle of attack is generally used as the state variable.

[0147]

[0148] Substituting into formula (25), we get:

[0149]

[0150] Observing equation (27), we find that the matrix contained in the simplified longitudinal motion equation is still very complex. Starting from the application of flight control engineering, we further simplify it. Longitudinal motion is generally divided into two modes. For flight control, we are generally more concerned with short-period modes. For short-period modes, they are mainly determined by two state variables: the angle of attack disturbance α and the pitch rate disturbance q. It is assumed that the speed has not had time to change, that is, u≈0. Starting from the actual values ​​of the aircraft, we find that the influence of the engine on the short period can be ignored, that is, the value containing δ T The term can be ignored. Considering the simplest case, Z q ,M q , The influence on the longitudinal motion of the aircraft is small and can be ignored, and the following formula is obtained:

[0151]

[0152] Among them, Z α , M α , is the large derivative in longitudinal motion, and the calculation formula is as follows:

[0153]

[0154] Where Q represents dynamic pressure, S represents wing area, d represents average aerodynamic chord length, I y represents the moment of inertia about the Y axis, C zα is the pitching force coefficient caused by the angle of attack, is the pitching force coefficient caused by elevator deflection, C mα is the pitching moment coefficient caused by the angle of attack, is the pitching moment coefficient caused by elevator deflection,

[0155] Step 6: Linearly simplify the lateral motion according to the small disturbance model. In order to directly use the results of LQG control theory, simplify it into the standard state space equation form.

[0156] Let the state variable be x = [v, p, r, φ], and the control variable be u = [δ r , δ a ]. Among them, δ r represents the rudder deflection angle, δ a Represents the aileron deflection angle. Similarly, first convert it into the form of equation (24), and use the small perturbation model to linearize it to obtain the lateral small perturbation equation:

[0157]

[0158] In order to facilitate the observation of state variables, the disturbance of the sideslip angle is usually taken as a state variable.

[0159]

[0160] Substituting into equation (33), and finally ignoring the smile factor, we can obtain the following equation:

[0161]

[0162] In practical applications, Y p and Y r It is generally very small and can be ignored. Formula (5-5) can be simplified to

[0163]

[0164] Among them, Y β , N β , L β , L p , L r , N p , N r , is the large derivative in the lateral heading motion, and the calculation formula is as follows:

[0165] in, is the side force coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the rolling angular rate, is the rolling moment coefficient caused by the yaw rate, is the yaw moment coefficient caused by the sideslip angle, is the yaw moment coefficient caused by the roll angular rate, is the yaw moment coefficient caused by the yaw rate, is the side force coefficient caused by rudder deflection, is the side force coefficient caused by aileron deflection, is the rolling moment coefficient caused by rudder deflection, is the rolling moment coefficient caused by aileron deflection, is the yaw moment coefficient caused by rudder deflection, is the yaw moment coefficient caused by aileron deflection.

[0166] Step 7: Use the lateral and longitudinal motions in the form of standard state-space equations to build a digital simulation model of a general aircraft, and load the model into the aircraft simulation system to achieve mission-level simulation.

[0167] like Figure 8As shown, it is a schematic diagram of the pitch rate error of a certain missile longitudinal control simulation system of the present invention, wherein the horizontal axis represents time, in seconds; the vertical axis represents the missile pitch rate error, in microradians / second; the curve is a curve showing the error between the actual value of the missile pitch rate and the control expected value over time.

[0168] like Fig. 9 As shown in the figure, it is a schematic diagram of the yaw rate error of a missile lateral heading control simulation system of the present invention, wherein the horizontal axis represents time, in seconds; the vertical axis represents the missile yaw rate error, in microradians per second; the curve in the figure is a curve showing the error between the actual value of the missile yaw rate and the control expected value over time.

[0169] like Fig.10 As shown in the figure, it is a schematic diagram of the roll angular rate error of a missile lateral heading control simulation system of the present invention, wherein the horizontal axis represents time, in seconds; the vertical axis represents the missile roll angular rate error, in microradians / second; the curve in the figure is a curve showing the error between the actual value of the missile roll angular rate and the control expected value over time.

Claims

1. A method for designing a general aircraft digital simulation model, characterized in that: The specific steps are as follows: Step 1: Establish four common coordinate systems to describe the motion of the aircraft: ground coordinate system, body coordinate system, velocity coordinate system and track coordinate system; Step 2: Obtain the transformation relationship and transformation matrix between coordinate systems; Step 3: Using Newton's second law and the momentum theorem, establish a mathematical model of the aircraft's six-degree-of-freedom motion, and obtain a group of kinematic equations based on the projection relationship between the attitude angle and the angular velocity and the relationship between the velocity component and the aircraft's position; Specifically include: The equation of motion for the center of mass is: m represents the mass of the aircraft; u, w, v represent the components of the velocity vector of the aircraft in the ground coordinate system in the body coordinate system; p, q, r represent the components of the angular velocity of the body relative to the ground coordinate system in the body coordinate system; T represents thrust, D represents drag, L represents lift; Y represents side force; θ represents the pitch angle; φ represents the roll angle; α represents the angle of attack; β represents the sideslip angle; Angular motion equations: M x ,M y ,M z are the components of the moment of the total external force on the center of mass of the aircraft on each axis of the body coordinate system, M x Denotes the rolling moment, M y is the pitching moment, M z I represents the yaw moment; x Indicates the aircraft's OX b Moment of inertia about the shaft, I y Indicates the aircraft's OY to the aircraft body b Moment of inertia about the shaft, I z Indicates the aircraft's position on the aircraft's OZ b Moment of inertia about the shaft, I xz Indicates the aircraft's axis OX b With OZ b The moment of inertia; Attitude motion equation: ψ is the yaw angle; Navigation equation: in, Represents the component of the aircraft's velocity in the ground coordinate system, V k It represents the speed of the aircraft in the track coordinate system, S χγ T is the rotation matrix from the track coordinate system to the ground coordinate system; Step 4: Divide the dynamic equation group into longitudinal motion and lateral heading motion with the smallest relative coupling; Longitudinal motion includes 1 rotation and 2 translations. When only considering the longitudinal motion, β=φ≡0, p=r≡0, so the variable is [uwqθ], and the following equations are obtained: The lateral motion includes two rotations and one translation. When only the lateral motion is considered, α=θ≡0, q=0, so the variable is [vprφ], and the following equations are obtained: Step 5: Linearly simplify the longitudinal motion according to the small disturbance model and simplify it into the standard state space equation form; Let the state variable be x = [u, w, q, θ], and the control variable be u = [δ e ,δ T ]; where δ e represents the elevator deflection angle, δ T represents the throttle lever deflection angle, and the longitudinal motion equations are simplified into the following form: By using the linear simplification of the small disturbance model and considering only two state variables, the angle of attack disturbance α and the pitch rate disturbance q, from the perspective of flight control engineering application, the speed change is u≈0, and the following formula is obtained: Among them, V m0 Indicates the flight speed of the aircraft, Z α , M α , is the large derivative in longitudinal motion, and the calculation formula is as follows: Where Q represents dynamic pressure, S represents wing area, d represents average aerodynamic chord length, I y represents the moment of inertia about the Y axis, C zα is the pitching force coefficient caused by the angle of attack, is the pitching force coefficient caused by elevator deflection, C mα is the pitching moment coefficient caused by the angle of attack, is the pitching moment coefficient caused by elevator deflection; Step 6: Simplify the lateral motion linearly according to the small disturbance model and simplify it into the standard state space equation form; Let the state variable be x = [v, p, r, φ], and the control variable be u = [δ r ,δ a ]; where δ r represents the rudder deflection angle, δ a Represents the aileron deflection angle; Similarly, using the small disturbance model linearization, and taking the disturbance of the sideslip angle as a state variable, the following formula is obtained: Among them, Y β , N β , L β , L p , L r , N p , N r , is the large derivative in the lateral heading motion, and the calculation formula is as follows: in, is the side force coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the sideslip angle, is the rolling moment coefficient caused by the rolling angular rate, is the rolling moment coefficient caused by the yaw rate, is the yaw moment coefficient caused by the sideslip angle, is the yaw moment coefficient caused by the roll angular rate, is the yaw moment coefficient caused by the yaw rate, is the side force coefficient caused by rudder deflection, is the side force coefficient caused by aileron deflection, is the rolling moment coefficient caused by rudder deflection, is the rolling moment coefficient caused by aileron deflection, is the yaw moment coefficient caused by rudder deflection, is the yaw moment coefficient caused by aileron deflection; Step 7: Use the lateral and longitudinal motions in the form of standard state-space equations to build a digital simulation model of a general aircraft, and load the model into the aircraft simulation system to achieve mission-level simulation.

2. The method according to claim 1, characterized in that: In the step 1, the ground coordinate system is O g X g Y g Z g , where the origin O g is the take-off point of the aircraft, O g X g The axis passes through the origin O g In the horizontal plane, pointing to the target is positive; O g Y g Axis passes through origin O g , perpendicular to the ground, with upward being positive; O g Z g Axis passes through origin O g , and O g X g Axis, O g Y g The axis is in right-hand relationship, and the four fingers are from O g X g Axis points to O g Y g Axis, the direction of the thumb is O g Z g The positive direction of the axis; The body coordinate system is OX b Y b Z b , where the origin O is the center of mass of the aircraft, OX b Axis points in the direction of the bullet; OZ b The axis is perpendicular to OX in the symmetry plane of the aircraft b Axis, pointing downward; OY b Axis and OX b Axis, OZ b The axis is in right-hand relationship, and the four fingers are from OZ b Axis points to OX b Axis, the direction of the thumb is OY b The positive direction of the axis; The velocity coordinate system is OX w Y w Z w , where the origin O is the center of mass of the aircraft, OX w Axis points to the direction of flight speed; OZ w The axis is perpendicular to OX in the symmetry plane of the aircraft w Axis, pointing downward; OY w Axis and OX w Axis, OZ w The axis is in right-hand relationship, and the four fingers are from OZ w Axis points to OX w Axis, the direction of the thumb is OY w The positive direction of the axis; The track coordinate system is OX k Y k Z k , where the origin O is the center of mass of the aircraft, OX k Axis points to the direction of flight speed; OZ k The axis is in the vertical plane containing the velocity vector and is perpendicular to OX k Axis, pointing downward; OY k Axis and OX k Axis, OZ k The axis is in right-hand relationship, and the four fingers are from OZ k Axis points to OX k Axis, the direction of the thumb is OY k The positive direction of the axis.

3. The method according to claim 1, characterized in that: The step 2 specifically includes: 1) Relationship between the ground coordinate system and the body coordinate system: The ground coordinate system is rotated three times around the axis in different directions to obtain the body coordinate system; The rotation angle is defined as follows: The yaw angle ψ is the longitudinal axis OX of the aircraft b Projection on the horizontal plane and ground coordinate system OX g The angle between them is positive in the clockwise direction from due north, and the range is [0°, 360°]; The pitch angle θ is the longitudinal axis OX of the aircraft b With ground plane O g X g Y g The angle is positive when the nose is raised, and the range is [-90°, 90°]; Roll angle φ is the vertical axis OZ of the machine body b With OX b The included angle between the plumb planes is positive when the right side drops, and the range is [-90°, 90°]; Rotate the yaw angle ψ clockwise around the vertical axis of the ground system according to the right-hand principle, rotate the pitch angle θ counterclockwise around the horizontal axis of the transition system according to the right-hand principle, and rotate the roll angle φ counterclockwise around the longitudinal axis of the aircraft system according to the right-hand principle. The rotation matrix is: Among them, S ψθφ is the rotation matrix from the ground coordinate system to the body coordinate system, and a vector is expressed in ground coordinates as In the body coordinate system, it is expressed as Then there is the following relationship: P b =S ψθφ P g 2) Relationship between body coordinate system and velocity coordinate system: The body coordinate system first revolves around its horizontal axis OY b Rotate the attack angle α clockwise to get the transition system, the transformation matrix is ​​L(α), and then rotate around the transition system vertical axis OZ w The axis rotates clockwise by the sideslip angle β to obtain the velocity coordinate system, and the transformation matrix is ​​L(β); S αβ Represents the rotation matrix from the body coordinate system to the velocity coordinate system: Let a vector be expressed in the body coordinate system as In velocity coordinates it is expressed as Then there is the following relationship: P w =S αβ P b 3) Relationship between track coordinate system and ground coordinate system: The ground coordinate system first revolves around the vertical axis OZ g Rotate a track azimuth angle χ, the transformation matrix is ​​L(χ), get the transition system, and then rotate around the horizontal axis OY of the transition system k Rotate the track by an inclination angle γ to obtain the track coordinate system, and the transformation matrix is ​​L(γ); S χγ Represents the rotation matrix from the ground coordinate system to the track coordinate system: Let a vector be expressed in the ground coordinate system as In track coordinates it is expressed as Then there is the following relationship: P k =S χγ P g .

Images