A Spacecraft Attitude Control Method Based on Fractional Sliding Mode and Actuators

Abstract

This invention discloses an attitude control method for aerospace vehicles based on fractional-order sliding mode considering actuators, belonging to the field of aircraft control technology. Addressing the performance degradation problem caused by traditional sliding mode attitude controllers neglecting actuator dynamics, this invention first integrates attitude dynamics, aerodynamic torque, and actuator models to construct a second-order linearized attitude control model. Subsequently, an extended state observer is designed to estimate and compensate for convergent disturbances in the system in real time. Furthermore, a fractional-order non-singular terminal sliding surface is designed, and combined with a reaching law using saturation functions, the desired intermediate control quantity is derived, ultimately calculating the rudder deflection command. Through the coordinated design of model construction, disturbance observation, and advanced control laws, this invention achieves rapid finite-time convergence of attitude angle tracking errors while fully considering the dynamic characteristics of the actuators, effectively suppressing control chattering and significantly improving the control accuracy and robustness of the system under parameter uncertainty and external disturbances.

Description

Technical Field

[0001] This invention belongs to the field of aerospace vehicle attitude control technology, and specifically relates to an aerospace vehicle attitude control method based on fractional sliding mode considering actuators. Background Technology

[0002] Due to the significant differences in aerodynamic characteristics between high and low altitudes, hypersonic vehicles experience substantial changes in their dynamic characteristics and model parameters during long-range, cross-airspace and high-speed flight. Furthermore, their control characteristics change drastically with altitude and speed. In addition, numerous unpredictable external disturbances occur during flight, making hypersonic vehicles highly nonlinear and uncertain systems. Sliding mode control, with its advantages of fast dynamic response, simple algorithms, easy physical implementation, insensitivity to parameter perturbations and external disturbances, robustness, and adaptability, is frequently applied in the design of hypersonic vehicle control systems. Compared to traditional integer-order calculus, fractional-order calculus adds variability to both the differentiation and integration degrees of freedom, thus bringing new flexibility to control system design. In recent years, fractional-order sliding mode control, which utilizes the memory and inheritance properties of fractional-order calculus operators and introduces them into traditional sliding mode control theory, has been extensively studied in various fields, further enhancing the flexibility of aerospace vehicle control system design.

[0003] Existing fractional-order sliding mode attitude controllers for aircraft do not consider the impact of actuator dynamics on the overall attitude control system during their design. Instead, they assume that the actual control deflection angle can instantaneously reach the commanded control deflection angle. When actuator dynamics are taken into account, the controller's control performance will decrease or even diverge. The traditional method of increasing the reaching law gain will produce obvious fluctuations or chattering phenomena. In addition, most fractional-order sliding mode controllers for aerospace vehicle attitude control are conventional fractional-order sliding mode controllers, while fractional-order terminal sliding mode attitude controllers with finite-time convergence characteristics are relatively rare. Summary of the Invention

[0004] To address the shortcomings of traditional sliding mode attitude controllers that neglect the dynamic characteristics of actuators, this invention proposes a fractional-order sliding mode attitude control method for aerospace vehicles that considers actuators. First, this invention combines the vehicle's attitude dynamics model with the actuator model to construct a second-order linear control model that better reflects the actual control scenario, thus overcoming the deficiency of traditional sliding mode attitude controllers that ignore the dynamic characteristics of actuators. Then, a state observer is used to accurately estimate the unknowns in this linear model, providing reliable data support for controller design. For this model, this invention further designs a fractional-order terminal sliding mode controller with finite-time convergence characteristics. This controller combines the flexibility of fractional-order calculus with the fast convergence advantage of terminal sliding mode control, ensuring that the vehicle's attitude angle stably converges to the desired command value within a set finite time. This method effectively improves the control accuracy and robustness of the system under parameter uncertainties and external disturbances, and has strong engineering application value.

[0005] This invention provides an attitude control method for aerospace vehicles based on fractional sliding mode considering actuators, comprising the following steps: Step S1: Establish the attitude dynamics model, aerodynamic torque model, and actuator model of the spacecraft with parameter uncertainties and aggregated disturbances; based on the feedback linearization method, integrate the attitude dynamics model, aerodynamic torque model, and actuator model to construct a second-order linearized attitude control model. Step S2: For the second-order linearized attitude control model, design an extended state observer to estimate the composite disturbance of attitude angular acceleration in the second-order linearized attitude control model in real time. Step S3: Establish a fractional-order terminal sliding mode function with finite-time convergence; Step S4: Based on the current state of the spacecraft, the composite disturbance estimate of the current attitude angular acceleration obtained by the fractional-order terminal sliding mode function with finite-time convergence and the extended state observer, the current expected intermediate control quantity is obtained by combining the second-order linearized attitude control model and using the approach law containing the saturation function. Step S5: Based on the current expected intermediate control quantity and the current state of the spacecraft, calculate the current rudder deflection command; based on the current rudder deflection command, apply it to the actuator model, aerodynamic torque model and attitude dynamics model to obtain the state of the spacecraft at the next moment. Step S6: Determine whether the state of the spacecraft at the next moment meets the convergence condition. If the convergence condition is not met, set the state of the spacecraft at the next moment to the current state of the spacecraft and return to step S4. If the convergence condition is met, realize the finite-time convergence control of the state of the spacecraft.

[0006] Optionally, the state of the spacecraft includes a system drift term matrix. F Control distribution matrix E Angle of attack, sideslip angle, roll angle, derivative of angle of attack, derivative of sideslip angle, derivative of roll angle, roll rate, pitch rate, yaw rate, derivative of roll rate, derivative of pitch rate, and derivative of yaw rate.

[0007] Optionally, the expression for the attitude dynamics model of the aerospace vehicle with parameter uncertainties and convergence perturbations in step S1 is:

[0008] in, For the angle of attack, Sideslip angle, For roll angle, For the roll rate, For pitch rate, The yaw rate, The first derivative of the angle of attack is represented by... The first derivative represents the sideslip angle. The first derivative of the roll angle is given by... The first derivative of the roll rate. The first derivative of the pitch rate. The first derivative of the yaw rate; For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, , , , , and All are aggregation perturbations.

[0009] Optionally, the expression for the aerodynamic moment model of the spacecraft in step S1 is:

[0010] In the formula, For the aerodynamic torque of a spacecraft; These represent the elements in the first row and first column to the third row and third column of the attitude angle-related aerodynamic moment coefficient matrix. These represent the elements in the first row and first column of the aerodynamic moment coefficient matrix related to the rudder deflection angle, from the elements in the first row and first column to the elements in the third row and third column. For the angle of attack; Sideslip angle; For roll angle; , , They represent x , y and z rudder deflection angle of the shaft, Atmospheric density, For the speed of aerospace vehicles, For reference area of ​​aerospace vehicles, This is a reference length for aerospace vehicles.

[0011] Optionally, the expression for the actuator model of the aerospace vehicle in step S1 is:

[0012] In the formula, The transfer function representing the actuator model; Represents the Laplace operator; Represents the time constant; This indicates damping in a second-order system.

[0013] Optionally, the specific steps in step S5 to obtain the state of the spacecraft at the next moment based on the current rudder deflection angle command and applied to the actuator model, aerodynamic moment model, and attitude dynamics model are as follows: Input the current rudder deflection command into the actuator model to obtain the actual rudder deflection angle of the spacecraft; then input the actual rudder deflection angle, the current angle of attack, sideslip angle, roll angle, velocity, and the reference area, reference length, and atmospheric density of the spacecraft into the aerodynamic moment model to calculate the torque acting on the spacecraft at the current moment; finally, input the torque acting on the spacecraft at the current moment into the attitude dynamics model to obtain the state of the spacecraft at the next moment.

[0014] Compared with the prior art, the present invention has at least the following beneficial effects: The method of this invention addresses the problem of performance degradation or even divergence in traditional sliding diaphragm controllers due to neglecting the dynamic characteristics of actuators. By integrating the attitude dynamics model and the actuator dynamics model, a second-order linear control model that is more in line with the actual control scenario is constructed, laying the model foundation for high-precision control.

[0015] Based on this, a state observer is introduced to perform real-time and accurate estimation and compensation of unknowns and aggregated disturbances in the system, which effectively improves the robustness of the system under parameter uncertainty and external disturbances.

[0016] Furthermore, fractional-order nonsingular terminal sliding mode control is applied to this model. Leveraging the memory inheritance properties of fractional calculus and the finite-time fast convergence advantage of terminal sliding mode control, the attitude angle tracking error is ensured to converge stably within a finite time. Simultaneously, boundary layer technology is employed to smooth the control signal, effectively suppressing the inherent high-frequency chattering problem of traditional sliding mode control. The method of this invention can guarantee that the aircraft's attitude angle converges quickly and accurately to the desired command in complex reentry environments, considering actuator dynamics. Compared to traditional methods, it significantly improves convergence speed, control accuracy, and stability, providing an efficient solution for high-reliability attitude control of aerospace vehicles and possessing significant engineering application value. Attached Figure Description

[0017] Figure 1 This is a flowchart of the aerospace vehicle attitude control method based on fractional sliding mode considering actuators according to the present invention.

[0018] Figure 2 The results show a comparison of the attitude angles simulated between the control method of this invention and the control method in the prior art.

[0019] Figure 3 The simulation results show the rudder deflection angle comparison between the control method of the present invention and the control method in the prior art. Detailed Implementation

[0020] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0021] One embodiment of the present invention is shown below. Figures 1-3 A method for attitude control of aerospace vehicles based on fractional sliding mode considering actuators is disclosed. The specific implementation method is as follows: Step 1: Establish an attitude dynamics model for an aerospace vehicle with parameter uncertainties and convergence perturbations, expressed as: (1) in, For the angle of attack, Sideslip angle, For roll angle, For the roll rate, For pitch rate, The yaw rate, The first derivative of the angle of attack is represented by... The first derivative represents the sideslip angle. The first derivative of the roll angle is given by... The first derivative of the roll rate. The first derivative of the pitch rate. The first derivative of the yaw rate; For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, , , , , and All are aggregation disturbances. , , , , and Used to reflect parameter uncertainty.

[0022] The x-axis, y-axis, and z-axis are the coordinate axes of the aerospace vehicle: the origin is fixed to the center of mass of the aerospace vehicle; the x-axis points forward along the longitudinal axis of the aerospace vehicle; the y-axis is perpendicular to the plane of symmetry and points to the right; the z-axis is determined by the right-hand rule and points downward.

[0023] Step 2: Establish the aerodynamic moment model of the spacecraft; Specifically, the aerodynamic moment model of the spacecraft is approximated using the following second-order system, expressed as: (2) In the formula, For the aerodynamic torque of a spacecraft; These represent the elements in the first row and first column to the third row and third column of the attitude angle-related aerodynamic moment coefficient matrix. These represent the elements in the first row and first column of the aerodynamic moment coefficient matrix related to the rudder deflection angle, from the elements in the first row and first column to the elements in the third row and third column. , , These are the rudder deflection angles along the x, y, and z axes, respectively. Atmospheric density, For the speed of the aircraft, For reference area of ​​aerospace vehicles, This is a reference length for aerospace vehicles.

[0024] Step 3: Establish the actuator model of the aerospace vehicle; Specifically, the actuator model of the aerospace vehicle is approximated using the following second-order system, expressed as: (3) In the formula, The transfer function representing the actuator model; Represents the Laplace operator; Represents the time constant; This indicates damping in a second-order system.

[0025] Preferably, , =0.7; Transforming the transfer function of the actuator model shown in equation (3) into a time-domain differential equation, we obtain the second-order differential equation between the actuator's rudder deflection command and the actual value: (4) In the formula, The first derivative represents the actual rudder deflection angle; The second derivative represents the actual rudder deflection angle; This refers to the actual deflection angle of the control wheel of an aerospace vehicle. This is the rudder deflection command. , and These are the rudder deflection commands for the x, y, and z axes, respectively.

[0026] Step 4: Establish a second-order linearized attitude control model to help solve for the desired intermediate control variables; The attitude dynamics model of the aerospace vehicle shown in equation (1) is linearized using the feedback linearization method, and the expression is: (5) in, The attitude angle vector, ; The first derivative of the attitude angle vector; The second derivative of the attitude angle vector; As an intermediate control variable, This refers to the uncertainties of the system. These represent the uncertainties affecting the second-order reciprocals of the three attitude angles, respectively, and the uncertainties are the combined disturbances.

[0027] Furthermore, ,in, The system drift term matrix is ​​a matrix that does not include control input. At that time, the state derivative components are caused by the system's own state coupling and nonlinear terms; The control distribution matrix describes the aerodynamic moments of the control input spacecraft. M to be an intermediate control variable A linear mapping relationship.

[0028] Among them, the system drift term matrix and control distribution matrix It can be obtained from the first derivative of the attitude angle vector Differentiation yields the expression:

[0029]

[0030]

[0031] in, - Representing the system drift term matrix respectively Intermediate state variables in.

[0032] The aerodynamic torque of the spacecraft can be obtained from equations (2)-(4). for: (6) in, Indicates the torque command of the aircraft; This represents the estimated increment of the torque; This represents the matrix of aerodynamic moment coefficients related to attitude angles; Represents the attitude angle vector; This represents the matrix of aerodynamic moment coefficients related to the rudder deflection angle; This represents the rudder deflection command vector; Indicates atmospheric density; Indicates the current speed of the spacecraft; Indicates the reference area of ​​an aerospace vehicle; This indicates the reference length of an aerospace vehicle.

[0033] in, and They are respectively: (7) (8).

[0034] Furthermore, intermediate control variables Transform into: (9) in, This is the desired intermediate control quantity.

[0035] (10) Therefore, the second-order linearized attitude control model is obtained, and its expression is: (11) Step 5: Use the extended state observer to estimate the composite disturbance of the angular acceleration vector of the attitude angle. .

[0036] Furthermore, the expression for the extended state observer is: (12) In the formula, This represents the attitude angle error vector; , , All of these are state variables of the extended state observer. Composite disturbance of the angular acceleration vector of the attitude angle The estimated value, Represents the first state variable The first derivative; Represents the second state variable The first derivative; Represents the third state variable The first derivative; Indicates the constant gain coefficient; This represents the first constant gain coefficient vector; This represents the second constant gain coefficient vector; ; To control the nonlinear function.

[0037] Furthermore, , , , Furthermore, The expression is: (13) (14) in, This represents the attitude angle error vector; Indicates the first j A vector of constant gain coefficients; Indicates the first iThe error of one attitude angle; Indicates the first j A vector of constant gain coefficients The Middle k A constant gain coefficient; Indicates constant coefficient parameters, ; Step 6: Establish a fractional-order terminal sliding mode function with finite-time convergence.

[0038] Let the state error be: (15) in, For attitude angle tracking error, The derivative of the attitude angle tracking error. The attitude angle vector, The desired attitude angle vector contains three components: For the desired angle of attack, For the desired sideslip angle, The desired roll angle.

[0039] Fractional terminal sliding mode function for: (16) in, , , , These represent the sliding mode functions corresponding to the angle of attack, sideslip angle, and roll angle, respectively. This is the error gain coefficient. For fractional terms, constant coefficients The error gain coefficient represents the angle of attack. The error gain coefficient represents the sideslip angle. The error gain coefficient representing the roll angle; The fractional-order gain coefficient representing the angle of attack; The fractional-order gain coefficient representing the sideslip angle; The fractional-order gain coefficients represent the roll angle; m and n are the exponential-order gain coefficients and satisfy... , For fractional operators, it means that for... beg Order integral, Indicates the order of a fraction. , Furthermore, satisfy:

[0040] in, Indicates the firsti One attitude angle, , ; , and These represent the expected values ​​of the angle of attack, sideslip angle, and roll angle, respectively.

[0041] Step 7: Calculate the expected intermediate control quantity .

[0042] For the fractional-order terminal sliding mode function of equation (16) Differentiation yields: (17) in, This represents the first derivative of the sliding mode function; express The first derivative; Furthermore, to address the chattering problem in sliding mode control, let the reaching law of the sliding mode function be: (18) In the formula, The constant gain coefficient matrix is ​​the approach law matrix. These represent the constant gain coefficients of the first to third reaching-laws, respectively. All are greater than or equal to 0. This is the gain coefficient matrix for the uncertainty term. These represent the gain coefficients for the first to third uncertainty terms, respectively. Correspondingly greater than or equal to ; Let be a saturated function, satisfying: (19) in, Indicates the first One sliding mode function, ; This is the boundary layer thickness, which can be set according to actual needs. It is typically set to... =0.01 can meet the requirements for high precision.

[0043] From equation (15), we can obtain: (20) in, express The first derivative; express The second derivative; express The second derivative of .

[0044] From equations (11) and (12), we can obtain: (twenty one) Therefore, the desired intermediate control quantity can be obtained from equations (17)-(21). for: (twenty two) Step 8: Obtain torque commands based on the state of the spacecraft Based on torque command and expected intermediate control quantity Request rudder deflection command .

[0045] Specifically, the torque command can be obtained from equation (10). for: (twenty three) Substituting equation (23) into equation (7) yields the rudder deflection command. for: (twenty four).

[0046] Step 9: Execute control commands.

[0047] Furthermore, the rudder deflection command Input the actuator model to obtain the current actual control deflection angle; input the current actual control deflection angle, current angle of attack, sideslip angle, roll angle, velocity, reference area, reference length, and atmospheric density of the aerospace vehicle into the aerodynamic moment model to calculate the torque of the aerospace vehicle at the current moment; then substitute the torque at the current moment into the attitude dynamics model of the aerospace vehicle to obtain the state of the aerospace vehicle at the next moment, where the attitude angle of the aerospace vehicle is obtained by integrating the first derivative of its attitude angle.

[0048] The simulation process involves determining whether the spacecraft's state at the next moment meets the convergence condition. If not, the state of the spacecraft at the next moment is set to the current state. Steps seven, eight, and nine are repeated until the convergence condition is met, thus achieving finite-time convergent control over the spacecraft's state. The convergence condition is the divergence of the spacecraft's attitude control, i.e., the divergence of the spacecraft's true attitude angles: angle of attack, sideslip angle, and roll angle, or the end of the control time. At the start of the simulation, the initial state of the spacecraft is given by initial values.

[0049] The state of the aerospace vehicle of this invention includes a system drift term matrix. F Control distribution matrix EAngle of attack, sideslip angle, roll angle, derivatives of angle of attack, derivatives of sideslip angle, derivatives of roll angle, roll rate, pitch rate, yaw rate, derivatives of roll rate, derivatives of pitch rate, derivatives of yaw rate, etc.; each derivative includes the first derivative and the second derivative.

[0050] The method of this invention first substitutes the state variables from the attitude dynamics model into a second-order linearized control model and an extended state observer. Then, the second-order linearized control model, combined with the desired attitude angle, constructs a fractional-order terminal sliding mode function. Next, using the fractional-order terminal sliding mode function, the error estimate of the second-order linearized control model obtained from the extended state observer, and the desired attitude angle, the desired intermediate control variable is obtained. Then, the desired intermediate control variable and the current state of the spacecraft are used to derive the rudder deflection command, which is then substituted into the actuator model to obtain the current rudder deflection angle. The current rudder deflection angle and the spacecraft state variables are then substituted into the aerodynamic moment model to obtain the aerodynamic moment. Finally, the aerodynamic moment is substituted into the attitude dynamics model to achieve a closed-loop attitude control.

[0051] Figure 2 Except for the key parameters that need to be compared, all other simulation conditions remain the same. For example... Figure 2 As shown, this invention achieves better convergence, while existing fractional sliding mode control methods fail to converge under the same gain conditions. Increasing the gain to overcome errors caused by the actuator model, while preventing divergence, results in a larger control error and worse control performance compared to the method proposed in this invention.

[0052] like Figure 3 As shown, existing methods exhibit divergence in normal gain rudder deflection angle. While existing methods overcome this divergence by increasing the gain, they suffer from significant fluctuations, resulting in a worse control effect compared to the method proposed in this invention.

[0053] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for space vehicle attitude control based on fractional order sliding mode considering actuators, characterized in that, Includes the following steps: Step S1: Establish the attitude dynamics model, aerodynamic torque model, and actuator model of the spacecraft with parameter uncertainties and aggregated disturbances; based on the feedback linearization method, integrate the attitude dynamics model, aerodynamic torque model, and actuator model to construct a second-order linearized attitude control model. Step S2: For the second-order linearized attitude control model, design an extended state observer to estimate the composite disturbance of attitude angular acceleration in the second-order linearized attitude control model in real time. Step S3: Establish a fractional-order terminal sliding mode function with finite-time convergence; Step S4: Based on the current state of the spacecraft, the composite disturbance estimate of the current attitude angular acceleration obtained by the fractional-order terminal sliding mode function with finite-time convergence and the extended state observer, the current expected intermediate control quantity is obtained by combining the second-order linearized attitude control model and using the approach law containing the saturation function. Step S5: Based on the current expected intermediate control quantity and the current state of the spacecraft, calculate the current rudder deflection command; based on the current rudder deflection command, apply it to the actuator model, aerodynamic torque model and attitude dynamics model to obtain the state of the spacecraft at the next moment. Step S6: Determine whether the state of the spacecraft at the next moment meets the convergence condition. If the convergence condition is not met, set the state of the spacecraft at the next moment to the current state of the spacecraft and return to step S4. If the convergence condition is met, realize the finite-time convergence control of the state of the spacecraft.

2. The attitude control method for aerospace vehicles according to claim 1, characterized in that, The state of the aerospace vehicle includes a system drift term matrix F , a control distribution matrix E , an angle of attack, a sideslip angle, a roll angle, a derivative of the angle of attack, a derivative of the sideslip angle, a derivative of the roll angle, a roll rate, a pitch rate, a yaw rate, a derivative of the roll rate, a derivative of the pitch rate, and a derivative of the yaw rate.

3. The attitude control method for aerospace vehicles according to claim 1, characterized in that, The expression for the attitude dynamics model of the aerospace vehicle with parameter uncertainties and convergence perturbations in step S1 is as follows: in, For the angle of attack, Sideslip angle, For roll angle, For the roll rate, For pitch rate, The yaw rate, The first derivative of the angle of attack is represented by... The first derivative represents the sideslip angle. The first derivative of the roll angle is given by... The first derivative of the roll rate. The first derivative of the pitch rate. The first derivative of the yaw rate; For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles Moment of inertia in the axial direction, For aerospace vehicles in Aerodynamic torque in the axial direction, For aerospace vehicles Aerodynamic torque in the axial direction, For aerospace vehicles in Aerodynamic torque in the axial direction, , , , , and All are aggregation perturbations.

4. The attitude control method for aerospace vehicles according to claim 3, characterized in that, The expression for the aerodynamic moment model of the spacecraft in step S1 is: In the formula, For the aerodynamic torque of aerospace vehicles; These represent the elements in the first row and first column to the third row and third column of the attitude angle-related aerodynamic moment coefficient matrix. These represent the elements in the first row and first column of the aerodynamic moment coefficient matrix related to the rudder deflection angle, from the elements in the first row and first column to the elements in the third row and third column. For the angle of attack; Sideslip angle; For roll angle; , , They represent x , y and z rudder deflection angle of the shaft, Atmospheric density, For the speed of aerospace vehicles, For reference area of ​​aerospace vehicles, This is a reference length for aerospace vehicles.

5. The attitude control method for aerospace vehicles according to claim 1, characterized in that, The expression for the actuator model of the aerospace vehicle in step S1 is: In the formula, The transfer function representing the actuator model; Represents the Laplace operator; Represents the time constant; This indicates damping in a second-order system.

6. The attitude control method for aerospace vehicles according to claim 1, characterized in that, The specific steps in step S5 to obtain the state of the spacecraft at the next moment based on the current rudder deflection angle command and applied to the actuator model, aerodynamic moment model, and attitude dynamics model are as follows: Input the current rudder deflection command into the actuator model to obtain the actual rudder deflection angle of the spacecraft; then input the actual rudder deflection angle, the current angle of attack, sideslip angle, roll angle, velocity, and the reference area, reference length, and atmospheric density of the spacecraft into the aerodynamic moment model to calculate the torque acting on the spacecraft at the current moment; finally, input the torque acting on the spacecraft at the current moment into the attitude dynamics model to obtain the state of the spacecraft at the next moment.

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