Attitude Fault-Tolerant Control Method for Reusable Launch Vehicles with Performance Constraints

Abstract

The present invention discloses a method for attitude fault-tolerant control of a reusable launch vehicle with performance constraints, belonging to the field of automatic control. A multivariable adaptive PI fault-tolerant controller is designed to achieve performance constraints for the attitude model of the reusable launch vehicle during the powered landing phase, considering the actual engineering applications. During the entire controller design process, the complexity brought by uncertainties, external disturbances, and engine failures is considered. First, performance constraint limits are designed for the transition variables including attitude angle error and attitude angular velocity error. Secondly, new variables are derived using performance conversion techniques, and by controlling the stability of these variables, the transition variables are restricted within the performance function. Finally, a multivariable adaptive PI fault-tolerant controller is designed to stabilize these variables. The present invention can handle the performance constraint problem during the rocket powered landing process, thereby improving the success rate of the rocket's soft landing.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and particularly to a reusable launch vehicle attitude fault-tolerant control method with performance constraints. Background Art

[0002] In the powered landing phase, the attitude control of a reusable launch vehicle is crucial for the success of a soft landing. There are certain deviations in the model of the reusable launch vehicle after it returns from performing a mission. At the same time, there are significant changes in the rocket's flight speed, altitude, atmospheric density, as well as the fuel and mass inside the rocket. This leads to great uncertainties and some unknown external disturbances in the reusable launch vehicle during the powered landing phase. In particular, a reusable launch vehicle that lands using a sea recovery method may encounter sudden bad weather, which may lead to engine failures. Therefore, the designed control method needs to have anti-interference and fault-tolerant capabilities. Although various advanced control methods have emerged in the past few decades, in engineering practice, the currently preferred method is still the PID (Proportional-Integral-Derivative) control method. Although the PID control method has a simple structure and is easy to implement, its parameters are designed offline and rely on an accurate rocket dynamics model. This results in poor anti-interference and fault-tolerant capabilities of the traditional PID control method, further leading to the possible instability of the reusable launch vehicle during the powered landing phase. At this stage, the premise for separately designing the attitude system and the guidance system is that the guidance command can be tracked without delay. However, the constraints of transient performance and steady-state performance cannot be guaranteed for traditional PID control. Therefore, PID control also cannot guarantee the successful soft landing of the rocket. In addition, the impact of rocket engine failures on the attitude control system is destructive. This requires that in practical engineering applications, when an engine failure occurs, the attitude control system of the reusable launch vehicle needs to have fault-tolerant control capabilities.

[0003] Currently, there have been some research results on the improvement of PID control. Based on the idea of PID control in a single-input single-output system, a single-variable adaptive PI control algorithm is designed to solve the problem that a nonlinear system can still achieve stable tracking and performance constraints under uncertainties and actuator failures. However, the above research only focuses on single-input single-output systems, while the attitude control system of a reusable launch vehicle is multi-input multi-output. Therefore, it is necessary to improve this algorithm to ensure the accurate tracking of the rocket's attitude angle. Summary of the Invention

[0004] The present invention provides a reusable launch vehicle attitude fault-tolerant control method with performance constraints, which can simultaneously handle the performance constraint problems of the rocket attitude control system, thereby improving the accuracy of the attitude control system, enhancing the success rate of the rocket's soft landing, and being closer to actual engineering applications while improving performance.

[0005] An embodiment of the present invention provides a reusable launch vehicle attitude fault-tolerant control method with performance constraints, including the following steps:

[0006] Step 1, establish an attitude control model for the powered landing section of the reusable launch vehicle;

[0007] Step 2, taking into account uncertainties and internal and external disturbances, obtain a rigid body attitude control model for the powered landing section of the rocket in the body coordinate system, using the attitude angle and attitude angular velocity of the reusable launch vehicle as the system outputs, and the engine gimbal angles of the pitch, yaw, and roll channels as the control system inputs;

[0008] Step 3, considering the situation where an engine failure occurs in the rigid body attitude control model, establish an engine failure model, and obtain an attitude control model of the reusable launch vehicle under the failure according to the engine failure model;

[0009] Step 4, define a transition variable based on the attitude angle error and attitude angular velocity error, and design performance constraints for the transition variable including the attitude angle and attitude angular velocity errors;

[0010] Step 5, according to the transition variable, construct a new error variable through performance conversion technology, and the new error variable includes constraint information, attitude angle, and attitude angular velocity error information;

[0011] Step 6, according to the new error variable, design a multivariable adaptive PI fault-tolerant controller to stabilize the new error variable, and obtain the engine gimbal angle input under the corresponding situation.

[0012] In an embodiment of the present invention, in Step 1, the established attitude control model for the powered landing section of the reusable launch vehicle is:

[0013]

[0014]

[0015] In the formula, is the attitude angle in the landing coordinate; ω b =[ω bx ω by ω bz T ​is the three-axis attitude angular velocity in the rocket body coordinate system; J is the moment of inertia matrix of the rocket in the rocket body coordinate system; matrices J, σ, B, and the control vector u are respectively:

[0016]

[0017] where, x R represents the distance from the swing point of the variable-thrust swivel engine of the rocket to the theoretical tip of the rocket; x T represents the distance from the center of mass of the rocket to the theoretical tip of the rocket; T represents the total thrust of the rocket; l RCS is the force arm of the attitude control nozzle in the roll channel; δ γ , δ ψ and are respectively the engine swing angles of the roll, yaw, and pitch channels.

[0018] In an embodiment of the present invention, in step 2, the rigid body attitude control model of the rocket during the powered landing phase in the rocket body coordinate system is:

[0019]

[0020]

[0021] where, Δd = [d1 d2 d3] T is the change in the moment of inertia caused by rocket fuel consumption, etc., and the external disturbances encountered by the rocket; Δf = [f1 f2 f3] T includes the uncertainties caused by the deviation of the model after the rocket returns from performing the mission.

[0022] In an embodiment of the present invention, in step 3, the engine fault model is:

[0023] u t = ρ u (t)u + ρ r (t)

[0024] where, u t is the true input of the system after the fault; ρ u (t) is the damage ratio of the engine, representing the severity of the fault, is the equivalent bias vector when the engine swing angle has a bias-type fault;

[0025] According to the engine fault model, the attitude control model of the reusable launch vehicle under the fault is:

[0026]

[0027] In one embodiment of the present invention, in step 4, the transition variable defined based on the attitude angle error and the attitude angular velocity error is:

[0028] ο(t) = aε1(t) + ε2(t)

[0029] where ε1 = η - η d is the attitude angle error; ε2 = ω b - ω d is the angular velocity error; is the desired attitude angle; ω d is the desired attitude angular velocity;

[0030] The performance constraint is:

[0031]

[0032] where μ = μ 1 μ 2 μ 3] T and respectively represent the upper and lower limits of the performance constraint and are always positive; t represents time.

[0033] In one embodiment of the present invention, in step 5, the new error variable ζ = [ζ1 ζ2 ζ3] T is:

[0034]

[0035] where i = 1, 2, 3 respectively represent the error variables of the roll, yaw and pitch channels.

[0036] In one embodiment of the present invention, in step 6, the multivariable adaptive PI fault-tolerant controller is:

[0037]

[0038] where the operation symbol is defined as: if α = [α1 α2 α3] T , β = [β1 β2 β3] T , then k ο = [k ο1 k ο2 k ο3 T , and any element is expressed as:

[0039]

[0040] k p and k ICan be respectively expressed as:

[0041]

[0042] k I = βk p

[0043] In the formula, and β are positive numbers that can be freely selected, and Δk p and Δk I are automatically updated according to the adaptation law, and the adaptation law is:

[0044]

[0045] Δk I = βΔk p

[0046] In the formula, is the estimated value of the auxiliary parameter variable b, The adaptation law of is:

[0047]

[0048] In the formula, κ and γ b are both positive numbers that can be freely selected; ι = [ι1 ι2 ι3] T , and any element of ι is a positive number.

[0049] The attitude fault-tolerant control method of the reusable launch vehicle with performance constraints in the embodiment of the present invention has the following technical effects compared with the prior art:

[0050] 1. Different from traditional PID control, the parameters of the present invention can be continuously updated according to the changes of the state and the adaptation law. At the same time, the multivariable adaptive PI control is an improvement based on PI control and is easier to implement compared with other non-linear control methods.

[0051] 2. The present invention does not require the information of an additional fault diagnosis link, can ensure that the system still shows fault-tolerant ability without fault information, can make full use of the control redundancy of the reusable launch vehicle, and ensure that the attitude angle error and angular velocity error are still within the performance constraint range in the case of uncertainties, disturbances and engine failures of the rocket.

[0052] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0053] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of embodiments in conjunction with the accompanying drawings, in which:

[0054] Figure 1 FIG. 4 is a flowchart of a method for attitude fault-tolerant control of a reusable launch vehicle with performance constraints according to an embodiment of the present invention;

[0055] Figure 2 FIG. 5 is a control structure diagram of the method for attitude fault-tolerant control of a reusable launch vehicle with performance constraints of the present invention;

[0056] Figure 3 FIG. 6 is a pitch angle command curve of a reusable launch vehicle during the powered landing phase;

[0057] Figure 4 FIG. 7 is a yaw angle command curve of a reusable launch vehicle during the powered landing phase;

[0058] Figure 5 FIG. 8 is a comparison diagram of roll angle errors of the control system under engine failure;

[0059] Figure 6 FIG. 9 is a comparison diagram of x-axis angular velocity errors of the control system under engine failure;

[0060] Figure 7 FIG. 10 is a comparison diagram of yaw angle errors of the control system under engine failure;

[0061] Figure 8 FIG. 11 is a comparison diagram of y-axis angular velocity errors of the control system under engine failure;

[0062] Figure 9 FIG. 12 is a comparison diagram of pitch angle errors of the control system under engine failure;

[0063] Figure 10 FIG. 13 is a comparison diagram of z-axis angular velocity errors of the control system under engine failure;

[0064] Figure 11 FIG. 14 is an engine swing angle curve under engine failure. Detailed Embodiment

[0065] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0066] As shown in FIGS. Figure 1 and Figure 2 , the method for attitude fault-tolerant control of a reusable launch vehicle with performance constraints includes the following steps:

[0067] Step 1: Establish the attitude control model for the powered landing phase of a reusable launch vehicle.

[0068] In Step 1, the attitude control model for the powered landing phase of a reusable launch vehicle is:

[0069]

[0070]

[0071] where is the attitude angle in the landing coordinate system; ω b = [ω bx ω by ω bz T is the three-axis attitude angular velocity in the body coordinate system of the rocket; J is the moment of inertia matrix of the rocket in the body coordinate system; the matrices J, σ, B and the control vector u are respectively:

[0072]

[0073] where x R represents the distance from the swing point of the variable-thrust swivel engine of the rocket to the theoretical tip of the rocket; x T represents the distance from the center of mass of the rocket to the theoretical tip of the rocket; T represents the total thrust of the rocket; l RCS is the force arm of the attitude control nozzle in the roll channel; δ γ , δ ψ and are the engine swing angles of the roll, yaw, and pitch channels respectively.

[0074] Step 2: Taking into account uncertainties and internal and external disturbances, obtain the rigid-body attitude control model of the rocket during the powered landing phase in the body coordinate system, with the attitude angle and attitude angular velocity of the reusable launch vehicle as the system outputs, and the engine swing angles of the pitch, yaw, and roll channels as the control system inputs.

[0075] Taking into account uncertainties and internal and external disturbances, the rigid-body attitude control model of the rocket during the powered landing phase in the body coordinate system is obtained, with the attitude angle η and attitude angular velocity ω b of the reusable launch vehicle as the system outputs, and the engine swing angles of the pitch, yaw, and roll channels as the control system inputs. The rigid-body attitude control model of the rocket during the powered landing phase in the body coordinate system is:

[0076]

[0077] ​

[0078] where Δd = [d1 d2 d3] T is the change in moment of inertia caused by rocket fuel consumption, etc., and the external disturbances encountered by the rocket, such as wind disturbances, etc.; Δf = [f1 f2 f3] T includes the uncertainty caused by the deviation of the model after the rocket returns from mission execution.

[0079] Step 3: Consider the situation where an engine fails in the rigid body attitude control model, establish an engine failure model, and obtain the attitude control model of the reusable launch vehicle under the failure according to the engine failure model.

[0080] Considering the situation where an engine fails in the attitude control model, the two most common engine failures of the rocket are the bias-type failures caused by the damage of the engine gimbal angle and the loose floating swing. The failure model is:

[0081] u t = ρ u (t)u + ρ r (t)

[0082] where u t is the true input of the system after the failure; ρ u (t) is the damage ratio of the engine, representing the severity of the failure, is the equivalent bias vector when the engine gimbal angle has a bias-type failure.

[0083] In the failure model, the true input of the system after the failure is not the control vector u. The real input is u t ; ρ u (t) and ρ r (t) will represent several different working conditions of the engine respectively.

[0084] (1) Normal situation

[0085] The output signal of the engine is equal to the ideal control signal: ρ u (t) = 1, ρ r (t) = 0.

[0086] (2) Engine gimbal angle damage failure

[0087] ρ u (t) is the damage ratio of the engine, representing the severity of the failure. Although a failure has occurred and the engine cannot fully perform its function, the engine gimbal angle is not completely unable to swing and is still effective, satisfying 0 < ρ ≤ ρ u (t) ≤ 1, ρ is an unknown positive number.

[0088] (3) Bias-type fault caused by loose swing

[0089] is the equivalent bias vector when the engine swing angle has a bias-type fault, satisfying is an unknown positive number.

[0090] According to the engine fault model, the attitude control model of the reusable launch vehicle under the fault is:

[0091]

[0092] Step 4: Define a transition variable based on the attitude angle error and the attitude angular velocity error, and design performance constraints for the transition variable containing the attitude angle and the attitude angular velocity error.

[0093] The transition variable ο(t) defined based on the attitude angle error and the attitude angular velocity error is:

[0094] ο(t) = aε1(t) + ε2(t)

[0095] where ε1 = η - η d is the attitude angle error; ε2 = ω b - ω d is the angular velocity error; is the desired attitude angle; ω d is the desired attitude angular velocity; it can be solved according to the guidance command, and the specific solution formula is:

[0096]

[0097] where T = [T x T y T z T is the thrust in the landing coordinate system; T x , T y , T z are the three-axis thrusts respectively. Set the roll angle command to γ c = 0. Design performance constraints for the variables containing the attitude angle and the attitude angular velocity, and the specific form is:

[0098]

[0099] where μ = μ 1 μ 2 μ 3] T and respectively represent the upper and lower limits of the performance constraints and are always positive, and t represents time.

[0100] Step 5: According to the transition variable, construct a new error variable through performance conversion technology. The new error variable includes constraint information, attitude angle, and attitude angular velocity error information.

[0101] For the transition variable in Step 4, construct a new error variable ζ = [ζ1 ζ2 ζ3] through performance conversion technology T , and this variable needs to include constraint information, attitude angle, and attitude angular velocity error information. First, design a new function as:

[0102] F(ζ) = [F(ζ1) F(ζ2) F(ζ3)] T

[0103] According to the equation ο(t) = F(ζ), the error variable can be expressed. F(ζ) needs to have the following two properties:

[0104] (1) No matter how ζ changes, each element in the variable satisfies

[0105] (2) F(ζ) is strictly increasing, and each element in the variable satisfies

[0106] According to these two properties, it can be guaranteed that as long as the controller is designed to make ζ bounded when t ≥ 0, the attitude angle and attitude angular velocity of the rocket can be guaranteed to be within the performance constraints. The designed F(ζ) is:

[0107]

[0108] In the formula, The arbitrary element of the error variable ζ can be obtained as:

[0109]

[0110] In the formula, i = 1, 2, 3 respectively represent the error variables of the roll, yaw, and pitch channels.

[0111] Taking the derivative of it can obtain:

[0112]

[0113] In the formula, k οi is the i-th element of k ο = [k ο1 k ο2 k ο2 T By designing the controller to stabilize the error variable, the purpose that the attitude angle and attitude angular velocity of the rocket are always within the performance constraints can be achieved.

[0114] ​Step 6: Design a multivariable adaptive PI fault-tolerant controller based on the new error variable to stabilize the new error variable and obtain the engine swing angle input under the corresponding conditions.

[0115] Based on the error variable in Step 5, design a multivariable adaptive PI fault-tolerant controller to stabilize this variable. The form of the multivariable adaptive PI fault-tolerant controller is:

[0116]

[0117] In the formula, the operation symbol is defined as: If Then:

[0118]

[0119] k ο =[k ο1 k ο2 k ο3 T , and any element of it can be expressed as:

[0120]

[0121] k p and k I can be expressed as:

[0122]

[0123] k I =βk p

[0124] In the formula, and β are positive numbers that can be freely selected, and Δk p and Δk I can be automatically updated according to the adaptation law, and its adaptation law is:

[0125]

[0126] In the formula, is the estimated value of the auxiliary parameter variable b, and the adaptation law of is:

[0127]

[0128] In the formula, κ and γ b are both positive numbers that can be freely selected; ι = [ι1 ι2 ι3] T , and any element of ι is a very small positive number.

[0129] Consider the following Lyapunov function​

[0130]

[0131] In the formula, Solving the Lyapunov function can obtain:

[0132]

[0133] In the formula, is the smallest element in And:

[0134]

[0135] It can be proved that the closed-loop system is stable, the error variable ζ is ultimately uniformly bounded, and all signals are bounded.

[0136] Next, the effectiveness of the present invention is verified through simulation. The simulation parameters are as follows:

[0137] Parameters of the reusable launch vehicle: m = 34530 kg, J zz = J yy = 167525 kg·m 2 , J xx = 5685 kg·m 2 , T = 845 kN, x R -x T = 3 m, l RCS = 2 m.

[0138] The initial values of the attitude angles are the same as those of the commanded attitude angles. The curves of the commanded pitch angle and yaw angle obtained by solving the guidance commands are as Figure 3 and Figure 4 shown, and the roll angle command is set to 0;

[0139] The parameters of the multivariable adaptive PI fault-tolerant controller are set as κ = 2, γ b = 1, a = 50, ι = [0.1 0.1 0.1] T , The set performance constraints are μ = [0.01 0.02 0.02] T ,

[0140] The disturbances and uncertainties encountered by the reusable launch vehicle are set as:

[0141] d1 = 800sin(t) N·m f1 = 800cos(t) N·m

[0142] d2 = 25000cos(t) N·m, f2 = 25000sin(t) N·m

[0143] d3 = 25000sin(t) N·m, f3 = 25000cos(t) N·m

[0144] Considering that the engine may simultaneously suffer from engine damage failure and engine offset-type failure, the failure can be expressed as:

[0145] u t = ρ u (t)u + ρ r (t)

[0146] ρ u (t) = 1, 0 ≤ t < 15s

[0147]

[0148] ρ r (t) = 0.05[sin(t) cos(t) sin(t)] T

[0149] The simulation results compared with the traditional PID control are as Figures 5 - 11 shown.

[0150] The parameter settings of the traditional PID control are: for the roll channel, k px = 150, k ix = 100, k dx = 50; for the yaw channel, k py = 200, k iy = 150, k dy = 80; for the pitch channel, k pz = 200, k iz = 150, k dz = 80.

[0151] Among them, Figures 3 - 4 reflects the guidance command that the reusable launch vehicle needs to track during the powered landing phase, Figures 5 - 10 reflects the tracking effect of the attitude angle and attitude angular velocity in the case of engine failure, Figure 11 reflects the output effect of the engine swing angle in the case of failure.

[0152] From Figures 5 - 10 the tracking effect, it can be seen that adding the offset-type failure ρ r and adding the engine damage failure ρ u 15s laterIn the case of (t) (the damage ratio gradually increases), the attitude angles of the traditional PID control tend to diverge, and the roll angle error gradually increases. In contrast, the multivariable adaptive PI control can still limit the attitude angle error within the set performance constraint range. Based on the fault-tolerant strategy of the multivariable adaptive PI control, the engine gimbal angles of the three channels change rapidly according to the control strategy to ensure the tracking performance under this fault. However, the robustness of the traditional PID control is not sufficient to compensate for this fault, resulting in an increase in the attitude angle error.

[0153] From Figure 11 It can be seen that the control commands of the multivariable adaptive PI control method are relatively smooth. In practical engineering applications, the performance of the actuator is limited. Compared with other nonlinear controllers that generate control command chattering, it has advantages. At the same time, the multivariable adaptive PI control is an improvement based on the PI control and is easier to implement compared with other nonlinear control methods.

[0154] In summary, the simulation results verify the effectiveness of the proposed fault-tolerant control strategy. The multivariable adaptive PI control can still exhibit fault-tolerant capabilities without fault information. This performance is crucial for the successful soft landing of reusable launch vehicles. The premise of separate design of the attitude system and the guidance system lies in that the guidance commands can be tracked without delay, so the error must always be within an acceptable range.

[0155] The attitude fault-tolerant control method for reusable launch vehicles with performance constraints in the embodiments of the present invention designs a multivariable adaptive PI fault-tolerant controller to achieve performance constraints for the attitude model of the reusable launch vehicle during the powered landing phase, considering the actual engineering applications. During the entire controller design process, the complexity brought by uncertainties, external disturbances, and engine faults is considered. First, design performance constraint limits for the transition variables including attitude angle error and attitude angular velocity error; secondly, use performance transformation techniques to derive new variables, and limit the transition variables within the performance function by controlling the stability of this variable; finally, design a multivariable adaptive PI fault-tolerant controller to stabilize this variable. The present invention can handle the performance constraint problem during the rocket powered landing process, thereby improving the success rate of the rocket soft landing.

[0156] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0157] In addition, the terms "first" and "second" are used only for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0158] Any process or method description, whether in a flowchart or described otherwise herein, can be understood to represent a module, segment, or portion of code including one or N executable instructions for implementing a customized logic function or process, and the scope of the preferred embodiments of the present invention includes additional implementations, where the functions can be executed in a substantially simultaneous manner or in a reverse order according to the functions involved, rather than in the order shown or discussed, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

Claims

1. A reusable launch vehicle attitude fault-tolerant control method with performance constraints, characterized in that It includes the following steps: Step 1, establish an attitude control model for the powered landing section of a reusable launch vehicle; Step 2, taking uncertainties and internal and external disturbances into account, obtain a rigid body attitude control model for the powered landing section of the rocket in the body coordinate system, with the attitude angles and attitude angular velocities of the reusable launch vehicle as the system outputs, and the engine gimbal angles of the pitch, yaw, and roll channels as the control system inputs; Step 3, considering the situation where an engine failure occurs in the rigid body attitude control model, establish an engine failure model, and obtain an attitude control model for the reusable launch vehicle under the failure according to the engine failure model; Step 4, define a transition variable based on the attitude angle error and attitude angular velocity error, and design performance constraints for the transition variable containing the attitude angle and attitude angular velocity errors; Step 5, according to the transition variable, construct a new error variable through performance conversion technology, and the new error variable contains constraint information, attitude angle, and attitude angular velocity error information; Step 6, according to the new error variable, design a multivariable adaptive PI fault-tolerant controller to stabilize the new error variable, and obtain the engine gimbal angle input under the corresponding situation; In Step 1, the established attitude control model for the powered landing section of the reusable launch vehicle is: In the formula, is the attitude angle at the landing coordinates; ω b = [ω bx ω by ω bz T is the three-axis attitude angular velocity in the body coordinates of the rocket; J is the inertia matrix of the rocket in the body coordinate system; the matrices J, σ, B and the control vector u are respectively:​ where x R represents the distance from the swing point of the variable-thrust swivel engine of the rocket to the theoretical tip of the rocket; x T represents the distance from the center of mass of the rocket to the theoretical tip of the rocket; T represents the total thrust of the rocket; l RCS is the force arm of the attitude control nozzle in the roll channel; δ γ , δ ψ and are the engine swing angles of the roll, yaw, and pitch channels, respectively; In Step 2, the rigid body attitude control model for the powered landing section of the rocket in the body coordinate system is: where Δd = [d1 d2 d3] T is the change in the moment of inertia caused by rocket fuel consumption, etc. and the external disturbances encountered by the rocket; Δf = [f1 f2 f3] T includes the uncertainty caused by the deviation of the model after the rocket returns from performing its mission; In Step 3, the engine failure model is: u t = ρ u (t)u + ρ r (t) where, u t is the true input of the system after the fault; ρ u (t) is the damage ratio of the engine, representing the severity of the fault, is the equivalent offset vector when the engine swing angle has an offset-type fault; The attitude control model for the reusable launch vehicle under the failure obtained according to the engine failure model is: In Step 4, the transition variable defined based on the attitude angle error and attitude angular velocity error is: ο(t) = aε1(t) + ε2(t) where ε1 = η - η d is the attitude angle error; ε2 = ω b - ω d is the angular velocity error; is the desired attitude angle; ω d is the desired attitude angular velocity; The performance constraints are: In the formula, μ = μ 1 μ 2 μ 3] T and represent the upper and lower limits of the performance constraints respectively, and are always positive; t represents time; In step 5, the new error variable ζ = [ζ1 ζ2 ζ3] T is as follows: where i = 1, 2, 3 represent the error variables of the roll, yaw, and pitch channels respectively; In Step 6, the multivariable adaptive PI fault-tolerant controller is: In the formula, the operation symbol is defined as: If α = [α1 α2 α3] T , β = [β1 β2 β3] T , then k ο = [k ο1 k ο2 k ο3 T , and any element is expressed as:​ k p and k I can be respectively expressed as: k I = βk p wherein, and β are positive numbers that can be freely selected, and Δk p and Δk I are automatically updated according to the adaptation law, and the adaptation law is: In the formula, is the estimated value of the auxiliary parameter variable b, The adaptation law of is: where κ and γ b are both freely selectable positive numbers; ι = [ι1 ι2 ι3] T , and any element of ι is a positive number.

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