Attitude constraint control method for wide-range reentry vehicle under dynamic pressure adaptive torque distribution

Abstract

The application discloses a wide-range reentry vehicle attitude constraint control method based on dynamic pressure adaptive torque distribution. The real-time aerodynamic moment is solved by relying on the aerodynamic fitting model, and the positive definite diagonal adaptive weight matrix is updated in combination with the dynamic pressure. The attitude and angular velocity of the vehicle are collected, and the attitude kinematics matrix and global torque mapping matrix are solved. The attitude tracking error, expected attitude angular velocity, angular velocity, attitude kinematics matrix and aerodynamic moment are input into an integrated backstepping control law, and the expected control torque is output. The expected torque, real-time torque and positive definite diagonal adaptive weight matrix are relied on to build a quadratic programming cost function to solve the optimal execution instruction, and the instruction amplitude is constrained by the saturation clamping according to the hardware limit, and the execution input vector is output to realize the closed-loop regulation and control of the whole airspace attitude. The attitude loop and the torque distribution module are integrated and coupled, the reentry strong aerodynamic disturbance tracking error can be effectively inhibited, the execution mechanism saturation and load distribution imbalance defects can be relieved, and the wide-range variable working condition reentry task can be adapted.

Description

Technical Field

[0001] This invention relates to the field of aircraft attitude control, and more specifically to a method for wide-range reentry vehicle attitude constraint control under dynamic pressure adaptive torque distribution. Background Technology

[0002] When lifting-body reentry vehicles perform transatmospheric return missions, their flight altitude, Mach number, and angle of attack vary greatly, and their flight pressure can fluctuate significantly between 1000 Pa and 60000 Pa. The complex and variable external airflow environment causes the vehicle's aerodynamic characteristics to exhibit strong nonlinearity, multivariable coupling, and significant time-varying features, greatly increasing the design difficulty of attitude stability control across the entire airspace. These vehicles generally employ a redundant control scheme combining aerodynamic control surfaces and RCS thrust nozzles. The X-33-like vehicle is a typical example, equipped with eight aerodynamic control surfaces and eight thrust nozzles, forming a sixteen-dimensional fully redundant actuator. Relying on the coordinated output torque of these two types of actuators, it completes attitude correction and trajectory tracking throughout the entire flight.

[0003] Existing torque distribution and closed-loop attitude control technologies for redundant actuators have multiple inherent defects, making it difficult to adapt to the high-precision reentry control requirements under large changes in operating conditions and strong external disturbances. These drawbacks can be summarized into four categories:

[0004] (1) Insufficient fidelity in aerodynamic modeling of actuators. Most existing studies simplify the actuator configuration to reduce computational overhead, but cannot reproduce the sixteen-dimensional fully redundant control layout of the X-33. In modeling, constant torque mapping matrices are generally used to describe the aerodynamic control efficiency, without fitting time-varying control efficiency coefficients related to angle of attack and Mach number based on wind tunnel measured data, and ignoring the objective law of control efficiency drift with flight parameters during wide-range flight. At the same time, existing schemes establish two independent models for RCS geometric mapping and aerodynamic control mapping, and there is no unified sixteen-dimensional composite actuator mapping framework. The simplified model has obvious deviations from the aerodynamic characteristics of the real aircraft, and the simulation conclusions have low engineering reuse value.

[0005] (2) The torque distribution optimization algorithm has weak adaptability under different working conditions. The mainstream distribution methods in the industry include fixed weight quadratic programming, pseudo-inverse distribution, etc. The weight parameters and constraint thresholds are all fixed offline, and it is impossible to dynamically adjust the output ratio of RCS and aerodynamic rudder according to real-time dynamic pressure. Even the few improved schemes that adopt segmented weight switching will introduce torque disturbance due to the step change of weight, which will destroy the closed-loop attitude stability.

[0006] (3) The control levels are decoupled from each other, resulting in insufficient collaborative control capabilities. Most current technologies separate the attitude control law and torque distribution algorithm into completely independent units. During the design phase, the coupling interference of time-varying pressure and hardware saturation nonlinearity on the closed loop is not comprehensively considered. A few integrated solutions simply stack modules without constructing complete linkage control logic. The real-time aerodynamic parameters output from the underlying model cannot be passed up to the distribution algorithm to participate in iterative optimization, making it difficult to fully utilize the collaborative manipulation potential of redundant actuators, and the system control performance has an upper limit.

[0007] (4) The technical solutions are fragmented and singular, lacking a complete engineering support design. Most of the published literature only focuses on optimizing a single module, or only improves the upper-level attitude control law, or optimizes the torque distribution strategy separately, lacking a complete integrated solution from bottom-level modeling to closed-loop stability proof. Most algorithms do not incorporate the hardware output limits of RCS thrust and rudder deflection angle, and the theoretically optimal commands obtained often exceed the physical limits of the mechanism, remaining only at the theoretical simulation level and difficult to be directly used for the development of aircraft models.

[0008] In summary, traditional technologies suffer from multiple bottlenecks, including modeling distortion, static and fixed weight allocation, lack of control-level linkage, and poor engineering adaptability. The underlying constant mapping modeling and the upper-level static / segmented weight allocation are disconnected, making it impossible to meet the development needs of high-precision attitude control for new-generation lifting body aircraft under complex conditions across the entire airspace. Summary of the Invention

[0009] The purpose of this application is to propose a method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution to address the aforementioned technical problems.

[0010] In a first aspect, the present invention provides a method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution, comprising the following steps:

[0011] Establish a torque coefficient fitting equation based on Mach number and angle of attack, and construct an aerodynamic torque calculation model based on dynamic pressure; construct the attitude kinematic model and attitude dynamics model of the aircraft; construct the control law corresponding to the backstepping controller based on the attitude kinematic model and attitude dynamics model;

[0012] Obtain the dynamic pressure at the current moment and calculate the positive definite diagonal adaptive weight matrix at the current moment. Calculate the aerodynamic torque at the current moment based on the dynamic pressure and aerodynamic torque calculation model at the current moment.

[0013] The attitude, desired attitude, and angular velocity of the aircraft at the current moment are obtained, and the attitude tracking error at the current moment and the first derivative of the desired attitude with respect to time are calculated. The attitude kinematic matrix at the current moment is calculated based on the attitude at the current moment.

[0014] Obtain the aircraft's Mach number and angle of attack at the current moment, and calculate the global moment mapping matrix at the current moment by combining the moment coefficient fitting equation; use the global moment mapping matrix at the current moment to calculate the control moment at the current moment;

[0015] The current attitude tracking error, the first derivative of the desired attitude with respect to time, angular velocity, attitude kinematic matrix, and aerodynamic torque are input into the control law corresponding to the backstep controller, which outputs the desired control torque at the current moment. A cost function is constructed based on the desired control torque, control torque, and positive definite diagonal adaptive weight matrix at the current moment. The optimal execution input vector is obtained by minimizing the cost function under unconstrained conditions. The optimal execution input vector is clamped and constrained to obtain the final execution input vector. The final execution input vector is input into the aircraft's actuators for execution to adjust the aircraft's attitude at the next moment so that it reaches the desired attitude.

[0016] Preferably, the aircraft's attitude is expressed using Euler angle vectors. To represent, where, For roll angle, The pitch angle, Let yaw angle be yaw angle, and T denote the transpose of the matrix;

[0017] The posture kinematic model is represented as:

[0018] ;

[0019] in, This represents the first derivative of the Euler angle vector with respect to time. Indicates angular velocity, For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; The attitude kinematics matrix is ​​expressed as follows:

[0020] ;

[0021] The attitude dynamics model is represented as follows:

[0022] ;

[0023] in, Represents the moment of inertia matrix. Represents a diagonal matrix. These are the roll axes of the aircraft around its fuselage. Pitch axis yaw axis The moment of inertia of the main shaft; Angular acceleration, Indicates aerodynamic torque. Indicates control torque. The antisymmetric matrix of the cross product of angular velocities is defined as:

[0024] .

[0025] As a preferred option, the expression for the aerodynamic torque calculation model is:

[0026] ;

[0027] in, For dynamic pressure, For the reference area of ​​the aircraft wing, For wingspan, The mean aerodynamic chord of the wing. These are the column vectors of moment coefficients corresponding to the roll axis, pitch axis, and yaw axis, respectively.

[0028] As a preferred embodiment, the control torque is expressed as:

[0029] ;

[0030] in, This represents the execution input vector corresponding to all actuators of the aircraft. Indicates the first The execution input variables of each actuator, The aircraft's actuators include 8 sets of RCS nozzles and 8 aerodynamic control surfaces. This refers to the thrust of the first group of RCS nozzles, and the second through eighth groups of RCS nozzles. This indicates the deflection angle of the first, second, through eighth aerodynamic rudders; This is the global torque mapping matrix. For the angle of attack of the aircraft, Represents the Mach number;

[0031] The global moment mapping matrix is ​​an RCS submatrix and aerodynamic rudder matrix It is constructed by vertical splicing, as shown in the following formula:

[0032] ;

[0033] The RCS submatrix is ​​represented as:

[0034] ;

[0035] in, Indicates the first The unit thrust of the RCS nozzle group is respectively at the roll axis Pitch axis yaw axis The resulting torque coefficients are all constant values. ;

[0036] The aerodynamic rudder matrix is ​​represented as:

[0037] ;

[0038] in, For the first The unit deflection angle of the blade aerodynamic rudder at the roll axis Pitch axis yaw axis The corresponding torque coefficient;

[0039] No. The unit deflection angle of the aerodynamic rudder is respectively at the th The moment coefficient corresponding to the shaft is calculated using the following moment coefficient fitting equation:

[0040] ;

[0041] in, Corresponding to the roll axis Pitch axis yaw axis ; and These are the polynomial powers of the angle of attack and the Mach number, respectively. and These are the highest-order powers of the polynomials for angle of attack and Mach number, respectively. is the least squares fitting constant.

[0042] Preferably, the control law corresponding to the backstepping controller includes a virtual angular velocity control law and a desired control torque control law. The construction process of the control law corresponding to the backstepping controller is as follows:

[0043] Define attitude tracking error as Its expression is ; Define angular velocity tracking error as Its expression is ,in, Indicates the desired posture, This refers to virtual angular velocity;

[0044] Taking the first derivative of the attitude tracking error with respect to time and substituting it into the attitude kinematics model, we obtain the following equation:

[0045] ;

[0046] in, This represents the first derivative of the attitude tracking error with respect to time. This represents the first derivative of attitude with respect to time. This represents the first derivative of the desired attitude with respect to time.

[0047] The virtual angular velocity control law is designed as follows:

[0048] ;

[0049] in, For attitude kinematics matrix The inverse matrix, The positive definite gain matrix of the attitude loop. These represent the adjustable gain parameters corresponding to roll angle, pitch angle, and yaw angle, respectively.

[0050] Substituting the virtual angular velocity The attitude error dynamic model is obtained as follows:

[0051] ;

[0052] Taking the first derivative of the angular velocity tracking error with respect to time and substituting it into the attitude dynamics model, we obtain the following equation:

[0053] ;

[0054] in, This represents the first derivative of the angular velocity tracking error with respect to time. Represents virtual angular acceleration;

[0055] Introducing torque distribution error Its expression is ,in, To achieve the desired control torque; Substitution From this, we obtain the following formula:

[0056] ;

[0057] The desired control torque control law is designed as follows:

[0058] ;

[0059] in, Here is the positive definite gain matrix of the angular velocity loop, where Adjustable gain parameters for roll rate, pitch rate, and yaw rate;

[0060] Substituting the desired control torque control law The dynamic model of angular velocity error is obtained as follows:

[0061] ;

[0062] The attitude error dynamics model and the angular velocity error dynamics model are used to construct a stable closed-loop error system.

[0063] As a preferred option, the construction and solution process of the cost function is as follows:

[0064] The cost function, based on the control objective and hardware constraints, is established in the form of a convex quadratic programming algorithm, as shown in the following equation:

[0065] ;

[0066] in, This represents a positive definite diagonal adaptive weight matrix. Represents the cost function, Represents the diagonal weight matrix. This represents the square of the weighted 2-norm;

[0067] Expanding the cost function in the convex quadratic programming form, we obtain the cost function as shown in the following equation:

[0068] ;

[0069] Under unconstrained conditions, there exists a first-order necessary condition: ;

[0070] Solving the cost function by taking its first derivative with respect to time and combining it with the first necessary condition, we obtain the following equation:

[0071] ;

[0072] The optimal execution input vector is obtained by rearranging and rewriting the above equation, as shown in the following equation:

[0073] .

[0074] As a preferred method, the final calculation process for the execution input vector is as follows:

[0075] By performing channel-by-channel amplitude limiting correction on the execution input variables corresponding to each actuator in the optimal execution input vector, the execution input variables corresponding to each actuator in the final execution input vector are obtained, as shown in the following formula:

[0076] ;

[0077] in, This represents the first element in the optimal execution input vector. The execution input variables corresponding to each actuator Indicates the execution of the first element in the input vector. The lower limit value of the execution input variable corresponding to each actuator. Indicates the execution of the first element in the input vector. The upper limit of the execution input variables corresponding to each actuator; This represents the first element in the final execution input vector. The execution input variables corresponding to each actuator; This represents the amplitude limiting function.

[0078] As a preferred embodiment, the construction process of the positive definite diagonal adaptive weight matrix is ​​as follows:

[0079] The positive definite diagonal adaptive weight matrix is ​​a diagonal matrix consisting of 8 sets of RCS weights and 8 sets of aerodynamic rudder weights, which are filled with diagonal elements in sequence.

[0080] The RCS weights are represented as follows:

[0081] ;

[0082] in, Represents the RCS weight. This represents the maximum value of the RCS weight. This indicates the maximum value of the dynamic pressure. Indicates dynamic pressure;

[0083] Aerodynamic rudder weights are expressed as:

[0084] ;

[0085] in, Indicates the weight of the aerodynamic rudder. This represents the maximum value of the aerodynamic rudder weight.

[0086] As a preferred method, the calculation process for the dynamic pressure at the current moment is as follows:

[0087] Obtain the atmospheric density corresponding to the aircraft's current flight speed and current altitude, and calculate the dynamic pressure at the current moment.

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] (1) The attitude constraint control method for wide-domain reentry vehicles under dynamic pressure adaptive torque distribution mentioned in this invention builds a high-precision continuous torque coefficient fitting equation and aerodynamic torque calculation model based on full-space wind tunnel test data, fully reproduces the configuration of 16-channel redundant actuators, and reduces the deviation between the simulation environment and the actual flight conditions; the control torque and aerodynamic torque are calculated using the torque coefficient fitting equation and aerodynamic torque calculation model, and the attitude kinematic model and attitude dynamic model are constructed on the basis of the attitude kinematic matrix. A continuous complementary positive definite diagonal adaptive weight matrix driven by real-time dynamic pressure is designed, the piecewise threshold structure is discarded, and the instantaneous disturbance caused by weight switching is eliminated.

[0090] (2) The attitude constraint control method for wide-domain reentry vehicles under dynamic pressure adaptive torque distribution mentioned in this invention constructs an integrated closed-loop framework for attitude control and quadratic programming torque distribution, breaking the traditional design of complete decoupling between attitude control and torque distribution. It fully considers the loop coupling interference caused by dynamic pressure time-varying and mechanism saturation, and improves the coordinated control capability under all working conditions. After obtaining the optimal execution input vector using the quadratic programming method, the out-of-limit data is uniformly constrained according to the hardware limits of rudder deflection and thrust. Under the premise of preserving the optimality of distribution, the final output execution input vector matches the physical boundary of the mechanism, solving the problem that the theoretically optimal execution input vector exceeds the hardware threshold and cannot be directly applied to the aircraft model.

[0091] (3) The attitude constraint control method for wide-range reentry vehicles under dynamic pressure adaptive torque distribution mentioned in this invention completes the stability derivation with the help of Lyapunov theory, and proves that it can achieve final uniform bounded convergence under the superposition of aerodynamic disturbance and saturation error. It can also improve the accuracy of three-axis attitude tracking error, reduce the saturation frequency of actuators, reduce fuel consumption, make up for the shortcomings of traditional fixed weight distribution algorithms, adapt to a wide range of variable working conditions and strong disturbance reentry flight environment, and can be transferred to various lifting body aircraft of the same series, providing a complete engineering control solution with high precision and strong robustness. Attached Figure Description

[0092] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0093] Figure 1 This is a flowchart illustrating a wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution, as an embodiment of this application.

[0094] Figure 2 This is a block diagram of the overall architecture of the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution, which is an embodiment of this application.

[0095] Figure 3 This is a graph showing the variation of the three-axis attitude tracking error of the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to an embodiment of this application under nominal operating conditions. Figure 3 (a) in the graph represents the change curve of the attitude tracking error of the roll axis. Figure 3 (b) in the figure represents the curve showing the change in attitude tracking error along the pitch axis. Figure 3(c) in the figure represents the curve showing the change in attitude tracking error of the yaw axis;

[0096] Figure 4 This is a graph showing the variation of the three-axis angular velocity tracking error of the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to an embodiment of this application under nominal operating conditions. Figure 4 (a) in the graph represents the variation curve of the angular velocity tracking error of the roll axis. Figure 4 (b) in the figure represents the curve showing the change in the pitch axis angular velocity tracking error. Figure 4 (c) in the figure represents the curve showing the change in the angular velocity tracking error of the yaw axis;

[0097] Figure 5 The graph shows the variation of the Lyapunov function of the closed-loop error system of the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution, as an embodiment of this application.

[0098] Figure 6 This is a graph showing the variation of the three-axis torque distribution error of the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to an embodiment of this application under nominal operating conditions. Figure 6 (a) in the graph represents the variation curve of the torque distribution error of the rolling shaft. Figure 6 (b) in the figure represents the curve showing the change in the pitch axis torque distribution error. Figure 6 (c) in the figure represents the curve showing the change in the torque distribution error of the yaw axis;

[0099] Figure 7 This is a comparison curve of the three-axis torque distribution error between the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to the embodiments of this application and the traditional fixed-weight quadratic programming scheme under the same reentry condition. Figure 7 (a) in the figure represents a comparison curve of the torque distribution error of the rolling shaft. Figure 7 (b) in the figure represents a comparison curve of the pitch axis torque distribution error. Figure 7 (c) in the figure represents a comparison curve of the torque distribution error of the yaw axis;

[0100] Figure 8 This is a bar chart comparing the actuator saturation rate and relative control energy consumption of the wide-domain reentry vehicle attitude constraint control method under dynamic adaptive torque distribution according to embodiments of this application with that of the traditional fixed-weight quadratic programming scheme. Figure 8 (a) in the chart represents a comparison of actuator saturation rates. Figure 8 (b) in the figure represents a comparative bar chart of relative control energy consumption;

[0101] Figure 9The figure shows a comparison of the maximum three-axis attitude tracking error between the wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution of the embodiments of this application under four typical reentry profiles and the traditional fixed-weight quadratic programming scheme. Detailed Implementation

[0102] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0103] Figure 1 This application illustrates an embodiment of a wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution, comprising the following steps:

[0104] S1. Establish the torque coefficient fitting equation based on Mach number and angle of attack, and construct the aerodynamic torque calculation model based on dynamic pressure; construct the attitude kinematic model and attitude dynamics model of the aircraft; construct the control law corresponding to the backstepping controller based on the attitude kinematic model and attitude dynamics model.

[0105] In a specific embodiment, the expression for the aerodynamic torque calculation model is as follows:

[0106] ;

[0107] in, For dynamic pressure, For the reference area of ​​the aircraft wing, For wingspan, The mean aerodynamic chord of the wing. These are the column vectors of moment coefficients corresponding to the roll axis, pitch axis, and yaw axis, respectively.

[0108] Specifically, the aircraft in the embodiments of this application takes the X-33-like aircraft as an example. The X-33-like aircraft includes 8 sets of RCS thrust nozzles and 8 aerodynamic rudders, and uses the 8 sets of RCS thrust nozzles and 8 aerodynamic rudders as actuators to achieve a 16-dimensional fully redundant actuator layout.

[0109] The embodiments of this application directly utilize NASA's publicly available complete wind tunnel test dataset during the modeling phase, collecting discrete data on the torque coefficients of the aircraft under different combinations of Mach numbers and angles of attack. A multivariate polynomial regression fitting method is used to construct torque coefficient fitting equations with Mach number and angle of attack as independent variables. Furthermore, the fitting accuracy of the torque coefficient fitting equations is verified by cross-referencing the discrete data with the curves corresponding to the torque coefficient fitting equations.

[0110] After the above-mentioned multi-source polynomial fitting modeling of the entire channel, the torque coefficient column vector corresponding to the roll axis can be obtained in batches. Column vector of moment coefficients corresponding to the pitch axis The column vector of moment coefficients corresponding to the yaw axis To achieve the conversion of dimensionless torque coefficients into real physical torques usable in aircraft dynamics, a high-precision, continuous aerodynamic torque calculation model is constructed. This abandons the traditional idealized constant parameter modeling mode and maximizes the reproduction of real flight aerodynamic characteristics. The aerodynamic torque calculated using this model can be embedded as a feedforward compensation term into the corresponding control law of the backstepping controller to offset time-varying aerodynamic disturbances in real time and reduce the torque distribution adjustment load. The aerodynamic field constructed based on measured data provides a realistic simulation environment, overcoming the shortcomings of traditional models that rely on ideal assumptions, suffer from simulation distortion, and have poor global adaptability. The polynomial coefficients are pre-calibrated offline, and only simple algebraic operations are performed during airborne operation, resulting in low computational overhead, strong real-time performance, and compatibility with embedded airborne control programs.

[0111] In a specific embodiment, the aircraft's attitude is expressed using Euler angle vectors. To represent, where, For roll angle, The pitch angle, Let yaw angle be yaw angle, and T denote the transpose of the matrix;

[0112] The posture kinematic model is represented as:

[0113] ;

[0114] in, This represents the first derivative of the Euler angle vector with respect to time. Indicates angular velocity. For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; The attitude kinematics matrix is ​​expressed as follows:

[0115] ;

[0116] The attitude dynamics model is expressed as:

[0117] ;

[0118] in, Represents the moment of inertia matrix. Represents a diagonal matrix. These are the roll axes of the aircraft around its fuselage. Pitch axis yaw axis The moment of inertia of the main shaft; Angular acceleration, Indicates aerodynamic torque. Indicates control torque. The antisymmetric matrix of the cross product of angular velocities is defined as:

[0119] .

[0120] Specifically, embodiments of this application utilize attitude kinematics matrices to construct attitude kinematics models. Within the normal reentry attitude range... Therefore, the attitude kinematics matrix Since it is a non-singular matrix, its inverse matrix exists, and therefore it can be used to design the control law corresponding to the subsequent backstepping controller.

[0121] The dynamics of an aircraft rotating about its center of mass are described by the Euler equations. Let the moment of inertia matrix be... For X-33-like aircraft, , , This characterizes the magnitude of the three-axis attitude rotational inertia of an aircraft; because the fuselage of an X-33-like aircraft along... Symmetrical, the moment of inertia matrix is ​​a diagonal matrix with the three elements as diagonal elements. It is the core intrinsic mass parameter for constructing six-degree-of-freedom attitude dynamics and designing upper-level attitude controllers and lower-level torque distribution algorithms.

[0122] Considering that the gravitational gradient torque is negligible, the external torques acting on the aircraft include aerodynamic torques. (Aircraft aerodynamic characteristics when rudder deflection is zero) and the control torque generated by the RCS thrust nozzle and aerodynamic rudder together. This led to the construction of an attitude dynamics model. The formula of this attitude dynamics model clearly separates the open-loop body dynamics from the closed-loop control effect, laying the foundation for the design of subsequent control allocation and backstepping controller.

[0123] In a specific embodiment, the control law corresponding to the backstepping controller includes a virtual angular velocity control law and a desired control torque control law. The construction process of the control law corresponding to the backstepping controller is as follows:

[0124] Define attitude tracking error as Its expression is ; Define angular velocity tracking error as Its expression is ,in, Indicates the desired posture, This refers to virtual angular velocity;

[0125] Taking the first derivative of the attitude tracking error with respect to time and substituting it into the attitude kinematics model, we obtain the following equation:

[0126] ;

[0127] in, This represents the first derivative of the attitude tracking error with respect to time. This represents the first derivative of attitude with respect to time. This represents the first derivative of the desired attitude with respect to time.

[0128] The virtual angular velocity control law is designed as follows:

[0129] ;

[0130] in, For attitude kinematics matrix The inverse matrix, The positive definite gain matrix of the attitude loop. These represent the adjustable gain parameters corresponding to roll angle, pitch angle, and yaw angle, respectively.

[0131] Substituting the virtual angular velocity The attitude error dynamic model is obtained as follows:

[0132] ;

[0133] Taking the first derivative of the angular velocity tracking error with respect to time and substituting it into the attitude dynamics model, we obtain the following equation:

[0134] ;

[0135] in, This represents the first derivative of the angular velocity tracking error with respect to time. Represents virtual angular acceleration;

[0136] Introducing torque distribution error Its expression is ,in, To achieve the desired control torque; Substitution From this, we obtain the following formula:

[0137] ;

[0138] The desired control torque control law is designed as follows:

[0139] ;

[0140] in, Here is the positive definite gain matrix of the angular velocity loop, where Adjustable gain parameters for roll rate, pitch rate, and yaw rate;

[0141] Substituting the desired control torque control law The dynamic model of angular velocity error is obtained as follows:

[0142] ;

[0143] The attitude error dynamics model and the angular velocity error dynamics model are used to construct a stable closed-loop error system.

[0144] Specifically, the embodiments of this application define two types of state variables, attitude tracking error and angular velocity tracking error, based on backstepping control theory. The attitude tracking error is dynamically calibrated by relying on virtual angular velocity. Simultaneously, auxiliary control terms such as gyro coupling torque compensation, aerodynamic feedforward compensation, angular acceleration feedforward compensation, and damping compensation are introduced to optimize the dynamic response quality and finally calculate the desired control torque.

[0145] Define the desired attitude of the aircraft as The desired attitude is a slowly varying signal, with its first and second derivatives being continuous and bounded. The goal of attitude control is to adjust the aircraft's attitude. Precise tracking of desired attitude The embodiments of this application employ a backstepping method to design the control law corresponding to the backstepping controller. This control law includes a virtual angular velocity control law and a desired control torque control law. The virtual angular velocity control law enables the aircraft's angular velocity to accurately track the virtual angular velocity. First, the virtual angular velocity is calculated using the virtual angular velocity control law, and then the desired control torque is calculated using the desired control torque control law. The physical meaning of each component in the desired control torque control law is as follows: First term... Used to counteract the nonlinear gyroscopic coupling torque of the aircraft body; second term Used to counteract the effects of aerodynamic torque, achieving aerodynamic feedforward compensation; the third item The feedforward compensation term for angular acceleration; the fourth term The main damping term drives the convergence of angular velocity tracking error; the fifth term... Used to compensate for kinematic coupling, ensuring that cross terms cancel each other out in subsequent stability proofs.

[0146] First, the virtual angular velocity is calculated using the virtual angular velocity control law based on the attitude tracking error, the first derivative of the desired attitude with respect to time, and the attitude kinematics matrix. Then, the angular velocity tracking error is calculated based on the angular velocity and the virtual angular velocity, and the first derivative of the angular velocity tracking error with respect to time is obtained. Finally, the desired control torque for all three axes is output using the desired control torque control law based on the angular velocity, the first derivative of the angular velocity tracking error with respect to time, the aerodynamic torque, the attitude tracking error, and the attitude kinematics matrix. .

[0147] Further construction yields attitude error dynamics and angular velocity error dynamics, which together constitute a closed-loop error system. From the formula of the angular velocity error dynamics model, it can be seen that: when the torque distribution error... The dynamic model of the angular velocity error transforms into an asymptotically stable linear error system; when When this occurs, it can be considered as an externally bounded disturbance.

[0148] S2, obtain the dynamic pressure at the current moment and calculate the positive definite diagonal adaptive weight matrix at the current moment, and calculate the aerodynamic torque at the current moment based on the dynamic pressure and aerodynamic torque calculation model at the current moment.

[0149] In a specific embodiment, the calculation process for the dynamic pressure at the current moment is as follows:

[0150] Obtain the atmospheric density corresponding to the aircraft's current flight speed and current altitude, and calculate the dynamic pressure at the current moment.

[0151] Specifically, the dynamic pressure mentioned in the embodiments of this application can be calculated using the following formula:

[0152] ;

[0153] In the formula, This represents the atmospheric density at the aircraft's current altitude. The real-time flight speed of the aircraft; dynamic pressure The unit of measurement is Pascal. The embodiments of this application are adapted to the complete reentry envelope of the aircraft, covering the dynamic pressure variation range. The dynamic pressure in the middle of the interval can be taken as the reference benchmark for dividing the high and low airspace operating conditions.

[0154] In a specific embodiment, the construction process of the positive definite diagonal adaptive weight matrix is ​​as follows:

[0155] The positive definite diagonal adaptive weight matrix is ​​a diagonal matrix consisting of 8 sets of RCS weights and 8 sets of aerodynamic rudder weights, which are filled with diagonal elements in sequence.

[0156] The RCS weights are represented as follows:

[0157] ;

[0158] in, Represents the RCS weight. This represents the maximum value of the RCS weight. This indicates the maximum value of the dynamic pressure. Indicates dynamic pressure;

[0159] Aerodynamic rudder weights are expressed as:

[0160] ;

[0161] in, Indicates the weight of the aerodynamic rudder. This represents the maximum value of the aerodynamic rudder weight.

[0162] Specifically, this invention employs two sets of continuous, non-jumping, complementary weights for real-time dynamic pressure drive, namely RCS weights and aerodynamic rudder weights, and combines eight identical RCS weights. 8 sets of identical aerodynamic rudder weights By sequentially filling in the diagonal elements, a 16th-order positive definite diagonal adaptive weight matrix is ​​constructed. As shown in the following formula:

[0163] .

[0164] Furthermore, the calculated dynamic pressure at the current moment is substituted into the aerodynamic torque calculation model constructed in step S1 to calculate the aerodynamic torque at the current moment.

[0165] S3: Obtain the aircraft's attitude, desired attitude, and angular velocity at the current moment, and calculate the attitude tracking error at the current moment and the first derivative of the desired attitude with respect to time. Calculate the attitude kinematic matrix at the current moment based on the current attitude.

[0166] Specifically, in the embodiments of this application, the current attitude, desired attitude, and angular velocity are first obtained. The attitude tracking error at the current moment is calculated using the current attitude and desired attitude, and the first derivative of the desired attitude is obtained. Then, the attitude kinematic matrix is ​​calculated using the current attitude. .

[0167] S4: Obtain the Mach number and angle of attack of the aircraft at the current moment, and calculate the global moment mapping matrix at the current moment by combining the moment coefficient fitting equation; use the global moment mapping matrix at the current moment to calculate the control moment at the current moment.

[0168] In a specific embodiment, the control torque is expressed as:

[0169] ;

[0170] in, This represents the execution input vector corresponding to all actuators of the aircraft. Indicates the first The execution input variables of each actuator, The aircraft's actuators include 8 sets of RCS nozzles and 8 aerodynamic control surfaces. This refers to the thrust of the first group of RCS nozzles, and the second through eighth groups of RCS nozzles. This indicates the deflection angle of the first, second, through eighth aerodynamic rudders; This is the global torque mapping matrix. For the angle of attack of the aircraft, Represents the Mach number;

[0171] The global moment mapping matrix is ​​an RCS submatrix and aerodynamic rudder matrix It is constructed by vertical splicing, as shown in the following formula:

[0172] ;

[0173] The RCS submatrix is ​​represented as:

[0174] ;

[0175] in, Indicates the first The unit thrust of the RCS nozzle group is respectively at the roll axis Pitch axis yaw axis The resulting torque coefficients are all constant values. ;

[0176] The aerodynamic rudder matrix is ​​represented as:

[0177] ;

[0178] in, For the first The unit deflection angle of the blade aerodynamic rudder at the roll axis Pitch axis yaw axis The corresponding torque coefficient;

[0179] No. The unit deflection angle of the aerodynamic rudder is respectively at the th The moment coefficient corresponding to the shaft is calculated using the following moment coefficient fitting equation:

[0180] ;

[0181] in, Corresponding to the roll axis Pitch axis yaw axis ; and These are the polynomial powers of the angle of attack and the Mach number, respectively. and These are the highest-order powers of the polynomials for angle of attack and Mach number, respectively. is the least squares fitting constant.

[0182] Specifically, the RCS nozzle installation position, spray direction, and lever arm are all fixed mechanical geometric parameters, and are related to the angle of attack. and Mach number Irrelevant, therefore the RCS submatrix All elements are constants; the aerodynamic control efficiency varies nonlinearly with angle of attack and Mach number; the moment coefficients of the aerodynamic control system per unit deflection angle along the three axes are solved in real time using the moment coefficient fitting equation obtained in step S1; therefore, the aerodynamic control system sub-matrix... This is a time-varying state matrix. The final RCS submatrix will be... with aerodynamic rudder matrix Vertical concatenation yields the global moment mapping matrix. Therefore, once the Mach number and angle of attack at the current moment are obtained, the global moment mapping matrix at the current moment can be calculated. Finally, the control torque at the current moment is calculated using the global torque mapping matrix at the current moment and the execution input vectors corresponding to all actuators of the aircraft to be solved.

[0183] S5 inputs the current attitude tracking error, the first derivative of the desired attitude with respect to time, angular velocity, attitude kinematic matrix, and aerodynamic torque into the control law corresponding to the backstep controller, and outputs the desired control torque at the current moment. Based on the desired control torque, control torque, and positive definite diagonal adaptive weight matrix at the current moment, a cost function is constructed. Under unconstrained conditions, the optimal execution input vector is obtained by minimizing the cost function as the optimization objective. The optimal execution input vector is clamped and constrained to obtain the final execution input vector. The final execution input vector is input into the actuator of the aircraft for execution to adjust the attitude of the aircraft at the next moment so that it reaches the desired attitude.

[0184] Specifically, the calculated attitude tracking error at the current moment, the first derivative of the desired attitude with respect to time, the angular velocity, the attitude kinematic matrix, and the aerodynamic torque are input into the control law corresponding to the backstepping controller to obtain the desired control torque at the current moment. First, the attitude tracking error at the current moment, the first derivative of the desired attitude with respect to time, and the attitude kinematic matrix are input into the virtual angular velocity control law to calculate the virtual angular velocity at the current moment. Based on the current angular velocity and the virtual angular velocity, the angular velocity tracking error at the current moment is calculated, and the first derivative of the current angular velocity tracking error with respect to time is obtained. Then, the current angular velocity, the first derivative of the angular velocity tracking error with respect to time, the aerodynamic torque, the attitude tracking error, and the attitude kinematic matrix are input into the desired control torque control law to obtain the desired control torque. .

[0185] The torque allocation solution must strictly adhere to the actuator output amplitude constraints. The goal is to accurately reproduce the desired control torque while suppressing the command amplitude, reducing system energy consumption, and ensuring smooth output. This is a multi-objective optimization problem with inequality constraints. Compared to traditional methods such as pseudo-inverse and cascade allocation, quadratic programming can uniformly consider tracking accuracy, energy consumption, and hardware constraints. The embodiments of this application use quadratic programming to complete the torque allocation solution.

[0186] In a specific embodiment, the construction and solution processes of the cost function are as follows:

[0187] The cost function, based on the control objective and hardware constraints, is established in the form of a convex quadratic programming algorithm, as shown in the following equation:

[0188] ;

[0189] in, This represents a positive definite diagonal adaptive weight matrix. Represents the cost function, Represents the diagonal weight matrix. This represents the square of the weighted 2-norm;

[0190] Expanding the cost function in the convex quadratic programming form, we obtain the cost function as shown in the following equation:

[0191] ;

[0192] Under unconstrained conditions, there exists a first-order necessary condition: ;

[0193] Solving the cost function by taking its first derivative with respect to time and combining it with the first necessary condition, we obtain the following equation:

[0194] ;

[0195] The optimal execution input vector is obtained by rearranging and rewriting the above equation, as shown in the following equation:

[0196] .

[0197] Specifically, in the cost function of the convex quadratic programming form proposed in the embodiments of this application, the first term is the output weighted penalty term of the actuator, used to smooth control commands and reduce system energy consumption; the second term is the torque distribution error weighted term, ensuring the torque following accuracy of the three-axis control. and All are positive definite symmetric matrices, and the cost function is a strictly convex quadratic function with a unique global optimum. We temporarily ignore the actuator amplitude constraint and focus on minimizing the cost function as the optimization objective. A necessary first-order condition for the extremum of a multivariate convex function is that the gradient of the cost function with respect to the control vector is zero. The gradient represents the instantaneous rate of change of the cost function with respect to the actuator output; even when the gradient is not zero, there is still room for optimization adjustment, but only when the gradient is zero can the global optimum balance between torque tracking and mechanism penalty be achieved.

[0198] Introducing a positive definite diagonal adaptive weight matrix into the cost function of the convex quadratic programming form. The positive definite diagonal adaptive weight matrix The included RCS weights and aerodynamic rudder weights are essentially secondary penalty coefficients for the output of each channel actuator: the smaller the weight value, the looser the constraint on the output amplitude of that channel, and the corresponding actuator takes priority in bearing the control torque; the larger the weight value, the more actively it can suppress the output of that actuator, reducing load occupancy. Combined with... Figure 3 The weighted dynamic pressure change curve is divided into two categories to explain the control logic:

[0199] (1) High-altitude low dynamic pressure condition: real-time dynamic pressure The value is too small. The value is too low. The value is too high. The embodiments of this application relax the RCS thrust constraint and tighten the control surface deflection constraint, prioritizing the generation of control torque based on the RCS to compensate for insufficient control effectiveness at high altitudes. Figure 3 This interval is designated as the RCS-dominant region.

[0200] (2) Low-altitude high dynamic pressure condition: As the flight altitude continues to decrease, the dynamic pressure gradually increases. A linear and steady increase, The synchronous linear reduction occurs. Embodiments of this application progressively strengthen the constraint on RCS output, relax the control surface deflection limit, and switch to aerodynamic rudders bearing the main torque output. Figure 3 This interval is defined as the aerodynamic rudder dominance zone.

[0201] Within the entire dynamic pressure variation range Monotonically increasing The two types of actuators are monotonically decreasing, forming a natural complementary pairing relationship. The weight curves transition smoothly without abrupt inflection points, and the working modes of the two types of actuators can be seamlessly switched, completely avoiding dynamic disturbances such as torque jumps and attitude oscillations caused by segmented weight switching.

[0202] The positive definite diagonal adaptive weight matrix based on dynamic pressure proposed in this application overcomes the inherent defect of traditional fixed weights being unable to adapt to the dynamic pressure-rudder effect coupling relationship from the underlying mechanism. It can dynamically adjust the output ratio of RCS and aerodynamic rudder according to the aerodynamic conditions of the flight airspace, effectively alleviating engineering problems such as torque distribution imbalance and frequent saturation of actuators.

[0203] With cost function Minimize as the optimization objective, and solve for the corresponding theoretically optimal execution input vector. . This is the theoretically optimal execution input vector that minimizes the global cost function under no hardware saturation constraints; the analytical process also embeds the constructed global moment mapping matrix. With positive definite diagonal adaptive weight matrix It only includes matrix multiplication and matrix inversion operations, with a small computational load and a simple operation form. The airborne controller can complete matrix operations in real time to meet the needs of rapid attitude adjustment of the aircraft.

[0204] In a specific embodiment, the final calculation process of the execution input vector is as follows:

[0205] By performing channel-by-channel amplitude limiting correction on the execution input variables corresponding to each actuator in the optimal execution input vector, the execution input variables corresponding to each actuator in the final execution input vector are obtained, as shown in the following formula:

[0206] ;

[0207] in, This represents the first element in the optimal execution input vector. The execution input variables corresponding to each actuator This represents the first element in the final execution input vector. The execution input variables corresponding to each actuator Indicates the execution of the first element in the input vector. The lower limit value of the execution input variable corresponding to each actuator. Indicates the execution of the first element in the input vector. The upper limit of the execution input variables corresponding to each actuator; This represents the amplitude limiting function.

[0208] Specifically, the embodiments of this application adopt a saturation processing architecture that first completes the unconstrained optimization solution and then performs channel-by-channel amplitude-limited projection, directly mapping all out-of-limit components to the hardware nominal boundary, and outputting execution input variables that can directly drive the actuator.

[0209] The embodiments of this application employ a segmented operation method to perform limit calculations on the execution input variables corresponding to each actuator in the optimal execution input vector. When the optimal execution input variable obtained by unconstrained solution is less than the hardware lower limit, the lower limit value is directly output; when the optimal execution input variable obtained by unconstrained solution falls within the rated range, the original optimal execution input variable is retained without modification; when the optimal execution input variable obtained by unconstrained solution exceeds the hardware upper limit, the upper limit value is directly output.

[0210] The entire clamping operation relies solely on simple interval comparison logic, eliminating the need for complex matrix iteration operations and resulting in extremely low computational overhead. This makes it well-suited to meet the high real-time performance requirements of airborne embedded controllers. By constraining all control commands with unified limiting rules, hardware wear and failure issues caused by long-term over-limit operation of actuators can be avoided, ensuring the safe operation of aircraft hardware.

[0211] The embodiments of this application combine the control law and cost function corresponding to the backstepping controller to build an integrated closed-loop coupled architecture for attitude-torque distribution. This architecture breaks away from the traditional design concept of independent decoupling of attitude control and torque distribution, integrating backstepping attitude control, dynamic pressure adaptive quadratic programming torque distribution, and saturation clamping correction into the same closed-loop system. This scheme fully considers the time-varying dynamic pressure characteristics and cross-loop coupling disturbances caused by actuator saturation, thereby improving the coordinated control performance of multiple actuators under all-airspace and wide-range operating conditions of the aircraft.

[0212] To verify the stability of the closed-loop error system, embodiments of this application construct a positive definite Lyapunov function, as shown in the following equation:

[0213] ;

[0214] in, For scalar Lyapunov functions, obviously If and only if attitude tracking error Angular velocity tracking error Both must be reduced to zero to achieve the desired result. .

[0215] The time derivative of the Lyapunov function is taken and substituted into the attitude error dynamics model and the angular velocity error dynamics model, as shown in the following equation:

[0216] ;

[0217] In the derivation of the above equation, the cross-coupling term This exactly cancels out the difference, thanks to the desired control torque. The compensation term set in the expression .

[0218] For the remaining coupling terms We apply Young's inequality for scaling. For any given positive constant... The following relationship holds:

[0219] ;

[0220] in, Let represent the Euclidean norm of the vector. The significance of this inequality lies in transforming the product of two different physical quantities (angular velocity tracking error and torque distribution error) into a weighted sum of the squares of their respective norms, thus facilitating the separation of variables in subsequent stability analysis. Parameters The introduction of provides a degree of freedom, allowing for optimization of the final convergence bound in subsequent analysis by appropriately choosing its value. In this proof, is selected... So that The coefficients of the term can be naturally combined with the damping term in the derivative of the Lyapunov function, where, This represents the smallest eigenvalue in the matrix.

[0221] Will Substituting into the formula for the first derivative of the Lyapunov function, we get the following equation:

[0222] ;

[0223] The following discusses torque distribution error. The boundedness of the force distribution is analyzed. In practical engineering, the torque distribution error comes from two parts: first, the positive definite diagonal adaptive weight matrix. The resulting reconstruction error can be addressed by increasing the diagonal weight matrix. The first part of the equation tends to zero due to the diagonal elements of the actuator; the second part is the constraint error introduced by the clamping projection when the actuator is saturated. This part is bounded, and its boundary value is determined by the global torque mapping matrix. Norm and upper and lower bounds of physical constraints of the actuator They are jointly determined. Therefore, there always exists a finite constant. , so that:

[0224] ;

[0225] Substituting it into the above inequality, we get the following equation:

[0226] ;

[0227] Considering Lyapunov functions satisfy:

[0228] ;

[0229] in, Represents the largest eigenvalue in the matrix;

[0230] Define the synthesis convergence factor :

[0231] ;

[0232] Wherein, min represents taking the minimum value;

[0233] Then we can obtain the following formula:

[0234] ;

[0235] According to the comparison lemma in Lyapunov stability theory, the above differential inequality yields:

[0236] ;

[0237] in, express time, express The Lyapunov function at time t, Indicates the initial time. The value of the Lyapunov function.

[0238] when hour, The exponential convergence to a radius of Within the steady-state neighborhood. Therefore, the attitude tracking error... and angular velocity tracking error Ultimately uniformly bounded (UUB), and the steady-state error bound and the upper bound of the distribution error. Proportional to the positive definite gain matrix of the angular velocity loop It is inversely proportional to the smallest eigenvalue. By increasing and The steady-state neighborhood can be arbitrarily reduced.

[0239] When the torque distribution achieves ideal distribution and the actuator does not trigger saturation. ,Right now ,but , and when When the time is strictly less than zero, the closed-loop error system is globally asymptotically stable.

[0240] Limiting correction causes a distribution deviation between the control torque and the desired control torque. This deviation is a globally bounded disturbance, and its upper and lower boundaries are uniquely defined by the global torque mapping matrix and the actuator hardware limits. In the closed-loop Lyapunov stability derivation, this torque distribution error is uniformly attributed to an external bounded disturbance, thus completing the robust convergence demonstration of the system under saturated disturbance conditions.

[0241] The above analysis rigorously proves from a theoretical perspective that the embodiments of this application can guarantee the eventual consistent bounded stability of the closed-loop error system under the conditions of bounded torque distribution error and saturation constraints of the actuator. Furthermore, the steady-state accuracy can be flexibly controlled by adjusting the positive definite gain matrix, providing a solid theoretical guarantee and engineering application foundation.

[0242] To verify the comprehensive performance of the attitude constraint control method for wide-domain reentry vehicles under dynamic pressure adaptive torque distribution proposed in the embodiments of this application, and to test the environmental adaptability, closed-loop stability characteristics and engineering feasibility of the entire control system under the full airspace reentry conditions of lifting body vehicles, a six-degree-of-freedom full-link closed-loop simulation platform was built based on the dynamic model of an X-33-like vehicle.

[0243] During the transatmospheric reentry phase, the dynamic pressure varies significantly, and the control efficiency of the air rudder differs markedly between high and low altitudes. Under highly nonlinear aerodynamic conditions, traditional fixed-parameter torque distribution algorithms struggle to match the full range of flight conditions, easily leading to output imbalances in multiple actuators. This simulation did not employ a simplified single-trajectory, fixed-point steady-state test mode. The experimental profile covered the complete reentry altitude, Mach number, and dynamic pressure variation range. The simulation environment superimposed various real-world flight disturbances, including aerodynamic coefficient perturbations, gyro-coupled interference, and thrust amplitude / rate saturation of control surfaces and RCS, thus reproducing the complex dynamic characteristics of wide-range reentry and ensuring the simulation results have engineering reference value.

[0244] Using the industry-standard fixed-weight quadratic programming allocation method as a benchmark, and under the premise of unified initial flight state, aerodynamic disturbances, and attitude tracking errors, the attitude constraint control method for wide-domain reentry vehicles under dynamic pressure adaptive torque allocation proposed in the embodiments of this application was tested in simulation, traditional allocation comparison experiments, and multi-profile generalization verification. Performance differences were quantitatively evaluated from multiple dimensions, including attitude error convergence rate, three-axis angular velocity smoothness, system anti-interference capability, torque tracking accuracy, actuator saturation frequency, and overall control energy consumption. This comprehensively demonstrates that the complete solution of the embodiments of this application, integrating high-fidelity modeling, continuous adaptive weights, saturation correction, and an integrated collaborative architecture, possesses significant innovative advantages and engineering practical value compared to traditional decoupled control allocation techniques.

[0245] The total simulation duration was set to 20 seconds, with a calculation step size of 0.01 seconds. Initial attitude and angular velocity tracking errors were artificially introduced to recreate the real-world conditions of attitude disturbances inherent in the initial reentry phase. The attitude tracking error used a smooth, gradually varying signal with bounded first and second derivatives to match the actual maneuvering limitations of the aircraft.

[0246] The simulation loads time-varying aerodynamic torque and aerodynamic parameters throughout the entire process, without using piecewise linear approximation, and fully reproduces the rudder effect differentiation caused by the difference in dynamic pressure at high and low altitudes, preserving the aerodynamic nonlinearity and time-varying characteristics in the entire airspace; at the same time, it gives the upper and lower limits of RCS thrust and rudder deflection angle hardware, strictly applies saturation constraints on the actuators, and the simulation environment is consistent with the real flight scenario.

[0247] Based on the aforementioned full-envelope standard reentry condition, a joint simulation was conducted, extracting four core data types: three-axis attitude tracking error, three-axis angular velocity tracking error, Lyapunov function, and three-axis torque distribution error. The corresponding curves are as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 The dynamic convergence capability and steady-state control effect of the system under the benchmark trajectory are comprehensively evaluated through multi-dimensional indicators.

[0248] Figure 3 The variation curves of the three-axis attitude tracking error of the aircraft are presented. An initial attitude tracking error was preset in the experiment. The closed-loop error system proposed in this application can quickly suppress the deviation, causing the three-axis attitude tracking error to converge to a very small range near zero and maintain stability. There is no significant overshoot throughout the dynamic adjustment process, and no adverse phenomena such as low-frequency oscillations or error divergence exist; the attitude output is stable. It can adapt to the time-varying characteristics of the full ballistic control system, effectively suppressing aerodynamic nonlinearity and multi-channel coupled disturbances, achieving high-precision and stable attitude angle tracking under a wide range of varying operating conditions, verifying the excellent basic steady-state control performance of this control system.

[0249] Figure 4 The curves show the variation of the three-axis angular velocity tracking error of the aircraft. As the simulation progresses, the angular velocity tracking error continues to decrease, eventually converging to a small fluctuation near zero. The dynamic adjustment process is smooth throughout, without any instability phenomena such as high-frequency jitter, numerical jumps, or periodic oscillations.

[0250] Simulation results show that the control law corresponding to the backstepping controller designed in the embodiments of this application, combined with the aerodynamic torque calculation model based on dynamic pressure, can effectively suppress angular velocity fluctuations caused by high and low altitude control effect switching and aerodynamic sudden changes, stabilize the airframe angular velocity, and meet the engineering requirements for long-term attitude maintenance and stable cruise of lifting body aircraft.

[0251] Figure 5The variation curve of the Lyapunov function of the closed-loop error system is presented. In the initial stage of the simulation, the function value is relatively high, and the curve monotonically decreases as the simulation progresses, eventually converging to a low numerical range. Throughout the simulation, the Lyapunov function remains positive definite, and its derivative remains negative definite, satisfying the stability criterion for nonlinear systems. This curve theoretically verifies the effectiveness of the entire control framework.

[0252] Figure 6 The error variation curves between the expected control torque and the actual control torque for the three axes are presented. As can be seen from the curves, the torque distribution errors of the three axes converge quickly and remain within a very small range over a long period, without any abnormal phenomena such as command jumps, mechanism mismatch, or execution channel saturation exceeding limits. The embodiments of this application dynamically adjust the positive definite diagonal adaptive weight matrix based on real-time dynamic pressure, and rationally allocate aerodynamic rudder and RCS output according to the differences in rudder effectiveness at various altitudes; simultaneously, saturation correction constraints are used to limit the upper and lower limits of the execution input vector to ensure stable operation of the attitude closed loop.

[0253] comprehensive Figures 3 to 6 Based on all simulation data, the wide-domain reentry vehicle attitude constraint control method proposed in the embodiments of this application under dynamic pressure adaptive torque distribution can adapt to the dynamic pressure time-varying and rudder effect nonlinear drift conditions throughout the reentry process. Under the standard full-envelope trajectory, this method can achieve high-precision three-axis attitude tracking and maintain asymptotic stability of the system, while also completing the optimal allocation of multiple redundant mechanisms. The dynamic response accuracy and steady-state control accuracy of this method can meet the requirements of transatmospheric reentry missions.

[0254] To visually demonstrate the performance differences between the embodiments of this application and traditional solutions, a comparative simulation under the same flight conditions was conducted. Initial flight parameters were standardized, and a standard full-airspace reentry trajectory was used. Closed-loop simulations were performed on the embodiments of this application and the fixed-weight quadratic programming allocation algorithm, respectively. The simulation comparison data for the two schemes are as follows: Figure 7 and 8 As shown.

[0255] Figure 7 The figures show a comparison curve of the three-axis torque distribution error between the embodiment of this application and the traditional fixed-weight allocation method under the same reentry condition. Throughout the reentry process, the dynamic pressure of the aircraft continuously changes, causing the aerodynamic control efficiency to constantly shift. Traditional solutions use fixed weight coefficients to decompose the torque, which cannot match the changes in aerodynamic control efficiency with the flight state. Under the dual disturbances of aerodynamic coupling and time-varying dynamic pressure, the amplitude of its three-axis torque distribution error is larger, the convergence speed is slower, and low-frequency periodic fluctuations still exist in the steady-state phase, making it difficult to converge the torque distribution error to the ideal range, resulting in insufficient adaptability across all operating conditions.

[0256] The embodiments of this application introduce real-time dynamic pressure as the adjustment basis, dynamically updating the positive definite diagonal adaptive weight matrix. Relying on complementary weight adjustment logic, it can adapt to different aerodynamic conditions at high and low altitudes, smoothly switching the primary and secondary output relationships of the aerodynamic rudder and RCS, and realizing the coordinated operation of the two types of actuators. Simulation curves show that this adaptive mechanism can significantly accelerate the convergence of torque distribution errors and reduce steady-state error oscillations. The overall torque tracking performance is superior to the fixed-weight scheme, proving that dynamic pressure adaptive adjustment can effectively improve the torque distribution accuracy across the entire airspace.

[0257] Figure 8 Bar charts were used to statistically analyze two quantitative indicators: the saturation rate of the mechanism and the overall energy consumption, under the same reentry trajectory, for two allocation schemes. Traditional fixed-weight algorithms cannot match the changes in the efficiency of the aerodynamic rudder control across the entire domain. This can easily lead to a single type of actuator bearing the majority of the adjustment torque for a long time, causing the execution input vector to frequently exceed hardware limits. Ultimately, this results in high saturation frequency, high ineffective energy consumption, and low utilization of execution resources, making it difficult to support long-term, large-scale trajectory change reentry missions.

[0258] The embodiments of this application rely on a positive definite diagonal adaptive weight matrix to adjust the output ratio of the aerodynamic rudder and RCS thruster in real time, perfectly conforming to the variation law of the aerodynamic rudder control efficiency throughout the entire ballistic trajectory, and achieving balanced torque distribution among multiple redundant mechanisms. Adaptive adjustment combined with post-saturation correction reduces the phenomenon of high-load operation of single mechanisms from the source, significantly reducing the probability of exceeding the limit of the executed input vector; at the same time, it optimizes the multi-channel output distribution relationship, reducing ineffective energy consumption. The comparison results of these two indicators show that the embodiments of this application have significant advantages in suppressing mechanism saturation and reducing system power consumption, and are more suitable for the long-term stable reentry engineering requirements of aircraft.

[0259] To verify the global adaptability of the embodiments of this application and demonstrate that the embodiments of this application are not limited to a single standard trajectory, multiple sets of differentiated reentry trajectories were designed to complete generalization tests. Four typical profiles were selected for the tests: reference nominal reentry, low-altitude high dynamic pressure high-speed dive, high-altitude low-speed descent, and large-angle lateral maneuver. Each set of trajectories showed significant differences in initial altitude, peak dynamic pressure, rate of pressure change, and maneuver amplitude, and could reproduce real flight conditions such as steady-state cruise, strong aerodynamic perturbation, extreme dynamic pressure, and large-angle deflection, fully covering the complex reentry environment of X-33-like lifting body aircraft. The comparison of the three-axis peak attitude errors of the two allocation strategies is shown below. Figure 9 As shown.

[0260] Figure 9 The data uses bar charts to display the error statistics under multiple operating conditions. Solid bars represent the method proposed in this invention, while hollow bars represent the traditional fixed-weight quadratic programming scheme. A horizontal comparison of the data shows that, under the four types of profiles, the embodiments of this application comprehensively outperform the traditional fixed-weight allocation in terms of peak attitude tracking errors across the roll, pitch, and yaw axes, demonstrating superior attitude suppression performance.

[0261] Different trajectories correspond to completely different dynamic pressure ranges, directly altering the control efficiency of aerodynamic control surfaces and RCS nozzles. Traditional algorithms, with their fixed weight parameters, cannot compensate for control surface drift caused by changes in operating conditions. This invention, relying on a positive definite diagonal adaptive weight matrix, coupled with hierarchical decoupling control and a post-saturation correction mechanism, can dynamically adjust the loads of the two types of actuators according to real-time dynamic pressure, balancing the output ratio of control surfaces and thrusters. Even with frequent changes in flight profiles and drastic aerodynamic nonlinearities, the system can still quickly converge attitude errors and maintain high-precision steady-state control. Experiments show that the embodiments of this application break away from the strong dependence of traditional algorithms on nominal trajectories, adapting to the aerodynamic characteristics of the entire airspace based on a high-fidelity aerodynamic fitting model, and can be adapted to various wide-range variable operating condition reentry missions.

[0262] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution, characterized in that, Includes the following steps: A torque coefficient fitting equation based on Mach number and angle of attack is established, and an aerodynamic torque calculation model based on dynamic pressure is constructed; an attitude kinematic model and an attitude dynamics model of the aircraft are constructed; and a control law corresponding to the backstepping controller is constructed based on the attitude kinematic model and attitude dynamics model. The dynamic pressure at the current moment is obtained and the positive definite diagonal adaptive weight matrix at the current moment is calculated. The aerodynamic torque at the current moment is calculated based on the dynamic pressure at the current moment and the aerodynamic torque calculation model. The attitude, desired attitude, and angular velocity of the aircraft at the current moment are obtained, and the attitude tracking error at the current moment and the first derivative of the desired attitude with respect to time are calculated. The attitude kinematic matrix at the current moment is calculated based on the attitude at the current moment. Obtain the aircraft's Mach number and angle of attack at the current moment, and calculate the global moment mapping matrix at the current moment by combining it with the moment coefficient fitting equation; use the global moment mapping matrix at the current moment to calculate the control torque at the current moment; The current attitude tracking error, the first derivative of the desired attitude with respect to time, angular velocity, attitude kinematic matrix, and aerodynamic torque are input into the control law corresponding to the backstepping controller, and the desired control torque at the current moment is output. A cost function is constructed based on the desired control torque, control torque, and positive definite diagonal adaptive weight matrix at the current moment. The optimal execution input vector is obtained by minimizing the cost function under unconstrained conditions. The optimal execution input vector is clamped and constrained to obtain the final execution input vector. The final execution input vector is input into the actuator of the aircraft for execution to adjust the attitude of the aircraft at the next moment so that it reaches the desired attitude.

2. The method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution according to claim 1, characterized in that, The attitude of the aircraft is expressed using Euler angle vectors. To represent, where, For roll angle, The pitch angle, Let yaw angle be yaw angle, and T denote the transpose of the matrix; The posture kinematic model is represented as follows: ； in, This represents the first derivative of the Euler angle vector with respect to time. Indicates angular velocity, For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; The attitude kinematics matrix is ​​expressed as follows: ； The attitude dynamics model is expressed as follows: ； in, Represents the moment of inertia matrix. Represents a diagonal matrix. These are the roll axes of the aircraft around its fuselage. Pitch axis yaw axis The moment of inertia of the main shaft; Angular acceleration, Indicates aerodynamic torque. Indicates control torque. The antisymmetric matrix of the cross product of angular velocities is defined as: 。 3. The wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to claim 2, characterized in that, The expression for the aerodynamic torque calculation model is as follows: ； in, For dynamic pressure, For the reference area of ​​the aircraft wing, For wingspan, The mean aerodynamic chord of the wing. These are the column vectors of moment coefficients corresponding to the roll axis, pitch axis, and yaw axis, respectively.

4. The wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to claim 2, characterized in that, The control torque is expressed as: ； in, This represents the execution input vector corresponding to all actuators of the aircraft. Indicates the first The execution input variables of each actuator, The aircraft's actuators include 8 sets of RCS nozzles and 8 aerodynamic control surfaces. This refers to the thrust of the first group of RCS nozzles, and the second through eighth groups of RCS nozzles. This indicates the deflection angle of the first, second, through eighth aerodynamic rudders; This is the global torque mapping matrix. For the angle of attack of the aircraft, Represents the Mach number; The global torque mapping matrix is ​​an RCS submatrix. and aerodynamic rudder matrix It is constructed by vertical splicing, as shown in the following formula: ； The RCS submatrix is ​​represented as follows: ； in, Indicates the first The unit thrust of the RCS nozzle group is respectively at the roll axis Pitch axis yaw axis The resulting torque coefficients are all constant values. ; The aerodynamic rudder matrix is ​​represented as follows: ； in, For the first The unit deflection angle of the blade aerodynamic rudder at the roll axis Pitch axis yaw axis The corresponding torque coefficient; No. The unit deflection angle of the aerodynamic rudder is respectively at the th The moment coefficient corresponding to the shaft is calculated using the following moment coefficient fitting equation: ； in, Corresponding to the roll axis Pitch axis yaw axis ; and These are the polynomial powers of the angle of attack and the Mach number, respectively. and These are the highest-order powers of the polynomials for angle of attack and Mach number, respectively. is the least squares fitting constant.

5. The wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to claim 4, characterized in that, The control law corresponding to the backstepping controller includes a virtual angular velocity control law and a desired control torque control law. The construction process of the control law corresponding to the backstepping controller is as follows: Define attitude tracking error as Its expression is ; Define angular velocity tracking error as Its expression is ,in, Indicates the desired posture, This refers to virtual angular velocity; Taking the first derivative of the attitude tracking error with respect to time and substituting it into the attitude kinematics model, we obtain the following equation: ； in, This represents the first derivative of the attitude tracking error with respect to time. This represents the first derivative of attitude with respect to time. This represents the first derivative of the desired attitude with respect to time. The virtual angular velocity control law is designed as follows: ； in, For attitude kinematics matrix The inverse matrix, The positive definite gain matrix of the attitude loop. These represent the adjustable gain parameters corresponding to roll angle, pitch angle, and yaw angle, respectively. Substitute the virtual angular velocity into The attitude error dynamic model is obtained as follows: ； Taking the first derivative of the angular velocity tracking error with respect to time and substituting it into the attitude dynamics model, we obtain the following equation: ； in, This represents the first derivative of the angular velocity tracking error with respect to time. Represents virtual angular acceleration; Introducing torque distribution error Its expression is ,in, To achieve the desired control torque; Substitution From this, we obtain the following formula: ； The desired control torque control law is designed as follows: ； in, Here is the positive definite gain matrix of the angular velocity loop, where Adjustable gain parameters for roll rate, pitch rate, and yaw rate; Substituting the desired control torque control law The dynamic model of angular velocity error is obtained as follows: ； The attitude error dynamics model and the angular velocity error dynamics model are constructed into a stable closed-loop error system.

6. The wide-domain reentry vehicle attitude constraint control method under dynamic pressure adaptive torque distribution according to claim 5, characterized in that, The construction and solution process of the cost function is as follows: The cost function, based on the control objective and hardware constraints, is established in the form of a convex quadratic programming algorithm, as shown in the following equation: ； in, This represents a positive definite diagonal adaptive weight matrix. Represents the cost function, This represents the diagonal weight matrix. This represents the square of the weighted 2-norm; Expanding the cost function of the convex quadratic programming form, we obtain the cost function as shown in the following equation: ； Under unconstrained conditions, there exists a first-order necessary condition: ; Taking the first derivative of the cost function with respect to time and combining it with the first-order necessary condition, we obtain the following equation: ； The optimal execution input vector is obtained by rearranging and rewriting the above equation, as shown in the following equation: 。 7. The method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution according to claim 1, characterized in that, The calculation process for the final execution input vector is as follows: The execution input variables corresponding to each actuator in the optimal execution input vector are subjected to channel-by-channel limiting correction to obtain the execution input variables corresponding to each actuator in the final execution input vector, as shown in the following formula: ； in, The first element in the optimal execution input vector represents the... The execution input variables corresponding to each actuator Indicates the execution of the first element in the input vector. The lower limit value of the execution input variable corresponding to each actuator. Indicates the execution of the first element in the input vector. The upper limit of the execution input variables corresponding to each actuator; This represents the first element in the final execution input vector. The execution input variables corresponding to each actuator; This represents the amplitude limiting function.

8. The method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution according to claim 1, characterized in that, The construction process of the positive definite diagonal adaptive weight matrix is ​​as follows: The positive definite diagonal adaptive weight matrix is ​​a diagonal matrix composed of 8 sets of RCS weights and 8 sets of aerodynamic rudder weights, which are filled with diagonal elements in sequence. The RCS weight is expressed as follows: ； in, Represents the RCS weight. This represents the maximum value of the RCS weight. This indicates the maximum value of the dynamic pressure. Indicates dynamic pressure; The weight of the aerodynamic rudder is expressed as follows: ； in, Indicates the weight of the aerodynamic rudder. This represents the maximum value of the aerodynamic rudder weight.

9. The method for attitude constraint control of a wide-domain reentry vehicle under dynamic pressure adaptive torque distribution according to claim 1, characterized in that, The calculation process for the dynamic pressure at the current moment is as follows: Obtain the atmospheric density corresponding to the aircraft's current flight speed and current altitude, and calculate the dynamic pressure at the current moment.

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