Energy / trajectory integrated planning method for variable thrust engines

Abstract

The present invention discloses a variable thrust engine energy / trajectory integrated planning method, including: establishing a variable thrust engine power and trajectory coupling longitudinal plane model, a variable thrust engine energy trajectory constraint optimization model; establishing a variable thrust engine energy trajectory integrated constraint optimization model; performing parameterized discretization based on Gaussian pseudo-spectral method, converting the variable thrust engine energy trajectory integrated constraint optimization model into a nonlinear variable thrust engine energy trajectory integrated direct optimization model; solving the variable thrust engine energy trajectory integrated direct optimization model based on sequential quadratic programming method, the corresponding relationship between the mass consumption per second of the variable thrust engine and the displacement of the throat plug, thereby obtaining the change curve of the throat plug displacement instruction. The present invention is applied to the field of variable thrust engine optimization design, taking into account the energy trajectory coupling characteristics and thrust constraint conditions, making the planning of the variable thrust engine more practical.

Description

Technical Field

[0001] The invention relates to the technical field of variable thrust engine optimization design, and in particular to a variable thrust engine energy / trajectory integrated planning method. Background Art

[0002] Variable thrust engines can adjust thrust in real time according to needs and distribute energy more reasonably, which is one of the important development directions of solid engines. Variable thrust aircraft have more powerful adjustment and maneuverability than traditional aircraft. Variable thrust engine trajectory planning is an important way to reflect this feature, and it is also one of the relatively difficult technologies at present.

[0003] At present, the commonly used planning methods are divided into indirect methods and direct methods. The indirect method is to use the Pontryagin minimum principle and the first-order optimal necessary conditions to convert the original problem into a two-point or multi-point boundary value problem, and further use a more mature numerical method to solve this boundary value; the basic idea of ​​the direct method to solve the optimal control problem is to discretize the original continuous optimal control problem and convert it into a parameter optimization problem, and then further use the relevant optimization algorithm to directly optimize the system performance indicators.

[0004] Most of the common trajectory planning methods in the current technology use pseudo-spectral method to transform the trajectory optimal control problem into a nonlinear programming problem, and then use SQP algorithm to solve the trajectory optimization design problem; or use HP adaptive pseudo-spectral method to perform offline trajectory optimization, obtain multiple optimal trajectory control data, and then train BP neural network to obtain neural network guidance controller; or establish a corresponding model for the aircraft optimization plan, and use the method of segmented optimization of the whole trajectory. However, there are few trajectory planning for variable thrust engine energy trajectory coupling characteristics, and the influence of variable thrust engine energy trajectory coupling characteristics is not considered. It is impossible to guide the operation of variable thrust engine according to the planned trajectory characteristics, and only according to the variable thrust engine thrust adjustable characteristics, a trajectory with better performance than the traditional engine is planned, and the thrust constraint conditions of the variable thrust engine are not considered, which has low practicality. Summary of the invention

[0005] In view of the problems of dynamic energy regulation and trajectory coupling of variable thrust engines in the above-mentioned prior art, the present invention provides a variable thrust engine energy / trajectory integrated planning method, which takes into account the energy-trajectory coupling characteristics and thrust constraint conditions, making the planning of variable thrust engines more practical.

[0006] To achieve the above object, the present invention provides a variable thrust engine energy / trajectory integrated planning method, comprising the following steps:

[0007] Step 1, establishing a variable thrust engine power and trajectory coupling longitudinal plane model, and a variable thrust engine energy trajectory constraint optimization model;

[0008] Step 2, based on the variable thrust engine power and trajectory coupled longitudinal plane model and the variable thrust engine energy trajectory constraint optimization model, a variable thrust engine energy trajectory integrated constraint optimization model is established;

[0009] Step 3, performing parameterized discretization based on Gaussian pseudo-spectral method, converting the variable thrust engine energy-trajectory integrated constraint optimization model into a nonlinear variable thrust engine energy-trajectory integrated direct optimization model;

[0010] Step 4, based on the sequential quadratic programming method, solve the variable thrust engine energy-trajectory integrated direct optimization model, the corresponding relationship between the mass consumption per second of the variable thrust engine and the displacement of the throat plug, so as to obtain the change curve of the throat plug displacement instruction.

[0011] Compared with the prior art, the present invention has the following beneficial technical effects:

[0012] 1. The present invention takes into account the energy-trajectory coupling characteristics and thrust constraint conditions, making the planning of variable thrust engines more practical;

[0013] 2. The present invention also takes thrust constraints into consideration during the planning process, and can guide the operation of the variable thrust engine according to the planned aircraft characteristics, further improving the practicability of the planning method. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0015] Figure 1 It is a flow chart of the energy / trajectory integrated planning method of a variable thrust engine in an embodiment of the present invention;

[0016] Figure 2 A schematic diagram of a predicted hit point in an embodiment of the present invention;

[0017] Figure 3 Schematic diagram of observation constraints in an embodiment of the present invention;

[0018] Figure 4 It is a trajectory planning diagram of an intelligent aircraft in an embodiment of the present invention;

[0019] Figure 5 Schematic diagram of a speed curve of a variable thrust aircraft in an embodiment of the present invention;

[0020] Figure 6 Schematic diagram of a mass curve of a variable thrust aircraft in an embodiment of the present invention;

[0021] Figure 7 Schematic diagram of a speed inclination curve of a variable thrust aircraft in an embodiment of the present invention;

[0022] Figure 8 Schematic diagram of the angle of attack curve of the variable thrust aircraft in an embodiment of the present invention;

[0023] Fig. 9 It is a schematic diagram of the mass consumption per second curve of the variable thrust aircraft in an embodiment of the present invention.

[0024] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0027] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0028] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0029] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0030] In view of the problem that the existing variable thrust engine trajectory planning does not reflect the energy-trajectory coupling characteristics and thrust constraints, this embodiment discloses a variable thrust engine energy / trajectory integrated planning method, which provides a planning method that reflects the energy change characteristics of the variable thrust engine for variable thrust engine planning. Figure 1 The variable thrust engine energy / trajectory integrated planning method in this embodiment specifically includes the following steps:

[0031] Step 1, establishing a variable thrust engine power and trajectory coupling longitudinal plane model, and a variable thrust engine energy trajectory constraint optimization model;

[0032] Step 2, based on the variable thrust engine power and trajectory coupling longitudinal plane model and the variable thrust engine energy trajectory constraint optimization model, a variable thrust engine energy trajectory integrated constraint optimization model is established;

[0033] Step 3, parameterized discretization is performed based on the Gaussian pseudo-spectral method to convert the variable thrust engine energy-trajectory integrated constraint optimization model into a nonlinear variable thrust engine energy-trajectory integrated direct optimization model;

[0034] Step 4, based on the sequential quadratic programming method, solve the energy-trajectory integrated direct optimization model of the variable thrust engine, the corresponding relationship between the mass consumption per second of the variable thrust engine and the displacement of the throat plug, so as to obtain the change curve of the throat plug displacement instruction.

[0035] In the specific implementation process of step 1, the variable thrust engine power and trajectory coupling longitudinal plane model is established in the aircraft body coordinate system, ignoring the earth's curvature and rotation, specifically:

[0036] ;

[0037] in, , are the coordinates of the aircraft in the inertial coordinate system, is the speed of the aircraft; is the velocity inclination angle of the aircraft, is the current mass of the aircraft, is the acceleration due to gravity, is the fuel mass consumption per second of the engine, The thrust follows the engine thrust. , are aerodynamic drag and aerodynamic lift, respectively. is the angle of attack of the aircraft;

[0038] The above variable thrust engine dynamics and trajectory coupling longitudinal plane model also has the following supplementary equations:

[0039]

[0040] in, is the air density, is the characteristic area of ​​the aircraft, , are the drag coefficient and lift coefficient, is the nozzle efficiency, is the engine specific impulse, is the propellant density, is the burning rate coefficient, is the pressure index, is the combustion chamber pressure, is the characteristic velocity of the gas, is the charge burning area, is the equivalent throat area.

[0041] This embodiment stipulates that the coordinates of the target motion in the inertial coordinate system are , , the target's velocity vector is , the velocity inclination is , because the motion model of the target aircraft is: .

[0042] In the process of constructing the variable thrust engine energy trajectory constraint optimization model, the main constraints include aircraft differential equations, aircraft control constraints, terminal constraints, and observation constraints. Among them, the aircraft differential equations are the variable thrust engine power and trajectory coupling longitudinal plane model.

[0043] Assumptions Indicates the overall weight of the aircraft when all the fuel is consumed; , are the minimum and maximum values ​​of the angle of attack respectively; , represents the minimum and maximum values ​​of the combustion chamber pressure; the angle between the target and the aircraft position and the horizontal plane is set to ; The aircraft observation angle is ; The angle between the observation window and the aircraft axis is λ; The angle between the position line of the target and the aircraft equipped with variable thrust and the aircraft axis is ; The angle between the target and the aircraft position line and the target axis is The aircraft is planned to move at a speed inclination angle in the inertial coordinate system at the end of the adjustment phase. . Constant speed Moving forward, the target moves at a speed inclination angle in the inertial coordinate system , constant speed go ahead.

[0044] The mass constraint of the aircraft is:

[0045]

[0046] The vehicle control constraints are:

[0047]

[0048] When the engine energy consumption is completed, the predicted hit point diagram is as follows: Figure 2 , then the terminal constraint is:

[0049]

[0050] When the aircraft and the target are at the predicted point, the observation constraint diagram is as follows: Figure 3 , so the observation constraint is:

[0051]

[0052] In summary, the energy-trajectory integrated constraint optimization model of the variable thrust engine in step 2 is:

[0053]

[0054] in, To optimize the index, the above formula combined with the differential equation constraint is the energy-trajectory integrated constraint optimization model of the variable thrust engine.

[0055] The kinematic equations of variable thrust solid aircraft are nonlinear first-order ordinary differential equations. The energy-trajectory integrated constraint optimization model of variable thrust engine formed by the original continuous-time system variables, multiple conditional constraints and indicators to be optimized is discretized into the state and control variables of the discrete system by Gaussian pseudo-spectral method and global polynomial interpolation estimation is performed, and finally transformed into a solution to a nonlinear programming problem (i.e., the energy-trajectory integrated direct optimization model of variable thrust engine). In the specific implementation process:

[0056] Let the state variables of the aircraft be , let the state variable of the target be , let the control variable , then the total state variable ,in, is the transpose of the matrix;

[0057] The dynamic differential equation based on the total state variables and the variable thrust engine power and trajectory coupling longitudinal plane model is:

[0058]

[0059] in, For aircraft t The total state variables at time , u ( t )for t The control variables at time, It is a longitudinal plane model of variable thrust engine power and trajectory coupling, that is:

[0060]

[0061] Get the interpolation basis function as:

[0062] ;

[0063]

[0064] in, is the interpolation basis function, is the Lagrange interpolation basis function for the control input, For the time interval N-order Legendre-Gauss interpolation points within;

[0065] In Legendre interpolation polynomial of the state value at for:

[0066]

[0067] exist Legendre interpolation polynomial of the control variable at u ( τ )for:

[0068]

[0069] in, for Control variables at the time;

[0070] have:

[0071]

[0072] in, is the differential of the Lagrange interpolation basis function at the interpolation point, which can be expressed as a differential approximation matrix. OK Column Elements It can be expressed as:

[0073]

[0074] Therefore, the equality constraints of the aircraft differential equations are parameterized as:

[0075] ;

[0076] in, is the initial time of the aircraft, for The differential matrix at time OK Column elements, for The total state variables at time , for The total state variables at time , for Control variables at the time;

[0077] The terminal constraints are parameterized as follows:

[0078] ;

[0079] ;

[0080]

[0081] in, is the intermediate parameter, for The thrust at the moment is controlled by the engine thrust. for The aircraft angle of attack at time, For Qi The dynamic resistance at the moment, for The mass of the aircraft at the time, for The aircraft speed inclination at the time, is the aircraft speed inclination angle at the end of the aircraft adjustment phase, is the velocity inclination angle of the aircraft at the terminal moment, for The aerodynamic lift at this moment, for The speed of the aircraft at the moment;

[0082] It can be expressed as:

[0083]

[0084] in, is the interpolation point;

[0085] The terminal constraint can be described as:

[0086]

[0087] Then, the vehicle mass constraint, vehicle control constraint, and observation constraint are parameterized respectively, and the energy-trajectory integrated direct optimization model of the variable thrust engine can be obtained as follows:

[0088]

[0089] in, for The mass of the aircraft at the time, for The aircraft angle of attack at time, for The engine fuel mass consumed per second at the time.

[0090] In step 4, the nonlinear programming problem corresponding to the variable thrust engine energy-trajectory integrated direct optimization model is solved using the sequential quadratic programming method until the vehicle state variables are obtained. , the state variables of the target And control variables At discrete points The optimal value on the control variable At discrete points The optimal value on can be used to obtain the change curve of the throat plug displacement instruction, and the process is as follows:

[0091] Get the mass consumption per second Equivalent throat area The corresponding relationship is:

[0092]

[0093] When the throat plug is in displacement At the nozzle profile function Take a little bit when you take office , in the throat plug surface function Take a little bit when you take office , traverse all points on the nozzle profile function and the throat plug profile function, and the minimum area solved is the displacement of the throat plug The equivalent throat area of ​​the nozzle at ,Right now:

[0094]

[0095] in, , The displacement of the laryngeal plug The equivalent throat area of ​​the nozzle at ;

[0096] Getting laryngeal plug displacement Equivalent throat area of ​​nozzle After the corresponding relationship, the mass consumption per second can be obtained Displacement with laryngeal plug The corresponding relationship between the displacement command and the displacement command of the throat plug can be obtained, thus completing the integrated planning of the energy / trajectory of the variable thrust engine.

[0097] The planning method in the embodiment is further described below with reference to specific examples.

[0098] For the energy-trajectory integrated constraint optimization model of variable thrust engine, the Gaussian pseudo-spectral method is used for discretization to obtain a nonlinear programming problem. The initial values ​​of the state variables are set as shown in Table 1, and the sequential quadratic programming algorithm is used to solve the problem.

[0099] Table 1 Initial value setting of state variables

[0100]

[0101] The main steps of carrying out the planning method in this embodiment are:

[0102] Establish a variable thrust engine power and trajectory coupling longitudinal plane model and a variable thrust engine energy trajectory constraint optimization model;

[0103] Establish an integrated energy-trajectory constraint optimization model for variable thrust engines;

[0104] Based on the Gaussian pseudo-spectral method, the energy-trajectory integrated direct optimization model of the variable thrust engine is obtained.

[0105] The problem corresponding to the energy-trajectory integrated direct optimization model of variable thrust engine is solved using sequential quadratic programming algorithm.

[0106] The solution curve result is as follows Figures 4 to 9 As shown by Figures 4 to 9 It can be seen that the optimal planned trajectory, state variables, and control quantity curve can be obtained through the planning method of this embodiment. Compared with the conventional variable thrust trajectory planning method, the energy-trajectory coupling characteristics and thrust constraint conditions are considered, making the variable thrust engine trajectory planning more practical.

[0107] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A variable thrust engine energy / trajectory integrated planning method, characterized in that: The steps include: Step 1, establishing a variable thrust engine power and trajectory coupling longitudinal plane model, and a variable thrust engine energy trajectory constraint optimization model; Step 2, based on the variable thrust engine power and trajectory coupled longitudinal plane model and the variable thrust engine energy trajectory constraint optimization model, a variable thrust engine energy trajectory integrated constraint optimization model is established; Step 3, performing parameterized discretization based on Gaussian pseudo-spectral method, converting the variable thrust engine energy-trajectory integrated constraint optimization model into a nonlinear variable thrust engine energy-trajectory integrated direct optimization model; Step 4, solving the variable thrust engine energy-trajectory integrated direct optimization model based on the sequential quadratic programming method, the corresponding relationship between the mass consumption per second of the variable thrust engine and the displacement of the throat plug, so as to obtain the change curve of the throat plug displacement instruction; In step 1, the variable thrust engine power and trajectory coupling longitudinal plane model is specifically: in, , are the coordinates of the aircraft in the inertial coordinate system, is the speed of the aircraft; is the velocity inclination angle of the aircraft, is the current mass of the aircraft, is the acceleration due to gravity, is the fuel mass consumption per second of the engine, P The thrust follows the engine thrust. X , Y are aerodynamic drag and aerodynamic lift, respectively. α is the angle of attack of the aircraft; The above variable thrust engine dynamics and trajectory coupling longitudinal plane model has the following supplementary equations: in, is the air density, is the characteristic area of ​​the aircraft, , are the drag coefficient and lift coefficient, is the nozzle efficiency, is the engine specific impulse, is the propellant density, is the burning rate coefficient, is the pressure index, is the combustion chamber pressure, is the characteristic velocity of the gas, is the charge burning area, is the equivalent throat area; In step 1, the variable thrust engine energy trajectory constraint optimization model specifically includes: The aircraft differential equation equality constraint is the variable thrust engine power and trajectory coupling longitudinal plane model; The vehicle mass constraint is: in, The total weight of the aircraft when all its fuel is consumed; The vehicle control constraints are: in, , are the minimum and maximum values ​​of the angle of attack, , are the minimum and maximum values ​​of the combustion chamber pressure respectively; The terminal constraints are: in, The velocity inclination angle in the inertial coordinate system at the end of the aircraft adjustment phase At a constant speed, is the angle between the target and the aircraft's position line and the aircraft's axis, θ t1 is the angle between the target and the aircraft position and the target axis, is the velocity inclination of the target in the inertial coordinate system Constant speed under The observation constraints are: in, is the angle between the line connecting the target and the aircraft and the horizontal plane, μ is the observation angle of the aircraft, λ is the angle between the observation window and the aircraft axis; That is, the variable thrust engine energy-trajectory integrated constraint optimization model in step 2 is: in, J To optimize the index, α ( t ) is the aircraft in t The angle of attack at the moment, m s ( t ) is the aircraft in t The quality of the moment in seconds, For the aircraft at the end moment The speed size, For the aircraft at the end moment The speed inclination angle.

2. The variable thrust engine energy / trajectory integrated planning method according to claim 1, characterized in that: Step 3 is as follows: Let the state variables of the aircraft be , let the state variable of the target be , let the control variable , then the total state variable ,in, T is the transpose of the matrix; The dynamic differential equation based on the total state variable and the variable thrust engine power and trajectory coupling longitudinal plane model is: in, X ( t ) is the aircraft in t The total state variables at time , for t The control variables at time, It is a longitudinal plane model of variable thrust engine dynamics and ballistic coupling; Get the interpolation basis function: in, is the Lagrange interpolation basis function of the state value, is the Lagrange interpolation basis function for the control input, is the Nth-order Legendre-Gauss interpolation point in the time interval [-1,1]; In Legendre interpolation polynomial of the state value at for: exist Legendre interpolation polynomial of the control input at for: in, for Control variables at the time; have: in, is the differential of the Lagrange interpolation basis function at the interpolation point, which can be expressed as a differential approximation matrix. OK Column Elements It can be expressed as: Therefore, the equality constraints of the aircraft differential equations are parameterized as: in, t 0 is the initial time of the aircraft, for The differential matrix at time OK Column elements, for The total state variables at time , for The total state variables at time , for Control variables at the time; The terminal constraints are parameterized as follows: It can be expressed as: in, for The thrust at the moment is controlled by the engine thrust. for The aircraft angle of attack at time, For Qi The dynamic resistance at the moment, for The mass of the aircraft at the time, for The aircraft speed inclination at the time, is the aircraft speed inclination angle at the end of the aircraft adjustment phase, is the velocity inclination angle of the aircraft at the terminal moment, for The aerodynamic lift at this moment, for The speed of the aircraft at the moment; Then, the vehicle mass constraint, vehicle control constraint, and observation constraint are parameterized respectively, and the variable thrust engine energy trajectory integrated direct optimization model can be obtained as follows: in, for The mass of the aircraft at the time, for The aircraft angle of attack at time, for The engine fuel mass consumed per second at the time.

3. The variable thrust engine energy / trajectory integrated planning method according to claim 2, characterized in that: Step 4 specifically includes: Based on the sequential quadratic programming method, the energy-trajectory integrated direct optimization model of the variable thrust engine is solved to obtain the control variables At discrete points The optimal value on ; Get the mass consumption per second Equivalent throat area The corresponding relationship is: When the throat plug is in displacement At the nozzle profile function Take a little bit when you take office , in the throat plug surface function Take a little bit when you take office , traverse all points on the nozzle profile function and the throat plug profile function, and the minimum area solved is the displacement of the throat plug The equivalent throat area of ​​the nozzle at ,Right now: in, , The displacement of the laryngeal plug The equivalent throat area of ​​the nozzle at ; Getting laryngeal plug displacement Equivalent throat area of ​​nozzle After the corresponding relationship, the mass consumption per second can be obtained Displacement with laryngeal plug The corresponding relationship between the displacement command and the displacement command of the throat plug can be obtained, thus completing the integrated planning of the energy / trajectory of the variable thrust engine.

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