Trajectory optimization and guidance method for mode transition of combined power aircraft

Abstract

The present application belongs to the field of hypersonic vehicle trajectory optimization and guidance control, and relates to a trajectory optimization and guidance method in the mode conversion process of a combined power vehicle. By establishing a vehicle particle dynamics model, trajectory optimization is performed on the climb segment and mode conversion segment in combination with an adaptive Gauss pseudospectral method, a flight strategy is designed to exchange potential energy for kinetic energy, and the vehicle is accelerated to cross the thrust trap through diving when the thrust is insufficient. At the same time, integrated flight and thrust control is realized based on a trajectory linearization control method, the linearized error equation along the optimized trajectory is designed, and a time-varying feedback control law is designed to realize high-precision stable tracking of the optimized trajectory through coordinated adjustment of the angle of attack and the throttle. An intelligent tracking method for online application trains a deep neural network to learn the mapping rule of the flight state, the error and the optimal parameters, and combines time and frequency domain performance indicators to select the optimal control parameters, thereby enhancing the tracking robustness in complex working conditions.

Description

Technical Field

[0001] This invention belongs to the field of hypersonic vehicle trajectory optimization and guidance control, and relates to a trajectory optimization and guidance method during the mode transition process of a combined propulsion vehicle. Background Technology

[0002] During wide-speed-range flight, combined-powered aircraft undergo a mode transition phase from turbofan engines to ramjet engines. During this process, because the turbofan engine has reached its operational limit while the ramjet engine has not yet entered its high-efficiency operating range, a "thrust trap" phenomenon often occurs, where the total thrust cannot meet the acceleration requirements for level flight, severely impacting the aircraft's acceleration and climb performance. Existing research largely focuses on engine performance improvement or inlet flow control, lacking a systematic solution to the thrust trap problem during the mode transition phase from the perspectives of trajectory optimization and integrated flight / propulsion control. Traditional trajectory optimization methods often suffer from limitations such as poor convergence, low computational efficiency, or inability to effectively overcome insufficient thrust when dealing with strongly coupled, multi-constraint problems like mode transitions.

[0003] The patent "A Trajectory Optimization Method for Combined-Powered Aircraft Based on Convex Hybrid Integer Programming" (CN113111434A) proposes a trajectory optimization method for combined-powered aircraft based on convex hybrid integer programming. This method can solve the problem of trajectory optimization involving integer variables and achieve aircraft mode selection and optimal trajectory optimization. However, this method uses equal time intervals to divide flight phases, which lacks flexibility and is difficult to adapt to complex and changing flight environments. Furthermore, the initial reference trajectory needs to be manually provided, which is highly subjective and may affect the rationality of the optimization starting point, potentially impacting flight safety.

[0004] The patent "A Method for Envelope Design and Trajectory Optimization of Combined-Power Air-breathing Mode Flight" (CN119249600A) proposes a method for envelope design and trajectory optimization of combined-power air-breathing mode flight, which can solve the design challenges of multiple constraints and high terminal window accuracy in the ascent phase of air-breathing combined-power aircraft. However, this method does not specify the method for determining the initial values ​​of the initial flight state, which may affect the accuracy of subsequent calculations. Furthermore, it does not mention the efficiency of angle-of-attack profile calculation and trajectory determination under complex operating conditions, and may have insufficient real-time performance, which is not conducive to engineering applications.

[0005] The patent "Control Method Based on Mode Transition Phase of Tilrotor Aircraft" (CN109581878A) proposes a control method based on the mode transition phase of a tiltrotor aircraft. This method features fast controller convergence and low input, effectively solving the control challenges of the mode transition phase. However, this method does not consider the impact of measurement errors on control accuracy during actual flight, relies on a specific toolkit, and its adaptability in engineering applications may be limited. Furthermore, this method only verifies its effectiveness through local simulations and does not address control stability under complex conditions such as external disturbances and component failures, which is detrimental to comprehensively ensuring flight safety.

[0006] The paper "An Optimization Method for Ascent Trajectory under RBCC Mode Transition [J]. Aerospace Technology, 2024, (05): 71-80" addresses the problems of multiple modes, complex transitions, stringent constraints, and strong nonlinearity in the ascent phase of RBCC-powered aerospace vehicles, as well as the difficulties in convergence and cumbersome constraint handling of existing methods. It proposes a parameter / trajectory co-optimization scheme that can adapt to different orbital insertion scenarios and solve the trajectory optimization problem under mode transitions. However, this method does not clearly define its robustness under complex operating conditions (such as atmospheric disturbances and engine performance deviations), nor does it address efficiency adaptation in real-time engineering applications. The trajectory reliability under extreme scenarios remains to be verified.

[0007] Therefore, there is an urgent need for a trajectory optimization and guidance method for the mode transition process of combined propulsion aircraft, which can avoid or reduce the impact of thrust traps through reasonable trajectory design, under the premise of satisfying multiple path and terminal constraints, and ensure that the aircraft can safely and efficiently complete the mode transition and acceleration tasks. Summary of the Invention

[0008] The purpose of this invention is to provide a trajectory optimization and guidance method for the mode transition process of a combined-powered aircraft. This method can effectively overcome the thrust trap problem in the mode transition stage and achieve smooth acceleration and climb of the aircraft.

[0009] The technical solution of the present invention is as follows:

[0010] A trajectory optimization and guidance method for a combined-powered aircraft during mode transition includes: constructing the three-variable centroid motion dynamic equations of the aircraft during the mode transition phase; optimizing the trajectory flight strategy during the mode transition phase, dividing the mode transition process into a climb preparation phase and a mode transition acceleration phase, and employing a trajectory optimization method based on the Gaussian pseudospectral method to transform the continuous optimal control problem of each sub-phase into a nonlinear programming problem; designing a tracking controller based on trajectory linearization control, linearizing the error state equation along the optimized trajectory, designing a time-varying feedback control law to achieve high-precision tracking of the optimized trajectory and improve system robustness; and designing an intelligent tracking method for online applications, using a trained neural network to filter controller parameters. Details are as follows:

[0011] Step 1: Construct the three-variable center-of-mass motion dynamics equations of the aircraft during the mode transition phase.

[0012] (1)

[0013] Among them, the superscript " " represents the first derivative; For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

[0014] Step 2: Trajectory Optimization Flight Strategy during Mode Transition Phase

[0015] The mode transition process is divided into a climb preparation phase and a mode transition acceleration phase. In the climb preparation phase, the turbine engine uses its power turbine to propel the aircraft to sufficient altitude and speed, accumulating kinetic and potential energy for the subsequent mode transition acceleration. In the mode transition acceleration phase, the turbine and ramjet engines work in tandem, employing an adaptive Gaussian pseudospectral method for trajectory optimization. A pre-set trajectory is used for further acceleration, bringing the aircraft into the normal operating speed range of the ramjet engine. Regarding trajectory planning, the first stage aims to bring the aircraft to the turbine engine's service ceiling; the second stage aims to bring the aircraft to the speed requirements for normal ramjet engine operation, while simultaneously relaxing altitude restrictions.

[0016] The Gaussian pseudospectral method is a direct optimization method based on spectral discretization, transforming the continuous-time optimal control problem into a nonlinear programming problem. Its core lies in: Discretizing the time domain: Dividing the time interval into multiple sub-segments, and selecting Gaussian collocation points within each sub-segment for discretizing state and control variables. Global polynomial approximation: Using Lagrange interpolation polynomials to approximate the state and control variables, ensuring the polynomial values ​​at the collocation points match the actual state. Differential-algebraic equation transformation: Transforming the constraints of the dynamic differential equations into algebraic constraints through differential matrices, avoiding the complexity of directly solving the differential equations. The specific implementation steps are as follows:

[0017] Step 2.1: Time Domain Segmentation and Discretization

[0018] The mode conversion process is divided into a climbing preparation stage and a mode conversion acceleration stage. The time domain of each stage is mapped to the interval [-1,1] through variable transformation, and N Gaussian collocation points are selected in each stage.

[0019] Step 2.2: Approximation of State Variables and Control Variables

[0020] State variables and control variables Represented by the Lagrange interpolation polynomial:

[0021] (2)

[0022] (3)

[0023] In the formula: For Lagrange basis functions; This represents the total number of Gaussian collocation points, i.e., the number of nodes in the time-domain discretization. The more collocation points, the higher the approximate accuracy. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points.

[0024] Step 2.3: Discretization of the dynamic equations

[0025] For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints:

[0026] (4)

[0027] In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions; Discrete index for Gaussian collocations. For the first Discretized vectors of the motion state of the aircraft's center of mass at each Gaussian collocation point. This refers to the terminal time of the mode transition phase. The start time, For the first The time of a Gaussian collocation point in the original time domain.

[0028] Step 2.4, Constraint Handling

[0029] Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the aircraft, respectively. , , These represent the maximum permissible values ​​for dynamic pressure, overload, and heat flux density of the aircraft. The terminal state should satisfy the constraints of the dynamic equations.

[0030] Step 2.5: Construction of the objective function

[0031] Performance metrics transformed into NLP objective functions :

[0032] (5)

[0033] In the formula: These are the state variables at the terminal moment, including key states such as velocity, altitude, trajectory inclination, and mass. It is the Gaussian integral weight of the kth collocation point, reflecting the importance of each collocation point in the time domain; It is the process performance index function of the kth collocation point, which quantifies the performance requirements at that moment, such as speed deviation, fuel consumption, etc. It is the control variable of the kth coordinate point, such as the angle of attack, throttle opening, etc., which can be actively adjusted; It is the time of the kth collocation point, that is, the terminal time after discretization. It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of mode transition trajectories. It is a terminal performance index function that describes the state performance requirements at the end of the mode transition, ensuring that key constraints are met when the transition is completed, such as the deviation between the terminal speed and the target speed, and the terminal height constraint.

[0034] Step 2.6: Solve the nonlinear programming problem.

[0035] The complete nonlinear programming problem constructed in steps 2.1-2.5 is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory. At this point, the original problem has been transformed into a discretized form, which can be solved by optimizing the discrete state variables. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function Obtain the minimum value.

[0036] Step 3: Tracking guidance strategy based on trajectory linearization control

[0037] The goal of guidance during the mode transition phase is to ensure stable flight of the aircraft along its nominal trajectory by controlling its angle of attack and throttle opening, adjusting parameters such as altitude, speed, and trajectory inclination. The guidance system adjusts control commands in real time based on the deviation between the aircraft's current state and the nominal trajectory to achieve precise control of key parameters such as altitude, speed, and trajectory inclination. The core of this approach lies in establishing a mathematical model of the aircraft's center of mass motion and designing corresponding control laws.

[0038] To facilitate guidance law design, velocity, height, and lateral position are taken as state variables, and the three-variable center-of-mass motion equations are extended to obtain:

[0039] (6)

[0040] In the formula: The flight distance of the aircraft in three-dimensional space. For the lateral direction of the aircraft in the ground coordinate system, i.e. Flight distance along the axial direction. Rearranging this into the error state equation form:

[0041] (7)

[0042] in, Let be the deviation vector between the actual extended dimension state of the spacecraft and the nominal trajectory extended dimension state at time t. , These are the state matrix and input matrix of the linear time-varying error system, respectively. To control the error vector, used for correction This causes the actual trajectory to converge to the nominal trajectory. , These are the nominal state vector and the nominal control vector, respectively. The linearized dynamic function, For the first The error state for the th error state The linearization coefficient of the rate of change of each error state. For the first The control error affects the first Linearization control gain for the rate of change of each error state.

[0043] For the obtained error state equation, a time-varying controller of the following form is adopted:

[0044] (8)

[0045] in, For time-varying control matrix No. Line number Column elements, Error state vector The Each component.

[0046] Expected closed-loop matrix for:

[0047] (9)

[0048] in, - for The corresponding 6 expected eigenvalues. The expected closed-loop matrix should satisfy... By adjusting the values ​​of the time-varying controller parameter matrix, the desired closed-loop matrix can be written in the form described above. Therefore, the control parameter matrix is:

[0049] (10)

[0050] (11)

[0051] (12)

[0052] in, For time-varying control matrix The control parameter elements of each decomposed subspace correspond to the second-order system control requirements of the three error subspaces (velocity, height, and lateral position). These control parameters are determined by the desired eigenvalues, so the core issue lies in selecting these desired eigenvalues.

[0053] From the expected closed-loop system matrix, it can be seen that all three error subspaces can be described as linear time-varying second-order systems, which can be described in the form of the characteristic equation:

[0054] (13)

[0055] Therefore:

[0056] (14)

[0057] In the formula: These represent the time-varying damping ratios for the velocity, height, and lateral position error subspaces, respectively. These represent the time-varying natural frequencies of the velocity, altitude, and lateral position error subspaces, respectively. The desired natural frequencies and damping ratios of the system can be determined by the required performance parameters (including rise time, overshoot, etc.), thereby enabling the design of controller parameters that meet the performance requirements.

[0058] Based on the current rise time of the step response of underdamped second-order linear systems and overshoot Estimation formula:

[0059] (15)

[0060] (16)

[0061] in, For general damping ratio, It is a universal natural frequency.

[0062] Given the required rise time and overshoot of the closed-loop control system, the damping ratio and frequency of the desired system can be solved simultaneously, and then the eigenvalues ​​of the desired system matrix can be determined to obtain the controller parameters.

[0063] Step 4: Design an intelligent tracking method for online applications.

[0064] To address the real-time and robustness requirements of tracking and guidance during mode transitions, this paper proposes an intelligent tracking method for online applications, combining the nonlinear fitting capability of deep neural networks with the optimization logic of control performance indicators. This method achieves real-time optimal adjustment of controller parameters through the synergy of offline training and online inference. The method takes flight state, error information, and aerodynamic uncertainties as inputs and outputs core controller parameters that meet performance requirements. It leverages the empirical knowledge accumulated from massive simulations to empower online decision-making. The specific implementation process is as follows:

[0065] First, a comprehensive training dataset is constructed. Using the climb preparation and acceleration phases of the mode transition stage as core operating conditions, and based on the three-variable center-of-mass motion dynamics equations and trajectory linearization error model, aerodynamic parameters for yaw (static stability coefficient uncertainty) are injected. Uncertainty of manipulation coefficients Typical uncertainties such as measurement errors alter the natural frequency. Damping ratio Massive simulations are performed on the controller parameters. The dataset input vector is defined as a fusion vector of flight state, error state, and uncertainty parameters:

[0066] (17)

[0067] in, For flight speed, For flight altitude, For the trajectory inclination angle, , , These represent the errors in flight speed, flight altitude, and trajectory inclination angle compared to the nominal trajectory, respectively; the output vector represents the optimal controller parameters. , The optimal natural frequency, The optimal damping ratio is the natural frequency and the optimal damping ratio that meet the performance requirements.

[0068] Secondly, a control performance evaluation model and parameter selection mechanism are established. Referring to the comprehensive performance requirements in the time and frequency domains, the rise time is selected. Overshoot As a core time-domain indicator, the magnitude margin is supplemented by the stability requirements of the mode transition stage. Phase margin Frequency domain metrics are used to construct a multi-objective optimization evaluation function.

[0069] (18)

[0070] In the formula, the subscript 0 represents the baseline value of the performance index, and the subscript nor represents the normalized value. , These represent the rise time. The baseline value, normalized value, , They represent overshoot. The baseline value, normalized value, , These represent the gain margin. The baseline value, normalized value, , They represent phase margins respectively. The baseline value and normalized value. Maximizing the evaluation function. Filter the optimal parameters for each set of inputs. , ,in and The following second-order system performance constraints must be satisfied:

[0071] (19)

[0072] Then, deep neural network training and optimization were performed. A 5-layer fully connected neural network structure was adopted, where the input layer dimension and input vector... With consistent settings, the number of neurons in the hidden layer is set to 10, 5, and 5 respectively, and the output layer outputs the optimal parameters. and During network training, 90% of the samples are used as the training set, and the predicted natural frequencies are output through forward propagation. Damping ratio prediction value The propagation relationship is as follows:

[0073] (20)

[0074] In the formula, , , , They are respectively the 1st floor, the 4th floor, and the 5th floor. Layer, First The layer's output vector; , Here are the weight matrix and bias vector for layer 1. , Here are the weight matrix and bias vector for layer 5. , These are the weight matrix and bias vector of the l-th layer, respectively. , , They are respectively the 1st floor, the 5th floor, and the 6th floor. The activation function of the layer; using 10% of the samples as the test set, the network parameters are iteratively updated through error backpropagation, minimizing the difference between the predicted value and the selected optimal parameters. , The root mean square error is calculated until the network fitting accuracy meets the engineering requirements, i.e., the root mean square error of the test set is ≤0.06.

[0075] During the online application phase, flight status is collected in real time through sensors. With trajectory error Real-time uncertainty parameters are obtained by combining recursive least squares aerodynamic parameter identification methods. Construct the input vector The input is then fed into the trained neural network. The network outputs the optimal natural frequency through real-time inference. With damping ratio Substituting the values ​​into the characteristic equation yields the desired eigenvalues, which are then used to solve for the time-varying control parameter matrix, enabling high-precision adaptive tracking of the optimized trajectory. This method eliminates the need for online solving of complex nonlinear programming problems. Real-time performance is ensured through the rapid inference capabilities of neural networks, while the availability of massive sample data covering complex operating conditions enhances the tracking robustness under parameter uncertainties and external disturbances during the mode transition stage.

[0076] The beneficial effects of this invention are:

[0077] This invention effectively solves the thrust trap problem faced by combined-powered aircraft during mode transitions through an integrated design of trajectory optimization and guidance control, significantly improving the success rate of flight missions and the overall system performance. First, this invention abandons the traditional approach of relying on adding auxiliary power units to improve the propulsion system. Instead, it designs a special flight trajectory, utilizing gravity assistance and potential energy conversion strategies to compensate for insufficient thrust during mode transitions, thus successfully overcoming the thrust trap phenomenon without increasing system complexity or weight. Specifically, this method divides the mode transition process into two stages: climb preparation and mode transition acceleration. By accumulating kinetic and potential energy during climb and employing an optimized dive acceleration trajectory during the transition stage, potential energy is effectively converted into kinetic energy, enabling continuous acceleration of the aircraft in the thrust-deficient range and ensuring its smooth transition to the effective operating speed range of the ramjet engine. Second, this invention combines trajectory linearization control methods with a high-precision integrated flight-thrust guidance law. By coordinating the adjustment of control variables such as angle of attack and throttle opening, stable tracking of the optimized trajectory is achieved. This guidance strategy transforms a nonlinear problem into a time-varying error adjustment problem, exhibiting good robustness even when facing uncertainties such as aerodynamic parameter deviation. The intelligent tracking method proposed in this invention for online applications balances real-time performance and robustness in mode transition control through a collaborative mechanism of offline training and online inference. In the offline phase, massive simulations cover multiple operating conditions and uncertainties, and optimal controller parameters are selected by combining time-frequency domain performance indicators. This allows the deep neural network to fully learn the mapping between flight state, error information, and optimal parameters, eliminating the need for solving complex nonlinear programming problems online. In the online phase, relying on the rapid inference capability of the neural network, core control parameters such as natural frequency and damping ratio are output in milliseconds, adapting to the dynamic changes in flight state during mode transitions and solving the real-time insufficiency problem of traditional guidance methods. Simultaneously, this method, combined with recursive least squares aerodynamic parameter identification technology, can capture aerodynamic uncertainties and measurement errors in real time, enabling adaptive adjustment of control parameters and further enhancing tracking robustness under complex conditions. Furthermore, the neural network model can be continuously optimized through feedback iteration of online flight data, achieving long-term improvement in control accuracy.

[0078] Simulation results demonstrate that this method effectively overcomes thrust trapping, improves aircraft acceleration performance, trajectory tracking accuracy, and mission success rate, and maintains stability and adaptability even under complex conditions such as aerodynamic parameter deviation and external disturbances. This invention not only provides an economical, efficient, and feasible new technical approach to solving the thrust trapping problem in combined-fuel aircraft, but also enhances the aircraft's adaptability and mission reliability in complex dynamic environments through an integrated flight-thrust control strategy, possessing significant engineering practical value and broad application prospects. Attached Figure Description

[0079] Figure 1 This is a general block diagram of the mode conversion trajectory optimization and guidance method for combined-propellant aircraft;

[0080] Figure 2 This is a flight strategy diagram for the mode transition phase of a combined-propellant aircraft.

[0081] Figure 3 This is a graph showing the altitude-time curve of a combined-powered aircraft.

[0082] Figure 4 This is a velocity-time curve of a combined-propellant aircraft.

[0083] Figure 5 This is a time curve of the trajectory inclination of a combined-propellant aircraft.

[0084] Figure 6 This is a mass-time curve of a combined-propellant aircraft.

[0085] Figure 7 This is a graph showing the angle-of-attack time of a combined-propellant aircraft.

[0086] Figure 8 These are the turbine throttle time curve and the ramjet fuel equivalence ratio time curve of the combined-power aircraft. Detailed Implementation

[0087] The embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0088] like Figure 1 As shown, the present invention provides a trajectory optimization and guidance method for a combined-powered aircraft during the mode transition phase, comprising:

[0089] Step 1: Construct the three-variable center-of-mass motion dynamics equations of the aircraft during the mode transition phase;

[0090] Step 2: Trajectory optimization flight strategy during mode transition. The mode transition process is divided into a climb preparation stage and a mode transition acceleration stage. A trajectory optimization method based on Gaussian pseudospectral method is adopted to transform the continuous optimal control problem of each sub-stage into a nonlinear programming problem.

[0091] Step 3: Design of a tracking controller based on trajectory linearization control. Linearize the error state equation along the optimized trajectory, design a time-varying feedback control law to achieve high-precision tracking of the optimized trajectory and improve system robustness.

[0092] Step 4: Intelligent tracking method for online applications, which filters controller parameters by training a neural network.

[0093] Specifically, the embodiments of the present invention are described as follows:

[0094] Step 1: Construct the three-variable center-of-mass motion dynamics equations of the aircraft during the mode transition phase;

[0095] (twenty one)

[0096] The superscript “ ” indicates the first derivative; For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

[0097] Step 2: Trajectory Optimization Flight Strategy during Mode Transition Phase

[0098] The mode transition process is divided into a climb preparation phase and a mode transition acceleration phase. In the climb preparation phase, the turbine engine uses its power turbine to propel the aircraft to sufficient altitude and speed, accumulating kinetic and potential energy for the subsequent mode transition acceleration. In the mode transition acceleration phase, the turbine and ramjet engines work in tandem, employing an adaptive Gaussian pseudospectral method for trajectory optimization. A pre-set trajectory is used for further acceleration, bringing the aircraft into the normal operating speed range of the ramjet engine. Regarding trajectory planning, the first stage aims to bring the aircraft to the turbine engine's service ceiling; the second stage aims to bring the aircraft to the speed requirements for normal ramjet engine operation, while simultaneously relaxing altitude restrictions.

[0099] The Gaussian pseudospectral method is a direct optimization method based on spectral discretization, transforming the continuous-time optimal control problem into a nonlinear programming problem. Its core lies in: Discretizing the time domain: Dividing the time interval into multiple sub-segments, and selecting Gaussian collocation points within each sub-segment for discretizing state and control variables. Global polynomial approximation: Using Lagrange interpolation polynomials to approximate the state and control variables, ensuring the polynomial values ​​at the collocation points match the actual state. Differential-algebraic equation transformation: Transforming the constraints of the dynamic differential equations into algebraic constraints through differential matrices, avoiding the complexity of directly solving the differential equations. The specific implementation steps are as follows:

[0100] Step 2.1: Time Domain Segmentation and Discretization

[0101] The mode conversion process is divided into a climbing preparation stage and a mode conversion acceleration stage. The time domain of each stage is mapped to the interval [-1,1] through variable transformation, and N Gaussian collocation points are selected in each stage.

[0102] Step 2.2: Approximation of State Variables and Control Variables

[0103] State variables and control variables Represented by the Lagrange interpolation polynomial:

[0104] (twenty two)

[0105] (twenty three)

[0106] In the formula: For Lagrange basis functions; The total number of Gaussian collocations. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points.

[0107] Step 2.3: Discretization of the dynamic equations

[0108] For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints:

[0109] (twenty four)

[0110] In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions. Discrete index for Gaussian collocations. For the first Discretized vectors of the motion state of the aircraft's center of mass at each Gaussian collocation point. This refers to the terminal time of the mode transition phase. The start time, For the first The time of a Gaussian collocation point in the original time domain.

[0111] Step 2.4, Constraint Handling

[0112] Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the aircraft, respectively. , , These represent the maximum permissible values ​​for dynamic pressure, overload, and heat flux density of the aircraft. The terminal state should satisfy the constraints of the dynamic equations.

[0113] Step 2.5: Construction of the objective function

[0114] Performance metrics are transformed into NLP objective functions:

[0115] (25)

[0116] In the formula: These are the state variables at the terminal moment, including key states such as velocity, altitude, trajectory inclination, and mass. It is the number of Gaussian collocation points, that is, the number of nodes in the time domain discretization. The more collocation points, the higher the approximate accuracy. It is the Gaussian integral weight of the kth collocation point, reflecting the importance of each collocation point in the time domain; It is the process performance index function of the kth collocation point, which quantifies the performance requirements at that moment, such as speed deviation, fuel consumption, etc. It is the state variable of the kth collocation point, which includes the velocity, altitude, and other states at that moment; It is the control variable of the kth coordinate point, such as the angle of attack, throttle opening, etc., which can be actively adjusted; It is the time of the kth collocation point, that is, the time node after discretization.

[0117] It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of mode transition trajectories. It is a terminal performance index function that describes the state performance requirements at the end of the mode transition, ensuring that key constraints are met when the transition is completed, such as the deviation between the terminal speed and the target speed, and the terminal height constraint.

[0118] Step 2.6: Solve the nonlinear programming problem.

[0119] The complete nonlinear programming problem constructed in steps 2.1-2.5 is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory. At this point, the original problem has been transformed into a discretized form, which can be solved by optimizing the discrete state variables. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function Obtain the minimum value.

[0120] Step 3: Tracking guidance strategy based on trajectory linearization control

[0121] Trajectory linearization control is an effective nonlinear tracking control method that can well solve the high-precision guidance problem under aerodynamic / propulsion coupling conditions during mode transitions. Compared with traditional trajectory tracking guidance methods based on gain scheduling between feature points, trajectory linearization control replaces linearization at discrete feature points with linearization along the entire flight trajectory. This allows for a more accurate characterization of the original guidance model's dynamics, reduces guidance errors caused by model approximation errors, and improves guidance accuracy during mode transitions in combined-power hypersonic vehicles. By linearizing the dynamic model along the entire flight trajectory, a time-varying feedback control law is designed, and the system performance is optimized using parameter tuning methods to verify the tracking accuracy of the guidance strategy in complex flight environments.

[0122] The goal of guidance during the mode transition phase is to ensure stable flight of the aircraft along its nominal trajectory by controlling its angle of attack and throttle opening, adjusting parameters such as altitude, speed, and trajectory inclination. The guidance system adjusts control commands in real time based on the deviation between the aircraft's current state and the nominal trajectory to achieve precise control of key parameters such as altitude, speed, and trajectory inclination. The core of this approach lies in establishing a mathematical model of the aircraft's center of mass motion and designing corresponding control laws.

[0123] To facilitate guidance law design, velocity, height, and lateral position are taken as state variables, and the three-variable center-of-mass motion equations are extended to obtain:

[0124] (26)

[0125] In the formula: The flight distance of the aircraft in three-dimensional space. Let be the lateral flight distance of the aircraft in the ground coordinate system, i.e., along the z-axis. Rearranging this into an error state equation, we have:

[0126] (27)

[0127] in, Let be the deviation vector between the actual extended dimension state of the spacecraft and the nominal trajectory extended dimension state at time t. , These are the state matrix and input matrix of the linear time-varying error system, respectively. To control the error vector, used for correction This causes the actual trajectory to converge to the nominal trajectory. , These are the nominal state vector and the nominal control vector, respectively. The linearized dynamic function, For the first The error state for the th error state The linearization coefficient of the rate of change of each error state. For the first The control error affects the first Linearization control gain for the rate of change of each error state.

[0128] For the obtained error state equation, a time-varying controller of the following form is adopted:

[0129] (28)

[0130] in, For time-varying control matrix No. Line number Column elements, Error state vector The Each component.

[0131] Expected closed-loop matrix for:

[0132] (29)

[0133] in, - for The corresponding 6 expected eigenvalues. The expected closed-loop matrix should satisfy... By adjusting the values ​​of the time-varying controller parameter matrix, the desired closed-loop matrix can be written in the form described above. Therefore, the control parameter matrix is:

[0134] (30)

[0135] (31)

[0136] (32)

[0137] in, For time-varying control matrix The control parameter elements of each decomposed subspace correspond to the second-order system control requirements of the three error subspaces (velocity, height, and lateral position). These control parameters are determined by the desired eigenvalues, so the core issue lies in selecting these desired eigenvalues.

[0138] From the expected closed-loop system matrix, it can be seen that all three error subspaces can be described as linear time-varying second-order systems, which can be described in the form of the characteristic equation:

[0139] (33)

[0140] Therefore:

[0141] (34)

[0142] In the formula: These represent the time-varying damping ratios for the velocity, height, and lateral position error subspaces, respectively. These represent the time-varying natural frequencies of the velocity, altitude, and lateral position error subspaces, respectively. The desired natural frequencies and damping ratios of the system can be determined by the required performance parameters (including rise time, overshoot, etc.), thereby enabling the design of controller parameters that meet the performance requirements.

[0143] Based on the current rise time of the step response of underdamped second-order linear systems and overshoot Estimation formula:

[0144] (35)

[0145] (36)

[0146] in, For general damping ratio, It is a universal natural frequency.

[0147] Given the required rise time and overshoot of the closed-loop control system, the damping ratio and frequency of the desired system can be solved simultaneously, and then the eigenvalues ​​of the desired system matrix can be determined to obtain the controller parameters.

[0148] Step 4: Intelligent Tracking Methods for Online Applications

[0149] To address the real-time and robustness requirements of tracking and guidance during mode transitions, this paper proposes an intelligent tracking method for online applications, combining the nonlinear fitting capability of deep neural networks with the optimization logic of control performance indicators. This method achieves real-time optimal adjustment of controller parameters through the synergy of offline training and online inference. The method takes flight state, error information, and aerodynamic uncertainties as inputs and outputs core controller parameters that meet performance requirements. It leverages the empirical knowledge accumulated from massive simulations to empower online decision-making. The specific implementation process is as follows:

[0150] First, a comprehensive training dataset is constructed. Using the climb preparation and acceleration phases of the mode transition stage as core operating conditions, and based on the three-variable center-of-mass motion dynamics equations and trajectory linearization error model, aerodynamic parameters for yaw (static stability coefficient uncertainty) are injected. Uncertainty of manipulation coefficients Typical uncertainties such as measurement errors alter the natural frequency. Damping ratio Massive simulations were performed on the controller parameters, generating no fewer than 50,000 sets of sample data. The dataset input vector is defined as a fusion vector of flight state, error state, and uncertainty parameters:

[0151] (37)

[0152] in, For flight speed, For flight altitude, For the trajectory inclination angle, , , These represent the errors in flight speed, flight altitude, and trajectory inclination angle compared to the nominal trajectory, respectively; the output vector represents the optimal controller parameters. , The optimal natural frequency, The optimal damping ratio is the natural frequency and the optimal damping ratio that meet the performance requirements.

[0153] Secondly, a control performance evaluation model and parameter selection mechanism are established. Referring to the comprehensive performance requirements in the time and frequency domains, the rise time is selected. Overshoot As a core time-domain indicator, the magnitude margin is supplemented by the stability requirements of the mode transition stage. Phase margin Frequency domain metrics are used to construct a multi-objective optimization evaluation function.

[0154] (38)

[0155] In the formula, the subscript 0 represents the baseline value of the performance index, and the subscript nor represents the normalized value. , These represent the rise time. The baseline value, normalized value, , They represent overshoot. The baseline value, normalized value, , These represent the gain margin. The baseline value, normalized value, , They represent phase margins respectively. The baseline value and normalized value. Maximizing the evaluation function. Filter the optimal parameters for each set of inputs. , ,in and The following second-order system performance constraints must be satisfied:

[0156] (39)

[0157] Then, deep neural network training and optimization were performed. A 5-layer fully connected neural network structure was adopted, where the input layer dimension and input vector... With consistent settings, the number of neurons in the hidden layer is set to 10, 5, and 5 respectively, and the output layer outputs the optimal parameters. and During network training, 90% of the samples are used as the training set, and the predicted natural frequencies are output through forward propagation. Damping ratio prediction value The propagation relationship is as follows:

[0158] (40)

[0159] In the formula, , , , They are respectively the 1st floor, the 4th floor, and the 5th floor. Layer, First The output vector of the layer, , Here are the weight matrix and bias vector for layer 1. , Here are the weight matrix and bias vector for layer 5. , These are the weight matrix and bias vector of the l-th layer, respectively. , , They are respectively the 1st floor, the 5th floor, and the 6th floor. The activation function of the layer; using 10% of the samples as the test set, the network parameters are iteratively updated through error backpropagation, minimizing the difference between the predicted value and the selected optimal parameters. , The root mean square error is calculated until the network fitting accuracy meets the engineering requirements, i.e., the root mean square error of the test set is ≤0.06.

[0160] During the online application phase, flight status is collected in real time through sensors. With trajectory error Real-time uncertainty parameters are obtained by combining recursive least squares aerodynamic parameter identification methods. Construct the input vector The input is then fed into the trained neural network. The network outputs the optimal natural frequency through real-time inference. With damping ratio Substituting the values ​​into the characteristic equation yields the desired eigenvalues, which are then used to solve for the time-varying control parameter matrix, enabling high-precision adaptive tracking of the optimized trajectory. This method eliminates the need for online solving of complex nonlinear programming problems. Real-time performance is ensured through the rapid inference capabilities of neural networks, while the availability of massive sample data covering complex operating conditions enhances the tracking robustness under parameter uncertainties and external disturbances during the mode transition stage.

[0161] To verify the feasibility of the proposed mode transition trajectory optimization and guidance method for combined-powered aircraft, simulation verification was conducted. In the simulation scenario, the aircraft undergoes a mode transition process from a turbine engine to a ramjet engine, which is divided into a climb preparation phase and a mode transition acceleration phase. The simulation-related parameters of this invention are shown in Table 1. Figure 2 A flight strategy for optimizing the aircraft's trajectory is presented, clearly depicting the complete flight trajectory from takeoff to the separation point of the combined aircraft. During the climb preparation phase, the aircraft steadily increases its altitude and speed to the turbine ceiling along the ascending trajectory using the turbine engines. Subsequently, it enters the mode transition acceleration phase, using a moderate dive trajectory to convert potential energy into kinetic energy. The reference signal is processed by the trajectory optimization and guidance system. The trajectory optimization method used is the Gaussian pseudospectral method, which transforms the continuous optimal control problem into a nonlinear programming problem. The optimization objective is to minimize fuel consumption. The guidance and control employ a combined strategy of trajectory linearization and intelligent tracking.

[0162] Table 1 Simulation-related parameters

[0163]

[0164] Simulation results are as follows Figures 3 to 8 As shown. Figures 3 to 4 Altitude-time curves and velocity-time curves of the combined-powered aircraft under the target of minimum fuel consumption during the mode transition phase are presented respectively. Within 0-50s, the aircraft's altitude first climbs from the initial value to about 21km. After a slight adjustment during the mode transition phase, it stabilizes at the target altitude and the velocity gradually increases to 850m / s. During the acceleration phase, the velocity increases uniformly, successfully enabling the aircraft to enter the normal operating speed range of the ramjet engine. Figure 5 The trajectory inclination time curve is given under the target of minimizing fuel consumption during the mode transition phase. The trajectory inclination gradually decreases from 10° to -20°. During the climb phase, a positive inclination is maintained to achieve altitude gain. During the dive acceleration phase, the inclination is turned to a negative inclination to accumulate kinetic energy. The trajectory gradually stabilizes in the later stage. Figure 6 The mass-time curve of the combined-powered aircraft is given. The mass of the aircraft gradually decreases from 14.73t to 14.64t, at which point the fuel consumption is the lowest. Figure 7 The curve of angle of attack of the combined propulsion aircraft as a function of time is presented. The angle of attack is dynamically adjusted within the range of -2° to 2° to adapt to the aerodynamic requirements of different flight stages and ensure flight stability. Figure 8The graphs showing the time-varying turbine throttle and ramjet fuel equivalence ratio of the combined-propellant aircraft are presented. The turbine throttle gradually increases from 0.8 to approximately 0.95, while the ramjet fuel equivalence ratio remains constant at 0.25. This demonstrates the coordinated operation of the turbine and ramjet engines during the mode transition phase, ultimately propelling the ramjet engine into its efficient operating state. In summary, using the trajectory optimization and guidance method proposed in this invention, the combined-propellant aircraft can successfully avoid thrust traps, smoothly complete mode transition acceleration tasks, and all flight parameters meet design requirements, verifying the effectiveness and engineering applicability of the proposed method.

Claims

1. A trajectory optimization and guidance method for a combined-powered aircraft during mode transition, characterized in that, Includes the following steps: Step 1: Construct the three-variable center-of-mass motion dynamics equations of the aircraft during the mode transition phase; Step 2: Optimize flight strategy for trajectory during mode transition phase; The mode transition process is divided into a climb preparation phase and a mode transition acceleration phase. In the climb preparation phase, the turbine engine is used to enable the aircraft to reach sufficient altitude and speed, accumulating kinetic and potential energy for subsequent mode transition acceleration. In the mode transition acceleration phase, the turbine and ramjet engines work together, and the adaptive Gaussian pseudospectral method is used for trajectory optimization. The aircraft is further accelerated through a preset trajectory to bring it into the normal operating speed range of the ramjet engine. In terms of trajectory planning, the goal of the first stage is to enable the aircraft to reach the service ceiling of the turbine engine. The goal of the second stage is to enable the aircraft to reach the normal operating speed requirements of the ramjet engine, while relaxing the altitude restrictions on the aircraft. Step 3: Tracking guidance strategy based on trajectory linearization control; The goal of guidance during the mode transition phase is to adjust the aircraft's altitude, speed, and trajectory tilt parameters by controlling the aircraft's angle of attack and throttle opening to ensure stable flight along the nominal trajectory. The guidance system adjusts the control commands in real time based on the deviation between the aircraft's current state and the nominal trajectory to achieve precise control of altitude, speed, and trajectory tilt parameters. Step 4: Design an intelligent tracking method for online applications; Combining the nonlinear fitting capability of deep neural networks with the optimization logic of control performance indicators, an intelligent tracking method for online applications is proposed. The method achieves real-time optimal adjustment of controller parameters through the synergy of offline training and online inference. Taking flight state, error information and aerodynamic uncertainty as inputs and the core controller parameters that meet performance requirements as outputs, the method empowers online decision-making through the experience knowledge accumulated from simulation.

2. The trajectory optimization and guidance method for the mode transition process of a combined-powered aircraft according to claim 1, characterized in that, Step 1 is as follows: (1) Among them, the superscript " " represents the first derivative; For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

3. The trajectory optimization and guidance method for the mode transition process of a combined-powered aircraft according to claim 1, characterized in that, Step 2 is as follows: Step 2.1: Time Domain Segmentation and Discretization The mode conversion process is divided into a climbing preparation stage and a mode conversion acceleration stage. The time domain of each stage is mapped to the interval [-1,1] through variable transformation, and N Gaussian collocation points are selected in each stage. Step 2.2: Approximation of State Variables and Control Variables State variables and control variables Represented by the Lagrange interpolation polynomial: (2) (3) In the formula: For Lagrange basis functions; This represents the total number of Gaussian collocation points, i.e., the number of nodes discretized in the time domain. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points; Step 2.3: Discretization of the dynamic equations For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints: (4) In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions; Discrete index for Gaussian collocations. For the first Discretized vectors of the motion state of the aircraft's center of mass at each Gaussian collocation point. This refers to the terminal time of the mode transition phase. The start time, For the first The time of a Gaussian collocation point in the original time domain; Step 2.4, Constraint Handling Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the aircraft, respectively. , , These are the maximum permissible values ​​for the aircraft's dynamic pressure, overload, and heat flux density, respectively; the terminal state should satisfy the constraints of the dynamic equations. Step 2.5: Construction of the objective function Performance metrics transformed into NLP objective functions : (5) In the formula: These are the state variables at the terminal moment, including key states such as velocity, altitude, trajectory inclination, and mass; It is the Gaussian integral weight of the kth collocation point, reflecting the importance of each collocation point in the time domain; It is the process performance index function of the kth collocation point; It is the control variable of the kth collocation point; It is the time of the kth collocation point, that is, the terminal time after discretization; It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of the mode transition trajectory; It is a terminal performance index function that describes the state performance requirements at the end of the mode transition, ensuring that key constraints are met when the transition is completed. Step 2.6: Solve the nonlinear programming problem. The complete nonlinear programming problem constructed in steps 2.1-2.5 is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory. At this point, the problem has been transformed into a discretized form, which is then optimized by refining the discrete state variables. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function Obtain the minimum value.

4. The trajectory optimization and guidance method for the mode transition process of a combined-powered aircraft according to claim 1, characterized in that, Step 3 is as follows: By taking velocity, height, and lateral position as state variables, the three-variable center-of-mass motion equations are expanded to: (6) In the formula: The flight distance of the aircraft in three-dimensional space. For the lateral direction of the aircraft in the ground coordinate system, i.e. Flight distance along the axial direction; rearranged into the error state equation form: (7) in, Let be the deviation vector between the actual extended dimension state of the spacecraft and the nominal trajectory extended dimension state at time t. , These are the state matrix and input matrix of the linear time-varying error system, respectively. To control the error vector, used for correction This causes the actual trajectory to converge to the nominal trajectory; , These are the nominal state vector and the nominal control vector, respectively. The linearized dynamic function, For the first The error state for the th error state The linearization coefficient of the rate of change of each error state. For the first The control error affects the first Linearization control gain for the rate of change of each error state; For the obtained error state equation, a time-varying controller of the following form is adopted: (8) in, For time-varying control matrix No. Line 1 Column elements, Error state vector The One component; Expected closed-loop matrix for: (9) in, - for The corresponding 6 expected eigenvalues; the expected closed-loop matrix should satisfy By adjusting the values ​​of the time-varying controller parameter matrix, the desired closed-loop matrix can be written in desired matrix form; therefore, the control parameter matrix is ​​rearranged as follows: (10) (11) (12) in, For time-varying control matrix The control parameter elements of each subspace after decomposition correspond to the second-order system control requirements of the three error subspaces; All three error subspaces are described as linear time-varying second-order systems, and can be represented by the characteristic equation in the form of: (13) Therefore: (14) In the formula: These represent the time-varying damping ratios for the velocity, height, and lateral position error subspaces, respectively. These represent the time-varying natural frequencies of the velocity, altitude, and lateral position error subspaces, respectively. Based on the current rise time of the step response of underdamped second-order linear systems and overshoot Estimation formula: (15) (16) in, For the damping ratio, It is the natural frequency; Given the required rise time and overshoot of the closed-loop control system, the damping ratio and frequency of the desired system can be solved simultaneously, and then the eigenvalues ​​of the desired system matrix can be determined to obtain the controller parameters.

5. The trajectory optimization and guidance method for mode transition process of a combined-powered aircraft according to claim 1, characterized in that, Step 4 is as follows: First, a comprehensive training dataset is constructed. Using the climb preparation and acceleration phases of the mode transition stage as core operating conditions, and based on the three-variable center-of-mass motion dynamics equations and trajectory linearization error model, aerodynamic parameters such as pull-off statics and measurement errors are injected. The pull-off statics parameters include the uncertainty of the stability coefficient. and uncertainty of manipulation coefficients Change the natural frequency Damping ratio The simulation is performed; the dataset input vector is defined as a fusion vector of flight state, error state, and uncertainty parameters: (17) in, For flight speed, For flight altitude, For the trajectory inclination angle, , , These represent the errors in flight speed, flight altitude, and trajectory inclination angle compared to the nominal trajectory, respectively; the output vector represents the optimal controller parameters. , The optimal natural frequency, The optimal damping ratio is the optimal value of the natural frequency and damping ratio that satisfies the performance requirements. Secondly, an evaluation model for control performance indicators and a parameter selection mechanism are established; the rise time is selected with reference to the comprehensive performance requirements in the time and frequency domain. Overshoot As a core time-domain indicator, the magnitude margin is supplemented by the stability requirements of the mode transition stage. Phase margin Frequency domain metrics are used to construct a multi-objective optimization evaluation function. (18) In the formula, the subscript 0 represents the baseline value of the performance index, and the subscript nor represents the normalized value; , These represent the rise time. The baseline value, normalized value, , They represent overshoot. The baseline value, normalized value, , These represent the gain margin. The baseline value, normalized value, , They represent phase margins respectively. The baseline value and normalized value; by maximizing the evaluation function Filter the optimal parameters for each set of inputs. , ,in and The following second-order system performance constraints must be satisfied: (19) Subsequently, deep neural network training and optimization were performed; a 5-layer fully connected neural network structure was adopted, where the input layer dimension and input vector were... With consistent settings, the number of neurons in the hidden layer is set to 10, 5, and 5 respectively, and the output layer outputs the optimal parameters. and During network training, 90% of the samples are used as the training set, and the predicted natural frequencies are output through forward propagation. Damping ratio prediction value The propagation relationship is as follows: (20) In the formula, , , , They are respectively the 1st floor, the 4th floor, and the 5th floor. Layer, First The layer's output vector; , Here are the weight matrix and bias vector for layer 1. , Here are the weight matrix and bias vector for layer 5. , These are the weight matrix and bias vector of the l-th layer, respectively. , , They are respectively the 1st floor, the 5th floor, and the 6th floor. The activation function of the layer; using 10% of the samples as the test set, the network parameters are iteratively updated through error backpropagation, minimizing the difference between the predicted value and the selected optimal parameters. , The root mean square error is calculated until the network fitting accuracy meets the engineering requirements, i.e., the root mean square error of the test set is ≤0.

06. During the online application phase, flight status is collected in real time through sensors. With trajectory error Real-time uncertainty parameters are obtained by combining recursive least squares aerodynamic parameter identification methods. Construct the input vector The input is then fed into the trained neural network; the network outputs the optimal natural frequency through real-time inference. With damping ratio Substituting these values ​​into the characteristic equation yields the desired characteristic roots, which are then used to solve for the time-varying control parameter matrix, enabling high-precision adaptive tracking of the optimized trajectory.

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