A method for attitude control of a reusable launch vehicle in aerodynamic deceleration phase under attitude constraints

Abstract

The present invention proposes a method for attitude control of the aerodynamic deceleration section of a reusable launch vehicle under attitude constraints. First, a VTLV aerodynamic deceleration section control model containing unknown interference and model uncertainty is established, and a dynamic surface control method is used to achieve attitude command tracking control; then, the interference and uncertainty in the model are estimated and compensated to the control law by the UDE method, thereby improving the control accuracy of the system; finally, in order to improve the transient performance of the system, a new error transformation method is adopted, and a dynamic surface control method with preset performance is designed. The present invention has the characteristics of high control accuracy, fast response speed, high safety, strong versatility, etc. It specifically overcomes the technical difficulties such as input saturation that are easily caused by traditional control methods, and can be widely used in important industrial fields such as aerospace, providing a safe and reliable general algorithm for the problem of rocket attitude control constraints.

Description

Technical Field

[0001] The invention relates to a method for controlling the attitude of a reusable carrier rocket in a pneumatic deceleration section under attitude constraints, and belongs to the technical field of attitude control of missiles and carrier rockets. Background Art

[0002] In order to reduce the cost of rocket launches and improve launch efficiency, reusable launch vehicles (RLVs) came into being. RLVs can return and land at a predetermined point after completing a given mission. Compared with "disposable" launch vehicles, RLVs can greatly reduce launch costs.

[0003] RLV has many key technologies. On the basis of conventional launch vehicles, it also includes technologies related to the return and recovery of the spacecraft, such as propulsion technology, landing cushion technology, detection and maintenance technology, etc. Generally speaking, the entire flight phase of a vertical takeoff vertical landing reusable launch vehicle (Vertical takeoff vertical landing RLV, VTVL-RLV, abbreviated as VTLV) consists of seven parts: active phase, attitude adjustment phase, flight repair phase, high-altitude descent phase, power deceleration phase, aerodynamic deceleration phase and vertical landing phase. The mission profile of the full flight phase of VTLV is as follows: Figure 1 As shown in the figure, the aerodynamic deceleration stage has the characteristics of large nonlinearity, strong coupling, and model parameter uncertainty. It is one of the most important stages in the vertical recovery of VTLV. Among them, attitude control technology is one of the key technologies affecting recovery. The existing control technology faces thorny problems. The main challenges are as follows:

[0004] (1) There are many control constraints:

[0005] Due to its own structural reasons, the launch vehicle cannot use high speed to reduce the impact of wind field interference like a missile, nor can it use wings to maintain its own stability like an airplane. Therefore, the recovery mission during the final landing stage is more difficult. In addition, the launch vehicle also has many constraints, such as engine swing angle, thrust size, number of ignitions, etc. These constraints pose huge challenges to control technology.

[0006] (2) Strong interference and uncertainty:

[0007] The flight conditions of RLV in the aerodynamic deceleration stage are quite special. Unlike flying outside the atmosphere, it needs to pass through the dense atmosphere, so the aerodynamic force cannot be ignored. In addition, due to the different atmospheric environments at different altitudes, for example, as the altitude decreases, the air density increases, so the flight environment at this stage is complex and changeable. At the same time, RLV will also be affected by various interferences, such as sensor measurement noise, modeling parameter deviation, etc. In summary, the flight environment of RLV in the aerodynamic deceleration stage is relatively harsh, and it is subject to strong interference and uncertainty.

[0008] (3) Strict landing requirements

[0009] The success or failure of RLV lies in whether the landing is successful. Compared with other spacecraft, RLV has more stringent requirements for landing, especially for vertical recovery, which not only requires the position accuracy to be met during landing, but also requires the speed to drop to zero and the attitude to remain vertical to the ground. Therefore, soft landing in a fixed attitude is a difficult problem.

[0010] (4) Failures are prone to occur

[0011] During the attitude adjustment process of RLV in the aerodynamic deceleration phase, the thrust vector engine and grid rudder play a major role. Due to the influence of the complex atmospheric environment, actuator and sensor failures are prone to occur. Therefore, a certain degree of redundancy must be ensured in the design, and a good control strategy must also be in place to compensate for the impact of failures on attitude control.

[0012] With the improvement of the carrying capacity of launch vehicles, their mass, thrust and slenderness ratio increase, and the booster and core stage engine are often used to swing together to participate in attitude control. At the same time, due to the effect of complex aerodynamic loads, the overall rocket presents elastic low-frequency and dense-frequency modes, strong coupling vibration, complex local deformation and other characteristics, resulting in a large degree of time-varying and uncertainty in the parameters of the rocket body model, which will lead to a reduction in the stability margin of the rocket attitude control system and even greatly increase the probability of instability. The US SpaceX company has successfully applied the reuse technology to the "Falcon 9" launch vehicle. Faced with many difficulties and pressures, my country should also accelerate the research process of rocket reuse technology. Summary of the invention

[0013] Technical problems solved by the present invention:

[0014] Since reusable launch vehicles have a lightweight structure and a large slenderness ratio, there is a large range of uncertainty in the modeling process of the rocket body itself. The traditional deviation-based PID control law has low design parameter margins and poor adaptability for attitude control. The technical problems solved by the present invention mainly include two points: one is to improve the adaptability of attitude control; the other is to improve the transient performance during attitude adjustment.

[0015] Purpose of the present invention:

[0016] The present invention overcomes the shortcomings of the prior art and innovatively proposes a design method for repeatable rocket aerodynamic deceleration stage attitude control, which effectively solves the attitude restriction problem of VTLV in the presence of external unknown disturbances and model uncertainty. The method has the characteristics of high control accuracy, fast response speed, high safety, and strong versatility. It specifically overcomes technical difficulties such as input saturation that are easily caused by traditional control methods, and can be widely used in important industrial fields such as aerospace, providing a safe and reliable general algorithm for the problem of rocket attitude control restriction.

[0017] The solution of the present invention:

[0018] For vertical take-off and landing reusable rockets with unknown disturbances, model uncertainties and attitude constraints, a dynamic surface control algorithm based on uncertainty and disturbance estimator (UDE) is proposed to achieve precise attitude control in the aerodynamic deceleration stage. Firstly, a control model of the aerodynamic deceleration stage of VTLV with unknown disturbances and model uncertainties is established, and the dynamic surface control method is used to achieve attitude command tracking control; then, the UDE method is used to estimate the disturbances and uncertainties in the model and compensate them to the control law, thereby improving the control accuracy of the system; finally, in order to improve the transient performance of the system, a new error transformation method is adopted, and a dynamic surface control method with preset performance (PPDSC) is designed.

[0019] The technical solution of the present invention is described in detail below:

[0020] (1) Rocket model establishment

[0021] In order to design the attitude control law of the VTLV aerodynamic deceleration stage, its mathematical model needs to be established first.

[0022] Taking into account the influence of the earth's rotation and oblateness, the translation equation of the rocket motion is described as follows:

[0023]

[0024] Where h is the altitude, V is the speed, ζ is the flight path angle, φ is the latitude, and R e is the radius of the earth, ψ is the heading angle, θ is the longitude, Y is the lateral force, L is the lift, D is the drag, m is the mass of the rocket, α, β, σ represent the angle of attack, sideslip angle and inclination angle respectively, g is the gravitational acceleration and the expression is g = μ / (R e +h) 2 (μ is the gravitational constant), ω eis the angular velocity of the Earth's rotation.

[0025] In the aerodynamic deceleration stage, the VTLV engine is in the off state, the engine thrust is 0N, and the changes in its speed and attitude are mainly affected by aerodynamic force and aerodynamic torque. The dynamic equation of the RLV rotating around the center of mass in the aerodynamic deceleration stage is as follows:

[0026]

[0027] In the formula, J kl (k, l = x, y, z) represents the moment of inertia, M m (m=x, y, z) represent the aerodynamic moments of the three channels, and p, q and r are the angular velocities of the three axes.

[0028] The aerodynamic forces and aerodynamic moments are described as follows:

[0029]

[0030]

[0031] In the formula, S r is the cross-sectional area of ​​VTLV, L r Its reference length, C L0 , and is the lift coefficient, C D0 , and is the drag coefficient, and are the damping moment coefficients for roll, pitch and yaw, respectively, and is the static stability moment coefficient, and Indicates the control torque coefficient, dynamic pressure q0=0.5ρV 2 , ρ is the air density (the atmospheric model uses the 1976 American Standard Atmospheric Model), δ a , δ e and δ r Represents the three-channel equivalent swing angle.

[0032] Define the attitude angle vector Ω = [αβσ] T , angular velocity vector ω = [pqr] T According to equations (2) and (3), considering and merging the unknown interference terms in the model, the rotation equation of VTLV around the center of mass can be further simplified as:

[0033]

[0034] Where d1 represents the sum of unknown parameters and external disturbances, d2 represents the sum of unknown disturbance torque and model uncertainty; δ = [δ a ,δ e .δ r ] T is the control input vector; J is the instantaneous moment of inertia matrix of VTLV, ω × is the skew-symmetric matrix of ω, R is the coordinate transfer matrix, and B is the instantaneous control input matrix. Their expressions are as follows:

[0035]

[0036] In the pneumatic deceleration section, due to the complex atmospheric environment, the VTLV may have an actuator failure, so the actual control input is expressed as follows:

[0037] δ f =D f δ+F δ

[0038] Where δ is the ideal control input, D f =diag(D f1 ,D f2 ,D f3 ) is a multiplicative fault, F δ =[F δ1 ,F δ2 ,F δ3 ] T It is an additive fault.

[0039] (2) Interference estimation based on UDE

[0040] Since the UDE method has the characteristics of simple structure and good interference estimation effect, the present invention adopts the UDE method to estimate the composite interferences d1 and d2 in the VTLV attitude model (6), and compensates them in the subsequent control law to improve the control accuracy.

[0041] According to formula (6), the unknown term in the VTLV attitude model can be expressed as:

[0042]

[0043] UDE estimates unknown interference through filters. For the interference of the VTLV model, the following interference estimation is designed:

[0044]

[0045] In the formula, are interference d i and interference estimation Pull transformation of G fn (s)=(τ ns+I) -1 represents a first-order filter matrix, where τ n ∈R 3×3 is the filter coefficient matrix to be designed.

[0046] Through the inverse transformation, we can get:

[0047]

[0048] Integrating both sides of the equal sign, we can get the expression of interference estimate as follows:

[0049]

[0050] Where t is the integration time. This formula will be used in subsequent controller design. The unknown term d i will be replaced.

[0051] (3) Design of dynamic surface controller with preset performance

[0052] In order to make the VTLV attitude controller have satisfactory transient performance and steady-state error and reduce the complexity of the control law, it is necessary to design a dynamic surface controller with preset performance.

[0053] The error performance function can be expressed as

[0054]

[0055] Where, the posture tracking error [e1(t)e2(t)e3(t)] T =Ω-Ω d , z min and z max is the positive parameter to be set, is a differentiable, bounded and strictly monotonically decreasing positive function. The present invention adopts an exponential performance function. The specific form is as follows:

[0056]

[0057] In the formula, m i 、b i,0 、b i,∞ is a positive constant, m i Represents the convergence speed, requiring z max b i,0 and z min b i,0 must be greater than the absolute value of the initial error |e(0)| and satisfy Choose the right b i,0 make,

[0058]

[0059] In the formula, e i The initial condition of (t) is e i (0)Satisfaction

[0060] The performance error function not only quantitatively describes the steady-state performance of the controlled system, but also describes its transient performance, introducing upper and lower bound constraints for the control system. In order to introduce the preset performance into the controller and realize the equivalent conversion from the performance constraint space to the unconstrained space, it is necessary to find an error transformation function that can perform homeomorphic mapping.

[0061] Define tracking error e i The lower and upper bounds of

[0062]

[0063] According to the above analysis, we first construct the following nonlinear transformation

[0064]

[0065] In the formula, S 1,i is the transformed error variable and satisfies the following three conditions:

[0066] 1) Strictly monotonically increasing;

[0067] 2) S 1,i = 0 if and only if e i =0;

[0068] 3)

[0069] The design steps of the controller are as follows:

[0070] Step 1, for S 1,i Taking the derivative we get:

[0071]

[0072] Among them, the variable χ i and κ i The expression is as follows:

[0073]

[0074] S 1,i Although the expression of meets the error requirements, z i When both tend to 0, χ i may become infinite, resulting in becomes infinite, and eventually the system will diverge. So modify S 1,i The expression is as follows:

[0075]

[0076] Same as above, taking the derivative of the new error variable gives:

[0077]

[0078] χ i and κ i The new expression is as follows:

[0079]

[0080] By simplifying χ i The numerator of can be obtained:

[0081]

[0082] Then the properties of S1 can be redefined as follows:

[0083] 1) S 1,i = 0 if and only if e i =0;

[0084] 2)

[0085] 3) Satisfy the conditions

[0086] The above design shows that the new dynamic surface S1 = [S 11 ,S 12 ,S 13 ] T Avoid system divergence. 1i In addition to e i =0 are both less than 0, but χ i The sign of e will change i The sign of Further deduction yields:

[0087]

[0088] In the formula, χ = diag (χ1, χ2, χ3), e(t) = [e1(t), e2(t), e3(t)] T , κ=[κ1,κ2,κ3] T .

[0089] Design of virtual control law as follows:

[0090]

[0091] Among them, K1 is a positive definite symmetric matrix.

[0092] Combining equations (10), (20) and (21), we can obtain The expression is as follows:

[0093]

[0094] In order to avoid the complexity of the virtual control law derivation, the virtual control law in equation (21) is passed through a first-order low-pass filter:

[0095]

[0096] In the formula, ω d ∈R 3 is the state vector of the first-order filter, T d >0 is the time constant matrix of the filter.

[0097] Step 2, define the attitude angular velocity error vector S2:

[0098]

[0099] By taking the derivative of S2, we can get:

[0100]

[0101] Finally, the actual control input vector designed is as follows:

[0102]

[0103] Where K2 is a positive definite diagonal matrix.

[0104] According to formula (10) and formula (26), we can get The expression is as follows:

[0105]

[0106] Beneficial effects of the present invention:

[0107] (1) The UDE method is used to estimate disturbances and uncertainties in real time, overcoming the conservatism of traditional robust control and greatly improving the adaptability of the VTLV control system.

[0108] (2) The designed tracking error envelope range can improve the transient performance of the system and further improve the reliability and adaptability of the system.

[0109] (3) The control scheme proposed in the present invention is simple and practical, can be used in general models, and is easy to implement in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 This is the VTLV flight mission profile.

[0111] Figure 2 For the control scheme architecture.

[0112] Figure 3 is the attitude angle tracking error curve.

[0113] Figure 4 is the attitude angle tracking curve.

[0114] Figure 5 Estimated effect diagram of the interference between the attitude angle subsystem and the angular rate subsystem d1.

[0115] Figure 6 Estimated effect diagram of the interference between the attitude angle subsystem and the angular rate subsystem d2.

[0116] Figure 7 is the equivalent control deflection curve. DETAILED DESCRIPTION

[0117] To further clarify the technical solution of the present invention, the specific implementation steps are as follows:

[0118] 1. Define the posture tracking error [e1(t)e2(t)e3(t)] T =Ω-Ω d , where the attitude angle vector Ω = [αβσ] T , the expected attitude angle vector Ω d Set to [180 0 0] T , which is the real-time value after passing through a first-order filter with a time constant of 1.

[0119] 2. Set the tracking error e i The lower and upper bounds of are:

[0120]

[0121] Choose a nonlinear transformation function:

[0122]

[0123] Design the virtual control signal as

[0124]

[0125] The estimated value of the selected interference is:

[0126]

[0127] Pass the virtual control signal through a first-order filter:

[0128]

[0129] Get the expected signal of angular rate ω d .

[0130] 3. Set the angular rate tracking error to:

[0131] S2=ω-ω d

[0132] Finally, the actual control signal is:

[0133]

[0134] Among them, the estimated value of interference for:

[0135]

[0136] The settings in the simulation are as follows:

[0137] The simulation time is set to 30 s and the step size is 0.001 s.

[0138] The initial state of VTLV is: h = 25000 (m), φ = 0 (deg), θ = 0 (deg), V = 1180 (m / s), ζ = -40 (deg), ψ = 0 (deg), Ω (0) = [175 5 -5] T (deg), ω(0) = [0 0 0] T (deg / s).

[0139] The interference and fault settings are as follows:

[0140] Δd=[2sin(0.5t+π / 3)2sin(0.5t+2π / 3)2sin(0.5t+π)] T

[0141]

[0142] The model and controller parameters are shown in Table 1 and Table 2.

[0143] Table 1 VTLV model parameters

[0144]

[0145] Table 2 Controller parameters

[0146]

[0147] Figure 3The VTLV attitude angle tracking error curve is shown in Figure 1, where the black dashed line is the preset performance. When the error is within the preset performance range, normal control can be guaranteed. It can be seen from the figure that the attitude angle error is within the envelope of the preset performance, and the control requirements can be met when interference exists and the actuator fails.

[0148] Figure 4 It is the attitude angle tracking curve. The attitude output curve in the figure is divided into two categories, one is the dynamic surface control without preset performance, and the other is the dynamic surface control with preset performance. There is little difference between the two in the first 15 seconds. After the actuator failure occurs 15 seconds later, the former has a larger deviation, and the latter has a smaller deviation and fluctuation. Therefore, the preset performance added by the present invention can make the control effect better.

[0149] Figure 5 , Figure 6 The estimated effect diagram of the interference between the attitude angle subsystem and the angular rate subsystem. It can be seen from the figure that the estimated value can track the actual interference in real time, so the UDE method adopted in the present invention has good real-time performance.

[0150] Figure 7 In order to control the deflection curve equivalently, the control input is adjusted quickly after the simulation starts so that the actual attitude angle tracks the expected value. Under the interference, the input is adjusted slightly according to the interference size. After the actuator fails, the input is adjusted in amplitude, and all changes are within the normal range.

Claims

1. A method for attitude control of a reusable launch vehicle in aerodynamic deceleration phase under attitude constraints, characterized in that: Step 1: Rocket model building: In order to design the attitude control law of the aerodynamic deceleration phase of the vertical take-off and landing reusable launch vehicle (VTLV), its mathematical model needs to be established first; Taking into account the influence of the earth's rotation and oblateness, the translation equation of the rocket motion is described as follows: Where h is the altitude, V is the speed, ζ is the flight path angle, φ is the latitude, and R e is the radius of the earth, ψ is the heading angle, θ is the longitude, Y is the lateral force, L is the lift, D is the drag, m is the mass of the rocket, α, β, σ represent the angle of attack, sideslip angle and inclination angle respectively, g is the gravitational acceleration and the expression is g = μ / (R e +h) 2 , μ is the gravitational constant, ω e is the angular velocity of the Earth's rotation; In the aerodynamic deceleration stage, the VTLV engine is in the off state, the engine thrust is 0N, and the changes in speed and attitude are affected by aerodynamic force and aerodynamic torque; the dynamic equation of the RLV rotating around the center of mass in the aerodynamic deceleration stage is as follows: In the formula, J kl (k, l = x, y, z) represents the moment of inertia, M m (m=x, y, z) represent the aerodynamic moments of the three channels, and p, q and r are the angular velocities of the three axes; Define the attitude angle vector Ω = [αβσ] T , angular velocity vector ω = [pqr] T According to equations (2) and (3), considering and merging the unknown interference terms, the rotation equation of VTLV around the center of mass is further simplified to: Where d1 represents the sum of unknown parameters and external disturbances, d2 represents the sum of unknown disturbance torque and model uncertainty; δ = [δ a ,δ e .δ r ] T is the control input vector; J is the instantaneous moment of inertia matrix of VTLV, ω × is the skew-symmetric matrix of ω, R is the coordinate transfer matrix, and B is the instantaneous control input matrix; Step 2: Interference estimation based on UDE: The UDE method is used to estimate the composite disturbances d1 and d2 in the VTLV attitude model and compensate them in the subsequent control law to improve the control accuracy. According to formula (6), the unknown term in the VTLV attitude model is expressed as: UDE estimates unknown interference through filters. For the interference of the VTLV model, the following interference estimation is designed: In the formula, are interference d i and interference estimation Pull transformation of G fn (s)=(τ n s+I) -1 represents a first-order filter matrix, where τ n ∈R 3×3 is the filter coefficient matrix to be designed; Through the inverse pull transform, we get: Integrating both sides of the equal sign, we get the following expression for interference estimation: Where t is the integration time. This formula (10) will be used in the subsequent controller design. The unknown term d i will be replaced; Step 3: Dynamic surface controller design with preset performance: In order to make the VTLV attitude controller have satisfactory transient performance and steady-state error and reduce the complexity of the control law, it is necessary to design a dynamic surface controller with preset performance; The error performance function is expressed as: Where, the posture tracking error [e1(t)e2(t)e3(t)] T =Ω-Ω d , z min and z max is the positive parameter to be set, is a differentiable, bounded and strictly monotonically decreasing positive function, using an exponential performance function. The specific form is as follows: In the formula, m i 、b i,0 、b i,∞ is a positive constant, m i Represents the convergence speed, requiring z max b i,0 and z min b i,0 must be greater than the absolute value of the initial error |e(0)| and satisfy Select b i,0 make, In the formula, e i The initial condition of (t) is e i (0)Satisfaction Define tracking error e i The lower and upper bounds of are: According to the analysis, construct a nonlinear transformation: In the formula, S 1,i is the transformed error variable.

2. The method for controlling the attitude of a reusable launch vehicle in aerodynamic deceleration stage under attitude restriction according to claim 1, characterized in that: In step 1, the aerodynamic forces and aerodynamic moments are described as follows: In the formula, S r is the cross-sectional area of ​​VTLV, L r Its reference length, C L0 , and is the lift coefficient, C D0 , and is the drag coefficient, and are the damping moment coefficients for roll, pitch and yaw, respectively, and is the static stability moment coefficient, and Indicates the control torque coefficient, dynamic pressure q0=0.5ρV 2 , ρ is the air density, δ a ,δ e and δ r Represents the three-channel equivalent swing angle.

3. The method for controlling the attitude of a reusable launch vehicle in aerodynamic deceleration stage under attitude restriction according to claim 2, characterized in that: In step 1, the expressions of J, R, and B are as follows:

4. The method for controlling the attitude of a reusable launch vehicle in aerodynamic deceleration stage under attitude restriction according to claim 1, characterized in that: In step 1, in the pneumatic deceleration section, due to the complex atmospheric environment, the VTLV may have an actuator failure, so the actual control input is expressed as follows: d f =D f d+F δ Where δ is the ideal control input, D f =diag(D f1 ,D f2 ,D f3 ) is a multiplicative fault, F δ =[F δ1 ,F δ2 ,F δ3 ] T It is an additive fault.

5. The method for controlling the attitude of a reusable launch vehicle in aerodynamic deceleration stage under attitude restriction according to claim 1, characterized in that: In step 3, S 1,i The following three conditions are met: 1) Strictly monotonically increasing; 2) S 1,i = 0 if and only if e i =0; 3) 6. The method for controlling the attitude of the aerodynamic deceleration stage of a reusable launch vehicle under attitude restriction according to claim 1 or 5, characterized in that: In step 3, S 1,i The derivative is: Among them, the variable χ i and κ i The expression is as follows: S 1,i Although the expression of meets the error requirements, z i When both tend to 0, χ i may become infinite, resulting in becomes infinite, the system will eventually diverge; so modify S 1,i The expression is as follows:

7. The method for controlling the attitude of a reusable launch vehicle in aerodynamic deceleration stage under attitude restriction according to claim 6, characterized in that: In step three, χ i and κ i The new expression is as follows: By simplifying χ i The numerator of , we get:

8. The method for controlling the attitude of the aerodynamic deceleration stage of a reusable launch vehicle under attitude restriction according to claim 1 or 7, characterized in that: In step 3, redefine the properties of S1 as follows: 1) S 1,i = 0 if and only if e i =0; 2) 3) Satisfy the conditions The above design shows that the new dynamic surface S1 = [S 11 ,S 12 ,S 13 ] T Avoid system divergence; although S 1i In addition to e i =0 are both less than 0, but χ i The sign of e will change i The sign of Further deduction yields: In the formula, x = diag(x1,x2,x3), e(t) = [e1(t),e2(t),e3(t)] T ,k=[k1,k2,k3] T ; Design of virtual control law as follows: Among them, K1 is a positive definite symmetric matrix.

9. The method for controlling the attitude of the aerodynamic deceleration stage of a reusable launch vehicle under attitude restriction according to claim 8, characterized in that: In step 3, combining equations (10), (20) and (21), we obtain The expression is as follows: In order to avoid the complexity of the virtual control law derivation, the virtual control law in equation (21) is passed through a first-order low-pass filter: In the formula, ω d ∈R 3 is the state vector of the first-order filter, T d >0 is the time constant matrix of the filter.

10. The method for attitude control of a reusable launch vehicle aerodynamic deceleration stage under attitude restriction according to claim 9, characterized in that: In step 3, define the attitude angular velocity error vector S2: S2=oh-oh d (24) By taking the derivative of S2, we get: Finally, the actual control input vector designed is as follows: Where K2 is a positive definite diagonal matrix; According to formula (10) and formula (26), we can get The expression is as follows:

Images