Reusable vehicle robust fault-tolerant control method

Abstract

The present application belongs to the technical field of reusable carrier control, and particularly relates to a strong robust fault-tolerant control method for a reusable carrier. The purpose of the present application is to provide a strong robust stable control method for a reusable carrier under the condition of stuck rudder, so as to solve the problem that the control efficiency of the aircraft is suddenly reduced or even out of control when the reusable carrier is in the stuck rudder state, which seriously threatens the safety of the task. The method comprises the construction of a six-degree-of-freedom model of the reusable carrier and a stuck rudder fault model; a reference controller is designed based on the nonlinear dynamic inverse theory; and an extended state observer is designed to estimate the system disturbance and improve the robustness of the control system. The method is a strong robust stable control method for a reusable carrier under the condition of stuck rudder fault, and has a broad application prospect.

Description

Technical Field

[0001] This invention belongs to the field of reusable launch vehicle control technology, specifically relating to a robust fault-tolerant control method for reusable launch vehicles. It is a robust fault-tolerant control method adapted to reusable launch vehicles under the fault condition of control surface jamming. Background Technology

[0002] Reusable launch vehicles, with their global rapid response and wide-area mission coverage capabilities, have become a core research direction in the aerospace field. However, their flight process traverses a wide speed range from subsonic and transonic to supersonic, with aerodynamic characteristics changing drastically with speed and altitude. Furthermore, the dynamic models exhibit strong nonlinearity, multivariable coupling, and time-varying parameters, leading to extremely high requirements for the fault tolerance of the flight control system. In particular, control surface jamming (such as mechanical jamming or hydraulic failure causing the control surface to be fixed at a certain deflection angle) directly cuts off the control channel in a specific direction, causing a sharp drop in control efficiency. If the control strategy cannot adapt in time, it can easily lead to attitude instability or even mission failure. Therefore, stable control technology under this fault condition is a key bottleneck for the safe operation of reusable launch vehicles.

[0003] The patent "Fault-Tolerant Control Method and Simulation Platform for Faulty Aircraft Based on Control Surface Deflection Angle Estimation" (CN118466251A) uses a visual estimation algorithm to achieve online detection of control surface jamming angle, and constructs a simulation system by combining an offline preset optimal lift-to-drag ratio trim scheme with an adaptive incremental backstepping controller. However, although the incremental backstepping control architecture can cope with conventional disturbances, it is not adaptable enough to extreme flight conditions with strong nonlinearity and rapid time variation, and the timeliness and stability of the control response need to be improved.

[0004] The patent "An Adaptive Backstepping Fault-Tolerant Control Method for Transport Aircraft Wing Surface Faults" (CN120215570A) focuses on the scenario of transport aircraft wing surface damage. It constructs an adaptive backstepping control law through a simplified dynamic model and combines it with a fixed-weight control allocation strategy to compensate for the loss of handling performance caused by wing surface faults. However, the single-channel simplified model used to reduce computational complexity ignores the strong coupling characteristics of multiple variables and cannot be transferred to reusable launch vehicles with complex aerodynamic coupling relationships; the fault tolerance capability of the fixed-weight compensation logic is obviously insufficient, and the control risks caused by control surface saturation constraints are not fully considered.

[0005] The patent "Active Disturbance Rejection and Fault-Tolerant Attitude Control Method for Flying-Wing UAV Considering Control Surface Faults" (CN114578691A) transforms control surface faults into lumped disturbances, achieves disturbance estimation and feedforward compensation through an extended state observer, and improves fault tolerance performance by combining a nonlinear dynamic inverse controller and pseudo-inverse control surface allocation. However, the fixed-bandwidth observer design makes it difficult to track the disturbance characteristics that dynamically change with Mach number and altitude during high-speed flight, thus limiting the accuracy of disturbance rejection.

[0006] The paper "Nussbaum Gain Adaptive Fault-Tolerant Control for Control Surface Faults in Hypersonic Vehicles" ([J]. Tactical Missile Technology, 2017, (04): 103-112.) constructs a basic control framework through feedback linearization, introduces Nussbaum gain to solve the problems of parameter uncertainty and unknown control direction, and combines adaptive laws to achieve control surface fault compensation. However, the modeling scope is limited to a single longitudinal channel and does not consider the strong coupling characteristics of multi-channel roll-yaw-pitch of reusable launch vehicles, thus failing to reflect the true dynamic behavior of all attitude motions.

[0007] Existing technologies are limited by factors such as the environmental adaptability of diagnostic solutions, the operational condition adaptability of models, or the fault response capabilities and real-time performance of control strategies, all of which have significant application limitations. Dedicated solutions designed for different launch vehicle types are insufficient to meet the fault-tolerant control requirements of reusable launch vehicles in wide speed ranges, strong coupling, multiple faults, and harsh environments. There is an urgent need for a control surface fault control method with strong environmental adaptability, wide operational condition coverage, and high fault-tolerant reliability. Summary of the Invention

[0008] The purpose of this invention is to provide a robust and stable control method adapted to reusable vehicles in the event of control surface jamming, thereby addressing the problem that the maneuverability of reusable vehicles drops sharply or even becomes uncontrollable when control surfaces are jammed, seriously threatening mission safety. The invention introduces a baseline controller designed based on nonlinear dynamic inverse theory, followed by an extended state observer to estimate system disturbances, reducing the control system's dependence on an accurate model and improving its robustness.

[0009] The technical solution of the present invention is as follows:

[0010] A robust fault-tolerant control method for reusable launch vehicles includes: constructing a six-degree-of-freedom model and a control surface jamming fault model for the reusable launch vehicle; introducing a baseline controller based on nonlinear dynamic inverse theory; and designing an extended state observer to estimate system disturbances, thereby improving the robustness of the control system. Details are as follows:

[0011] Step (1) Construct a six-degree-of-freedom dynamic model of the reusable launch vehicle

[0012] The reusable launch vehicle adopts a lifting body configuration and an integrated design of the airframe and engine. Its six-degree-of-freedom rigid body model can fully reflect the typical operating conditions of wide-range flight. In the modeling process, the elastic deformation effect of the launch vehicle structure is ignored, and the sloshing effect of fuel and propellant is neglected. Only the rigid body motion characteristics are considered.

[0013] This six-degree-of-freedom rigid body model contains 12 state variables. With 3 control inputs The dynamic equations of the center of mass motion are as follows:

[0014] (1)

[0015] In the formula, the superscript " " represents the first derivative; and These are speed, track inclination angle, and track yaw angle, respectively. For engine thrust, For flight drag, For lift, It is a lateral force; For the mass of the launch vehicle, It is the gravitational constant. This is the distance from the launch vehicle to the Earth's center. and These are the angle of attack, sideslip angle, and roll angle, respectively.

[0016] The specific kinematic equations for the motion of the center of mass are as follows:

[0017] (2)

[0018] In the formula, and These represent the displacements of the launch vehicle in the ground coordinate system.

[0019] The specific equations of motion about the center of mass are as follows:

[0020] (3)

[0021] In the formula, and The carrier orbits the fuselage. and Angular velocity of the axis; and These are the rolling moment, yaw moment, and pitch moment, respectively. and The moment of inertia of the three axes of the launch vehicle. and This is the derivative of the moment of inertia with respect to time.

[0022] The specific kinematic equations for motion about the center of mass are as follows:

[0023] (4)

[0024] In the formula, and These are pitch angle, yaw angle, and roll angle, used to describe the aircraft's attitude state.

[0025] The calculation relationships between some physical quantities and the conversion logic between state quantities are as follows:

[0026] (5)

[0027] In the formula, For the Earth's radius, The flight altitude of the launch vehicle; For the engine's specific impulse. This refers to the rate of change in quality. and These are the initial moment of inertia and the initial mass, respectively, used to describe the relationship between the moment of inertia and the mass.

[0028] Aerodynamics (lift) ,resistance Lateral force ) and aerodynamic torque (rolling torque) , yaw moment Pitch moment The calculation expression for ) is as follows:

[0029] (6)

[0030] in, For dynamic pressure, The atmospheric density at the flight altitude. For the reference area of ​​the launch vehicle, and These are the horizontal and vertical reference lengths, respectively. , , These are the lift coefficient, drag coefficient, and lateral force coefficient, respectively. and These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively. All of these aerodynamic coefficients are multivariable high-order polynomials relating to flight state parameters. Among the control inputs, and These correspond to the left elevator deflection angle, right elevator deflection angle, and rudder deflection angle, respectively. Adjusting these control parameters allows for control of the launch vehicle's flight status.

[0031] Step (2) Construction of the control surface jamming fault model

[0032] Control surface jamming refers to a situation where one or more control surfaces in the flight control system fail to move normally according to control commands or remain completely stationary due to mechanical failure, hydraulic system failure, or other reasons, resulting in a "jammed" state. This causes the aircraft to lose effective control in the corresponding direction, thereby seriously affecting flight safety and performance. The control surface jamming fault model is represented as follows:

[0033] (7)

[0034] In the formula: Indicates in Time of the first The control surface deflection output by each control surface feedback. The value for the control surface jamming is a constant.

[0035] Step (3) Design of a reference controller based on nonlinear dynamic inverse theory

[0036] First, a reference control law for the aircraft based on nonlinear dynamic inverse is designed. Unlike traditional linear methods, which require controller design based on small disturbance linearization, nonlinear dynamic inverse can design the controller directly on the nonlinear model without multiple parameter adjustments. The nonlinear dynamic inverse control method essentially eliminates the nonlinearity and coupling of the controlled object by inversion, and then replaces the original nonlinear system with a pseudolinear system, thereby achieving the goal of linearization.

[0037] Consider an affine nonlinear system as shown in the equation:

[0038] (8)

[0039] Among them, state variables for Step, control input quantity for Order, output for Order, state matrix for Step, control input for Rank. When and For all possible values Both can be reversed. By processing equation (8), we can obtain:

[0040] (9)

[0041] Using pseudo-control input In the substitution formula (9) We can obtain:

[0042] (10)

[0043] Substituting equation (10) into equation (8), we get:

[0044] (11)

[0045] The tracking error of the system is defined as:

[0046] (12)

[0047] in, This is the instruction value for the state variable.

[0048] Differentiating both sides of equation (12) with respect to time, we get:

[0049] (13)

[0050] The nonlinear dynamic inverse control law is designed as follows:

[0051] (14)

[0052] Substituting equation (14) into equation (13) yields:

[0053] (15)

[0054] This can be expressed as:

[0055] (16)

[0056] in, This represents the bandwidth of the circuit.

[0057] Combining equations (15) and (16), we can obtain:

[0058] (17)

[0059] By selecting appropriate parameters, the control law of equation (17) can guarantee the tracking error. It converges to 0.

[0060] As described above, the dynamic inverse control law form for conventional systems was derived. For flight systems, the dynamic inverse control law is generally based on the singular perturbation method, dividing the system into multiple loops on a time scale, and then designing the feedback linearization for each set of separated variables. This invention chooses to divide the reusable launch vehicle control system into inner and outer loops, with the state variables of each loop being: the aircraft attitude angular velocity of the inner loop. Aircraft attitude angles of the outer loop .

[0061] The control objective of the inner loop is to track the attitude angular velocity commands generated by the outer loop. The control input is a three-axis torque command. .

[0062] From equation (3), we can obtain:

[0063] (18)

[0064] in:

[0065] (19)

[0066] (20)

[0067] Design a nonlinear dynamic inverse control law:

[0068] (twenty one)

[0069] in:

[0070] (twenty two)

[0071] In the formula, These represent the error gain in the three directions of the inner loop, respectively.

[0072] The control objective of the external loop is to track a given attitude angle command. The control input is the attitude angular velocity command. .

[0073] From equation (4), we can obtain:

[0074] (twenty three)

[0075] in:

[0076] (twenty four)

[0077] (25)

[0078] Design a nonlinear dynamic control law:

[0079] (26)

[0080] In the formula:

[0081] (27)

[0082] in, , , These represent the error gain in the three directions of the external loop, respectively.

[0083] In summary, a nonlinear dynamic inverse control law for reusable launch vehicles was designed.

[0084] Step (4) Robust control based on extended state observer compensation

[0085] Based on the nonlinear dynamic inverse reference control law of step (3), this invention uses an extended state observer to design an adaptive disturbance observer for a reusable vehicle control system, compensating for the inner loop to reduce the impact of the system on model accuracy and improve system robustness. The derivation process of the extended state observer is then presented.

[0086] Assume the nonlinear system model is as follows:

[0087] (28)

[0088] in, It is the system's output. External disturbances It is the input quantity. The nominal control gain (which may include modeling errors) ), This is the system's own nonlinear dynamic term. Total disturbance Defined as:

[0089] (29)

[0090] Rewrite the system as follows:

[0091] (30)

[0092] Total disturbance Considered a new state And assume its dynamic ( (Unknown but bounded). The expanded state-space equation is:

[0093] (31)

[0094] in, It is a system state variable. It is the total disturbance The goal of the extended state observer is to obtain input... and output estimate .

[0095] for The estimated value. Based on this, the dynamic equations for the linear extended state observer can be designed:

[0096] (32)

[0097] in, To output the estimation error, For gain, at this time, the parameter The bandwidth method can be used for design:

[0098] Let the observer bandwidth be Then we have:

[0099] (33)

[0100] Higher bandwidth leads to faster convergence, but also increases noise sensitivity.

[0101] Next, the nonlinear dynamic inverse control law based on the extended state observer is derived. Since this extended state observer is designed only to compensate for the influence of external disturbances on the torque, it does not involve outer-loop control. The system's control torque deviates from the required value due to the disturbance caused by the control surface jamming in step (2). In cases where disturbances necessitate torque compensation, the angular rate dynamic equation of the reusable launch vehicle can be expressed as follows:

[0102] (34)

[0103] in, This represents the torque used to compensate for external disturbances.

[0104] Based on the derivation of the extended state observer in active disturbance rejection control, extended state observers for three angular rate channels are designed respectively:

[0105] (35)

[0106] In the formula, It is angular velocity Observations It is an external disturbance observation. and These are the observer coefficients. The observed torque that produces the angular rate in that direction can be solved as follows:

[0107] (36)

[0108] In the formula, It is the rudder effectiveness coefficient of each rudder surface in that direction. This refers to the rudder deflection of each rudder surface in that direction. By incorporating the observed external disturbance torque into the solution of the nonlinear dynamic inverse, and rearranging, the inner loop control command can be obtained as shown in equation (37):

[0109] (37)

[0110] The beneficial effects of this invention are:

[0111] This invention addresses the problems of "difficult-to-handle strong nonlinear coupling, poor adaptability over wide speed range, high model dependence, and difficulty in suppressing complex disturbances" under the control surface jamming fault of reusable launch vehicles. It proposes a collaborative architecture of "nonlinear dynamic inverse + extended state observer compensation" to make up for the shortcomings of existing technologies.

[0112] This invention's wide-velocity-domain modeling more closely resembles real flight conditions, laying a reliable foundation for stable control. A six-DOF rigid body model is constructed, and key parameters such as lift coefficient and moment coefficient are dynamically updated through real-time interpolation algorithms. Simultaneously, the time-varying characteristics of rotational inertia caused by fuel consumption are considered, avoiding the control mismatch problem caused by incomplete velocity-domain coverage in traditional models. Throughout the entire flight, the deviation between the model and the real system can be controlled within engineering-allowable limits, eliminating the need for extensive additional wind tunnel testing to supplement data and reducing upfront development costs.

[0113] Existing fault-tolerant control systems often rely on linearization or complex adaptive laws, requiring repeated adjustments to sub-controller parameters to adapt to different flight states. This is cumbersome and prone to introducing coupling errors. This invention employs a nonlinear dynamic inverse directly applied to the full nonlinear model, actively eliminating the multi-channel coupling effects of pitch, roll, and yaw through feedback linearization, transforming the complex nonlinear system into a easily controllable pseudo-linear system. By partially decoupling the state, computational steps are reduced while maintaining control accuracy. The extended state observer introduced in this invention treats the "total disturbance," including modeling errors, control surface jamming torque deviations, and external atmospheric disturbances, as real-time estimates of the extended state. It eliminates the need for pre-set disturbance models or offline training, achieving millisecond-level response using only easily measurable signals such as attitude angles and angular velocities. Furthermore, it directly offsets disturbance effects through feedforward compensation, reducing reliance on high-precision sensors and complex parameter identification algorithms. Attached Figure Description

[0114] Figure 1 This is a technical block diagram of a robust stability control method for reusable launch vehicles under rudder surface jamming.

[0115] Figure 2 It is a pitch angle-time curve of a reusable launch vehicle;

[0116] Figure 3 It is a graph of the angle-of-attack time of a reusable launch vehicle;

[0117] Figure 4 It is a roll angle-time curve of a reusable launch vehicle;

[0118] Figure 5 It is a yaw angle-time curve of a reusable launch vehicle;

[0119] Figure 6 It is a side-slip angle-time curve of a reusable launch vehicle;

[0120] Figure 7 It is a perturbation time curve observed by a reusable launch vehicle extended observer;

[0121] Figure 8 This is a time curve of the right elevator deflection of a reusable launch vehicle.

[0122] Figure 9 This is a time curve of the left elevator deflection of a reusable launch vehicle.

[0123] Figure 10 It is a time curve of rudder deflection for a reusable launch vehicle. Detailed Implementation

[0124] The embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0125] like Figure 1 As shown, robust fault-tolerant control methods for reusable launch vehicles include:

[0126] (1) Construct a six-degree-of-freedom dynamic model of a reusable launch vehicle, which can fully reflect the typical operating conditions of wide-range flight.

[0127] (2) Constructing the control surface jamming fault model to obtain the mathematical model of the control surface jamming state;

[0128] (3) Design a reference controller based on nonlinear dynamic inverse theory, eliminate the nonlinearity and coupling of the controlled object by inversion, and then replace the original nonlinear system with a pseudolinear system.

[0129] (4) Robust control based on extended state observer compensation to reduce the system's dependence on model accuracy and improve system robustness.

[0130] Specifically, the embodiments of the present invention are described as follows:

[0131] (1) Construct a six-degree-of-freedom dynamic model of the reusable vehicle. This six-degree-of-freedom rigid body model contains 12 state variables. With 3 control inputs The definitions of the main variables are given below: and These are speed, track inclination angle, and track yaw angle, respectively. For engine thrust, For flight drag, For lift, It is a lateral force; For the mass of the launch vehicle, It is the gravitational constant. This is the distance from the launch vehicle to the Earth's center. and These are the angle of attack, sideslip angle, and roll angle, respectively. and These represent the displacements of the launch vehicle in the ground coordinate system. and The carrier orbits the fuselage. and Angular velocity of the axis; and These are the rolling moment, yaw moment, and pitch moment, respectively. and The moment of inertia of the three axes of the launch vehicle. and This is the derivative of the moment of inertia with respect to time. and These are pitch angle, yaw angle, and roll angle, respectively. For the Earth's radius, The flight altitude of the launch vehicle; For the engine's specific impulse. This refers to the rate of change in quality. and These are the initial moment of inertia and the initial mass, respectively. For dynamic pressure, The atmospheric density at the flight altitude. For the reference area of ​​the launch vehicle, and These are the horizontal and vertical reference lengths, respectively. , , These are the lift coefficient, drag coefficient, and lateral force coefficient, respectively. and These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively. Combining dynamics and kinematics, the six-degree-of-freedom model of the reusable launch vehicle is represented as follows:

[0132] (38)

[0133] (39)

[0134] (40)

[0135] (41)

[0136] (42)

[0137] In the formula: control input quantity, and These correspond to the left elevator deflection angle, right elevator deflection angle, and rudder deflection angle, respectively. By adjusting these control values, the flight status of the reusable launch vehicle can be controlled.

[0138] (2) Modeling of Control Surface Jamming Failure: Control surface jamming failure refers to a situation where one or more control surfaces in the flight control system fail to move normally according to control commands or remain completely stationary due to mechanical failure, hydraulic system failure, or other reasons, resulting in a "jammed" state. This causes the aircraft to lose effective control over the corresponding direction, thereby seriously affecting flight safety and performance. In its mathematical model, Indicates in Time of the first The control surface deflection output by each control surface feedback. The value at which the control surface is stuck is a constant. The mathematical model is expressed as follows:

[0139] (43)

[0140] (3) Based on the nonlinear dynamic inverse theory, a reference controller is designed. Using equations (8)-(17), based on the model established in step (2), the reusable launch vehicle control system is divided into inner and outer loops. The state variables of each loop are: the attitude angular velocity of the inner loop and the attitude angle of the outer loop. The state variables of each loop are: the aircraft attitude angular velocity of the inner loop. Aircraft attitude angles of the outer loop .

[0141] The control objective of the inner loop is to track the attitude angular velocity commands generated by the outer loop. The control input is a three-axis torque command. .

[0142] From equation (3), we can obtain:

[0143] (44)

[0144] in:

[0145] (45)

[0146] (46)

[0147] Design a nonlinear dynamic inverse control law:

[0148] (47)

[0149] in:

[0150] (48)

[0151] in , , These represent the error gains in the three directions of the inner loop, respectively, and are set to 8.0, 7.5, and 9.0.

[0152] The control objective of the external loop is to track a given attitude angle command. The control input is the attitude angular velocity command. .

[0153] From equation (4), we can obtain:

[0154] (49)

[0155] in:

[0156] (50)

[0157] (51)

[0158] Design a nonlinear dynamic control law:

[0159] (52)

[0160] In the formula:

[0161] (53)

[0162] in , , These represent the error gains in the three directions of the external loop, respectively, and are set to 2.0, 1.8, and 2.2.

[0163] In summary, a nonlinear dynamic inverse control law for reusable launch vehicles was designed.

[0164] (4) Robust control based on extended state observer compensation, based on the nonlinear dynamic inverse reference control law derived in step (3) above. Since we designed this extended state observer only to compensate for the influence of external disturbances on the torque, it does not involve the control of the outer loop. The system is affected by the disturbance caused by the control surface jamming in step (2), which causes the control torque to deviate from the required value. In the case where there is a disturbance that requires torque compensation, the angular rate dynamic equation of the reusable launch vehicle can be expressed as follows:

[0165] (54)

[0166] in, This represents the torque used to compensate for external disturbances.

[0167] Based on the derivation of the extended state observer in active disturbance rejection control, extended state observers for three angular rate channels are designed respectively:

[0168] (55)

[0169] In the formula, It is angular velocity Observations It is an external disturbance observation. and These are the observer coefficients, taken as 10 and 100 respectively. The observed torque that produces the angular rate in that direction can be solved as follows:

[0170] (56)

[0171] In the formula, It is the rudder effectiveness coefficient of each rudder surface in that direction. It refers to the rudder deflection of each rudder surface in that direction.

[0172] By incorporating the observed external disturbance torque into the solution of the nonlinear dynamic inverse, the inner loop control command can be obtained as shown in equation (57):

[0173] (57)

[0174] To verify the feasibility of the proposed robust stability control method for reusable launch vehicles under rudder surface jamming conditions, the following verification simulation was conducted. The initial values ​​of the relevant state variables in the simulation scenario are given in Table 1. At 16s, the right elevator was set to jam at 3°, and the launch vehicle was instructed to always follow the pitch angle command.

[0175] Table 1 Initial and Expected Values ​​of Flight Status

[0176]

[0177] The relevant simulation results are as follows Figures 2 to 10 As shown. Figure 2 This demonstrates that the reusable launch vehicle data-driven learning control method designed in this invention can achieve rapid tracking of pitch angle reference commands and exhibits relatively small tracking errors. Furthermore, Figures 3 to 6 The curves showing the changes in angle of attack, roll angle, yaw angle, and sideslip angle over time demonstrate the good performance of reusable launch vehicle attitude angles. Figure 7 The extended observer's observation time curve is given, which can be used to compensate for the amount of disturbance. Figures 8 to 10 The time-varying curves of the control commands in the verification simulation are presented. After the right elevator jams at 16 seconds, the input quantities of the other two control surfaces change to maintain stability. In summary, the robust stability control method for control surface jamming proposed in this invention can achieve satisfactory results.

Claims

1. A robust fault-tolerant control method for reusable launch vehicles, characterized in that, Includes the following steps: Step (1) Construct a six-degree-of-freedom dynamic model of the reusable launch vehicle; Step (2) Construction of the control surface jamming fault model; Step (3) Design of a reference controller based on nonlinear dynamic inverse theory: First, a reference control law for the aircraft based on nonlinear dynamic inverse is designed. Then, the system is divided into multiple loops on a time scale, and the feedback linearization is achieved by designing each set of variables separately. The reusable launch vehicle control system is divided into inner and outer loops, with the state variables of each loop being: the aircraft attitude angular velocity of the inner loop. Aircraft attitude angles of the outer loop ; Step (4) Robust control based on extended state observer compensation: Based on the nonlinear dynamic inverse of the reference control law in step (3), an adaptive disturbance observer for the reusable vehicle control system is designed using an extended state observer to compensate the inner loop, thereby reducing the impact of the system on model accuracy and improving the system robustness. Step (3) is as follows: Consider an affine nonlinear system as shown in the equation: (8) Among them, the superscript " " represents the first derivative; state variable for Step, control input quantity for Order, output for Order, state matrix for Step, control input for Rank; when Step For all possible values Both can be reversed. By processing equation (8), we get: (9) Using pseudo-control input In the substitution formula (9) have to: (10) Substituting equation (10) into equation (8), we get: (11) The tracking error of the system is defined as: (12) in, The state variable instruction value; Differentiating both sides of equation (12) with respect to time, we get: (13) The nonlinear dynamic inverse control law is designed as follows: (14) Substituting equation (14) into equation (13) yields: (15) Expressed as: (16) in, This is the bandwidth of the circuit; Combining equations (15) and (16), we get: (17) By selecting appropriate parameters, the control law of equation (17) ensures the tracking error is controlled. Converging to 0; The control objective of the inner loop is to track the attitude angular velocity commands generated by the outer loop. The control input is a three-axis torque command. ; From equation (3), we get: (18) in: (19) (20) In the formula, and The moment of inertia of the three axes of the launch vehicle. and These are the rolling moment, yaw moment, and pitch moment, respectively. and This is the derivative of the moment of inertia with respect to time. and The carrier orbits the fuselage. and Angular velocity of the axis; Design a nonlinear dynamic inverse control law: (21) in: (22) In the formula, These represent the error gains in the three directions of the inner loop, respectively. The control objective of the external loop is to track a given attitude angle command. The control input is the attitude angular velocity command. ; From equation (4), we get: (23) in: (24) (25) Design a nonlinear dynamic control law: (26) In the formula: (27) in, , , These represent the error gains in the three directions of the external loop, respectively. and These are pitch angle, yaw angle, and roll angle, respectively.

2. The robust fault-tolerant control method for reusable launch vehicles according to claim 1, characterized in that, Step (1) is as follows: The six-degree-of-freedom rigid body model contains 12 state variables. With 3 control inputs The dynamic equations of the center of mass motion are as follows: (1) In the formula, the superscript " " represents the first derivative; and These are speed, track inclination angle, and track yaw angle, respectively. For engine thrust, For flight drag, For lift, It is a lateral force; For the mass of the launch vehicle, It is the gravitational constant. This is the distance from the launch vehicle to the Earth's center. and These are the angle of attack, sideslip angle, and roll angle, respectively. The specific kinematic equations for the motion of the center of mass are as follows: (2) In the formula, and These represent the displacements of the launch vehicle in the ground coordinate system; The specific equations of motion about the center of mass are as follows: (3) In the formula, The specific kinematic equations for motion about the center of mass are as follows: (4) The calculation relationships between some physical quantities and the conversion logic between state quantities are as follows: (5) In the formula, For the Earth's radius, The flight altitude of the launch vehicle; For the engine's specific impulse. This refers to the rate of change in quality. and These are the initial moment of inertia and the initial mass, respectively, used to describe the relationship between the moment of inertia and the mass. Includes lift ,resistance Lateral force Aerodynamic forces and including rolling torque , yaw moment Pitch moment The expression for calculating the aerodynamic torque is as follows: (6) in, For dynamic pressure, The atmospheric density at the flight altitude. For the reference area of ​​the launch vehicle, and These are the horizontal and vertical reference lengths, respectively. , , These are the lift coefficient, drag coefficient, and lateral force coefficient, respectively. and These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively; among the control inputs, and These correspond to the left elevator deflection angle, the right elevator deflection angle, and the rudder deflection angle, respectively.

3. The robust fault-tolerant control method for reusable launch vehicles according to claim 1, characterized in that, Step (2) is as follows: The control surface jamming fault model is represented as follows: (7) In the formula: Indicates in Time of the first The control surface deflection output by each control surface feedback. The value for the control surface jamming is a constant.

4. The robust fault-tolerant control method for reusable launch vehicles according to claim 1, characterized in that, Step (4) is as follows: Assume the nonlinear system model is as follows: (28) in, It is the system's output. External disturbances It is the input quantity. The nominal control gain. For modeling error, It is the system's own nonlinear dynamic term; total disturbance Defined as: (29) Rewrite the system as follows: (30) Total disturbance Considered a new state And assume its dynamic , The state is unknown but bounded; the extended state-space equation is: (31) in, It is a system state variable. It is the total disturbance The goal of the extended state observer is to obtain input and output estimate ; for The estimated value is used to design the dynamic equations for the linearly extended state observer: (32) in, To output the estimation error, For gain, the design is performed using the bandwidth method: Let the observer bandwidth be Then we have: (33) The interference caused by the control surface jamming in step (2) causes the control torque to deviate from the required value; in the case where the torque needs to be compensated due to the interference, the angular rate dynamic equation of the reusable launch vehicle can be expressed as follows: (34) in, The torque representing compensation for external disturbances; Based on the derivation of the extended state observer in active disturbance rejection control, extended state observers for three angular rate channels are designed respectively: (35) In the formula, It is angular velocity Observations It is an external disturbance observation. and These are the observer coefficients. The observed torque that produces the angular rate in that direction is solved as follows: (36) In the formula, It is the rudder effectiveness coefficient of each rudder surface in that direction. This refers to the rudder deflection of each rudder surface in that direction; the observed external disturbance torque is added to the solution of the nonlinear dynamic inverse, and the inner loop control command is obtained as shown in equation (37): (37)。

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