Adaptive fault compensation control method and system for hypersonic aircraft based on matrix decomposition and multiple models

Abstract

The invention discloses a hypersonic aircraft adaptive fault compensation control method and system based on matrix decomposition and multiple models, and relates to the field of aerospace control, and the method comprises the steps: firstly constructing a nonlinear dynamic model containing an actuator fault, and converting the nonlinear dynamic model into a matrix form; aiming at four typical actuator fault modes, respectively designing a corresponding parameter updating law and a state feedback control law, and parameterizing an unknown control gain matrix in a non-singularity manner by using SDU matrix decomposition; and a cost function based on performance indexes is further constructed, and an optimal controller is automatically selected through an online supervision switching mechanism. The fault occurrence time, position or amplitude does not need to be known in advance, the problem of control gain singularity can be effectively avoided, it is guaranteed that all signals of a closed-loop system are bounded, meanwhile, asymptotic tracking of speed and height instructions is achieved, and the robustness and stability of a hypersonic aircraft in a complex fault scene are remarkably improved.

Description

An Adaptive Fault Compensation Control Method and System for Hypersonic Vehicles Based on Matrix Decomposition and Multiple Models Technical Field

[0001] This application relates to the field of aerospace control, and in particular to an adaptive fault compensation control method and system for hypersonic aircraft based on matrix decomposition and multiple models. Background Technology

[0002] Hypersonic vehicles are characterized by a large flight envelope, drastic changes in aerodynamic characteristics, strong nonlinearity, and strong coupling. Their control systems have extremely high requirements for reliability and robustness. In actual flight, actuators (such as throttle and control surfaces) may malfunction due to mechanical wear, jamming, or signal interruption. If these malfunctions are not compensated for in time, they may lead to mission failure or even loss of control of the aircraft.

[0003] Existing fault-tolerant control methods mainly fall into two categories: passive fault tolerance and active fault tolerance. Passive methods rely on robust control and are difficult to cope with severe faults; while active methods can be dynamically adjusted, most of them rely on precise fault detection and diagnosis (FDD) modules, and are prone to the "singularity problem" when dealing with unknown control gains—that is, when the adaptive parameter update causes the control gain matrix to become irreversible, the control law diverges and the system becomes unstable.

[0004] Furthermore, traditional adaptive control struggles to simultaneously address parameter uncertainties, external disturbances, and various actuator failures when dealing with hypersonic vehicle models of relative order [3,4]. Therefore, a unified adaptive fault compensation framework that is independent of FDD, avoids singularities, and possesses strong robustness is urgently needed. Summary of the Invention

[0005] The purpose of this application is to provide an adaptive fault compensation control method and system for hypersonic aircraft based on matrix decomposition and multiple models, so as to solve the problems of control gain singularity, unknown fault information, and multiple interference coupling in the prior art.

[0006] To achieve the above objectives, this application provides the following solution: Firstly, this application provides an adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models, comprising: establishing a longitudinal dynamic model of the hypersonic vehicle including actuator faults; representing the longitudinal dynamic model of the hypersonic vehicle including actuator faults in matrix form; constructing corresponding parameter update laws for various preset actuator fault modes to estimate unknown parameters in the system in real time; designing state feedback adaptive control laws corresponding to each fault mode based on the parameter update laws and state feedback matrix decomposition technology to generate control inputs for throttle opening and elevator deflection angle; defining a corresponding cost function for each fault mode, and selecting the control input that optimizes system performance online based on the cost function to achieve adaptive compensation for the current fault mode.

[0007] Optionally, the expression for the longitudinal dynamics model of the hypersonic vehicle including actuator failure is as follows: ;in, The third derivative representing velocity; The fourth derivative representing altitude; For nonlinear terms related to velocity; For unknown external disturbances; The control gain is unknown. Failure mode coefficient; For highly correlated nonlinear terms; This refers to the throttle opening. To model unknown parameters for faults, , , , The basis functions are known for fault modeling; This is due to elevator deflection.

[0008] Optionally, the longitudinal dynamics model of the hypersonic vehicle containing actuator failure can be expressed in matrix form using the following formula: ;in, ; Indicates speed, Indicates altitude; Represents the failure mode coefficient matrix; It is the identity matrix; , as well as All represent unknown parameters; , as well as Both represent known basis functions; This represents the aircraft's state vector.

[0009] Optionally, the expression for the parameter update law is as follows: ;in, Representing unknown parameters The OK; Indicates control gain The One sequence of principal expressions; Indicates adjustment of gain; Indicates estimation error The OK; Indicates auxiliary signal; Indicates the parameter projection term; Indicates the parameter update law; Indicates adjustment of gain; Indicates the estimation error; Indicates auxiliary signal; Indicates a normalized signal; This indicates the parameter projection term.

[0010] Optionally, the expression for the adaptive control law is as follows: ;in, This represents an adaptive controller; Represents the control allocation matrix; Represents the aircraft state vector; This indicates the auxiliary signal for the adaptive controller; It is the identity matrix; Indicates an unknown parameter; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; This represents the asymptotic convergence reference signal.

[0011] Optionally, the expression for the cost function is as follows: ;in, Represents the cost function; Represents the cost function coefficients; Indicates time; Represents the integral variable; Represents the residual term; Indicates vector transpose; This represents the normalization parameter.

[0012] Secondly, this application provides an adaptive fault compensation control system for hypersonic vehicles based on matrix decomposition and multiple models, comprising: a dynamic model construction module for establishing a longitudinal dynamic model of the hypersonic vehicle including actuator faults; a transformation module for representing the longitudinal dynamic model of the hypersonic vehicle including actuator faults in matrix form; a parameter update law construction module for constructing corresponding parameter update laws for various preset actuator fault modes, used to estimate unknown parameters in the system in real time; an adaptive control law design module for designing state feedback adaptive control laws corresponding to each fault mode based on the parameter update laws and state feedback matrix decomposition technology, to generate control inputs for throttle opening and elevator deflection angle; and an adaptive compensation module for defining a corresponding cost function for each fault mode, and selecting the control input that optimizes system performance online based on the cost function, thereby achieving adaptive compensation for the current fault mode.

[0013] Optionally, the dynamic model construction module specifically adopts the following formula: ;in, The third derivative representing velocity; The fourth derivative representing altitude; For nonlinear terms related to velocity; For unknown external disturbances; The control gain is unknown. Failure mode coefficient; For highly correlated nonlinear terms; This refers to the throttle opening. To model unknown parameters for faults, , , , The basis functions are known for fault modeling; This is due to elevator deflection.

[0014] Optionally, the conversion module specifically adopts the following formula: ;in, ; Indicates speed, Indicates altitude; Represents the failure mode coefficient matrix; It is the identity matrix; , as well as All represent unknown parameters; , as well as Both represent known basis functions; This represents the aircraft's state vector.

[0015] Optionally, the expression for the parameter update law is as follows: ;in, Representing unknown parameters The OK; Indicates control gain The One sequence of principal expressions; Indicates adjustment of gain; Indicates estimation error The OK; Indicates auxiliary signal; Indicates the parameter projection term; Indicates the parameter update law; Indicates adjustment of gain; Indicates the estimation error; Indicates auxiliary signal; Indicates a normalized signal; This indicates the parameter projection term.

[0016] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides an adaptive fault compensation control method and system for hypersonic aircraft based on matrix decomposition and multiple models, which has the following significant advantages: Completely avoids singularity problems: Through SDU matrix decomposition technology, the unknown control gain matrix is ​​transformed into the product of a symmetric positive definite matrix and a unit upper triangular matrix, ensuring that the control law is bounded under any parameter update path, thus structurally avoiding the singularity problem in the adaptive control law; No prior fault information is required: A multi-model + online switching mechanism is adopted to automatically match the current fault mode, without needing to know the fault location, occurrence time, or amplitude information in advance. Information-free, independent of Fault Detection and Isolation (FDI) systems; Dynamic compensation: Designed with an online switching mechanism based on cost functions, it can quickly and autonomously select the controller that matches the current fault mode, achieving dynamic compensation for time-varying faults; Strong robustness and stability: Under multiple uncertainties such as unknown mass and moment of inertia, external disturbances, and partial or complete failure of actuators, it can still ensure that all signals of the closed-loop system are bounded; High-precision tracking capability: Achieves asymptotic tracking of time-varying speed and altitude commands, meeting the high-dynamic mission requirements of hypersonic vehicles; Strong engineering feasibility: All control laws and update laws are based on measurable states and known basis functions, facilitating deployment in the flight control computer. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 is a flowchart illustrating an adaptive fault compensation control method for hypersonic aircraft based on matrix decomposition and multiple models in one embodiment of this application; Figure 2 is a schematic diagram illustrating a control mechanism provided in one embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] This embodiment presents a state feedback adaptive actuator fault compensation control method designed for NASA's X-43A hypersonic vehicle. This control method uses throttle opening and elevator deflection as control inputs to the vehicle. Even with unknown vehicle mass and moment of inertia, and with disturbances in the sensor measurement system (hereinafter referred to as the system) and time-varying actuator faults, it ensures that all vehicle states are bounded and achieves tracking of time-varying speed and altitude commands.

[0022] In an exemplary embodiment, as shown in Figure 1, an adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models is provided. This method is executed by computer equipment, specifically by a computer device such as a terminal or server alone, or by a terminal and a server together. In this embodiment, the method includes the following steps: Step 101: Establish a longitudinal dynamic model of the hypersonic vehicle that includes actuator faults.

[0023] Using aerodynamics and flight mechanics theories, an analytical longitudinal dynamic model of a hypersonic vehicle is established. Considering actuator failure, the model expression is as follows: (1) Among them, The third derivative representing velocity; The fourth derivative representing altitude; For the nonlinear term related to velocity, For highly correlated nonlinear terms, which contain unknown mass. Moment of inertia ; For unknown external disturbances, the expression is: , It is an unknown parameter. These are known basis functions; The control gain is unknown; For throttle opening, Elevator deflection is the control input to be designed in this application.

[0024] by For example, when hour, ,at this time The coefficient is 1, representing No fault occurred; the actual input for this item is: The value, and Failure; when hour, ,at this time The coefficient is 0, representing A malfunction occurs at this time. Failure, this is the actual input of the failure model. The remaining items are similar to this one.

[0025] Step 102: Represent the longitudinal dynamics model of the hypersonic vehicle containing actuator failures in matrix form.

[0026] For the convenience of subsequent control scheme design, this application rewrites formula (1) in matrix form, as follows: (2) Among them, ; ; It is the identity matrix; All are unknown parameters; See the appendix for specific expressions.

[0027] All of them are known basis functions.

[0028] It is important to note the aircraft status. These are known parameters that can be measured using sensors. However, there are unknown parameters in the aircraft model. Furthermore, some intermediate variables need to be updated in real time when designing the controller in subsequent steps. Therefore, it is necessary to design a parameter update law to estimate some control law parameters.

[0029] Step 103: For the preset failure modes of various actuators (i.e., sub-controller 1, sub-controller 2, sub-controller 3 and sub-controller 4 in Figure 2), construct corresponding parameter update laws for real-time estimation of unknown parameters in the system.

[0030] In this embodiment, the following four possible failure modes are considered: ,represent Fault; ,represent Fault; ,represent Fault; ,represent and Fault. Record the fault actuator number corresponding to the fault mode as... ,For example, The actuator number corresponding to the fault mode is , The actuator number corresponding to the fault mode is .

[0031] For the above four fault modes The parameter update law for formula (2) is designed using the Lyapunov method: (3) Among them, , yes The estimated value, , ; represent The List, , , yes The OK. yes The estimated value. (Symbol) They are The symbols for the first and second sequential principal forms can be easily obtained from the wind test data and physical characteristics of the aircraft. It's about adjusting the gain. It is used to guarantee Bounded projection terms. This application hereby provides... Detailed form, Similar in form. Definition .in, They represent The One component, here ,and yes The dimension of . Considering In this application, the initial estimate is selected as .So, The expression is as follows: (4) Furthermore, in the above formula (3) The expression is as follows: (5) Among them, , These are arbitrarily chosen 3rd and 4th order Hurwitz polynomials, respectively. It is a filter used to filter out unknown highest-order signals. . , .

[0032] In addition, in the above formula (3) The expression is as follows: (6) Among them, in the above formulas (3)(5)(6) , The expression is as follows: (7) Wherein, in the above formula (7) The expression is as follows: (8) (9) Among them, represent The Line number Column elements, ; It is the control law to be designed; These are the given known speed command signal and its derivative, respectively; These are the given known altitude command signal and its derivative, respectively; These are the parameters for the designed control law.

[0033] Specifically, It can be calculated using the following formula: (10) At the same time It can be calculated using the following formula: (11) Thus, we obtained The estimated value The expression is (10), and these quantities will be used in the design of the control law for subsequent steps.

[0034] That is, based on the known aircraft state obtained in the above steps. Substituting into formulas (8)-(9), we obtain the parameters. ;Will Substituting into formula (7) yields the parameter. ;Will and Substituting into formula (6), we obtain The obtained Substituting into formula (5), calculate ;Will Substitute into formula (3) to calculate Finally, Substituting into formula (10), we can obtain .

[0035] Step 104: Based on the parameter update law and state feedback matrix decomposition technology, design a state feedback adaptive control law corresponding to each fault mode to generate control inputs for throttle opening and elevator deflection angle.

[0036] Based on the above formula (2) and parameter update law formula (3), the adaptive control law of state feedback matrix decomposition is designed, namely the throttle opening. and elevator deflection The control law expression aims to track time-varying commands related to speed and altitude. : (12) Among them, , The calculation is performed using formula (10). In order to meet The solution.

[0037] Due to the aircraft's status It is known. All of these can be calculated from known quantities. Thus, the aircraft control law, formula (12), is obtained and used to characterize the real-time control law expressions for throttle opening and elevator deflection. Note that, due to... and For a unique unit upper triangular matrix, such that It is always reversible, and the control gain has no singularity problem, which avoids the loss of control of the aircraft due to infinite control law, and ensures the stability of the flight control system, as well as realizes the speed and altitude tracking of the aircraft.

[0038] Step 105: Define a corresponding cost function for each fault mode, and select the control input that optimizes system performance online based on the cost function to achieve adaptive compensation for the current fault mode.

[0039] Currently, this application has designed corresponding control laws and parameter update laws for four fault modes. Since it is unknown which fault will occur, in order to enable the aircraft to automatically switch to the corresponding control scheme and achieve the control objective, the following mechanism is designed to switch the control signal (see Figure 2 for the specific process).

[0040] For each failure mode Define the corresponding cost function : (13) Evaluate all candidate cost functions , choose to The minimum candidate control input. This cost function measures the normalized estimate residuals under each candidate mode. The system can use its energy to identify and select the controller that best matches the actual fault mode online, so that the system can maintain closed-loop stability under unknown fault conditions and achieve asymptotic tracking of speed and altitude commands.

[0041] appendix ; ; ; ; ; ;in, Indicates the moment of inertia. For quality, For pitch rate, For the angle of attack, For the track angle, air density, For thrust, As resistance, The gravitational constant, This is the thrust coefficient.

[0042] The calculation expressions for the remaining parameters are as follows: (14) (15) (16) (17) Based on the same inventive concept, this application also provides a hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models for implementing the hypersonic vehicle adaptive fault compensation control method based on matrix decomposition and multiple models described above. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models provided below can be found in the limitations of the hypersonic vehicle adaptive fault compensation control method based on matrix decomposition and multiple models described above, and will not be repeated here.

[0043] In an exemplary embodiment, a hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models is provided, comprising: a dynamic model construction module for establishing a longitudinal dynamic model of the hypersonic vehicle including actuator faults; a transformation module for representing the longitudinal dynamic model of the hypersonic vehicle including actuator faults in matrix form; a parameter update law construction module for constructing corresponding parameter update laws for various preset actuator fault modes, for real-time estimation of unknown parameters in the system; an adaptive control law design module for designing state feedback adaptive control laws corresponding to each fault mode based on the parameter update laws and state feedback matrix decomposition technology, to generate control inputs for throttle opening and elevator deflection angle; and an adaptive compensation module for defining a corresponding cost function for each fault mode, and selecting the control input that optimizes system performance online based on the cost function, thereby achieving adaptive compensation for the current fault mode.

[0044] Specifically, the dynamic model construction module uses the following formula: ;in, The third derivative representing velocity; The fourth derivative representing altitude; For nonlinear terms related to velocity; For unknown external disturbances; The control gain is unknown. Failure mode coefficient; For highly correlated nonlinear terms; This refers to the throttle opening. To model unknown parameters for faults, , , , The basis functions are known for fault modeling; This is due to elevator deflection.

[0045] The conversion module uses the following formula: ;in, ; Indicates speed, Indicates altitude; Represents the failure mode coefficient matrix; It is the identity matrix; , as well as All represent unknown parameters; , as well as Both represent known basis functions; This represents the aircraft's state vector.

[0046] The expression for the parameter update law is as follows: ;in, Representing unknown parameters The OK; Indicates control gain The One sequence of principal expressions; Indicates adjustment of gain; Indicates estimation error The OK; Indicates auxiliary signal; Indicates the parameter projection term; Indicates the parameter update law; Indicates adjustment of gain; Indicates the estimation error; Indicates auxiliary signal; Indicates a normalized signal; This indicates the parameter projection term.

[0047] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0048] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. An adaptive fault compensation control method for hypersonic aircraft based on matrix decomposition and multiple models, characterized in that, The hypersonic vehicle adaptive fault compensation control method based on matrix factorization and multiple models includes: establishing a longitudinal dynamic model of the hypersonic vehicle including actuator faults; representing the longitudinal dynamic model of the hypersonic vehicle including actuator faults in matrix form; constructing corresponding parameter update laws for various preset actuator fault modes to estimate unknown parameters in the system in real time; designing state feedback adaptive control laws corresponding to each fault mode based on the parameter update laws and state feedback matrix factorization technology to generate control inputs for throttle opening and elevator deflection angle; defining a corresponding cost function for each fault mode, and selecting the control input that optimizes system performance online based on the cost function to achieve adaptive compensation for the current fault mode.

2. The adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models according to claim 1, characterized in that, The expression for the longitudinal dynamics model of the hypersonic vehicle, which includes actuator failure, is as follows: ;in, The third derivative representing velocity; The fourth derivative representing altitude; For nonlinear terms related to velocity; For unknown external disturbances; The control gain is unknown. Failure mode coefficient; For highly correlated nonlinear terms; This refers to the throttle opening. To model unknown parameters for faults, ， ， ， The basis functions are known for fault modeling; This is due to elevator deflection.

3. The adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models according to claim 2, characterized in that, The longitudinal dynamics model of the hypersonic vehicle, which includes actuator failure, is expressed in matrix form using the following formula: ;in, ； Indicates speed, Indicates altitude; Represents the failure mode coefficient matrix; It is the identity matrix; 、 as well as All represent unknown parameters; 、 as well as Both represent known basis functions; This represents the aircraft's state vector.

4. The adaptive fault compensation control method for hypersonic aircraft based on matrix decomposition and multiple models according to claim 1, characterized in that, The expression for the parameter update law is as follows: ;in, Representing unknown parameters The OK; Indicates control gain The One sequence of principal expressions; Indicates the adjustment of gain; Indicates estimation error The OK; Indicates auxiliary signal; Indicates the parameter projection term; Indicates the parameter update law; Indicates the adjustment of gain; Indicates the estimation error; Indicates auxiliary signal; Indicates a normalized signal; This indicates the parameter projection term.

5. The adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models according to claim 1, characterized in that, The expression for the adaptive control law is as follows: ;in, This represents an adaptive controller; Represents the control allocation matrix; Represents the aircraft state vector; This indicates the auxiliary signal for the adaptive controller; It is the identity matrix; Indicates an unknown parameter; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; Represents known basis functions; Indicates an unknown parameter; This represents the asymptotic convergence reference signal.

6. The adaptive fault compensation control method for hypersonic vehicles based on matrix decomposition and multiple models according to claim 1, characterized in that, The expression for the cost function is as follows: ;in, Represents the cost function; Represents the cost function coefficients; Indicates time; Represents the integral variable; Represents the residual term; Indicates vector transpose; This represents the normalization parameter.

7. An adaptive fault compensation control system for hypersonic aircraft based on matrix decomposition and multiple models, characterized in that, The hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models includes: a dynamic model construction module for establishing a longitudinal dynamic model of the hypersonic vehicle including actuator faults; a transformation module for representing the longitudinal dynamic model of the hypersonic vehicle including actuator faults in matrix form; a parameter update law construction module for constructing corresponding parameter update laws for various preset actuator fault modes, used to estimate unknown parameters in the system in real time; an adaptive control law design module for designing state feedback adaptive control laws corresponding to each fault mode based on the parameter update laws and state feedback matrix decomposition technology, to generate control inputs for throttle opening and elevator deflection angle; and an adaptive compensation module for defining a corresponding cost function for each fault mode, and selecting the control input that optimizes system performance online based on the cost function to achieve adaptive compensation for the current fault mode.

8. The hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models according to claim 7, characterized in that, The dynamic model construction module specifically adopts the following formula: ;in, The third derivative representing velocity; The fourth derivative representing altitude; For nonlinear terms related to velocity; For unknown external disturbances; The control gain is unknown. Failure mode coefficient; For highly correlated nonlinear terms; This refers to the throttle opening. To model unknown parameters for faults, ， ， ， The basis functions are known for fault modeling; This is due to elevator deflection.

9. The hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models according to claim 8, characterized in that, The conversion module specifically uses the following formula: ;in, ； Indicates speed, Indicates altitude; Represents the failure mode coefficient matrix; It is the identity matrix; 、 as well as All represent unknown parameters; 、 as well as Both represent known basis functions; This represents the aircraft's state vector.

10. The hypersonic vehicle adaptive fault compensation control system based on matrix decomposition and multiple models according to claim 7, characterized in that, The expression for the parameter update law is as follows: ;in, Representing unknown parameters The OK; Indicates control gain The One sequence of principal expressions; Indicates adjustment of gain; Indicates estimation error The OK; Indicates auxiliary signal; Indicates the parameter projection term; Indicates the parameter update law; Indicates the adjustment of gain; Indicates the estimation error; Indicates auxiliary signal; Indicates a normalized signal; This indicates the parameter projection term.

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