Physical information driven high-speed aircraft flight quality analysis and intelligent control method

Abstract

The present application belongs to the technical field of high-speed aircraft control, and relates to a physical information driven high-speed aircraft flight quality analysis and intelligent control method. The purpose of the present application is to provide an intelligent control method based on data and knowledge driving. The method comprises the following steps: establishing a high-speed aircraft dynamics model based on a rigid body mathematical model and an aerodynamic coupling model; evaluating the flight quality of the longitudinal and lateral directions of the aircraft to provide a reference for controller design; performing neural network training based on data and knowledge driving under a large number of flight sample data; and designing an intelligent controller based on the physical information neural network to realize stable tracking of the reference instruction. The method is a data and knowledge driven learning control method for high-speed aircrafts, and has a broad application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed aircraft control and relates to a physical information driven high-speed aircraft flight quality analysis and intelligent control method. BACKGROUND

[0002] High-speed aircraft has great application value due to its fast speed, long range, and strong penetration capability. The speed and height of high-speed aircraft change greatly during flight, resulting in a large flight envelope. Within the large envelope, the aerodynamic coefficients of the aircraft change significantly, and there is significant coupling between the roll channel, pitch channel, and yaw channel of the aircraft. These conditions make the dynamic model of the aircraft highly nonlinear and time-varying, and there is large model uncertainty and external disturbance, which leads to significant deviation of the model parameters of the aircraft during flight compared to the ground calculation results, making it difficult to obtain a high-precision dynamic coupling model and increasing the difficulty of control system design. Therefore, in order to ensure the safe flight of high-speed aircraft and have good flight quality, it is necessary to carry out research on the coupled dynamics modeling and flight quality analysis method of high-speed aircraft under the stacking of multiple physical fields, and design a multiple-input multiple-output controller based on the consideration of complex dynamic characteristics to improve the flight quality.

[0003] To solve the above problems, many scholars use advanced control theory to design the attitude control of high-speed aircraft, but the control method based on advanced control theory relies on high-precision modeling of the controlled object, which is difficult to meet the high-precision and fast-response attitude requirements of modern high-speed aircraft. If the contradiction between the existing attitude control method and the actual demand is to be fundamentally solved, the dependence of the control method on the model must be reduced to improve the adaptability to model uncertainty and enhance the generality to different aerodynamic shapes.

[0004] Dong Zhaoyang, Lu Yao, and Wang Qing proposed an inversion control method based on command filter in "Command Filtered Backstepping Control for Hypersonic Vehicles" (see Journal of Astronautics, August 2016, Vol. 37 No. 8, page 957-963), which can realize stable tracking of speed and track angle reference signals. However, the compensation accuracy of the inversion control method completely depends on the accuracy of the aerodynamic data and the high-precision aircraft model. When the parameters change in a large range, the compensation effect will usually decrease, resulting in a decrease in control performance.

[0005] Tubular algae, Jiang Heng, Gao Xingsheng in "Terminal sliding mode attitude control of hypersonic vehicles" (see "Missiles and space launch technology", June 2017, total 357, page 60-64) proposed a terminal sliding mode control method based on singular perturbation theory, which can track the attitude angle signal command well under the change of aerodynamic parameters. However, the sliding mode control still depends on the high-precision vehicle model, and for the strong uncertain model with large parameter deviation or unknown parameter in the flight process, the sliding mode variable structure control cannot achieve the expected control effect.

[0006] Pei Pei, He Shaoming, Wang Jiang, etc. in "A deep reinforcement learning guidance control integrated algorithm" (see "Journal of Aerospace Science", October 2021, Vol. 42, No. 10, pp. 1293-1304) proposed a guidance control integrated method based on deep reinforcement learning, which generates rudder angle control commands through observation of the missile by the agent, so as to accurately intercept the target. However, this method directly outputs control quantities based on deep neural networks, lacks robustness analysis, and is difficult to use in engineering practice and meet the general design requirements.

[0007] Liu Zibo, Liu Xiaodong, Xue Wenchao, etc. in "Adaptive active disturbance rejection attitude control method for high-speed vehicles in the lower section" (see "Journal of Command and Control", October 2024, Vol. 10, No. 5, pp. 521-533) proposed an adaptive active disturbance rejection attitude control method, which has strong robustness, high precision and adaptive ability through simulation analysis. However, this method requires an accurate dynamic model to obtain the aerodynamic parameters through the extended Kalman filter (EKF) method, but the actual flight process may have unmodeled dynamics or errors in the ground-derived model, resulting in large parameter identification errors of EKF and reducing control accuracy.

[0008] Xu Shengyuan, Hu Yang, Guo Jian, etc. in "Fault-tolerant control method for hypersonic vehicles based on long short-term memory neural network linear active disturbance rejection control" (CN 116755337 A) proposed a fault-tolerant control method for hypersonic vehicles based on long short-term memory neural network linear active disturbance rejection control, which ensures the safe operation of hypersonic vehicles. However, this modeling method based on statistical learning theory is based on large data samples for model accuracy, but it is difficult to provide a large database to support the training needs of complex multi-layer neural networks, and long short-term memory neural networks only focus on the time dependence in sequence data, without integrating physical knowledge, and the generalization ability of neural networks is not enough.

[0009] Li Siyuan, Yuan Yuqi, Zhou Di, et al. in "A Model Uncertainty Considered Direct-lift-gas Hybrid Aircraft Model-free Attitude Control Method" (CN 119861552 A) proposes a model uncertainty considered direct-lift-gas hybrid aircraft model-free attitude control method, which proves that the proposed method is superior to other adaptive sliding mode control methods. However, the calculation complexity of LSTM neural network is high, especially in the scene of aircraft attitude control which requires high real-time performance, it may not meet the control requirements. Moreover, the design of sliding mode control parameters is complex, which increases the difficulty of controller design.

[0010] To solve the above problems, it is necessary to design an intelligent control method that fully utilizes physical knowledge to reduce the dependence on databases and models and reduces the difficulty of controller parameter tuning. This method aims to promote high-speed aircraft towards higher reliability and better stability. In the current technology development trend, data-driven and intelligent learning technology (such as machine learning and artificial intelligence) plays an important role in improving the performance and adaptability of the system. Physics-informed neural networks (PINN) is a deep learning framework that combines physical law prior knowledge and data-driven learning ability. It breaks the traditional data-driven model's limitation of being independent of physical mechanism and relying on massive labeled data. By embedding the physical equation of the target system as a constraint into the training process of the neural network, the network learns the data distribution characteristics while strictly following the objective physical law, ultimately realizing the integration optimization of "modeling-prediction-control" for complex nonlinear systems. The high-speed aircraft flight quality analysis and intelligent control method based on physics-informed driving first evaluates the flight quality of high-speed aircraft, obtains the dynamic characteristics of the aircraft, ensures the safe and stable flight of high-speed aircraft, and guides the subsequent controller design. Then by processing a large amount of aircraft state database, using the data-driven part and the physics-driven part of the loss function, the mutual mapping relationship between the physical state of the aircraft and the control parameters is better established, the patterns and features in the data are learned, and a data and knowledge dual-driven active disturbance rejection controller parameter setting neural network is formed. SUMMARY

[0011] To address the complex dynamic characteristics of high-speed aircraft multiple-input multiple-output (MIMO) control, this invention proposes a physics-information-driven method for high-speed aircraft flight quality analysis and intelligent control. First, a high-speed aircraft dynamic model is established, integrating rigid body, aerodynamic, and structural elastic coupling models to comprehensively describe the aircraft's dynamic characteristics. Then, flight quality is evaluated based on the established dynamic model, providing a basis for controller design. Next, massive simulations are performed on a ground-designed active disturbance rejection controller (APDC) based on adaptive control bandwidth, while torque coefficients and atmospheric density are adjusted to optimize ADC parameters. After obtaining a large amount of flight sample data under different operating conditions, the data is preprocessed to construct a training dataset. Furthermore, an offline mapping relationship is established between the aircraft state and the optimized control parameters and rudder deflection, forming a data- and knowledge-driven neural network for ADC parameter optimization. Finally, during online use, the aircraft's physical state variables are collected in real-time as input to the PINN (Physical Input Multiple Output) network. Optimized controller parameters and rudder deflection are obtained through real-time inference and physical constraint verification. The optimized parameters are then substituted into the feedback control law and extended observer to output control commands, thereby achieving real-time optimization of ADC parameters.

[0012] The technical solution of the present invention is as follows:

[0013] A physical information-driven method for flight quality analysis and intelligent control of high-speed aircraft, comprising the following steps:

[0014] Step 1: Construction of high-speed aircraft dynamics model

[0015] A dynamic model of a high-speed aircraft is established based on a rigid body mathematical model and an aerodynamic coupling model.

[0016] (1)

[0017] In the formula, the superscript " " represents the first derivative; It's an attack angle. It is the sideslip angle. It's the yaw angle. It is the roll rate. It is the yaw rate. It is the pitch rate. It is the trajectory angle. For quality, It is the acceleration due to gravity. For flight speed, , , They represent along , , Moment of inertia of the shaft; It is the product of inertia; is the dynamic pressure, is the wing reference area, is the wing reference length; are the roll, yaw and pitch moment coefficients, respectively, are the roll, yaw and pitch damping moment coefficients, respectively, are the side force, lift and drag, respectively, and are expressed as:

[0018] (2)

[0019] where, are the axial, normal and side force coefficients, respectively. are functions of , is the Mach number, and the control variables , are the aileron, rudder and elevator deflections. The actuator dynamics are described using a second order element as follows:

[0020] (3)

[0021] where, is the Laplace variable; denotes the actual deflection of the corresponding channel, denotes the commanded deflection of the corresponding channel, where the corresponding channel refers to the roll, yaw and pitch directions; and denote the natural frequency and damping ratio of the servo system, respectively.

[0022] Step 2, High-speed aircraft flight quality evaluation

[0023] Step 2.1, Longitudinal flight quality evaluation

[0024] Equation (1) is divided into longitudinal and lateral equations, where the longitudinal equation is:

[0025] (4)

[0026] Equation (4) is linearized in small perturbations to obtain the state space equation with as the state variable and the elevator deflection as the input variable as follows:

[0027] (5)

[0028] where, is the perturbation of the angle of attack, is the perturbation of the pitch rate, is the perturbation of the elevator deflection, is the partial derivative of the angle of attack, is the partial derivative of the pitch rate, , is the change in lift due to the change in angle of attack, , is the change in lift due to the change in elevator deflection, ; , is the derivative of the pitching moment coefficient with respect to the angle of attack, , is the change in pitching moment due to the change in elevator deflection.

[0029] Let where is a constant, substitute into equation (5) and let and eliminate , the characteristic equation is:

[0030] (6)

[0031] Compare equation (6) with the standard second order equation , where are the natural frequency and damping ratio, respectively, and the expressions are .

[0032] After obtaining the natural frequency and damping ratio, there are two methods to evaluate the flight quality.

[0033] Step 2.1.1, short period pitch response

[0034] According to GJB185 "Manned Aircraft (Fixed Wing) Flight Quality", the flight quality specification has requirements for short period mode characteristics, and the short period mode evaluation index is damping ratio and natural frequency. After obtaining the damping ratio and natural frequency of the aircraft, the flight quality of the aircraft is evaluated by judging its belonging range in different flight stages.

[0035] Step 2.1.2, evaluation according to CAP parameters

[0036] The control anticipation parameter CAP is the association of the pilot's sensitivity to the pitch rate with the perceived aircraft normal acceleration, which predicts the final situation of the flight path from the initial attitude response, and the expression of CAP is:

[0037] (7)

[0038] where is the normal acceleration, which is specifically defined as After obtaining the CAP parameters, the flight quality of the pitch axis of the aircraft is evaluated according to the CAP regulation range to which the aircraft belongs in different flight stages according to GJB185 “Flight Quality of Manned Aircraft (Fixed Wing)”.

[0039] Step 2.2, lateral flight quality evaluation

[0040] Step 2.2.1, roll mode time constant

[0041] Roll mode time constant The roll damping characteristics of the aircraft are described as follows:

[0042] (8)

[0043] In the formula, is the derivative of the roll moment coefficient with respect to the sideslip angle, is the derivative of the yaw moment coefficient with respect to the sideslip angle. According to GJB185 “Flight Quality of Manned Aircraft (Fixed Wing)”, the roll mode time constant has a maximum value. After obtaining the roll mode time constant , the flight quality of the roll axis of the aircraft is evaluated by judging the regulation range to which it belongs.

[0044] Step 2.2.2, Dutch roll mode

[0045] Dutch roll mode frequency and damping ratio The calculation formula is:

[0046] (9)

[0047] (10)

[0048] In the formula, is the atmospheric density; is the derivative of the lateral force with respect to the sideslip angle. According to GJB185 “Flight Quality of Manned Aircraft (Fixed Wing)”, the Dutch roll mode flight quality specification standard is determined. After obtaining the Dutch roll mode frequency and damping ratio , the flight quality of the heading axis of the aircraft is evaluated by judging the regulation range to which it belongs.

[0049] Step 3, neural network training based on data and knowledge driving

[0050] First, the adaptive control bandwidth-based active disturbance rejection controller designed on the ground is simulated, and the torque coefficient and atmospheric density are pulled to obtain the optimal active disturbance rejection control parameters. After obtaining a large number of flight sample data under different flight conditions to form a training data set, the mapping relationship between the aircraft state and the gain adjustment parameter and the rudder deflection is established offline to form a neural network for active disturbance rejection control parameter optimization driven by data and knowledge. In the offline neural network training process, the data set generation, training, validation and testing steps are mainly included.

[0051] Step 3.1, data set generation: first, the flight state database covering multiple flight conditions and flight tasks, model uncertainties needs to be collected and generated. Then under the same flight condition and task, the controller parameters are continuously adjusted until the optimal controller parameters are found, and finally a large amount of training data is generated. Specifically, first, change the aerodynamic force and moment model parameters to generate data containing model errors, and realize the simulation of model uncertainties. Second, change the atmospheric density to simulate different environmental conditions, generate external disturbance data, and realize the simulation of environmental disturbances. Third, for the same flight condition and flight task, continuously adjust the parameters of the active disturbance rejection controller to find the best control effect parameter set, and realize the optimal setting of the controller parameters. Finally, the data set is divided into training set, validation set and test set in a certain distribution ratio for the later design verification.

[0052] Step 3.2, training, validation and testing: after the data set is generated, the data set is divided into input data samples and target data samples. The input data samples are historical data for model input, and the target data samples are future data to be predicted. Train these data, and the neural network used for training is the physical information neural network (PINN).

[0053] The input data sample, i.e. the input of the neural network, is , , and , wherein represents the time variable; represents the state variable group, including flight state data , is the flight altitude; is the model error, which is the error between the actual state of the aircraft and the reference model; is the angular rate sensor signal after band-pass filtering. The target data sample, i.e. the output of the neural network, is the predicted gain adjustment parameter and rudder effect , wherein , is the maximum value of the gain.

[0054] The loss function includes data fitting loss and physical consistency loss. Defined as the error between the network output value and the true value:

[0055] (11)

[0056] In the formula, The number of real data points that have been obtained. and These are the neural network pairs of the first... Predictive rudder effectiveness and predictive control bandwidth gain for each data point and They are the first The true rudder effect and optimal control bandwidth gain for each data point.

[0057] For the physical constraint part of the loss function, the automatic differentiation module in the neural network toolkit is used to calculate the time derivative of the gain adjustment parameter predicted by the neural network, thus obtaining the physical bias. :

[0058] (12)

[0059] In the formula, and These are the neural network's first... Model error and sensor signal for each data point , These represent the strength of the impact of error on bandwidth and the strength of the impact of chatter on bandwidth, respectively.

[0060] initial deviation Used to ensure that the network's output at the initial time is consistent with the given initial conditions, boundary deviation This involves comparing the adaptive gain predicted by the network with the range of the adaptive gain, as shown in the following formula:

[0061] (13)

[0062] (14)

[0063] In the formula, and These are the initial prediction of rudder effectiveness and the prediction of control bandwidth gain via neural network. and These are the initial true steering effect and the optimal control bandwidth gain, respectively.

[0064] Loss function of physical information neural network It consists of a weighted sum of the data-driven part and the physical-driven part, and can be represented as:

[0065] (15)

[0066] wherein, are weights used to balance their influence on the total loss function.

[0067] After obtaining the loss function, the trainable variables in the neural network need to be optimized according to the loss function value, and Adam is adopted, and the specific updating method is as follows:

[0068] (16)

[0069] (17)

[0070] (18)

[0071] (19)

[0072] (20)

[0073] wherein, is the current iteration number, represents the current momentum at the optimization step, represents the current momentum at the optimization step, represents its deviation correction value, is the to-be-optimized parameter at the th iteration, represents the loss function with respect to , the gradient, represents the current second-order momentum at the optimization step, represents the current second-order momentum at the optimization step, represents its deviation correction value; is the first-order momentum history momentum retention rate, is the second-order momentum history momentum retention rate, is the product of one multiplication, is the product of one multiplication; is the learning rate, is a very small number, used to prevent the denominator from being 0.

[0074] In this step, the physical information neural network obtained through training, verification, and testing based on a valid dataset has the function of updating controller parameters and will be used as a parameter optimizer for the subsequent design of the intelligent controller.

[0075] Step 4: Design of an intelligent controller based on a physical information neural network

[0076] The following longitudinal feedback control law is designed to have adaptive control gain and can adapt to model bias in real time: (twenty one)

[0077] In the formula, It is feedback control of the rudder deflection. These are the angle error and angular velocity error, respectively, and the adaptive control gain. As shown in the following formula:

[0078] (twenty two)

[0079] In the formula, It is the rudder effect, one of the outputs of the physical information neural network; It is a preset fixed damping ratio. This indicates the adaptive bandwidth, which adjusts the offline control gain based on the actual control effect. The update law is as follows:

[0080] (twenty three)

[0081] In the formula, For the adaptive gain of bandwidth, where, and These represent the minimum and maximum values ​​of the bandwidth adaptive gain. This refers to the nominal control bandwidth. Here is the gain adjustment parameter, where This is the maximum value. It is the sensor signal of angular rate after passing through a bandpass filter. , These represent the strength of the impact of error on bandwidth and the strength of the impact of chatter on bandwidth, respectively. This represents the error between the actual state of the aircraft and the reference model.

[0082] The extended state observer is used to estimate the system state and total disturbance. Based on the disturbance estimate, the system is compensated for the disturbance. The longitudinal attitude dynamics equation is shown below:

[0083] (twenty four)

[0084] In the formula: for ; For ; Including unmodeled dynamics and dynamic coupling terms; Is the rudder effect; Is the elevator deflection angle; Is the output of the system.

[0085] The longitudinal linear extended state observer equation is designed as:

[0086] (25)

[0087] In the formula: The observation value of ; The observation value of ; The observation value of total disturbance ; Is the rudder effect, which is also the compensation factor that determines the strength of compensation; The difference between the observation value and the system output; The observer gain, which is represented by the observer bandwidth The observer gain is represented by the observer bandwidth:

[0088] (26)

[0089] The process of compensating the total disturbance by using the extended observer for real-time estimation is called dynamic compensation linearization, and the disturbance compensation rudder deflection of the extended state observer is Designed as follows:

[0090] (27)

[0091] The control quantity of the pitch channel Can be represented as the sum of the feedback control rudder deflection and the extended state observer disturbance compensation rudder deflection:

[0092] (28)

[0093] The beneficial effects of the present application are:

[0094] This invention presents a physics-information-driven method for high-speed aircraft flight quality analysis and intelligent control, addressing the stability and robustness requirements faced by hypersonic vehicles during wide-speed-range, cross-airspace flight. Compared to traditional control methods, this physics-information-driven method addresses two key aspects: First, it fully considers the difficulties in modeling aircraft across wide speed and large airspace regions, particularly the challenge of obtaining accurate aircraft dynamics models. By constructing a wide-speed-range aircraft dynamics model to represent the aircraft's motion equations, it employs a data- and knowledge-driven neural network to ensure that the model output strictly satisfies the differential equations, thus reducing dependence on models and data. Second, to address the significant model errors arising from the complex environments encountered by wide-speed-range aircraft, it designs a variable-gain active disturbance rejection controller based on a physics-information neural network. This allows the control law to adapt in real-time to changes caused by model deviations, thereby improving overall control performance. Therefore, the designed physics-information-driven method significantly reduces dependence on models and data, achieving rapid iterative information feedback under a data- and knowledge-driven neural network, and optimizing control law gain and rudder effectiveness in real-time, effectively improving control efficiency and the dynamic performance of the control system. Attached Figure Description

[0095] Figure 1 This is a flowchart of the overall process for intelligent control of high-speed aircraft driven by physical information.

[0096] Figure 2 It is a framework for intelligent control methods driven by physical information;

[0097] Figure 3 It is a curve showing the flight altitude of a high-speed aircraft;

[0098] Figure 4 It is a curve showing the flight speed of a high-speed aircraft;

[0099] Figure 5 It is a curve showing the change of elevator deflection over time for a high-speed aircraft;

[0100] Figure 6 It is the curve of aileron deflection of a high-speed aircraft over time. Detailed Implementation

[0101] The embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0102] like Figure 1 and Figure 2 As shown, this invention provides a physical information-driven method for analyzing and intelligently controlling the flight quality of a high-speed aircraft, wherein the mass of the high-speed aircraft is... kg. The specific control process is as follows:

[0103] Step 1: Construction of high-speed aircraft dynamics model

[0104] Based on the rigid body mathematical model and the aerodynamic coupling model, the high-speed aircraft dynamic model is established:

[0105] (1)

[0106] where the superscript " denotes the first derivative; respectively are the roll angle rate, the yaw angle rate and the pitch angle rate, is the ballistic angle, is the mass, is the gravity acceleration, is the velocity, , , , respectively denote the moment of inertia along the x, y and z axes. is the inertia product; is the dynamic pressure, is the wing reference area, is the wing reference length; respectively are the roll moment coefficient, the yaw moment coefficient and the pitch moment coefficient, respectively are the roll damping moment coefficient, the yaw damping moment coefficient and the pitch damping moment coefficient, respectively are the side force, the lift and the drag, and the specific expressions are: (2)

[0107]

[0108] where, respectively are the axial force coefficient, the normal force coefficient and the side force coefficient. are all functions related to , is the Mach number, the control variable , respectively are the aileron deflection angle, the rudder deflection angle and the elevator deflection angle. In addition to the attitude motion equation, the influence of the actuator on the control process needs to be considered in the control system design, and the second-order link is used to describe the dynamic process of the actuator.

[0109] (3)

[0110] where, is the Laplace variable, denotes the actual deflection of the corresponding channel, denotes the command deflection of the corresponding channel, and the corresponding channel refers to the corresponding roll, yaw and pitch directions; and​​​​ respectively represent the natural frequency and damping ratio of the servo system. Due to the introduction of the actuator dynamic process, the system will bring phase lag and delay, reduce the system margin, and even cause the attitude motion to appear chattering and instability when the controller bandwidth does not match the available bandwidth of the actuator, which is one of the difficulties to be overcome.

[0111] Step 2, high-speed aircraft flight quality evaluation

[0112] Based on the high-speed aircraft dynamic model constructed in step 1, the longitudinal and lateral flight qualities of the aircraft will be evaluated in this step to provide a reference for controller design.

[0113] Step 2.1, longitudinal flight quality evaluation

[0114] Divide equation (1) into longitudinal and lateral equations, where the longitudinal equation is:

[0115] (4)

[0116] Linearize equation (4) for small disturbances to obtain the state space equation with as the state variable and as the input variable as follows

[0117] (5)

[0118] In the equation, is the attack angle deviation, is the pitch rate deviation, is the elevator deflection deviation, is the attack angle derivative deviation, is the pitch rate derivative deviation, and the deviation refers to the difference between the disturbance and the undisturbed value; , is the lift change caused by the change in attack angle; , is the lift change caused by the unit change in pitch deflection; ; , is the derivative of the pitch moment coefficient with respect to the attack angle; , is the pitch moment change caused by the unit change in pitch deflection.

[0119] Let , where is a constant, substitute it into the above equation, let , and eliminate , to obtain the characteristic equation as follows:

[0120] (6)

[0121] Equation (6) above and the standard second-order equation Compare the corresponding items. These are the natural frequency and the damping ratio, respectively, expressed as: .

[0122] After obtaining the short-period natural frequency and damping ratio, there are two methods for flight quality assessment.

[0123] Step 2.1.1, Short-period pitch response

[0124] The longitudinal disturbance motion of an aircraft is typically composed of a superposition of two different types of motion: fast decay and slow decay. The fast decay motion is referred to as short-period motion. Conventional aircraft use maneuverability as a metric, and flight phases can be divided into three categories: Category A is the mission phase, requiring rapid maneuvers and precise tracking, such as air combat, ground attack, and aerial refueling. Category B requires precise control of the flight trajectory, but can be achieved through slow maneuvers without precise tracking, such as climb, cruise, and airdrop. Category C requires slow maneuvers with accurate trajectory control, such as takeoff, approach, and landing. According to GJB185 "Flight Quality of Manned Aircraft (Fixed-Wing)", flight quality specifications have strict requirements for short-period modal characteristics. The evaluation indicators for short-period modes are damping ratio and natural frequency, as shown in the table below. After obtaining the aircraft's damping ratio and natural frequency, the longitudinal flight quality is assessed by determining their range in different flight phases.

[0125] Table 1 Requirements for short-period modal damping ratio and natural frequency

[0126]

[0127] Step 2.1.2: Evaluate based on CAP parameters.

[0128] CAP (Control Anticipation Parameter), also known as the control expectation parameter, correlates the pilot's sensitivity to pitch rate with the perceived aircraft normal overload, predicting the final trajectory from the initial attitude response. The CAP expression is:

[0129] (7)

[0130] In the formula, Normal overload, specifically defined as After obtaining the CAP parameters, the flight quality of the aircraft pitch axis is evaluated based on the CAP specification range for different flight phases, according to GJB185 "Flight Quality of Manned Aircraft (Fixed Wing)".

[0131] Step 2.2, lateral-directional flying quality evaluation

[0132] The lateral-directional motion of the aircraft is to study the motion of the aircraft around the longitudinal symmetry plane, such as roll, yaw and other motion, and the corresponding aerodynamic force and aerodynamic moment change is more complex, which needs to evaluate the lateral-directional flying quality of the aircraft.

[0133] Step 2.2.1, roll mode time constant

[0134] Roll mode is the initial stage of the lateral perturbation motion of the aircraft, which describes the motion of the roll rate / roll angle of the aircraft, and the roll mode time constant Describes the roll damping characteristics of the aircraft, the expression is as follows:

[0135] (8)

[0136] In the formula, is the derivative of the roll moment coefficient with respect to the sideslip angle, is the derivative of the yaw moment coefficient with respect to the sideslip angle. According to GJB185 "manned aircraft (fixed wing) flying quality", the roll mode time constant has a maximum value. After obtaining the roll mode time constant , the flying quality evaluation of the roll axis of the aircraft is carried out by judging its belonging to the specified range.

[0137] Table 2 maximum value of roll mode time constant (unit: s)

[0138]

[0139] Step 2.2.12, Dutch roll mode

[0140] Dutch roll mode is only obvious in the later stage of lateral perturbation of the aircraft. Because it is a small real root, it shows that the yaw angle and the tilt angle change monotonously and slowly. It describes the mode that the sideslip angle, yaw angle / yaw rate of the aircraft after disturbance changes periodically with time, and the Dutch roll mode frequency And the damping ratio The calculation formula is

[0141] (9)

[0142] (10)

[0143] In the formula, is the atmospheric density; ​is the derivative of the lateral force to the sideslip angle. According to GJB185 "Manned Aircraft (Fixed Wing) Flight Quality", the roll mode flight quality specification standard of the Netherlands is shown in the following table. After obtaining the roll mode frequency and damping ratio of the Netherlands, the flight quality evaluation of the aircraft heading axis is carried out by judging the specified range to which it belongs.

[0144] Table 3 Roll mode quality judgment standard of the Netherlands

[0145]

[0146] Step 3, data and knowledge driven neural network training

[0147] This step will first carry out mass simulation on the basis of the adaptive control bandwidth based active disturbance rejection controller designed on the ground, and pull the bias of the moment coefficient and atmospheric density to obtain the optimal active disturbance rejection control parameters. After obtaining a large number of flight sample data under different working conditions to form a training data set, the mapping relationship between the aircraft state and the gain adjustment parameter and the rudder deflection is established offline to form a neural network of data and knowledge mixed driven active disturbance rejection control parameter optimization. In the offline neural network training process, it mainly includes data set generation, training, verification and testing steps.

[0148] Step 3.1, data set generation: this step is to generate data of optimal controller parameters under complex flight conditions and flight tasks of the aircraft, so as to train a neural network prior knowledge model that can optimize the controller parameters with high accuracy and high generalization. First, the flight state database covering multiple flight conditions and flight tasks, model uncertainties needs to be collected and generated. These data need to simulate the performance of the actual aircraft under various complex environments and tasks as much as possible to ensure the sufficiency and generalization ability of the model training. Then under the same flight condition and task, the controller parameters are continuously adjusted until the optimal controller parameters are found, and finally a large amount of training data is generated. Specifically, first, change the aerodynamic force and moment model parameters to generate data containing model errors, and realize the simulation of model uncertainty. Second, change the atmospheric density to simulate different environmental conditions and generate external disturbance data to realize the simulation of environmental disturbance. Third, for the same flight condition and flight task, continuously adjust the parameters of the active disturbance rejection controller to find the best control effect parameter, and realize the optimal setting of the controller parameters. Finally, the data set is divided into training set, verification set and test set with certain allocation ratio for the later design verification.

[0149] Step 3.2, training, validation and testing: After the dataset is generated, the dataset is divided into input data samples and target data samples, the input data samples are historical data for model input, and the target data samples are future data to be predicted. Train these data, the neural network used for training is the physical information neural network (PINN). PINN is based on a fully connected deep neural network (FNN), combining traditional neural networks and physical laws, and is a method of embedding physical principles into neural networks. The basic idea of PINN is to use a neural network as an approximation function to fit the solution of the differential equation, and at the same time, the physical constraints are part of the loss function, so as to ensure that the results solved by the network comply with the physical properties of the differential equation. The neural network selects 5 hidden layers, 64 neurons in each layer, and the activation function is selected function, which is specifically shown as follows:

[0150] (11)

[0151] The input of the neural network is , , and , wherein represents a time variable, represents a state variable group, including flight state data , is the flight altitude, is the model error, which is the error between the actual state of the aircraft and the reference model, is the angular rate sensor signal after band-pass filtering. The output of the neural network is the predicted gain adjustment parameter and the rudder effect , wherein , is the maximum value of the gain.

[0152] The loss function includes data fitting loss and physical consistency loss. In detail, the sampling points of the data-driven part are selected in the same way as the training set in traditional deep learning technology, which can be obtained through experimental observation, numerical simulation, etc. These data are usually regarded as true values. The data fitting loss can be defined as the error between the network output value and the true value:

[0153] (12)

[0154] In the formula, is the number of real data points obtained, is 1000, and are the first Predictive rudder effectiveness and predictive control bandwidth gain for each data point and They are the first The true rudder effect and optimal control bandwidth gain for each data point.

[0155] For the physical constraint part of the loss function, we aim to fit the solution of the differential equation using a neural network; therefore, we need to construct the differential equation bias. We use the automatic differentiation module in the neural network toolkit to calculate the time derivative of the gain adjustment parameter predicted by the neural network, thus obtaining the physical bias. :

[0156] (13)

[0157] In the formula, The number of real data points that have been obtained. For 1000, and These are the neural network's first... Model error and sensor signal for each data point , These represent the strength of the impact of error on bandwidth and the strength of the impact of chatter on bandwidth, respectively.

[0158] initial deviation Used to ensure that the network's output at the initial time is consistent with the given initial conditions, boundary deviation This involves comparing the adaptive gain predicted by the network with the range of the adaptive gain, as shown in the following formula:

[0159] (14)

[0160] (15)

[0161] In the formula, The number of real data points that have been obtained. For 1000, and These are the initial prediction of rudder effectiveness and the prediction of control bandwidth gain via neural network. and These are the initial true steering effect and the optimal control bandwidth gain, respectively.

[0162] The loss function of a physical information neural network is a weighted sum of the data-driven part and the physical-driven part (physical bias, boundary bias, initial bias), which can be expressed as:

[0163] (16)

[0164] In the formula, are weights used to balance their influence on the overall loss function. Set , .

[0165] After getting the loss function, the trainable variables in the neural network need to be optimized according to the loss function value. For problems with a large training set and high-dimensional parameters, the Adam optimizer has the characteristics of high efficiency and rapidity, and its specific updating method is as follows:

[0166] (17)

[0167] (18)

[0168] (19)

[0169] (20)

[0170] (21)

[0171] In the formula, is the current iteration number, 1000 times are selected, and the size of each batch is 512, represents the current momentum of the optimization step, represents the current momentum of the optimization step, represents its bias correction value, is the to-be-optimized parameter of the th iteration, represents the loss function with respect to , represents the current second-order momentum of the optimization step, represents the current second-order momentum of the optimization step, represents its bias correction value; is the first-order momentum history momentum retention rate, which is 0.9, is the second-order momentum history momentum retention rate, which is 0.999, is the product of , is the product of ; is the learning rate, which is 0.001, is a very small number, which is , used to prevent the denominator from being 0.

[0172] ​​In this step, the physical information neural network trained, validated and tested based on the effective data set has the function of updating the controller parameters and will be used as a parameter optimizer for the design of the subsequent intelligent controller.

[0173] Step 4, intelligent controller design based on physical information neural network

[0174] This step makes full use of the physical information neural network generated by data fitting constraints and physical information constraints in step 3 to carry out intelligent controller design. Specifically as follows:

[0175] Considering that the actual flight state of the aircraft in a complex environment will deviate greatly from the reference model, the control effect of the traditional method of using offline fixed controller gain will be significantly reduced. To solve this problem, an adaptive control gain is designed, which can adapt to the model deviation in real time. The longitudinal feedback control rate is as follows: (22)

[0176] In the formula, is the feedback control rudder deflection, is the angle error and the angular velocity error, respectively, and the time-varying gain is as follows:

[0177] (23)

[0178] In the formula, is the rudder effect, which is one of the outputs of the physical information neural network; is a preset fixed damping ratio, which functions to ensure the stability in the attitude control process and avoid overshoot or chattering. represents the adaptive bandwidth, which corrects the offline control gain according to the actual control effect, The update law is as follows:

[0179] (24)

[0180] In the formula, is the adaptive gain of the bandwidth, which is the core adjustment factor and determines the degree of deviation of the actual bandwidth from the nominal bandwidth, wherein and are the minimum value and the maximum value of the bandwidth adaptive gain. is the nominal control bandwidth, which is the reference bandwidth calculated offline in the traditional method. is the gain adjustment parameter, wherein is the maximum value. is the sensor signal of the angular rate after the band-pass filter. , respectively represent the influence intensity of the error on the bandwidth and the influence intensity of the chattering on the bandwidth, Take 12, Take 8. Error between actual state of aircraft and reference model.

[0181] Extended state observer is the core technology of active disturbance rejection controller, which can accurately estimate the state and total disturbance of the system, and compensate the disturbance of the system according to the estimated value of the disturbance. The longitudinal attitude dynamics equation is as follows:

[0182] (25)

[0183] In the formula: is ; is ; Contains unmodeled dynamics and dynamic coupling terms; is the rudder effect; is the elevator deflection angle; is the output of the system.

[0184] The designed longitudinal linear extended state observer equation is:

[0185] (26)

[0186] In the formula: is the observation value of ; is the observation value of ; is the rudder effect, which is also the compensation factor that determines the strength of compensation; is the difference between the observation value and the system output; is the observer gain, which is represented by the observer bandwidth , which is generally taken as 10:

[0187] (27)

[0188] The process of using extended observer to estimate and compensate the total disturbance in real time is called dynamic compensation linearization. The disturbance compensation rudder deflection of extended state observer is designed as follows:

[0189] (28)

[0190] The control amount of pitch channel can be represented as the sum of feedback control rudder deflection and extended state observer disturbance compensation rudder deflection:

[0191] (29)​

[0192] To verify the effectiveness of this physical information-driven high-speed aircraft flight quality analysis and intelligent control method, the simulation experiment results are shown in Figures 3-6 Figure 3 The effect curve of angle of attack tracking is given. The command signal and the real attitude angle signal first flatten and then decline, indicating that the control system has excellent tracking effect on the speed reference command. Figure 4 The effect curve of roll angle tracking is shown. In the first 80 seconds, there is a gap between the command signal and the real roll angle, and the real roll angle value is higher than the command. The gap between the two gradually narrows; after 80 seconds, they almost completely coincide, indicating that the real roll angle gradually coincides with the tracking signal. Figure 5 The elevator deflection angle command change is given. In the first 100 seconds, the elevator command is relatively stable; after 100 seconds, the elevator command has significant fluctuations, reflecting the adjustment process of the angle of attack. Figure 6 The aileron deflection angle command curve over time is shown. In the first 20 seconds, the deflection command has significant fluctuations, reflecting the adjustment process of the roll angle. After 20 seconds, the deflection command basically stays in a small amplitude range, indicating that the aircraft has entered a relatively stable flight state and no longer needs frequent control surface adjustment. The above simulation tests prove the effectiveness of this physical information-driven high-speed aircraft flight quality analysis and intelligent control method, which can improve the performance and stability of the control system and ensure that the hypersonic aircraft can achieve high-precision and high-reliability autonomous control in practical applications.​

Claims

1. A physical information-driven method for analyzing and intelligently controlling the flight quality of high-speed aircraft, characterized in that, The steps are as follows: Step 1: Construction of high-speed aircraft dynamics model A dynamic model of a high-speed aircraft is established based on a rigid body mathematical model and an aerodynamic coupling model. (1) In the formula, the superscript " " represents the first derivative; It's an attack angle. It is the sideslip angle. It is the yaw angle. It is the roll rate. It is the yaw rate. It is the pitch rate. It is the trajectory angle. For quality, It is the acceleration due to gravity. For flight speed, , , They represent along , , Moment of inertia of the shaft; It is the product of inertia; For dynamic pressure, It is the wing reference area. This is the reference length for the wing; These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively. These are the roll damping moment coefficient, yaw damping moment coefficient, and pitch damping moment coefficient, respectively. These are lateral force, lift, and drag, respectively, and their specific expressions are as follows: (2) In the formula, These are the axial force coefficient, normal force coefficient, and lateral force coefficient, respectively. All are with Related functions, Mach number, control quantity , These are the aileron deflection angle, rudder deflection angle, and elevator deflection angle, respectively. The dynamic process of the actuator is described using a second-order element as follows: (3) In the formula, It is a Laplace variable; This indicates the actual rudder deflection for the corresponding channel. This indicates the command rudder deflection for the corresponding channel, which refers to the direction corresponding to roll, yaw, and pitch. and These represent the natural frequency and damping ratio of the servo system, respectively. Step 2: High-speed aircraft flight quality assessment Step 2.1, Longitudinal Flight Quality Evaluation Equation (1) is divided into longitudinal and lateral equations, where the longitudinal equation is: (4) Linearizing equation (4) with small perturbations, we obtain: State quantity, with elevator deflection angle The state-space equations for the input variables are shown below: (5) In the formula, This is the offset of the angle of attack. This is the deflection of the pitch rate. This represents the deflection of the elevator angle. Let be a partial derivative of the angle of attack. This is the deviator of the derivative of the pitch rate; the deviator refers to the difference between the disturbance and the undisturbed quantity. , The change in lift caused by the change in angle of attack; , The change in lift caused by a unit pitch rudder deflection; ; , This is the derivative of the pitch moment coefficient with respect to the angle of attack; , The change in pitch moment caused by a unit pitch rudder deflection; set up ,in Let be a constant, substitute it into equation (5), and let And eliminate The characteristic equation is obtained as follows: (6) Equation (6) and the standard second-order equation Compare the corresponding items. These are the natural frequency and the damping ratio, respectively, expressed as: ; After obtaining the natural frequency and damping ratio, there are two methods for flight quality assessment; Step 2.1.1, Short-period pitch response According to GJB185 "Flight Quality of Manned Aircraft (Fixed Wing)", the flight quality specification has requirements for short-period modal characteristics. The evaluation indicators for short-period modal characteristics are damping ratio and natural frequency. After obtaining the damping ratio and natural frequency of the aircraft, the longitudinal flight quality of the aircraft is evaluated by determining the range to which they belong in different flight phases. Step 2.1.2: Evaluate based on CAP parameters. The desired control parameter (CAP) correlates the pilot's sensitivity to pitch rate with the perceived aircraft normal overload, predicting the final trajectory from the initial attitude response. The CAP expression is: (7) In the formula, For normal overload, specifically defined as After obtaining the CAP parameters, the flight quality assessment of the aircraft pitch axis is carried out based on the CAP specification range of GJB185 "Flight Quality of Manned Aircraft (Fixed Wing)" for different flight phases. Step 2.2, Evaluation of Lateral Flight Quality Step 2.2.1, Rolling Mode Time Constant Roll mode time constant The roll damping characteristics of the aircraft are described, and the expression is as follows: (8) In the formula, This is the derivative of the rolling moment coefficient with respect to the sideslip angle. The derivative of the yaw moment coefficient with respect to the sideslip angle; according to GJB185 "Flight Quality of Manned Aircraft (Fixed Wing)", the roll mode time constant has a maximum value; after obtaining the roll mode time constant... Then, by determining the scope of the regulations to which it belongs, the flight quality of the aircraft roll shaft is assessed. Step 2.2.2, Dutch Roll Mode Dutch rolling modal frequency Damping ratio The calculation formula is: (9) (10) In the formula, It is atmospheric density; It is the derivative of the lateral force with respect to the sideslip angle; according to GJB185 "Flight Quality of Manned Aircraft (Fixed Wing)", the Dutch roll mode flight quality specification standard is determined; after obtaining the Dutch roll mode frequency... Damping ratio Then, by determining the prescribed range to which it belongs, the flight quality of the aircraft's heading axis is assessed; Step 3: Data- and Knowledge-Driven Neural Network Training First, based on the adaptive control bandwidth-based active disturbance rejection controller designed on the ground, massive simulations were conducted, and the torque coefficient and atmospheric density were adjusted to obtain the optimal active disturbance rejection control parameters. After obtaining a large amount of flight sample data under different operating conditions to form a training dataset, the mapping relationship between the aircraft state and the gain adjustment parameters and rudder deflection was established offline to form a neural network for optimizing active disturbance rejection control parameters driven by a combination of data and knowledge. The obtained physical information neural network has the function of updating controller parameters and will be used as a parameter optimizer for the subsequent design of intelligent controllers. Step 4: Design of an intelligent controller based on a physical information neural network The following longitudinal feedback control law is designed to have adaptive control gain and can adapt to model bias in real time: (21) In the formula, It is feedback control of rudder deflection. These are the angle error and angular velocity error, respectively, and the adaptive control gain. As shown in the following formula: (22) In the formula, It is the rudder effect, one of the outputs of the physical information neural network; It is a preset fixed damping ratio; This indicates the adaptive bandwidth, which adjusts the offline control gain based on the actual control effect. The update law is as follows: (23) In the formula, For the adaptive gain of bandwidth, where, and These are the minimum and maximum values ​​of the bandwidth adaptive gain; The nominal control bandwidth; Here is the gain adjustment parameter, where It is the maximum value; It is the sensor signal of angular velocity after passing through a bandpass filter; , These represent the intensity of the impact of error on bandwidth and the intensity of the impact of chatter on bandwidth, respectively. This represents the error between the actual state of the aircraft and the reference model. The extended state observer is used to estimate the system state and total disturbance. Based on the disturbance estimate, the system is compensated for the disturbance. The longitudinal attitude dynamics equation is shown below: (24) In the formula: for ; for ; Includes unmodeled dynamic and dynamically coupled terms; It's the rudder effect; Elevator deflection angle; This is the system output; The equations for designing the longitudinal linear expansion state observer are as follows: (25) In the formula: for Observed values; for Observed values; For total disturbance Observed values; It is the rudder effect, and also the compensation factor that determines the strength of the compensation. This is the difference between the observed value and the system output. For observer gain, use observer bandwidth. To represent the observer gain: (26) The process of using an extended state observer to estimate and compensate for the total disturbance in real time, transforming the original system into a linear integrator series system, is called dynamic compensation linearization. Extended state observer disturbance compensation for rudder deflection. The design is as follows: (27) Pitch channel control quantity This is expressed as the sum of the feedback control rudder deflection and the extended state observer disturbance compensation rudder deflection: (28)。 2. The method for analyzing and intelligently controlling the flight quality of a high-speed aircraft driven by physical information according to claim 1, characterized in that, Step 3 is as follows: Step 3.1, Dataset Generation: First, a flight state database covering various flight conditions and missions, as well as model uncertainties, needs to be collected and generated. Then, under the same flight conditions and missions, the controller parameters are continuously adjusted until the optimal controller parameters are found, and finally, a large amount of training data is generated. Specifically, first, the aerodynamic force and torque model parameters are changed to generate data containing model errors, thereby simulating model uncertainties; second, the atmospheric density is changed to simulate different environmental conditions, generating external disturbance data, thereby simulating environmental disturbances; third, for the same flight conditions and missions, the parameters of the active disturbance rejection controller are continuously adjusted to find the set of parameters with the best control effect, thereby achieving optimal tuning of the controller parameters; finally, the dataset is divided into training, validation, and test sets according to a certain allocation ratio for subsequent design verification. Step 3.2, Training, Validation and Testing: After the dataset is generated, it is divided into input data samples and target data samples. The input data samples are historical data used for model input, and the target data samples are future data to be predicted. The neural network used for training is the Physical Information Neural Network (PINN). The input data sample, i.e., the input to the neural network, is... , , and ,in, Represents a time variable; This represents a group of state variables, including flight state data. , Flight altitude; Model error is the error between the actual state of the aircraft and the reference model. The angular rate is the sensor signal after passing through a bandpass filter; the target data sample, i.e., the output of the neural network, is the predicted gain adjustment parameter. and rudder effect ,in , This represents the maximum gain. The loss function includes data fitting loss and physical consistency loss; data fitting loss Defined as the error between the network output value and the true value: (11) In the formula, The number of real data points that have been obtained. and These are the neural network pairs of the first... Predictive rudder effectiveness and predictive control bandwidth gain for each data point and They are the first The true rudder effectiveness and optimal control bandwidth gain of each data point; For the physical constraint part of the loss function, the automatic differentiation module in the neural network toolkit is used to calculate the time derivative of the gain adjustment parameter predicted by the neural network, thus obtaining the physical bias. : (12) In the formula, and These are the neural network's first... Model error and sensor signal for each data point , These represent the intensity of the impact of error on bandwidth and the intensity of the impact of chatter on bandwidth, respectively. initial deviation Used to ensure that the network's output at the initial time is consistent with the given initial conditions, boundary deviation This involves comparing the adaptive gain predicted by the network with the range of the adaptive gain, as shown in the following formula: (13) (14) In the formula, and These are the initial prediction of rudder effectiveness and the prediction of control bandwidth gain via neural network. and These are the initial true rudder effect and the optimal control bandwidth gain, respectively. Loss function of physical information neural network It consists of a weighted sum of the data-driven and physical-driven components, expressed as: (15) In the formula, These are weights, used to balance their impact on the total loss function.

3. The method for analyzing and intelligently controlling the flight quality of a high-speed aircraft driven by physical information according to claim 2, characterized in that, After obtaining the loss function, the trainable variables in the neural network need to be optimized based on the loss function value. Adam is used, and its specific update method is as follows: (16) (17) (18) (19) (20) In the formula, It is the current iteration number. express Optimize the current momentum in the next step. express Optimize the current momentum in the next step. This indicates its deviation correction value. It is the first The parameters to be optimized in the next iteration. Represents the loss function about gradient, express Optimize the current second-order momentum in the next step. express Optimize the current second-order momentum in the next step. This indicates its deviation correction value; The first-order momentum history momentum retention rate, The second-order momentum history momentum retention rate. for indivual The product of multiplication, for indivual The product of multiple products; It's the learning rate. It is a very small number used to prevent the denominator from being 0.

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