Adaptive Fault-Tolerant Backstep Attitude Control Design Method for Launch Vehicles

Abstract

This invention addresses the common failure problems encountered by actuators during the flight of heavy-lift launch vehicles in disturbed environments. It studies a method for achieving rocket attitude stabilization and tracking under complex conditions, proposing an adaptive fault-tolerant backstepping attitude control design method. First, to avoid attitude singularities, a quaternion-based kinematic and dynamic model of the launch vehicle oriented towards actuator failures is established. Based on this model, an adaptive fault-tolerant backstepping attitude controller is designed to adaptively estimate and compensate for uncertainties and external disturbances, handling potential failures and ensuring the stability of the control system. The algorithm proposed in this invention is more effective and superior than traditional adaptive backstepping methods.

Description

Technical Field

[0001] This invention belongs to the field of launch vehicle attitude control and relates to an effective fault-tolerant attitude control design method, which is applicable to attitude control under the fault and disturbance conditions of rockets and other aircraft. Background Technology

[0002] The motion model of a heavy-lift launch vehicle is a typical nonlinear system. With the development of nonlinear control theory, methods for directly designing controllers based on nonlinear models have emerged. The backstepping method, as a typical design approach, has excellent capabilities for solving nonlinear problems. Furthermore, the heavy-lift launch vehicle system is a rapidly time-varying system, with its relevant states changing quickly, and it experiences complex and variable environments during flight, subject to disturbances from unknown external factors that significantly impact its flight attitude, leading to uncertainties. Adaptive control technology is an effective solution to the uncertainties in the spacecraft model.

[0003] Heavy-lift launch vehicles often encounter problems such as actuator failures and nonlinear dead zones during flight, which can lead to unsatisfactory control effects or even system instability, resulting in unacceptable and serious consequences. Therefore, studying fault-tolerant control of spacecraft to ensure the stability and reliability of their control systems during flight has significant theoretical and engineering value. Fault-tolerant control of spacecraft has two main characteristics: proactive preventive control and rapid emergency control. By utilizing fault diagnosis information, the control system is reconstructed, and the deflection of the actuators is reconfigured to compensate for faults. Summary of the Invention

[0004] Technical problems to be solved

[0005] To address the problem that controllers designed using the traditional adaptive backstepping method cannot effectively control the attitude of a spacecraft under fault conditions, this invention proposes an adaptive fault-tolerant backstepping attitude control design method for rockets with actuator faults and bounded external disturbances.

[0006] Technical solution

[0007] An adaptive fault-tolerant backstepping attitude control method for a launch vehicle, characterized by the following steps:

[0008] Step 1: Identify the four types of actuator malfunctions, including jamming, saturation, looseness, and damage.

[0009] Step 2: Establish a quaternion-based mathematical model for launch vehicles oriented towards actuator failures;

[0010] Step 3: Design an adaptive fault-tolerant backstepping attitude controller for the launch vehicle mathematical model based on quaternions and oriented towards actuator faults, and adaptively estimate and compensate for four types of actuator faults and external disturbances.

[0011] A further technical solution of the present invention: Step 2 is as follows:

[0012] Actuator failure can be described by the following formula:

[0013]

[0014] In the formula, u F ∈R 4＝1 The input form of the attitude control system under fault conditions is represented by Λ = diag{κ1,κ2,κ3,κ4}, which represents the gain coefficient matrix of the actuator, and H = diag[h1,h2,h3,h4] which represents the damage factor matrix. When the i-th actuator experiences a jamming failure, i = 1, 2, 3, 4, that is... hour, hour, I4 is a 3×3 identity matrix; The input u of the attitude control system under fault conditions. F The first derivative of ; u is the input pendulum angle matrix;

[0015] Since the object studied in this invention has four engines as actuators, the fault mathematical model of each engine includes h and With two parameters, the system becomes very complex. To simplify the fault model and facilitate the design of the subsequent control law, the mathematical model of actuator faults is reasonably transformed, and h is represented by a parameter matrix M. i and Let matrix D represent (I4-Σ)u F As shown in the following formula:

[0016]

[0017] In the formula, M = diag[m1,m2,m3,m4] is defined as an occasional gain fault in the attitude control system, and because h i and Since M is a bounded positive constant, it is obvious that M is a symmetric positive definite matrix; the occasional deviation fault of the attitude control system is defined as D=[d1(t),d2(t),d3(t),d4(t)] T We get the following formula:

[0018] u F =Mu+D (3)

[0019] Based on the kinematic dynamics model of a heavy-lift launch vehicle under nominal conditions, the input matrix u under fault conditions is used. F Instead of the input matrix u in nominal form, a kinematic and dynamic model of the heavy-lift launch vehicle under fault conditions is established:

[0020]

[0021]

[0022] In the formula: state X1 represents a unit quaternion describing the attitude azimuth angle of the projectile coordinate system relative to the navigation coordinate system, i.e., X1 = [q1 q2 q3 q0] T =[q T q0] T The state variable X2 is the angular velocity vector in the projectile coordinate system, i.e. For roll angular velocity, For yaw rate, denoted as pitch angular velocity; J is the inertia tensor in the projectile coordinate system; u is the input swing angle matrix; B is the control allocation matrix, where x... R x is the distance from the engine hinge point to the theoretical tip of the rocket body. g d is the distance from the rocket's center of mass to the tip of the rocket body; f is the nonlinear torque of the system, d ext I3 is the disturbance torque of the model, and I3 is a 3×3 identity matrix.

[0023] A further technical solution of the present invention: Step 3 is as follows:

[0024] Since the dynamic equations for attitude angle tracking and attitude angular velocity have different time scales, the attitude control state-space model can be divided into first-order and second-order systems. In the first-order system, a virtual control law must be designed to force the attitude angle tracking error to converge to zero, as shown in the following equation:

[0025] X 2e,virtual =-kq e (5)

[0026] In the formula, k > 0 is a design parameter, and the estimated error of attitude angular velocity tracking error is defined as follows:

[0027]

[0028] X 2e,virtual This represents the designed virtual control law;

[0029] To force the angular velocity error to track the virtual control input of the first-order system, a second-order control input needs to be synthesized. In the second-order system, a nonlinear feedback term is introduced to overcome the known nonlinear term, as shown in the following equation:

[0030]

[0031] k1 > 0 is a design parameter; The first derivative of the designed virtual control law; the angular velocity error X is defined. 2e =X2-R(X 1e )X 2d =[X 2e，1 X 2e,2 X 2e,3 ] T , Define the attitude transition matrix R(X) 1e )=(q e0 2 -q e T q e )I3+2q e q e T -2q e0 S(q e In the formula, ||R(X) 1e )||=1, It is the first derivative of the desired angular velocity in the projectile coordinate system;

[0032] Secondly, due to the existence of deviation faults and external disturbances, a compensation control law with adaptive parameters was designed; because the control input and state variables of the feedback attitude control system are inconsistent, control allocation is required.

[0033]

[0034] In the formula, B is the control allocation matrix. It is an estimate of Γ, defined as:

[0035] Γ=BD+d ext (9)

[0036] To address the input uncertainty caused by actuator gain failure, an additional adaptive compensation law needs to be added to the conventional control signal:

[0037]

[0038] In the formula, This is an estimate of W, defined as follows:

[0039] W = [MI] / M (11)

[0040] M represents the occasional gain fault of the attitude control system, which is a symmetric positive definite matrix; I represents the identity matrix.

[0041] Design the final second-order system control law:

[0042] u = u c +u a (12)

[0043] And select the update pattern for the adaptive parameters:

[0044]

[0045]

[0046] Define η2:

[0047]

[0048] These are design parameters.

[0049] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0050] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0051] Beneficial effects

[0052] This invention provides an adaptive fault-tolerant backstepping attitude control design method for launch vehicles. Addressing actuators with gain and deviation faults, it designs a quaternion-based adaptive fault-tolerant backstepping attitude controller for heavy-lift launch vehicles. The main reason this controller can achieve accurate tracking is that the actuator employs an adaptive control method to handle potential faults: firstly, it combines the uncertainty Γ = BD + d caused by deviation faults and external disturbances. ext Adaptive estimation and compensation were performed, and then an additional control law was used. Force the nonlinear term B(MI)u c +BMu a Converges to 0, and let The desired value W = [MI] / M is reached. In this way, accurate angle-tolerant tracking is maintained. Simulation analysis and comparison with controllers designed using the traditional backstepping method show that the controller designed in this invention has excellent performance. Attached Figure Description

[0053] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0054] Figure 1 This is a structural diagram of the adaptive fault-tolerant backstepping attitude control system of the present invention;

[0055] Figure 2 This is a schematic diagram of the rocket's engine tilt angle.

[0056] Figure 3 Fault mode diagram of rocket engine servo mechanism;

[0057] Figure 4 The output diagrams show the attitude angles and desired attitude angles, comparing the adaptive fault-tolerant backstep attitude control design based on Euler angles with the traditional backstep attitude control design under simulation conditions.

[0058] Figure 5 The output diagrams show the attitude angular velocity and desired attitude angular velocity compared to the traditional backstep attitude control design under simulation conditions.

[0059] Figure 6 The output diagrams show the attitude angles and desired attitude angles, comparing the adaptive fault-tolerant backstep attitude control design based on Euler angles with the traditional backstep attitude control design under simulation conditions 2.

[0060] Figure 7 The diagram shows the output of attitude angular velocity and desired attitude angular velocity, comparing the adaptive fault-tolerant backstep attitude control design with the traditional backstep attitude control design under simulation condition 2. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0062] This invention provides an adaptive fault-tolerant backstepping attitude control design method. Based on the backstepping method, the nonlinear feedback term and the nonlinear uncertain adaptive compensation term are redistributed according to the control allocation law, and then the input uncertain adaptive compensation term is introduced to obtain the final control input. Its control block diagram is shown below. Figure 1 As shown in the figure. This method improves the safety and reliability of the attitude control system while also enhancing the system's control accuracy.

[0063] First, a rigid body kinematics and dynamics model of the rocket based on quaternions is established.

[0064] The motion of a rocket is a complex motion highly coupled with rigid body motion and non-rigid body motion, with rigid body motion being the fundamental motion of the rocket. This invention mainly discusses the attitude control of the rocket, therefore focusing on the angular motion around the three principal axes of inertia, and neglecting the influence of deviations in the center of mass motion parameters on the motion around the center of mass. It is assumed that the elastic deformation displacement and rotation angle during rocket flight are small, and the dynamic modeling ignores the non-rigid body motion of the rocket, simplifying it to a rigid body with its center of mass position unchanged; the influence of structural parameter errors (such as mass and inertia deviations) on the disturbing motion is ignored; and the influence of altitude on aerodynamic coefficients and thrust is also not considered.

[0065] The four engines of a launch vehicle are defined as C j (j=1,2,3,4), the corresponding engine tilt angle is δ j (j=1,2,3,4), r c This represents the distance from the engine's oscillating nozzle to the rocket's axial centerline. Assume all engine thrusts are equal, i.e., P1 = P2 = P3 = P4. The rocket's engine oscillation angle is illustrated below. Figure 2 As shown, the swing angle amplitude is limited to ±18°.

[0066] The rigid body kinematics and dynamics model of a rocket based on quaternions is shown in equation (1).

[0067]

[0068] In the formula: state X1 represents a unit quaternion describing the attitude azimuth angle of the projectile coordinate system relative to the navigation coordinate system, i.e., X1 = [q1 q2 q3 q0] T =[q T q0] T The state variable X2 is the angular velocity vector in the projectile coordinate system, i.e. (roll velocity) Yaw angular velocity Pitch angular velocity J is the inertia tensor in the projectile coordinate system; u is the input swing angle matrix; B is the control allocation matrix, where x R x is the distance from the engine hinge point to the theoretical tip of the rocket body. g M is the distance from the rocket's center of mass to the tip of the rocket body; f is the nonlinear torque of the system. Rst It is the aerodynamic stabilizing torque, M RD It is the aerodynamic damping torque, M δ It is the engine's oscillating inertial torque, M' k It is an additional Coriolis moment; d ext It is the disturbance torque of the model, MB It is the structural disturbance torque or other external disturbance torque in the rocket's mechanical environment; I3 is a 3×3 identity matrix.

[0069]

[0070]

[0071]

[0072] u = [δ1 δ2 δ3 δ4] T ;

[0073] f = M Rst +M RD +M δ +M' k ;

[0074] d ext =[M Bx M By M Bz ] T .

[0075] Consider the common failure modes of the swing angle δ(t) in the control torque output of the swing angle actuator of four rocket attitude control systems, such as Figure 3 As shown.

[0076] The faults can be categorized as follows: (1) Stuck fault: In the case of a stuck fault, the actuator is stuck in a fixed position and cannot respond to the controller signal; (2) Saturation fault: The saturation fault mode refers to the actuator gradually reaching the maximum or minimum output value and remaining unchanged. Similarly, this type of fault will not respond to the controller signal; (3) Loose fault: The loose fault refers to the operating mechanism moving freely without producing any action. The actuator will be stuck at the zero position. After the fault occurs, it will bring time-varying disturbances to the system; (4) Damaged fault: The damaged fault is caused by the change in the control gain of the actuator, which causes the response of the control command to deviate, ultimately leading to a reduction in control performance.

[0077] Considering the four failure modes of the actuators mentioned above, the actual swing angle δ output by the i-th engine actuator is... i (t)(i=1,2,3,4) can be expressed by the following formula.

[0078]

[0079] In the formula, δ i,normal The swing angle output by the actuator under nominal conditions. h is the time when the i-th actuator fails. i (t) is the damage factor, and h i (t)∈[himin ,1], where h imin >0 represents the minimum damage factor.

[0080] Based on the theoretical input u of the attitude control system and the swing angle δ output by the actuator under fault-free conditions... i The relationship between the above-mentioned actuator failures can be described by the following formula.

[0081]

[0082] In the formula, u F ∈R 4×1 This represents the input format of the attitude control system under fault conditions. Λ=diag{κ1,κ2,κ3,κ4} represents the gain coefficient matrix of the actuator. H=diag[h1,h2,h3,h4] represents the damage factor matrix. This can be understood as when the i-th actuator (i = 1, 2, 3, 4) experiences a jamming failure, i.e. hour, hour,

[0083] Since the object studied in this invention has four engines as actuators, the fault mathematical model of each engine includes h and With two parameters, the system becomes very complex. To simplify the fault model and facilitate subsequent control law design, the actuator fault mathematical model is appropriately transformed, using a parameter matrix M to represent h. i and Let matrix D represent (I4-Σ)u F Then we have equation (4).

[0084]

[0085] In the formula, M = diag[m1,m2,m3,m4] is defined as an occasional gain fault in the attitude control system, and because h i and j i Since M is a bounded positive constant, it is obvious that M is a symmetric positive definite matrix; D = [d1(t), d2(t), d3(t), d4(t)] T , is defined as an occasional deviation fault of the attitude control system, resulting in (5).

[0086] u F =Mu+D (1)

[0087] Considering occasional gain and deviation faults in the actuators, based on the kinematic dynamics model of the heavy launch vehicle under the nominal state described by equation (1), the input matrix u under the fault form in equation (5) is used. FInstead of the input matrix u in nominal form, a kinematic and dynamic model of a heavy launch vehicle under fault conditions can be established as shown in equation (6).

[0088]

[0089] For the attitude tracking problem, the desired rocket attitude motion is given in the projectile coordinate system, and the azimuth angle relative to the navigation coordinate system is expressed as a unit quaternion X. 1d =[q d T q d0 ] T To express, and satisfy q d T q d +q d0 2 =1.

[0090] Define attitude tracking error X 1e As shown in equation (7).

[0091]

[0092] In the formula, X 1d -1 =[-q d T q d0 ] T ; It is a quaternion multiplication operation.

[0093] Define angular velocity error X 2e As shown in equation (8).

[0094] X 2e =X2-R(X 1e )X 2d (8) In the formula, X 2d It is the desired angular velocity in the projectile coordinate system; R(X) 1e ) is the attitude transition matrix.

[0095] Define the attitude transition matrix R(X) 1e ) is shown in equation (9).

[0096] R(X 1e )=(q e0 2 -q e T q e )I3+2q e q e T -2q e0 S(q e (9)

[0097] In the formula, R(X) 1e )||=1;

[0098] After incorporating occasional gain and deviation faults in the actuator, and considering the attitude tracking problem, the dynamic equation for the attitude tracking error of the attitude control system can be established as follows.

[0099]

[0100] The control objective of this invention is to achieve precise attitude stabilization and tracking in the presence of gain faults and deviation faults in the actuator.

[0101] The virtual control law for a first-order system is designed as shown in equation (11).

[0102] X 2e,virtual =-kq e (11)

[0103] In the formula, k > 0 is a design parameter.

[0104] The estimation error of attitude angular velocity tracking error is now defined as shown in equation (12).

[0105]

[0106] The outer-loop theoretical control law containing nonlinear feedback terms is designed as shown in equation (13).

[0107]

[0108] In the formula, k1 > 0 is a design parameter. It is an estimate of Γ, defined as in equation (14).

[0109] Γ=BD+d ext (14)

[0110] Consider the following L2 optimal control assignment problem to calculate the theoretical outer-loop control signal u. c The outer loop control signal, which includes an adaptive compensation control law, is designed as shown in equation (15).

[0111]

[0112] From equation (15), it is clear that if u is used c Make an input, the input uncertainty is B(MI)u c Unable to obtain compensation. To address this problem, an additional adaptive compensation law u is designed to compensate for input uncertainty. a As shown in equation (16).

[0113]

[0114] In the formula, It is an estimate of W, defined as in equation (17).

[0115] W = [MI] / M (17)

[0116] The final second-order system control law is designed as shown in equation (18).

[0117] u = u c +u a (18)

[0118] If we choose the update rules for adaptive parameters as shown in equations (19) and (20).

[0119]

[0120]

[0121] Define η2 as in equation (21).

[0122]

[0123] In the formula, These are design parameters.

[0124] Then the attitude angle will converge precisely to the desired value, thus achieving accurate tracking.

[0125] The adaptive parameter estimation error is defined as follows.

[0126]

[0127] The Lyapunov function is defined as follows.

[0128]

[0129] Since M is a positive definite matrix, we can conclude that the Lyapunov function is positive definite.

[0130] The derivative of V1 is given by equation (24).

[0131]

[0132] By simplification, the derivative of V2 can be obtained as shown in equation (25).

[0133]

[0134] Substituting the adaptive parameter update law into the above equation and then combining it with equation (24), we can obtain equation (26).

[0135]

[0136] It can be obtained. Outside of set Ω.

[0137]

[0138] Therefore, we can conclude that: q e , Both are bounded signals. From equation (1-2), we know that u and u... c u a Both are bounded. However, the system state q e , converges to And from then on, it remains within the set. As can be seen from the equation, by appropriately choosing the design parameters k and k1, Ω can be arbitrarily small, thus the proof is complete.

[0139] To verify the control performance of the aforementioned Adaptive Fault Tolerant Control (AFTC), it is compared with the traditional Adaptive Backstepping Control (BC). The specific implementation steps are as follows:

[0140] First, select data at a specific feature point for single-point test simulation analysis.

[0141] Considering the heavy-lift launch vehicle will be launched from the Wenchang Space Launch Site in Hainan, with a launch azimuth A0 = 90°, geographical latitude B0 = 19.61N, launch point longitude λ0 = 110.95E, launch point altitude 20m, and the average angular velocity of the Earth's rotation ω... e =7.292×10 -5 rad / s.

[0142] The parameters for a certain feature point are set as follows: the rocket's flight speed is V = 20 m / s.

[0143] The rocket's moment of inertia J xx =10 7 ×5.1497Kg·m 2 J yy =J zz =10 8 ×7.7999Kg·m 2 The thrust of a single first-stage engine is P1 = 10. 6 ×5.6482N. Engine mounting radius r C = 3.47m, distance from engine hinge point to arrow tip x R = 94.3m, distance from the center of mass to the tip of the arrow body x g =66.6678m, x p =75m. Dynamic pressure is q=900Pa. Rocket reference area is S.M =56.74m 2 The rocket's reference length L = 95.383 m. Damping moment coefficient. Aerodynamic torque coefficient

[0144] Considering Q0 = [0.5; 0.2; 0.1; 0.8366], with initial attitude angular velocities all at zero, and adaptive parameters... The initial value is also zero, and the adaptive parameter is... The initial value is estimated to be -9I4. The desired attitude angle is designed to be... Design desired attitude angular rate

[0145] Design parameters η1 = 2, η 20 =1. Assume external disturbance d ext = [0.1; 0.1; 0.1]. Assume the deviation fault D = 0.005·[1 1 1 1] T .

[0146] The simulation is performed under the following two conditions:

[0147] (1) Gain fault M = 0.8I4, assuming control gain k = 2.5, k1 = 2.5, the simulation output diagram is as follows. Figure 4 — Figure 5 ;

[0148] (2) Gain fault M = 0.2I4, assuming control gain k = 1.0, k1 = 1.4, the output simulation output diagram is as follows. Figure 6 — Figure 7 .

[0149] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. An adaptive fault-tolerant backstepping attitude control method for launch vehicles, characterized in that The steps are as follows: Step 1: Identify the four types of actuator malfunctions, including jamming, saturation, looseness, and damage. Step 2: Establish a quaternion-based mathematical model for launch vehicles oriented towards actuator failures; Step 3: Design an adaptive fault-tolerant backstepping attitude controller for the launch vehicle mathematical model based on quaternions and oriented towards actuator faults, adaptively estimating and compensating for four types of actuator faults and external disturbances; details are as follows: Since the dynamic equations for attitude angle tracking and attitude angular velocity have different time scales, the attitude control state-space model is divided into first-order and second-order systems. In the first-order system, a virtual control law must be designed to force the attitude angle tracking error to converge to zero, as shown in the following equation: (5) wherein is a design parameter that defines the estimation error of the tracking error of the attitude angular velocity as follows: (6) This represents the designed virtual control law; To force the angular velocity error to track the virtual control input of the first-order system, a second-order control input needs to be synthesized. In the second-order system, a nonlinear feedback term is introduced to overcome the known nonlinear term, as shown in the following equation: (7) It is a design parameter; The first derivative of the designed virtual control law; definition of angular velocity error. , Define the attitude transition matrix. In the formula, , ; It is the first derivative of the desired angular velocity in the projectile coordinate system; Secondly, due to the existence of deviation faults and external disturbances, a compensation control law with adaptive parameters was designed; because the control input and state variables of the feedback attitude control system are inconsistent, control allocation is required. (8) In the formula, It is a control allocation matrix. yes The estimated value, defined : (9) To address the input uncertainty caused by actuator gain failure, an additional adaptive compensation law needs to be added to the conventional control signal: (10) In the formula, yes The estimated value, defined : (11) The occasional gain fault of the attitude control system is represented by a symmetric positive definite matrix. Represents the identity matrix; Design the final second-order system control law: (12) And select the update pattern for the adaptive parameters: (13) (14) definition : (15) , These are design parameters.

2. The adaptive fault-tolerant backstepping attitude control method for a launch vehicle according to claim 1, characterized in that: Step 2 is as follows: Actuator failure can be described by the following formula: (1) In the formula, This indicates the input format of the attitude control system under fault conditions. This represents the gain coefficient matrix of the actuator. This represents the damage factor matrix. , for the first When an actuator malfunctions and becomes stuck... ,Right now hour, ; hour, ; for The identity matrix; Indicates the input of the attitude control system under fault conditions. The first derivative; It is the input pendulum angle matrix; Since the object under study has four engines as actuators, the fault mathematical model of each engine contains... and With two parameters, the system becomes very complex. To simplify the fault model and facilitate the design of the subsequent control law, the actuator fault mathematical model is reasonably transformed using a single parameter matrix. to indicate and Using matrices to indicate As shown in the following formula: (2) In the formula, It is defined as an occasional gain fault in the attitude control system, and because and It is a bounded positive number, so we get It is a symmetric positive definite matrix; the occasional deviation fault of the attitude control system is defined as... We obtain the following formula: (3) Based on the kinematics and dynamics model of a heavy-lift launch vehicle under nominal conditions, the input matrix under fault conditions is used. Instead of the input matrix in nominal form Establish kinematic and dynamic models of heavy-lift launch vehicles under failure conditions: (4) In the formula: state The unit quaternion representing the attitude azimuth angle of the projectile's coordinate system relative to the navigation coordinate system is... ; State variables It is the angular velocity vector in the projectile coordinate system, that is... , For roll angular velocity, For yaw rate, It is the pitch angular velocity; It is the inertia tensor in the projectile coordinate system; It is the input pendulum angle matrix; It is a control allocation matrix, where This represents the distance from the engine hinge point to the theoretical tip of the rocket body. This is the distance between the rocket's center of mass and the tip of the rocket body. It is the nonlinear torque of the system. It is the disturbance torque of the model. for The identity matrix.

3. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

4. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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