A Dynamic Modeling Method for Attitude Control Systems under Dynamic Faults

Abstract

This invention relates to a dynamic modeling method for attitude control systems under dynamic failures, including: defining the modeling assumptions of the nonlinear dynamic model; establishing a coordinate system for modeling; obtaining rocket configuration parameters and engine-related parameters; establishing displacement and acceleration descriptions for three types of structures on the rocket; establishing rigid body translation equations, rigid body rotation equations, rocket body elastic vibration equations, propellant sloshing equations, and sensitive element measurement equations; summarizing the five equations established above to form a set of nonlinear dynamic equations; and performing a small-perturbation linearization expansion of the nonlinear dynamic equations based on the nominal reconstructed trajectory to obtain a linearized small-deviation equation set suitable for controller design and stability analysis. This invention achieves a comprehensive consideration of the impact of thrust reduction failures, and the model can be used to conduct more accurate dynamic response analysis and reconstruction scheme design under failure conditions.

Description

Technical Field

[0001] This invention belongs to the fields of overall design of launch vehicles, dynamics and control technology of launch vehicles, and relates to a dynamic modeling method for attitude control system under dynamic failure. Background Technology

[0002] To meet the needs of space exploration, countries around the world are vigorously developing a new generation of high-thrust launch vehicles. Because the thrust of a single engine is limited, most bare-barreled or bundled rockets currently use a dozen or even dozens of engines. This significantly increases the number of engines compared to traditional rockets, greatly increasing the probability of thrust reduction or even engine shutdown due to malfunctions.

[0003] A decrease in thrust has multiple impacts on a launch vehicle: (1) a decrease in thrust can affect orbital accuracy and may even require trajectory reconfiguration and degradation; (2) a decrease in thrust can lead to a shift in the center of mass and changes in overall parameters; (3) a decrease in thrust can generate unbalanced disturbance torques; (4) changes in the dynamic characteristics of the liquid sloshing and the overall elastic modes of the rocket; and (5) a decrease in the control capability of the attitude control system. Obviously, after a decrease in thrust, the dynamic characteristics of the launch vehicle have deviated far from the nominal design conditions. Some of the assumptions used in the derivation of the traditional dynamic model have become invalid. The dynamic model derived based on normal operating conditions and the linearized small deviation model can no longer be used to describe the flight state under fault conditions. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the inaccuracy of existing dynamic models under power system failures, and to propose a dynamic modeling method for attitude control systems under power failures. This method fully considers the impact of thrust reduction failures, and the model can be used to conduct more accurate dynamic response analysis and reconfiguration scheme design under failures.

[0005] The solution of this invention is: a dynamic modeling method for attitude control systems under dynamic faults, comprising the following steps:

[0006] Establish coordinate systems for modeling, including launch coordinate system a, rocket body coordinate system b, half-velocity coordinate system h, elastic coordinate system E, and local elastic follower coordinate system e. k(x) Nozzle coordinate system N ks ;

[0007] Based on the launch vehicle object description, obtain the rocket configuration parameters and engine-related parameters;

[0008] Based on launch coordinate system a, rocket body coordinate system b, and local elastic follower coordinate system e k(x) Nozzle coordinate system N ksThe displacement and acceleration descriptions of three types of structures on the rocket are established, including the displacement and acceleration descriptions of any point on the rocket body structure under the consideration of rocket elastic deformation, the displacement and acceleration descriptions of the swaying mass points when the propellant sways, and the displacement and acceleration descriptions of the center of mass of the nozzle of the k-th booster and s-th engine.

[0009] Based on the half-velocity coordinate system h, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, the rigid body translation equations are established.

[0010] Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, a rigid body rotation equation is established.

[0011] Based on the elastic coordinate system E, and according to the rocket configuration parameters and engine-related parameters, the elastic vibration equation of the rocket body is established.

[0012] Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, the propellant sloshing equation is established.

[0013] Based on the output of the rigid body rotation equation and the mode at the installation position of the inertial device, the measurement equation of the sensing element is established;

[0014] The equations of rigid body translation, rigid body rotation, rocket body elastic vibration, propellant sloshing, and sensitive element measurement are summarized to form a set of nonlinear dynamic equations.

[0015] By performing a small-perturbation linearization expansion of the nonlinear dynamic equations based on the nominal reconstructed trajectory, a linearized small-deviation equation set suitable for controller design and stability analysis is obtained.

[0016] Furthermore, before performing dynamic modeling, the following modeling assumptions for the nonlinear dynamic model are defined:

[0017] Assume that the strain and rotation caused by the elastic deformation of the arrow body are 1% of the arrow body structural dimensions;

[0018] Assume the liquid surface sloshing angle is less than 10°;

[0019] Assuming the engine sway angle is less than 10°;

[0020] Ignoring the effects of Earth's rotation;

[0021] Only the reaction force generated by the ejection of propellant combustion products is considered and included in the thrust, while the additional Coriolis force, additional Coriolis moment and additional relative moment generated are ignored.

[0022] Furthermore, the coordinate system b of the rocket body is defined as follows:

[0023] The origin of the rocket body coordinate system is the projection point O1 of the instantaneous center of mass O2 of the rocket onto the longitudinal axis of the core stage. The O1X1 axis is the longitudinal axis of the core stage, pointing towards the head of the core stage. The O1Y1 axis is located within the main symmetry plane of the rocket. The O1X1Y1 plane coincides with the OXY plane of the launch coordinate system at the instant of launch. The O1Z1 axis is determined according to the right-hand rule.

[0024] The nozzle coordinate system N ks The definition is as follows:

[0025] Nozzle coordinate system N ks The nozzle of the k-th booster engine is fixedly connected to the s-th engine nozzle, with the origin O. δks Located at the engine's swing point, O δ ks X δks The thrust P is directed along the axis of symmetry of the nozzle housing towards the nose of the rocket body. ks For a single-pendulum engine, the positive direction of the servo direction swing angle is defined as O. δks Y δks Axis, O δks Z δks The axis is determined according to the right-hand rule. For an orthogonal double-pendulum engine, after the positive polarity of the pendulum angle in the servo direction is determined, a unique O is determined according to the right-hand rule. δks Y δks Axis and O δks Z δks The positive direction of the axis.

[0026] Furthermore, the rocket configuration parameters and engine-related parameters include:

[0027] The rocket configuration parameters include: the number of boosters N. zt The total number of engines on the k-th booster is The total number of storage tanks is When k=0, it represents the core stage rocket body, that is, the total number of core stage rocket engines is... The total number of storage tanks is Boost installation radius L k This represents the distance between the longitudinal axis of booster k and the longitudinal axis of the core stage, and the booster installation azimuth angle μ. k This represents the angle between the plane formed by the k-booster longitudinal axis and the core stage longitudinal axis and the O1X1Z1 plane;

[0028] The engine-related parameters include: the engine installation position X of each module. kR The distance from the swing point of booster k to the theoretical vertex; the installation radius L of the s-th booster in the module. δks δ represents the distance from the engine sway point to the module's longitudinal axis; qks The azimuth angle for the engine is the angle between the line connecting the engine swing point to the module's longitudinal axis and the O1Y1 axis. The engine yaw azimuth angle represents the rotation from the rocket body coordinate system O1Y1 axis to the nozzle coordinate system O. δks Y δks The angle.

[0029] Furthermore, the description of displacement and acceleration at any point on the rocket body structure includes:

[0030] The radius vector at any point on the arrow's structure:

[0031]

[0032] The acceleration of the structural particle is:

[0033]

[0034] In the formula, This represents the absolute derivative in the launch coordinate system a. This represents the velocity of the origin O1 of the rocket's coordinate system relative to the launch coordinate system. This represents the local derivative in the arrow's coordinate system b. In the locally elastic follower coordinate system e k(x) Local derivatives in u k(x) Let o be the origin of the local elastic follower coordinate system after the projectile deforms. ek(x) The elastic translational displacement, R c.m R is the position vector of the origin O1 of the rocket body coordinate system in the launch coordinate system a. k(x) Let ω1 be the radius vector of the projection point from O1 of any point on the structure onto the longitudinal axis of booster k before deformation, and let ω1 be the rigid body rotational angular velocity of the rocket relative to the launch coordinate system a. ek(x) For the local dynamic elastic coordinate system e k(x) The elastic rotational angular velocity relative to the arrow body coordinate system b, In the coordinate plane o ek(x) y ek(x) z ek(x) origin o ek(x) The position vector to any structural point. The position vector of any structural point when the rocket is considered a rigid body;

[0035] The description of the displacement and acceleration of the sloshing particles during propellant sloshing includes:

[0036] When the rocket deforms and the propellant sloshes, the sloshing mass point m kp The position vector in the launch coordinate system a can be expressed as:

[0037]

[0038] The acceleration of the shaking particle is:

[0039]

[0040] In the formula, Let be the radius vector of the rocket's center of sway before deformation in the rocket's coordinate system b. The center of the sway is located in the local elastic follower coordinate system e. k(x) Translational displacement, h kp For the swaying mass in the locally elastic follower coordinate system e k(x) The swaying displacement;

[0041] The displacement and acceleration description of the nozzle center of mass of the k-th booster s-th engine includes:

[0042] In launch coordinate system a, the position vector of the center of mass of the nozzle of the k-th booster s-th engine is:

[0043]

[0044] The acceleration of the nozzle's center of mass is:

[0045]

[0046] In the formula, For the kth booster s engine swing center O δks The projection point on the longitudinal axis of the booster has a position vector in the rocket body coordinate system b. To establish the origin elastic translational displacement of a local elastic follower coordinate system at this projection point, ρ rks For the local elastic follower coordinate system e k(x) The oscillating point radius vector, ρ Rks In the nozzle coordinate system N ks The radius vector of the center of mass of the nozzle, ρ r1ks To treat the rocket as a rigid body, the radius vector at the oscillation point, ρ R1ks Let the radius vector be the center of mass of the nozzle when the engine is not swaying. For a locally elastic follower coordinate system The angular velocity of rotation relative to the arrow's coordinate system b, ω δks Let the nozzle be relative to the local elastic coordinate system e k(x) angular velocity of rotation.

[0047] Furthermore, establishing the equations of rigid body translation includes:

[0048] According to Newton's second law, the rigid body translation equations of the entire rocket system are:

[0049]

[0050] In the formula, mg is gravity, P is engine thrust, and F is... aero For aerodynamic forces, F wind For wind interference force, Fstructure For structural interference force, For volume fraction, For point Structural density at m kp For the swaying mass of the p-th order swaying assisted by the k-th boost, m Rks For the k-th booster s-th engine sway mass, N zt For the number of boosters, The total number of storage tanks, The total number of engines on the k-th booster;

[0051] In the half-velocity coordinate system h, the coefficient-reduced rigid body translation equations are obtained as follows:

[0052]

[0053] At the same time, the apparent acceleration in the arrow body coordinate system is established as:

[0054]

[0055] Where g is the acceleration due to gravity, V is the flight velocity, θ is the trajectory angle, σ is the trajectory deflection angle, and α is the trajectory angle of attack. wp —Stable wind angle of attack, α wq —Angle of attack of shear wind, β —Side slip angle of ballistic trajectory, β wp —Steady wind sideslip angle, β wq —Side slip angle of shear wind, —Arrow body pitch velocity, —Yaw rate of the rocket body, q i —Elastic generalized displacement, —Elastic generalized displacement velocity, δ Yks , Let δ represent the sway angle and angular acceleration of the oscillating engine in the Y direction, respectively. Zks , Let c be the sway angle and angular acceleration of the oscillating engine in the Z direction, respectively. X_aero —Axial force coefficient, —Aerodynamic coefficients of the pitch channel, — Yaw channel aerodynamic coefficient, —Aerodynamic damping force coefficient of the pitch channel, —Aerodynamic damping force coefficient of the yaw channel —The i-th order elastic additional aerodynamic coefficient of the pitch channel, —The i-th order elastic additional aerodynamic coefficient for the yaw channel. —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, c 1P —Axial thrust coefficient, These are the oscillation control force coefficients of the engine in the Y and Z directions, respectively, for the pitch control channel. These are the yaw control force coefficients for the yaw channel engine in the Y and Z directions, respectively. These are the oscillation inertial force coefficients of the engine in the Y and Z directions, respectively, for the pitch channel. These are the oscillating inertial force coefficients of the yaw channel engine in the Y and Z directions, respectively. —The coefficient of cross-linking force for pitch channel swaying. —Yaw channel sway cross-linking force coefficient, —The i-th order elastic additional thrust coefficient of the pitch channel, —The i-th order elastic additional thrust coefficient in the yaw channel, —The structural interference force coefficient of the pitch channel, —Yaw channel structural interference force coefficient, —Coordinate transformation matrix from the rocket body coordinate system to the half-velocity coordinate system, The projection of the swaying acceleration onto the O1Y1 axis of the rocket body coordinate system. The projection of the swaying acceleration onto the O1Z1 axis of the rocket body coordinate system. —Axial acceleration of the rocket body in coordinate system O1X1 —The apparent acceleration along the O1Y1 axis of the rocket's coordinate system. —Axis acceleration of the rocket body coordinate system O1Z1.

[0056] Furthermore, establishing the rigid body rotation equation includes:

[0057] The rigid body rotation equations for the entire rocket system are:

[0058]

[0059] In the formula, M CM_g M represents the torque exerted by the gravity of each component about the origin O1 of the rocket's coordinate system. CM_P M is the torque of the engine thrust about the origin O1 of the rocket body coordinate system. CM_aero M is the torque of the aerodynamic force about the origin O1 of the rocket's coordinate system. CM_wind M is the torque of the wind interference force about the origin O1 of the rocket's coordinate system. CM_structure The torque of the structural disturbance force about the origin O1 of the rocket body coordinate system;

[0060] After expanding and substituting the external torque terms, we obtain the coefficient-reduced full rigid body rotation equation in the arrow coordinate system:

[0061]

[0062]

[0063] In the formula, —Rolling angular velocity of the rocket body, —Roll channel yaw angle acceleration coupling coefficient, —Roll path pitch angle acceleration coupling coefficient, d PX — The transverse displacement coefficient of the center of mass in the fault rolling channel, d1 — The rolling damping moment coefficient, d 3Yks —k booster engine Y-axis oscillating roll control torque coefficient, d″ 3Yks —Y-direction oscillating moment coefficient of the rolling channel, d 3Zks —Z-axis oscillating rolling control force coefficient, d″ 3Zks —The Z-axis oscillating moment of inertia coefficient of the rolling channel, d hykp — The cross-linking coefficient of the Y-axis sloshing displacement of the propellant in the tank to the rolling channel, d″ hykp —Y-axis swaying acceleration as a function of the cross-linking coefficient of the rolling channel, d hzkp — Cross-linking coefficient of Z-axis sway displacement to rolling channel, d″ hzkp — Cross-linking coefficient of Z-axis swaying acceleration to the rolling channel, d 1i —The i-th order elastic aerodynamic damping moment coefficient of the rolling channel, d 2i —The i-th order elastic moment coefficient of the rolling channel, —Disturbing moment coefficient of the rolling channel structure, —Yaw channel roll angle acceleration coupling coefficient, —Yaw channel pitch angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of gravity in the fault yaw channel. — Yaw channel aerodynamic damping moment coefficient. — Yaw channel aerodynamic moment coefficient, —Engine Y-axis yaw control moment coefficient, —Engine Y-axis oscillation moment coefficient, —Engine Z-axis yaw control moment coefficient, —Engine Z-axis oscillation moment coefficient, —Yaw channel sway moment coupling coefficient, —Yaw channel sway center of mass coherence coefficient, —The i-th order elastic additional aerodynamic damping moment coefficient of the yaw channel. —The coefficients of the i-th order elastic additional aerodynamic moment and additional thrust moment in the yaw channel. —Engine thrust yaw channel torque, — Yaw channel structural disturbance moment, —Pitch channel roll angle acceleration coupling coefficient, —Pitch channel yaw angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of mass in the pitch channel during a fault. —Pitch channel aerodynamic damping moment coefficient, —Aerodynamic moment coefficient of the pitch passage, —Engine Y-axis yaw and pitch control torque coefficient, Engine Y-axis pitch inertia moment coefficient, Engine Z-axis yaw and pitch control torque coefficient —Engine Z-axis yaw pitch moment coefficient, —Coupling coefficient of pitch channel sway moment, —Coefficient of coherence of the center of mass of the pitch channel sway. —The i-th order elastic additional aerodynamic damping moment coefficient of the pitch channel. —The i-th order elastic additional aerodynamic moment and additional thrust moment coefficient of the pitch channel, —Engine thrust pitch channel torque, — Pitch channel structural disturbance moment, Y kp —Swaying normal displacement, Z kp —Swaying and lateral displacement.

[0064] Furthermore, establishing the elastic vibration equation of the arrow body includes:

[0065]

[0066] In the formula, q i —The generalized displacement of the i-th order elastic vibration, ξ i —The damping ratio of the i-th mode, ω i —The i-th elastic frequency, D 4i —Additional aerodynamic generalized force coefficient to the rolling channel, —The i-th order generalized aerodynamic damping force coefficient of the yaw channel. —The i-th order generalized aerodynamic damping force coefficient of the pitch channel. —The i-th order generalized aerodynamic coefficient of the pitch channel, —The i-th order generalized aerodynamic coefficient of the yaw channel, D 3iYks —Generalized control force coefficient for engine Y-axis oscillation, D″ 3iYks —Generalized inertial force coefficient of engine Y-axis oscillation, D 3iZks —Generalized control force coefficient for engine Z-axis oscillation, D″ 3iZks —The generalized inertial force coefficient of the engine's Z-axis oscillation. —The generalized force coefficient resulting from the p-th tank sway displacement and the i-th order elastic coupling in the pitch channel. —The generalized force coefficient resulting from the swaying acceleration of the p-th tank in the pitch channel and the elastic coupling of the i-th order. —The generalized force coefficient resulting from the sway displacement of the p-th tank in the yaw channel and the elastic coupling of the i-th order. —The generalized force coefficient R resulting from the sway acceleration of the p-th tank in the yaw channel and the elastic coupling of the i-th order. ij —The generalized force coefficient, R′, for the coupling of the j-th elastic element to the i-th elastic element. ij —The generalized damping force coefficient of the coupling between the j-th order elasticity and the i-th order elasticity. The generalized force generated by the thrust of the s-th engine in the k-th module. Generalized force generated by structural disturbance, Y kp —Swaying normal displacement, Z kp —Swaying lateral displacement, —Swaying normal acceleration, — Lateral acceleration due to swaying.

[0067] Furthermore, establishing the propellant sloshing equation includes:

[0068] The propellant sloshing equation in the rocket body coordinate system b is:

[0069]

[0070] These represent the swaying displacement, velocity, and acceleration of the swaying mass in the arrow body coordinate system, where... m kp For the propellant mass under thrust reduction failure, The matrix represents the coupling coefficients between the rocket body rotation and the liquid sloshing under thrust reduction failure. This is the coupling term caused by the displacement of the rocket's center of mass due to a thrust reduction fault. This is the equivalent damping coefficient matrix. This is the equivalent stiffness coefficient matrix. For the system's downward-looking acceleration, The elastic motion-liquid sloshing coupling coefficient matrix is ​​given. The angular acceleration of the arrow body, For elastic generalized acceleration;

[0071] Expanding the above equation, we derive the following equation for liquid sloshing:

[0072]

[0073] ζ kpy ζ kpz These are the normal and lateral sway damping ratios, Ω kp — Shaking frequency, Z Lkp—The Z-axis position of the p-tank rocket body in the coordinate system of the k-th booster, Y-axis position Lkp —The Y-position of the p-tank rocket body in the coordinate system of the k-th booster, E kpz —The distance from the center of mass to the center of mass during shaking. —The force coefficient coupling between the i-th order elastic deformation displacement of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation displacement of the yaw channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the yaw channel and the p-th tank sway. —Arrow body pitch acceleration, —Yaw acceleration of the rocket body, —Rolling angular acceleration of the rocket body, n —Number of non-zero natural frequencies.

[0074] Furthermore, establishing the measurement equation for the sensitive element includes:

[0075] The inertial measurement equation is:

[0076]

[0077] In the formula, φ 0ix (x gz ) represents the torsional vibration mode at the core stage of the rocket, φ 0iy (x gz ) and φ 0ix (x gz ) represents the mode shape slope at the core stage of the rocket. —Inertial measurement values ​​of pitch attitude angle considering elasticity, — Arrow body pitch angle, ψ gz —Yaw attitude angle measured by inertial navigation system considering elasticity, ψ —Yaw attitude angle of the rocket body, γ gz —Measured value of the rocket body roll attitude angle considering elasticity, γ —Rocket body roll attitude angle;

[0078] Assuming the rate gyroscope is mounted on the k-th booster, its measurement equation is:

[0079]

[0080] In the formula, φ kix (x st ) represents the torsional vibration mode at the mounting location of the k-th boost rate gyroscope, φ kiy (x st ) and φ kiz (x st ω is the mode shape slope at the mounting point of the k-th booster rate gyroscope.Z1_st —Gyroscope measurements of the rocket's pitch angular velocity rate. —Arrow body pitch velocity, —Yaw rate angular velocity of the rocket body measured by gyroscope. —Yaw rate of the rocket body, —Gyroscope measurement of the rocket's roll angular velocity rate. —Rolling angular velocity of the rocket body, — Elastic generalized velocity.

[0081] Furthermore, the linearized small-deviation equation set includes:

[0082] 1) Equation for small deviation of the center of mass motion:

[0083]

[0084] —Pitch channel dynamic coefficient, —Yaw channel dynamic coefficient, —Gravity coefficient of the pitch channel, — Gravity coefficient of the yaw channel —The i-th order elastic additional aerodynamic force and thrust coefficient of the pitch channel, —The i-th order elastic additional aerodynamic force and thrust coefficient of the yaw channel, Δ represents the deviation perturbation of the state quantity based on the nominal reconstructed trajectory;

[0085] 2) Equation for small deviations in rigid body rotation:

[0086]

[0087]

[0088] 3) Linearization results of the elastic motion equations:

[0089]

[0090] 4) The equation for small deviation of swaying is:

[0091]

[0092] The advantages of this invention compared to the prior art are:

[0093] This invention establishes a nonlinear dynamic model for a large, clustered launch vehicle considering rigid-sloshing-elastic coupling under the condition of thrust reduction failure from any number of engines. This dynamic model includes equations for rigid body translation, rigid body rotation, overall elastic vibration, fluid sloshing, and measurement of sensitive elements. The established nonlinear dynamic model has a certain degree of universality, reflecting not only the rocket's mass eccentricity, changes in moment of inertia and inertia product, unbalanced disturbance torque caused by thrust asymmetry, and the coupling characteristics of the center of mass and motion around the center of mass that may result from thrust reduction from any number of engines, but also its applicability to general, normally-flying clustered launch vehicles with asymmetric distribution of any number of boosters and engines. Attached Figure Description

[0094] Figure 1 A flowchart of a dynamic modeling method for an attitude control system under dynamic faults;

[0095] Figure 2 A schematic diagram defining the arrow body coordinate system and the elastic coordinate system;

[0096] Figure 3 (a) is a schematic diagram of the engine installation orientation. Figure 3 (b) Schematic diagram of engine sway direction;

[0097] Figure 4 A schematic diagram showing the radius vectors at different mass point positions;

[0098] Figure 5 Force analysis diagram of the interface between the central body and substructures; Detailed Implementation

[0099] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0100] This invention proposes a dynamic modeling method for attitude control systems under dynamic faults, such as... Figure 1 As shown, it includes the following steps:

[0101] (1) Define the modeling assumptions of the nonlinear dynamics model;

[0102] (2) Establish the coordinate systems used for modeling, including the launch coordinate system a, the rocket body coordinate system b, the half-velocity coordinate system h, the elastic coordinate system E, and the local elastic follower coordinate system e. k(x) Nozzle coordinate system N ks ;

[0103] (3) Based on the launch vehicle object description, obtain the rocket configuration parameters and engine-related parameters;

[0104] (4) Based on launch coordinate system a, rocket body coordinate system b, and local elastic follower coordinate system e k(x) Nozzle coordinate system N ksThe displacement and acceleration descriptions of three types of structures on the rocket are established, including the displacement and acceleration descriptions of any point on the rocket body structure under the consideration of rocket elastic deformation, the displacement and acceleration descriptions of the swaying mass points when the propellant sways, and the displacement and acceleration descriptions of the center of mass of the nozzle of the k-th booster and s-th engine.

[0105] (5) Based on the half-velocity coordinate system h, and according to the rocket configuration parameters, engine-related parameters, displacement and acceleration descriptions of the three types of structures on the rocket, establish the rigid body translation equation;

[0106] (6) Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, displacement and acceleration descriptions of the three types of structures on the rocket, establish the rigid body rotation equation;

[0107] (7) Based on the elastic coordinate system E, establish the elastic vibration equation of the rocket body according to the rocket configuration parameters and engine-related parameters;

[0108] (8) Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, displacement and acceleration descriptions of the three types of structures on the rocket, establish the propellant sloshing equation;

[0109] (9) Based on the output of the rigid body rotation equation and the mode at the installation position of the inertial device, establish the measurement equation of the sensitive element;

[0110] (10) Summarize the equations of rigid body translation, rigid body rotation, rocket body elastic vibration, propellant sloshing, and sensitive element measurement to form a set of nonlinear dynamic equations;

[0111] (11) Perform small perturbation linearization expansion of the nonlinear dynamic equations on the basis of nominal reconstructed trajectory to obtain a linearized small deviation equation set suitable for controller design and stability analysis.

[0112] Example 1

[0113] Step 1: Define the modeling assumptions of the nonlinear dynamics model.

[0114] When deriving the nonlinear dynamic model, the following assumptions are made:

[0115] (1) Assuming that the elastic deformation of the arrow body is small, the strain and rotation caused by the elastic deformation are very small relative to the original size of the arrow body, about 1% of the structural size of the arrow body;

[0116] (2) Assuming that the liquid sloshing is a small sloshing, it is generally believed that the assumption is met when the liquid surface sloshing angle is less than 10°.

[0117] (3) Assume that the rocket body rotates slowly around the center of mass (the rotational angular velocity ω1 is a small quantity, and the rotational angular velocity of a typical launch vehicle satisfies the assumption).

[0118] (4) Assuming the engine sway angle is small, it is assumed that the assumption is satisfied when the sway angle is less than 10°;

[0119] (5) Ignore the effects of Earth's rotation;

[0120] (6) Only the reaction force generated by the ejection of propellant combustion products is considered and included in the thrust, while the additional Coriolis force, additional Coriolis moment and additional relative moment generated are not considered.

[0121] Step 2: Establish the coordinate system used for modeling.

[0122] The following coordinate system was used in the modeling process:

[0123] (1) Launch coordinate system a: O-XYZ;

[0124] (2) Arrow body coordinate system b: O1-X1Y1Z1;

[0125] (3) Velocity coordinate system c: O2-X c Y c Z c ;

[0126] (4) Half-velocity coordinate system h: O2-X h Y h Z h ;

[0127] (5) Elastic coordinate system E:O E -X E Y E Z E ;

[0128] (6) Local elastic follower coordinate system e k(x) :O ek(x) -X ek(x) Y ek(x) Z ek(x) ;

[0129] (7) Nozzle coordinate system N ks :O δks -X δks Y δks Z δks .

[0130] The coordinate system is defined in addition to the rocket body coordinate system b and the nozzle coordinate system N. ks Apart from that, the other coordinate systems are defined as in the traditional sense. The rocket body coordinate system b and the nozzle coordinate system N are defined as follows. ks The detailed definition is as follows:

[0131] Rocket body coordinate system b: The origin is the projection point O1 of the rocket's instantaneous center of mass O2 (referring to the rocket body's center of mass without considering liquid sloshing and engine oscillation) onto the longitudinal axis of the core stage (note that points O1 and O2 do not necessarily coincide, such as...). Figure 2 As shown, the O1X1 axis is the longitudinal axis of the core stage, pointing towards the head of the core stage. The O1Y1 axis is located within the main symmetry plane of the rocket. The O1X1Y1 plane coincides with the launch coordinate system OXY plane at the moment of launch. The O1Z1 axis is determined according to the right-hand rule.

[0132] Nozzle coordinate system N ks Nozzle coordinate system N ks The nozzle of the k-th booster engine is fixedly connected to the s-th engine nozzle, with the origin O. δks Located at the engine's swing point, O δks X δks The thrust P is directed along the axis of symmetry of the nozzle housing towards the nose of the rocket body. ks For a single-pendulum engine, the positive direction of the servo direction swing angle is defined as O. δks Y δks Axis, O δks Z δks The axis is determined according to the right-hand rule. For an orthogonal double-pendulum engine, after determining the positive polarity of the pendulum angle in the servo direction, a unique O can be determined according to the right-hand rule. δks Y δks Axis and O δks Z δks The positive direction of the axis. For example... Figure 3 (a) Figure 3 As shown in (b).

[0133] Step 3: Based on the launch vehicle object description, obtain the rocket configuration parameters and engine-related parameters.

[0134] The rocket configuration parameters include: the number of boosters N. zt The total number of engines on the k-th booster is The total number of storage tanks is Specifically, when k=0, it represents the core stage rocket body, that is, the total number of core stage rocket engines is... The total number of storage tanks is Boost installation radius L k This represents the distance between the longitudinal axis of booster k and the longitudinal axis of the core stage, and the booster installation azimuth angle μ. k This represents the angle between the plane formed by the longitudinal axis of the k-booster and the longitudinal axis of the core stage and the O1X1Z1 plane. With the tail view as a reference, the O1X1Z1 plane is positive when rotated clockwise.

[0135] The engine-related parameters include: the engine installation position X of each module. kR The distance from the swing point of booster k to the theoretical vertex; the installation radius L of the s-th booster in the module. δks That is, the distance from the engine sway point to the module's longitudinal axis; δ qksThe engine is installed with an azimuth angle, which describes the angle between the line connecting the engine swing point to the module's longitudinal axis and the O1Y1 axis. With the rear view as a reference, clockwise rotation of O1Y1 is considered positive. The engine yaw azimuth angle represents the rotation from the rocket body coordinate system O1Y1 axis to the nozzle coordinate system O. δks Y δks The angle is referenced from the tail view, with clockwise being positive.

[0136] Step 4: Based on launch coordinate system a, rocket body coordinate system b, and local elastic follower coordinate system e k(x) Displacement and acceleration descriptions for three types of structures on the arrow are established. A schematic diagram of the radius vector at different mass point positions is shown below. Figure 4 .

[0137] 1) Description of displacement and acceleration at any point on the rocket body structure:

[0138] The radius vector at any point on the arrow's structure:

[0139]

[0140] The acceleration of the structural particle is:

[0141]

[0142] In the formula, This represents the absolute derivative in the launch coordinate system a. V1 represents the velocity of the origin O1 of the rocket body coordinate system relative to the launch coordinate system. This represents the local derivative in the arrow's coordinate system b. In the locally elastic follower coordinate system e k(x) Local derivatives in u k(x) Let o be the origin of the local elastic follower coordinate system after the projectile deforms. ek(x) The elastic translational displacement, R c.m R is the position vector of the origin O1 of the rocket body coordinate system in the launch coordinate system a. k(x) Let ω1 be the radius vector of the projection point from O1 of any point on the structure onto the longitudinal axis of booster k before deformation, and let ω1 be the rigid body rotational angular velocity of the rocket relative to the launch coordinate system a. ek(x) For the local dynamic elastic coordinate system e k(x) The elastic rotational angular velocity relative to the arrow body coordinate system b, In the coordinate plane origin o ek(x) The position vector to any structural point. Let be the position vector of any structural point when the rocket is considered as a rigid body.

[0143] 2) Description of the displacement and acceleration of the sloshing particles when the rocket deforms and the propellant sloshes:

[0144] When the rocket deforms and the propellant sloshes, the sloshing mass point m kp The position vector in the launch coordinate system a can be expressed as:

[0145]

[0146] The acceleration of the shaking particle is

[0147]

[0148] In the formula, Let be the radius vector of the rocket's center of sway before deformation in the rocket's coordinate system b. The center of the sway is located in the local elastic follower coordinate system e. k(x) Translational displacement, h kp For the swaying mass in the locally elastic follower coordinate system e k(x) The swaying displacement.

[0149] 3) Description of the displacement and acceleration of the center of mass of the nozzle of the k-th booster engine (s-th engine):

[0150] In launch coordinate system a, the position vector of the center of mass of the nozzle of the k-th booster s-th engine is:

[0151]

[0152] The acceleration of the nozzle's center of mass is:

[0153]

[0154] In the formula, For the kth booster s engine swing center O δks The projection point on the longitudinal axis of the booster has a position vector in the rocket body coordinate system b. To establish the origin elastic translational displacement of a local elastic follower coordinate system at this projection point, ρ rks For the local elastic follower coordinate system e k(x) The oscillating point radius vector, ρ Rks In the nozzle coordinate system N ks The radius vector of the center of mass of the nozzle, ρ r1ks To treat the rocket as a rigid body, the radius vector at the oscillation point, ρ R1ks Let the radius vector be the center of mass of the nozzle when the engine is not swaying. For a locally elastic follower coordinate system The angular velocity of rotation relative to the arrow's coordinate system b, ω δks Let the nozzle be relative to the local elastic coordinate system e k(x) angular velocity of rotation.

[0155] Step 5: Based on the half-velocity coordinate system h, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, establish the rigid body translation equations.

[0156] According to Newton's second law, the rigid body translation equations of the entire rocket system are:

[0157]

[0158] In the formula, mg is gravity, P is engine thrust (including control force), and F is... aero For aerodynamic forces (including aerodynamic forces and aerodynamic damping forces), F wind For wind interference force, F structure For structural interference force, For volume fraction, For point Structural density at m kp For the swaying mass of the p-th order swaying assisted by the k-th boost, m Rks For the s-th engine oscillation mass of the k-th booster, N zt For the number of boosters, The total number of storage tanks, The total number of engines on the k-th booster.

[0159] In the half-velocity coordinate system h, the coefficient-reduced rigid body translation equations are obtained as follows:

[0160]

[0161] At the same time, the apparent acceleration in the arrow body coordinate system is established as:

[0162]

[0163] Where g is the acceleration due to gravity, V is the flight velocity, θ is the trajectory angle, σ is the trajectory deflection angle, and α is the trajectory angle of attack. wp —Stable wind angle of attack, α wq —Angle of attack of shear wind, β —Side slip angle of ballistic trajectory, β wp —Steady wind sideslip angle, β wq —Side slip angle of shear wind, — Arrow body pitch angular velocity, ω Y1 —Yaw rate of the rocket body, q i —Elastic generalized displacement, —Elastic generalized displacement velocity, δ Yks , Let δ represent the sway angle and angular acceleration of the oscillating engine in the Y direction, respectively. Zks , Let c be the sway angle and angular acceleration of the oscillating engine in the Z direction, respectively.X_aero —Axial force coefficient, —Aerodynamic coefficients of the pitch channel, — Yaw channel aerodynamic coefficient, —Aerodynamic damping force coefficient of the pitch channel, —Aerodynamic damping force coefficient of the yaw channel —The i-th order elastic additional aerodynamic coefficient of the pitch channel, —The i-th order elastic additional aerodynamic coefficient for the yaw channel. —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, c 1P —Axial thrust coefficient, These are the oscillation control force coefficients of the engine in the Y and Z directions, respectively, for the pitch control channel. These are the yaw control force coefficients for the yaw channel engine in the Y and Z directions, respectively. These are the oscillation inertial force coefficients of the engine in the Y and Z directions, respectively, for the pitch channel. These are the oscillating inertial force coefficients of the yaw channel engine in the Y and Z directions, respectively. —The coefficient of cross-linking force for pitch channel swaying. —Yaw channel sway cross-linking force coefficient, —The i-th order elastic additional thrust coefficient of the pitch channel, —The i-th order elastic additional thrust coefficient in the yaw channel, —The structural interference force coefficient of the pitch channel, —Yaw channel structural interference force coefficient, —Coordinate transformation matrix from the rocket body coordinate system to the half-velocity coordinate system, The projection of the swaying acceleration onto the O1Y1 axis of the rocket body coordinate system. The projection of the swaying acceleration onto the O1Z1 axis of the rocket body coordinate system. —Axial acceleration of the rocket body in coordinate system O1X1 —The apparent acceleration along the O1Y1 axis of the rocket's coordinate system. —Axis acceleration of the rocket body coordinate system O1Z1.

[0164] Step 6: Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, establish the rigid body rotation equation.

[0165] According to d'Alembert's principle, the sum of the moments of the net forces acting on the launch vehicle about the origin O1 of the rocket's coordinate system is zero. The rigid body rotation equations of the entire rocket system are:

[0166]

[0167] In the formula, M CM_g M represents the torque exerted by the gravity of each component about the origin O1 of the rocket's coordinate system. CM_P M is the torque of the engine thrust (including control force) about the origin O1 of the rocket body coordinate system. CM_aero M is the torque of the aerodynamic force (including aerodynamic torque and aerodynamic damping torque) about the origin O1 of the rocket body coordinate system. CM_wind M is the torque of the wind interference force about the origin O1 of the rocket's coordinate system. CM_structure The torque of the structural disturbance force about the origin O1 of the rocket body coordinate system is given by the force.

[0168] After expanding and substituting the external torque terms, we can obtain the coefficient-reduced equation of rotation of the entire rigid body in the arrow coordinate system:

[0169]

[0170]

[0171] In the formula, —Rolling angular velocity of the rocket body, —Roll channel yaw angle acceleration coupling coefficient, —Roll path pitch angle acceleration coupling coefficient, d PX — The transverse displacement coefficient of the center of mass in the fault rolling channel, d1 — The rolling damping moment coefficient, d 3Yks —k booster engine Y-axis oscillating roll control torque coefficient, d″ 3Yks —Y-direction oscillating moment coefficient of the rolling channel, d 3Zks —Z-axis oscillating rolling control force coefficient, d″ 3Zks —The Z-axis oscillating moment of inertia coefficient of the rolling channel, d hykp — The cross-linking coefficient of the Y-axis sloshing displacement of the propellant in the tank to the rolling channel, d″ hykp —Y-axis swaying acceleration as a function of the cross-linking coefficient of the rolling channel, d hzkp — Cross-linking coefficient of Z-axis sway displacement to rolling channel, d″ hzkp — Cross-linking coefficient of Z-axis swaying acceleration to the rolling channel, d 1i —The i-th order elastic aerodynamic damping moment coefficient of the rolling channel, d 2i —The i-th order elastic moment coefficient of the rolling channel, —Disturbing moment coefficient of the rolling channel structure, —Yaw channel roll angle acceleration coupling coefficient, —Yaw channel pitch angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of gravity in the fault yaw channel. — Yaw channel aerodynamic damping moment coefficient. — Yaw channel aerodynamic moment coefficient, —Engine Y-axis yaw control moment coefficient, —Engine Y-axis oscillation moment coefficient, —Engine Z-axis yaw control moment coefficient, —Engine Z-axis oscillation moment coefficient, —Yaw channel sway moment coupling coefficient, —Yaw channel sway center of mass coherence coefficient, —The i-th order elastic additional aerodynamic damping moment coefficient of the yaw channel. —The coefficients of the i-th order elastic additional aerodynamic moment and additional thrust moment in the yaw channel. —Engine thrust yaw channel torque, — Yaw channel structural disturbance moment, —Pitch channel roll angle acceleration coupling coefficient, —Pitch channel yaw angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of mass in the pitch channel during a fault. —Pitch channel aerodynamic damping moment coefficient, —Aerodynamic moment coefficient of the pitch passage, —Engine Y-axis yaw and pitch control torque coefficient, Engine Y-axis pitch inertia moment coefficient, Engine Z-axis yaw and pitch control torque coefficient —Engine Z-axis yaw pitch moment coefficient, —Coupling coefficient of pitch channel sway moment, —Coefficient of coherence of the center of mass of the pitch channel sway. —The i-th order elastic additional aerodynamic damping moment coefficient of the pitch channel. —The i-th order elastic additional aerodynamic moment and additional thrust moment coefficient of the pitch channel, —Engine thrust pitch channel torque, — Pitch channel structural disturbance moment, Y kp —Swaying normal displacement, Z kp —Swaying and lateral displacement.

[0172] Step 7: Based on the elastic coordinate system E, establish the elastic vibration equation of the rocket body according to the rocket configuration parameters and engine-related parameters.

[0173] Taking the interfacial force analysis between a single nozzle and a single swaying oscillator and the central body as an example, this paper provides an opinion. Figure 5Based on the force and moment balance equations in the elastic coordinate system, and considering the compatibility conditions of force and displacement, the overall rocket vibration equation considering liquid sloshing and engine oscillation can be simplified as follows:

[0174]

[0175] The equation for the undamped free vibration of a rocket is:

[0176]

[0177] Where M is the central body mass matrix considering liquid sloshing and engine oscillation. Let F be the nodal elastic vibration displacement vector (including elastic deformation linear displacement and angular displacement); C and K are the damping matrix and stiffness matrix, respectively; and F is the nodal external load vector acting on the central body (including active forces such as gravity, thrust, aerodynamic force, and disturbance force). These are the vectors of inertial forces and torques acting on a rigid body in a spring oscillator (equivalent to a liquid sloshing mechanical model). These are the vectors of rigid body inertial forces and torques acting on the nozzle structure. This represents the vector of additional inertial forces and torques during rigid body motion.

[0178] Solve The generalized eigenvalues ​​of the system give the n non-zero natural frequencies ω1, ω2, ..., Ω,ω. n and the corresponding modal column vector make It is called the mode matrix.

[0179] According to the modal superposition method, elastic vibration displacement It can be expanded using non-zero frequency modes, i.e.

[0180]

[0181] In the formula, q = [q1, q2, q3, ..., q n ] T Let Φ be the generalized coordinate array. Substitute the above equation into the overall rocket vibration equation, and use Φ... T Multiply by the preceding terms to obtain

[0182]

[0183] make

[0184]

[0185] The equation for elastic vibration can then be simplified as follows:

[0186]

[0187] In the formula, Here is the modal mass matrix. Here is the modal stiffness matrix. Let Q be the modal damping matrix. A A generalized force, referring to the external force (active force) acting on the central body. This refers to the generalized force corresponding to the inertial force of rigid body motion acting on the central body. This refers to the generalized force corresponding to the inertial force of rigid body motion acting on the spring oscillator. This is the generalized force corresponding to the inertial force of the rigid body acting on the nozzle.

[0188] If we consider the sloshing of all the liquid in the reservoir and the oscillating of all the engine nozzles, the overall vibration equation of the rocket can be written as follows:

[0189]

[0190] Thus, the generalized coordinate form of the whole arrow vibration equation is obtained, where the modal mass matrix is... The effects of liquid sloshing in all tanks and the oscillating nozzles of all engines must be considered.

[0191] Because the modes are orthogonal with respect to the mass matrix and stiffness matrix, i.e.

[0192]

[0193] In the formula, and Let be the generalized mass (also called modal mass) and generalized stiffness (also called modal stiffness) corresponding to the i-th mode, respectively. Therefore, both the generalized mass matrix and the generalized stiffness matrix are diagonal matrices, i.e.

[0194]

[0195] In the formula, ω i Let i be the frequency of the i-th mode. When the damping matrix C is Rayleigh damped, i.e., C = αM + βK, the modal damping matrix is:

[0196]

[0197] In the formula, ξ i Let be the damping ratio of the i-th mode.

[0198] Expanding the generalized forces corresponding to inertial forces and active forces, the expanded form of the elastic vibration equation can be derived:

[0199]

[0200] In the formula, q i —The generalized displacement of the i-th order elastic vibration, ω i —The i-th elastic frequency, D4i —Additional aerodynamic generalized force coefficient to the rolling channel, —The i-th order generalized aerodynamic damping force coefficient of the yaw channel. —The i-th order generalized aerodynamic damping force coefficient of the pitch channel. —The i-th order generalized aerodynamic coefficient of the pitch channel, —The i-th order generalized aerodynamic coefficient of the yaw channel, D 3iYks —Generalized control force coefficient for engine Y-axis oscillation, D″ 3iYks —Generalized inertial force coefficient of engine Y-axis oscillation, D 3iZks —Generalized control force coefficient for engine Z-axis oscillation, D″ 3iZks —The generalized inertial force coefficient of the engine's Z-axis oscillation. —The generalized force coefficient resulting from the p-th tank sway displacement and the i-th order elastic coupling in the pitch channel. —The generalized force coefficient resulting from the swaying acceleration of the p-th tank in the pitch channel and the elastic coupling of the i-th order. —The generalized force coefficient resulting from the sway displacement of the p-th tank in the yaw channel and the elastic coupling of the i-th order. —The generalized force coefficient R resulting from the sway acceleration of the p-th tank in the yaw channel and the elastic coupling of the i-th order. ij —The generalized force coefficient, R′, for the coupling of the j-th elastic element to the i-th elastic element. ij —The generalized damping force coefficient of the coupling between the j-th order elasticity and the i-th order elasticity. The generalized force generated by the thrust of the s-th engine in the k-th module. Generalized forces generated by structural disturbances;

[0201] Step 8: Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, establish the propellant sloshing equation;

[0202] The propellant sloshing equation in the rocket body coordinate system b is written as:

[0203]

[0204] Compared with existing equations for liquid sloshing, the above equation... These represent the swaying displacement, velocity, and acceleration of the swaying mass in the arrow body coordinate system, where... m kp The propellant mass under thrust reduction failure conditions; The coupling coefficient matrix of rocket body rotation and liquid sloshing under thrust reduction fault; C is the coupling term caused by the displacement of the rocket's center of mass due to a thrust reduction fault. kp This is the equivalent damping coefficient matrix. This is the equivalent stiffness coefficient matrix. For the system's downward-looking acceleration, The elastic motion-liquid sloshing coupling coefficient matrix is ​​given. The angular acceleration of the arrow body, It is the elastic generalized acceleration.

[0205] Expanding and deriving the above equation, we obtain the following equation for liquid sloshing:

[0206]

[0207] In the formula, Y kp Z kp —representing the swaying normal and lateral displacement, ζ kpy ζ kpz —These are the normal and lateral sway damping ratios, respectively, Ω kp — Shaking frequency, Z Lkp —The Z-axis position of the p-tank rocket body in the coordinate system of the k-th booster, Y-axis position Lkp —The Y-position of the p-tank rocket body in the coordinate system of the k-th booster, E kpz —The distance from the center of mass to the center of mass during shaking. —The force coefficient coupling between the i-th order elastic deformation displacement of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation displacement of the yaw channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the yaw channel and the p-th tank sway. —Arrow body pitch acceleration, —Yaw acceleration of the rocket body, —Rolling angular acceleration of the rocket body, n —Number of non-zero natural frequencies.

[0208] Step 9: Based on the output of the rigid body rotation equation and the mode shape and mode slope at the elastic node position of the inertial device, establish the measurement equation of the sensitive element.

[0209] The inertial navigation system (INS) is mounted on the core stage rocket. The elastic deformation of the core stage affects its measurements; therefore, the INS measurement equation is:

[0210]

[0211] In the formula, φ 0ix (x gz ) represents the torsional vibration mode at the core stage of the rocket, φ 0iy (x gz ) and φ 0ix (x gzThe slopes of the mode shapes at the core stage of the rocket are shown in the elastic coordinate system o. E -x E y E z E The following is given; —Inertial measurement values ​​of pitch attitude angle considering elasticity, — Arrow body pitch angle, ψ gz —Yaw attitude angle measured by inertial navigation system considering elasticity, ψ —Yaw attitude angle of the rocket body, γ gz —Measured value of the rocket body roll attitude angle considering elasticity, γ —Rocket body roll attitude angle.

[0212] Assuming the rate gyroscope is mounted on the k-th booster, its measurement equation is:

[0213]

[0214] In the formula, φ kix (x st ) represents the torsional vibration mode at the mounting location of the k-th boost rate gyroscope, φ kiy (x st ) and φ kiz (x st Let be the mode shape slope at the mounting point of the k-th booster rate gyroscope, and both are in the elastic coordinate system o. E -x E y E z E The following is given; —Gyroscope measurements of the rocket's pitch angular velocity rate. —Arrow body pitch velocity, —Yaw rate angular velocity of the rocket body measured by gyroscope. —Yaw rate of the rocket body, —Gyroscope measurement of the rocket's roll angular velocity rate. —Rolling angular velocity of the rocket body, — Elastic generalized velocity.

[0215] Step 10: Summarize the equations of rigid body translation, rigid body rotation, rocket body elastic vibration, propellant sloshing, and sensitive element measurement to form a set of nonlinear dynamic equations.

[0216] Step 11: Perform small-perturbation linearization expansion of the nonlinear dynamic equations based on the nominal reconstructed trajectory to obtain a linearized small-deviation equation set suitable for controller design and stability analysis.

[0217] The linearized small-deviation equation set includes:

[0218] 1) Equation for small deviation of the center of mass motion:

[0219]

[0220] —Pitch channel dynamic coefficient, —Yaw channel dynamic coefficient, —Gravity coefficient of the pitch channel, — Gravity coefficient of the yaw channel —The i-th order elastic additional aerodynamic force and thrust coefficient of the pitch channel, —The i-th order elastic additional aerodynamic force and thrust coefficient of the yaw channel, Δ represents the deviation perturbation of the state quantity based on the nominal reconstructed trajectory.

[0221] 2) Equation for small deviations in rigid body rotation:

[0222]

[0223]

[0224] 3) Linearization results of the elastic motion equations:

[0225]

[0226] 4) The equation for small deviation of swaying is:

[0227]

[0228] This invention proposes a universal nonlinear dynamics modeling method for large liquid launch vehicles, applicable to the dynamics description of rockets under normal conditions and propulsion system failures of different configurations. It ensures the accuracy of the model under failure conditions and provides a basis for analyzing the impact of thrust reduction on rocket characteristics and dynamic behavior, as well as for formulating fault-tolerant and reconfigurable control strategies for attitude control systems.

[0229] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0230] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A dynamic modeling method for an attitude control system under dynamic faults, characterized in that, Includes the following steps: Establish coordinate systems for modeling, including launch coordinate system a, rocket body coordinate system b, half-velocity coordinate system h, elastic coordinate system E, and local elastic follower coordinate system e. k(x) Nozzle coordinate system N ks ; Based on the launch vehicle object description, obtain the rocket configuration parameters and engine-related parameters; Based on launch coordinate system a, rocket body coordinate system b, and local elastic follower coordinate system e k(x) Nozzle coordinate system N ks The displacement and acceleration descriptions of three types of structures on the rocket are established, including the displacement and acceleration descriptions of any point on the rocket body structure under the consideration of rocket elastic deformation, the displacement and acceleration descriptions of the swaying mass points when the propellant sways, and the displacement and acceleration descriptions of the center of mass of the nozzle of the k-th booster and s-th engine. Based on the half-velocity coordinate system h, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, the rigid body translation equations are established. Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, a rigid body rotation equation is established. Based on the elastic coordinate system E, and according to the rocket configuration parameters and engine-related parameters, the elastic vibration equation of the rocket body is established. Based on the rocket body coordinate system b, and according to the rocket configuration parameters, engine-related parameters, and displacement and acceleration descriptions of the three types of structures on the rocket, the propellant sloshing equation is established. Based on the output of the rigid body rotation equation and the mode at the installation position of the inertial device, the measurement equation of the sensing element is established; The equations of rigid body translation, rigid body rotation, rocket body elastic vibration, propellant sloshing, and sensitive element measurement are summarized to form a set of nonlinear dynamic equations. By performing a small-perturbation linearization expansion of the nonlinear dynamic equations based on the nominal reconstructed trajectory, a linearized small-deviation equation set suitable for controller design and stability analysis is obtained.

2. The dynamic modeling method for an attitude control system under dynamic faults according to claim 1, characterized in that, Before performing dynamic modeling, the following modeling assumptions for the nonlinear dynamic model are defined: Assume that the strain and rotation caused by the elastic deformation of the arrow body are 1% of the arrow body structural dimensions; Assume the liquid surface sloshing angle is less than 10°; Assuming the engine sway angle is less than 10°; Ignoring the effects of Earth's rotation; Only the reaction force generated by the ejection of propellant combustion products is considered and included in the thrust, while the additional Coriolis force, additional Coriolis moment and additional relative moment generated are ignored.

3. The dynamic modeling method for an attitude control system under dynamic faults according to claim 1, characterized in that, The definition of the arrow body coordinate system b is as follows: The origin of the rocket body coordinate system is the projection point O1 of the instantaneous center of mass O2 of the rocket onto the longitudinal axis of the core stage. The O1X1 axis is the longitudinal axis of the core stage, pointing towards the head of the core stage. The O1Y1 axis is located within the main symmetry plane of the rocket. The O1X1Y1 plane coincides with the OXY plane of the launch coordinate system at the instant of launch. The O1Z1 axis is determined according to the right-hand rule. The nozzle coordinate system N ks The definition is as follows: Nozzle coordinate system N ks The nozzle of the k-th booster engine is fixedly connected to the s-th engine nozzle, with the origin O. δks Located at the engine's swing point, O δks X δks The thrust P is directed along the axis of symmetry of the nozzle housing towards the nose of the rocket body. ks For a single-pendulum engine, the positive direction of the servo direction swing angle is defined as O. δks Y δks Axis, O δks Z δks The axis is determined according to the right-hand rule. For an orthogonal double-pendulum engine, after the positive polarity of the pendulum angle in the servo direction is determined, a unique O is determined according to the right-hand rule. δks Y δks Shaft and O δks Z δks The positive direction of the axis.

4. The dynamic modeling method for an attitude control system under dynamic faults according to claim 3, characterized in that, The rocket configuration parameters and engine-related parameters include: The rocket configuration parameters include: the number of boosters N. zt The total number of engines on the kth booster is The total number of storage tanks is When k=0, it represents the core stage rocket body, that is, the total number of core stage rocket engines is... The total number of storage tanks is Boost installation radius L k This represents the distance between the longitudinal axis of booster k and the longitudinal axis of the core stage, and the booster installation azimuth angle μ. k This represents the angle between the plane formed by the k-booster longitudinal axis and the core stage longitudinal axis and the O1X1Z1 plane; The engine-related parameters include: the engine installation position X of each module. kR The distance from the swing point of booster k to the theoretical vertex; the installation radius L of the s-th booster in the module. δks δ represents the distance from the engine sway point to the module's longitudinal axis; qks The azimuth angle for the engine is the angle between the line connecting the engine swing point to the module's longitudinal axis and the O1Y1 axis. The engine yaw azimuth angle represents the rotation from the rocket body coordinate system O1Y1 axis to the nozzle coordinate system O. δks Y δks The angle.

5. The dynamic modeling method for an attitude control system under dynamic faults according to claim 4, characterized in that, The description of displacement and acceleration at any point on the rocket body structure includes: The radius vector at any point on the arrow's structure: The acceleration of the structural particle is: In the formula, This represents the absolute derivative in the launch coordinate system a. This represents the velocity of the origin O1 of the rocket's coordinate system relative to the launch coordinate system. This represents the local derivative in the arrow's coordinate system b. In the locally elastic follower coordinate system e k(x) Local derivatives in u k(x) Let o be the origin of the local elastic follower coordinate system after the projectile deforms. ek(x) The elastic translational displacement, R c.m R is the position vector of the origin O1 of the rocket body coordinate system in the launch coordinate system a. k(x) Let ω1 be the radius vector of the projection point from O1 of any point on the structure onto the longitudinal axis of booster k before deformation, and let ω1 be the rigid body rotational angular velocity of the rocket relative to the launch coordinate system a. ek(x) For the local dynamic elastic coordinate system e k(x) The elastic rotational angular velocity relative to the arrow body coordinate system b, In the coordinate plane o ek(x) y ek(x) z ek(x) origin o ek(x) The position vector to any structural point. The position vector of any structural point when the rocket is considered a rigid body; The description of the displacement and acceleration of the sloshing particles during propellant sloshing includes: When the rocket deforms and the propellant sloshes, the sloshing mass point m kp The position vector in the launch coordinate system a can be expressed as: The acceleration of the shaking particle is: In the formula, Let be the radius vector of the rocket's center of sway before deformation in the rocket's coordinate system b. The center of the sway is located in the local elastic follower coordinate system e. k(x) Translational displacement, h kp For the swaying mass in the locally elastic follower coordinate system e k(x) The swaying displacement; The displacement and acceleration description of the nozzle center of mass of the k-th booster s-th engine includes: In launch coordinate system a, the position vector of the center of mass of the nozzle of the k-th booster s-th engine is: The acceleration of the nozzle's center of mass is: In the formula, For the kth booster s engine swing center O δks The projection point on the longitudinal axis of the booster has a position vector in the rocket body coordinate system b. To establish the origin elastic translational displacement of a local elastic follower coordinate system at this projection point, ρ rks For the local elastic follower coordinate system e k(x) The oscillating point radius vector, ρ Rks In the nozzle coordinate system N ks The radius vector of the center of mass of the nozzle, ρ r1ks To treat the rocket as a rigid body, the radius vector at the oscillation point, ρ R1ks Let the radius vector be the center of mass of the nozzle when the engine is not swaying. For a locally elastic follower coordinate system The angular velocity of rotation relative to the arrow's coordinate system b, ω δks Let the nozzle be relative to the local elastic coordinate system e k(x) angular velocity of rotation.

6. The dynamic modeling method for an attitude control system under dynamic faults according to claim 5, characterized in that, The establishment of the rigid body translation equations includes: According to Newton's second law, the rigid body translation equations of the entire rocket system are: In the formula, mg is gravity, P is engine thrust, and F is... aero For aerodynamic forces, F wind For wind interference force, F structure For structural interference force, For volume fraction, For point Structural density at m kp For the swaying mass of the p-th order swaying assisted by the k-th boost, m Rks For the k-th booster s-th engine sway mass, N zt For the number of boosters, The total number of storage tanks, The total number of engines on the k-th booster; In the half-velocity coordinate system h, the coefficient-reduced rigid body translation equations are obtained as follows: At the same time, the apparent acceleration in the arrow body coordinate system is established as: Where g is the acceleration due to gravity, V is the flight velocity, θ is the trajectory angle, σ is the trajectory deflection angle, and α is the trajectory angle of attack. wp —Stable wind angle of attack, α wq —Angle of attack of shear wind, β —Side slip angle of ballistic trajectory, β wp —Steady wind sideslip angle, β wq —Side slip angle of shear wind, —Arrow body pitch velocity, —Yaw rate of the rocket body, q i —Elastic generalized displacement, —Elastic generalized displacement velocity, δ Yks , Let δ represent the sway angle and angular acceleration of the oscillating engine in the Y direction, respectively. Zks , Let c be the sway angle and angular acceleration of the oscillating engine in the Z direction, respectively. X_aero —Axial force coefficient, —Aerodynamic coefficients of the pitch channel, — Yaw channel aerodynamic coefficient, —Aerodynamic damping force coefficient of the pitch channel, —Aerodynamic damping force coefficient of the yaw channel —The i-th order elastic additional aerodynamic coefficient of the pitch channel, —The i-th order elastic additional aerodynamic coefficient for the yaw channel. —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, —The i-th order elastic additional damping aerodynamic coefficient of the pitch channel, c 1P —Axial thrust coefficient, These are the oscillation control force coefficients of the engine in the Y and Z directions, respectively, for the pitch control channel. These are the yaw control force coefficients for the yaw channel engine in the Y and Z directions, respectively. These are the oscillation inertial force coefficients of the engine in the Y and Z directions, respectively, for the pitch channel. These are the oscillating inertial force coefficients of the yaw channel engine in the Y and Z directions, respectively. —The coefficient of cross-linking force for pitch channel swaying. —Yaw channel sway cross-linking force coefficient, —The i-th order elastic additional thrust coefficient of the pitch channel, —The i-th order elastic additional thrust coefficient in the yaw channel, —The structural interference force coefficient of the pitch channel, —Yaw channel structural interference force coefficient, —Coordinate transformation matrix from the rocket body coordinate system to the half-velocity coordinate system, The projection of the swaying acceleration onto the O1Y1 axis of the rocket body coordinate system. The projection of the swaying acceleration onto the O1Z1 axis of the rocket body coordinate system. —Axial acceleration of the rocket body in coordinate system O1X1 —The apparent acceleration along the O1Y1 axis of the rocket's coordinate system. —Axis acceleration of the rocket body coordinate system O1Z1.

7. The dynamic modeling method for an attitude control system under dynamic faults according to claim 6, characterized in that, The establishment of the rigid body rotation equation includes: The rigid body rotation equations for the entire rocket system are as follows: In the formula, M CM_g M represents the torque exerted by the gravity of each component about the origin O1 of the rocket's coordinate system. CM_P M is the torque of the engine thrust about the origin O1 of the rocket body coordinate system. CM_aero M is the torque of the aerodynamic force about the origin O1 of the rocket's coordinate system. CM_wind M is the torque of the wind interference force about the origin O1 of the rocket's coordinate system. CM_structure The torque of the structural disturbance force about the origin O1 of the rocket body coordinate system; After expanding and substituting the external torque terms, we obtain the coefficient-reduced full rigid body rotation equation in the arrow coordinate system: In the formula, —Rolling angular velocity of the rocket body, —Roll channel yaw angle acceleration coupling coefficient, —Roll path pitch angle acceleration coupling coefficient, d PX — The transverse displacement coefficient of the center of mass in the fault rolling channel, d1 — The rolling damping moment coefficient, d 3Yks —k booster engine Y-axis oscillation and rolling control torque coefficient, d3″ Yks —Y-direction oscillating moment coefficient of the rolling channel, d 3Zks —Z-axis oscillating rolling control force coefficient, d3″ Zks —The Z-axis oscillating moment of inertia coefficient of the rolling channel, d hykp — The cross-linking coefficient of the Y-axis sloshing displacement of the propellant in the tank to the rolling channel, d h " ykp —Y-axis swaying acceleration as a function of the cross-linking coefficient of the rolling channel, d hzkp — Cross-linking coefficient of Z-axis sway displacement to rolling channel, d h " zkp — Cross-linking coefficient of Z-axis swaying acceleration to the rolling channel, d 1i —The i-th order elastic aerodynamic damping moment coefficient of the rolling channel, d 2i —The i-th order elastic moment coefficient of the rolling channel, —Disturbing moment coefficient of the rolling channel structure, —Yaw channel roll angle acceleration coupling coefficient, —Yaw channel pitch angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of gravity in the fault yaw channel. — Yaw channel aerodynamic damping moment coefficient. — Yaw channel aerodynamic moment coefficient, —Engine Y-axis yaw control moment coefficient, —Engine Y-axis oscillation moment coefficient, —Engine Z-axis yaw control moment coefficient, —Engine Z-axis oscillation moment coefficient, —Yaw channel sway moment coupling coefficient, —Yaw channel sway center of mass coherence coefficient, —The i-th order elastic additional aerodynamic damping moment coefficient of the yaw channel. —The coefficients of the i-th order elastic additional aerodynamic moment and additional thrust moment in the yaw channel. —Engine thrust yaw channel torque, — Yaw channel structural disturbance moment, —Pitch channel roll angle acceleration coupling coefficient, —Pitch channel yaw angle acceleration coupling coefficient, —The lateral displacement coefficient of the center of mass in the pitch channel during a fault. —Pitch channel aerodynamic damping moment coefficient, —Aerodynamic moment coefficient of the pitch passage, —Engine Y-axis yaw and pitch control torque coefficient, Engine Y-axis pitch inertia moment coefficient, Engine Z-axis yaw and pitch control torque coefficient —Engine Z-axis yaw pitch moment coefficient, —Coupling coefficient of pitch channel sway moment, —Coefficient of coherence of the center of mass of the pitch channel sway. —The i-th order elastic additional aerodynamic damping moment coefficient of the pitch channel. —The i-th order elastic additional aerodynamic moment and additional thrust moment coefficient of the pitch channel, —Engine thrust pitch channel torque, — Pitch channel structural disturbance moment, Y kp —Swaying normal displacement, Z kp —Swaying and lateral displacement.

8. The dynamic modeling method for an attitude control system under dynamic faults according to claim 7, characterized in that, The establishment of the elastic vibration equation of the arrow body includes: In the formula, q i —The generalized displacement of the i-th order elastic vibration, ξ i —The damping ratio of the i-th mode, ω i —The i-th elastic frequency, D 4i —Additional aerodynamic generalized force coefficient to the rolling channel, —The i-th order generalized aerodynamic damping force coefficient of the yaw channel. —The i-th order generalized aerodynamic damping force coefficient of the pitch channel. —The i-th order generalized aerodynamic coefficient of the pitch channel, —The i-th order generalized aerodynamic coefficient of the yaw channel, D 3iYks —Generalized control force coefficient for engine Y-axis oscillation, D3″ iYks —Generalized inertial force coefficient of engine Y-axis oscillation, D 3iZks —Generalized control force coefficient for engine Z-axis oscillation, D3″ iZks —The generalized inertial force coefficient of the engine's Z-axis oscillation. —The generalized force coefficient resulting from the p-th tank sway displacement and the i-th order elastic coupling in the pitch channel. —The generalized force coefficient resulting from the swaying acceleration of the p-th tank in the pitch channel and the elastic coupling of the i-th order. —The generalized force coefficient resulting from the sway displacement of the p-th tank in the yaw channel and the elastic coupling of the i-th order. —The generalized force coefficient R resulting from the sway acceleration of the p-th tank in the yaw channel and the elastic coupling of the i-th order. ij —The generalized force coefficient, R′, for the coupling of the j-th elastic element to the i-th elastic element. ij —The generalized damping force coefficient of the coupling between the j-th order elasticity and the i-th order elasticity. The generalized force generated by the thrust of the s-th engine in the k-th module. Generalized force generated by structural disturbance, Y kp —Swaying normal displacement, Z kp —Swaying lateral displacement, —Swaying normal acceleration, — Lateral acceleration due to swaying.

9. The dynamic modeling method for an attitude control system under dynamic faults according to claim 8, characterized in that, The establishment of the propellant sloshing equation includes: The propellant sloshing equation in the rocket body coordinate system b is: These represent the swaying displacement, velocity, and acceleration of the swaying mass in the arrow body coordinate system, where... m kp For the propellant mass under thrust reduction failure, The matrix represents the coupling coefficients between the rocket body rotation and the liquid sloshing under thrust reduction failure. This is the coupling term caused by the displacement of the rocket's center of mass due to a thrust reduction fault. This is the equivalent damping coefficient matrix. This is the equivalent stiffness coefficient matrix. For the system's downward-looking acceleration, The elastic motion-liquid sloshing coupling coefficient matrix is ​​given. The angular acceleration of the arrow body, For elastic generalized acceleration; Expanding the above equation, we derive the following equation for liquid sloshing: ζ kpy ζ kpz These are the normal and lateral sway damping ratios, Ω kp — Shaking frequency, Z Lkp —The Z-axis position of the p-tank rocket body in the coordinate system of the k-th booster, Y-axis position Lkp —The Y-position of the p-tank rocket body in the coordinate system of the k-th booster, E kpz —The distance from the center of mass to the center of mass during shaking. —The force coefficient coupling between the i-th order elastic deformation displacement of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation displacement of the yaw channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the pitch channel and the p-th tank sway. —The force coefficient coupling between the i-th order elastic deformation acceleration of the yaw channel and the p-th tank sway. —Arrow body pitch acceleration, —Yaw acceleration of the rocket body, —Rolling angular acceleration of the rocket body, n —Number of non-zero natural frequencies.

10. A dynamic modeling method for an attitude control system under dynamic faults according to claim 9, characterized in that, The establishment of the measurement equation for the sensitive element includes: The inertial measurement equation is: In the formula, φ 0ix (x gz ) represents the torsional vibration mode at the core stage of the rocket, φ 0iy (x gz ) and φ 0ix (x gz ) represents the mode shape slope at the core stage of the rocket. —Inertial measurement values ​​of pitch attitude angle considering elasticity, — Arrow body pitch angle, ψ gz —Yaw attitude angle measured by inertial navigation system considering elasticity, ψ —Yaw attitude angle of the rocket body, γ gz —Measured value of the rocket body roll attitude angle considering elasticity, γ —Rocket body roll attitude angle; Assuming the rate gyroscope is mounted on the k-th booster, its measurement equation is: In the formula, φ kix (x st ) represents the torsional vibration mode at the mounting location of the k-th boost rate gyroscope, φ kiy (x st ) and φ kiz (x st ) represents the mode slope at the mounting location of the k-th booster rate gyroscope. —Gyroscope measurements of the rocket's pitch angular velocity rate. —Arrow body pitch velocity, —Yaw rate angular velocity of the rocket body measured by gyroscope. —Yaw rate of the rocket body, —Gyroscope measurement of the rocket's roll angular velocity rate. —Rolling angular velocity of the rocket body, — Elastic generalized velocity.

11. The dynamic modeling method for an attitude control system under dynamic faults according to claim 10, characterized in that, The linearized small-deviation equation set includes: 1) Equation for small deviation of the center of mass motion: —Pitch channel dynamic coefficient, —Yaw channel dynamic coefficient, —Gravity coefficient of the pitch channel, — Gravity coefficient of the yaw channel —The i-th order elastic additional aerodynamic force and thrust coefficient of the pitch channel, —The i-th order elastic additional aerodynamic force and thrust coefficient of the yaw channel, Δ represents the deviation perturbation of the state quantity based on the nominal reconstructed trajectory; 2) Equation for small deviations in rigid body rotation: 3) Linearization results of the elastic motion equations: 4) The equation for small deviation of swaying is:

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