A three-stage solid carrier rocket trajectory design method

Abstract

The present application relates to a kind of three-stage solid carrier rocket trajectory design method, first design carrier rocket flight program angle, select the parameter of solving all range trajectory, make the target orbit parameter deviation satisfy the threshold set by iteration solving trajectory launch parameter, design threshold reasonable, ensure that the iteration number is not too high, finally complete all range trajectory calculation;For parameter selection, the four launch parameters selected are one-to-one corresponding with target orbit parameter, with the advantages of simple principle, fast calculation, strong operability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aircraft guidance control, in particular to a three-stage solid carrier rocket trajectory design method. BACKGROUND

[0002] In the overall design and flight test of a carrier rocket system, a flight trajectory that can be used is usually generated quickly according to task requirements, that is, in the case of a known launch point, launch parameters that satisfy terminal orbit constraints are solved.

[0003] For the selection of launch parameters, the prior art has a solid carrier rocket ascent trajectory rapid design method that selects four pitch angle control parameters and a three-stage carrier rocket with sliding section entry trajectory design method and device that selects one-stage pitch angle parameters, two-stage pitch angle parameters, three-stage start time, three-stage working time, three-stage pitch angle and six parameters of launch azimuth. Due to the complexity of the motion model of the carrier rocket, the launch parameter calculation is generally solved by iterative calculation.

[0004] However, for the solid carrier rocket ascent trajectory rapid design method, there is a disadvantage that the total flight time of the rocket is fixed, and there is no sliding section in the middle of each section, which cannot optimize the flight time according to the task. And for the three-stage carrier rocket with sliding section entry trajectory design method and device, there is a disadvantage of insufficient calculation efficiency due to too many iterative parameters. SUMMARY

[0005] The technical problem to be solved by the present application is how to overcome the technical defects of too many iterations and inability to optimize flight time according to the task in three-stage solid carrier rocket trajectory design. In order to overcome the defects of the prior art, the present application provides a three-stage solid carrier rocket trajectory design method.

[0006] The three-stage solid carrier rocket trajectory design method provided by the present application comprises the following steps:

[0007] S1: set the rocket trajectory as: after the first stage of take-off vertical ascent time, turn with negative attack angle, turn with gravity in the second stage of flight, the program angle of the second stage and above flight section is a constant attack angle, and the third stage engine is ignited to enter the orbit after the second stage separation sliding ends;

[0008] S2: set the program as: turn according to the following program after the first stage of take-off:

[0009]

[0010] In the formula,

[0011]

[0012] t1 is the vertical ascent time of the rocket;

[0013] t2 is the time when the angle of attack turn ends;

[0014] fig is the program turn angle;

[0015] is the turn angle;

[0016] S3: setting the program as: the secondary and above flight segment program angle is a constant angle of attack, and the flight program is:

[0017]

[0018] wherein,

[0019] θ(t) is the rocket trajectory inclination angle;

[0020] α cz is a constant angle of attack;

[0021] S4: taking the launch azimuth angle, the program turn angle, the final stage ignition time and the final stage working time length as the launch parameters, and taking the standard orbit altitude, the standard orbit speed, the local standard trajectory inclination angle and the standard orbit inclination angle as the standard target orbit parameters;

[0022] S5: using the rocket initial state and the initial launch parameters, obtaining the corresponding target orbit parameters by the shooting integral trajectory equation;

[0023] S6: calculating the deviation of the target orbit parameters relative to the standard target orbit parameters, and judging whether the terminal time orbit eccentricity deviation is less than 0.001, the orbit altitude deviation is less than 1km, and the orbit inclination angle deviation is less than 0.0001° based on the deviation; if all the conditions are met, stop calculation and output the trajectory; otherwise, execute the next step:

[0024] S7: respectively adding small amounts of ±Δfig to the program turn angle, ±Δt 23 to the final stage ignition time and ±ΔT MZT to the final stage working time length, and obtaining the corresponding orbit altitude R + , orbit speed V + , orbit inclination angle Θ + , orbit altitude R - , orbit speed V - and orbit inclination angle Θ - by the shooting integral trajectory equation. Calculating the partial derivatives of the orbit altitude, the orbit speed and the local trajectory inclination angle relative to the program turn angle, the final stage working time length and the final stage ignition time: wherein, ±Δfig is the program turn angle change amount, ±Δt 23 is the final stage ignition time change amount, and ±ΔT MZT is the final stage working time length change amount;

[0025] S8: iterates the current launch element by a Newton iteration process, obtains an iterated launch element, and then executes the step S5 again with the iterated launch element as the initial launch element.

[0026] The disclosed three-stage solid carrier rocket trajectory design method first designs a carrier rocket flight program angle, selects full-range trajectory elements for solving parameters, and solves trajectory launch elements through iteration to make target orbit parameter deviations meet a set threshold. The threshold specification is reasonable, ensuring that the iteration number is not too high, and finally completing full-range trajectory calculation. When selecting parameters, the four launch elements selected correspond one-to-one to target orbit parameters, have the advantages of simple principle, fast calculation, and strong operability, thereby realizing fast launch element solution with fewer iterations, obtaining a full-range trajectory meeting task requirements, and overcoming the technical defects of many iterations and inability to optimize flight time according to tasks in the prior art.

[0027] In one possible implementation, in the step S6, the calculation formula of the deviation amount of the target orbit element relative to the standard target orbit element is as follows:

[0028]

[0029] In the formula,

[0030] H is the standard orbit height;

[0031] V is the standard orbit speed;

[0032] Θ is the local standard trajectory inclination;

[0033] i is the standard orbit inclination;

[0034] R f H is the orbit height in the target orbit element obtained through the shooting integral trajectory equation;

[0035] V f V is the orbit speed in the target orbit element obtained through the shooting integral trajectory equation;

[0036] Θ f Θ is the trajectory inclination in the target orbit element obtained through the shooting integral trajectory equation;

[0037] i f i is the orbit inclination in the target orbit element obtained through the shooting integral trajectory equation;

[0038] This scheme can realize the purpose of obtaining the terminal orbit height, orbit speed, orbit inclination and local trajectory inclination according to the initial state of the rocket, initial launch parameters and initial trajectory integral equation, and through calculating the deviation amount of the same relative to the standard target orbit parameters and obtaining the corresponding operation according to the deviation amount, the high efficiency operation of the trajectory acquisition is ensured.

[0039] In a possible implementation, the calculation formula of the partial derivative of the orbit height, orbit speed and local trajectory inclination relative to the program turn angle, the final stage working time and the final stage ignition time is:

[0040]

[0041] This scheme ensures the iterative update of the launch parameters by the Newton iteration method in the later stage, so as to ensure the orderly operation.

[0042] In a possible implementation, the current launch parameters are iterated by the Newton iteration process in the step S8, and the process is as follows:

[0043]

[0044] In the formula,

[0045] A0 is the launch azimuth angle;

[0046] n is the iteration number.

[0047] Further, the launch parameter calculation can be quickly completed with less iteration number, and the whole trajectory meeting the task requirement is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0048] Fig. 1 It is a flow chart of the trajectory design method of the three-stage solid carrier rocket in the embodiments of the present application.

[0049] Fig. 2 It is the rocket trajectory simulation curve obtained in the embodiments of the present application. DETAILED DESCRIPTION

[0050] Firstly, those skilled in the art should understand that these embodiments are only used for explaining the technical principles of the embodiments of the present application, and are not intended to limit the protection scope of the embodiments of the present application. Those skilled in the art can adjust them as needed to adapt to specific application occasions.

[0051] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0052] Referring to Figs. 1-2 The embodiments of the present application disclose a trajectory design method of a three-stage solid carrier rocket, referring to Fig. 1As shown, the method comprises the following steps:

[0053] S1: set the rocket trajectory as: after vertical ascent time of first stage, turn with negative attack angle, turn with gravity after the later stage of first stage flight, the program angle of the flight segment of second stage and above is a constant attack angle, and the final stage engine is ignited after the second stage separation glide ends until entering the orbit.

[0054] As a specific example, the rocket trajectory can be set as: after the rocket first stage takes off and flies vertically for 4 seconds, it turns with negative attack angle, and after the first stage flies for 18 seconds, it turns with gravity; the program angle of the flight segment of second stage is flown with a constant attack angle due to the thin air; after the second stage engine is exhausted, it separates at a predetermined time, the rocket starts to glide, and after the glide ends, the final stage engine is ignited until entering the orbit. According to the motion state of each segment of the carrier rocket, the whole trajectory can be divided into a first stage boost segment, a first stage glide segment, a second stage boost segment, a second stage glide segment, and a third stage boost segment.

[0055] S2: set the program as: after the first stage takes off, turn according to the following program:

[0056]

[0057] In the formula,

[0058]

[0059] t1 is the vertical ascent time of the rocket;

[0060] t2 is the time when the attack angle turning ends;

[0061] fig is the program turning angle;

[0062] is the turning angle.

[0063] S3: set the program as: the program angle of the flight segment of second stage and above is a constant attack angle, and the flight program is:

[0064]

[0065] In the formula,

[0066] θ(t) is the rocket trajectory inclination angle;

[0067] α cz is the constant attack angle.

[0068] S4: use the launch azimuth angle, the program turning angle, the final stage ignition time, and the final stage working time length as the launch parameters, and use the standard orbit altitude, the standard orbit speed, the local standard trajectory inclination angle, and the standard orbit inclination angle as the standard target orbit parameters.

[0069] S5: Using the initial state of the rocket, initial launch parameters, the corresponding target orbit parameters are obtained by shooting the integral trajectory equation.

[0070] The shooting integral trajectory equation is expressed as follows:

[0071]

[0072] In the formula,

[0073] [V x ,V y ,V z ] T is the velocity component in the launch system;

[0074] [X,Y,Z] T is the position component in the launch system;

[0075] m is the mass of the rocket;

[0076] P is the engine thrust;

[0077] [R x ,R y ,R z ] T is the resultant of aerodynamic force and control force;

[0078] [g x ,g y ,g z ] T ,[a cx ,a cy ,a cz ] T ,[a ex ,a ey ,a ez ] T are the components of gravitational acceleration, Coriolis acceleration and dependent acceleration in the launch system, respectively;

[0079] B is the conversion matrix from the body coordinate system to the launch coordinate system, and

[0080] B = W·A;

[0081] At time t after the rocket takes off, the rotation angle of the launch coordinate system relative to the inertial coordinate system is ω·t (ω is the earth rotation angular velocity). The conversion matrix W from the inertial coordinate system to the launch coordinate system is:

[0082]

[0083] In the formula: ω x = cosB·cosA, ω y = sinB, ω z= -cosB*sinA, c w = 1-cos(ω·t), s w = sin(ω·t).

[0084] The conversion matrix A from the arrow body coordinate system to the inertial coordinate system is:

[0085]

[0086] The process of obtaining the target orbit elements corresponding to the initial state of the rocket and the initial launch elements by solving this equation can be realized by the Runge-Kutta algorithm.

[0087] S6: Calculate the deviation of this target orbit element from the standard target orbit element, and determine whether the terminal time orbit eccentricity deviation is less than 0.001, the orbit height deviation is less than 1km, and the orbit inclination deviation is less than 0.0001° based on the deviation. If all conditions are met, stop calculation and output the trajectory; otherwise, perform the next step: wherein the calculation formula of the deviation is as follows:

[0088]

[0089] In the formula,

[0090] is the standard orbit height;

[0091] is the standard orbit velocity;

[0092] is the local standard trajectory inclination;

[0093] is the standard orbit inclination;

[0094] R f is the orbit height in the target orbit elements obtained by the shooting integral trajectory equation;

[0095] V f is the orbit velocity in the target orbit elements obtained by the shooting integral trajectory equation;

[0096] Θ f is the trajectory inclination in the target orbit elements obtained by the shooting integral trajectory equation;

[0097] i f is the orbit inclination in the target orbit elements obtained by the shooting integral trajectory equation;

[0098] S7: Apply small amounts of ±Δfig on the program turn angle, ±Δt 23 on the final stage firing time, and ±ΔT on the final stage working time, respectivelyMZT , the orbit height R + , the orbit velocity V + , the orbit inclination Θ + , the orbit height R - , the orbit velocity V - and the orbit inclination Θ - . The partial derivatives of the orbit height, the orbit velocity and the local ballistic inclination with respect to the program turn angle, the final stage working time and the final stage firing time are calculated: where ±Δfig is the program turn angle variation, ±Δt 23 is the final stage firing time variation and ±ΔT MZT is the final stage working time variation;

[0099]

[0100] S8: iterates the current launch parameters in a Newton iteration process, and the process is as follows:

[0101]

[0102] The iterated launch parameters are obtained, and then the iterated launch parameters are taken as the initial launch parameters to execute step S5.

[0103] The technical effects of the method will be described in detail below with a specific example;

[0104] Taking a certain three-stage solid carrier rocket as an example, the main overall data of the rocket are shown in Table 1.

[0105] Table 1 Main overall parameters of the rocket

[0106]

[0107] Two groups of examples are set to verify the above ballistic design method.

[0108] Example 1: the launch point latitude B0=39°, the launch point longitude L0=111°, the launch point height H0=1400m, the target orbit height 500km, and the target orbit inclination 97.4°.

[0109] Example 2: the launch point latitude B0=41°, the launch point longitude L0=100°, the launch point height H0=1000m, the target orbit height 300km, and the target orbit inclination 96.7°.

[0110] The attack angles of the second stage and the third stage are taken as 0, and the full-range ballistic design results are shown in Table 3.2.

[0111] Table 2 Ballistic design conditions

[0112]

[0113] According to Table 2 and Fig. 2 As shown in Table 2 and

[0114] In summary, the three-stage solid carrier rocket trajectory design method disclosed in the embodiment first designs the carrier rocket flight program angle, selects the full-range trajectory element solving parameters, and solves the trajectory launch elements through iteration so that the target orbit parameter deviation meets the set threshold value. The design threshold value is reasonable to ensure that the iteration number is not too high, and finally the full-range trajectory calculation is completed. When selecting parameters, the four launch elements selected correspond one-to-one to the target orbit parameters, have the advantages of simple principle, fast calculation, and strong operability, and further realize the rapid completion of launch element solution with less iteration number, obtain the full-range trajectory meeting the task requirements, and overcome the technical defects of many iteration numbers and inability to optimize flight time according to the task in the prior art

[0115] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "in this embodiment", "specific examples", or "some examples" means that the specific features, mechanisms, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, mechanisms, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, different embodiments or examples described in the specification and the features of different embodiments or examples can be combined and combined by those skilled in the art without contradiction.

[0116] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of three-stage solid launch vehicle trajectory design, characterized by, The method comprises the following steps: S1: setting a rocket trajectory as: after a vertical ascending time of a first stage, turning with a negative attack angle, turning with gravity in a later stage of the first stage, and turning with a constant attack angle in a stage above the second stage, and igniting a final stage engine after the second stage separation glide ends to enter an orbit; S2: setting a program as: turning after the first stage launch according to the following program: wherein, t1 is a vertical ascending time of the rocket; t2 is a time when the attack angle turning ends; fig is a program turning angle; for the turning angle; S3: setting a program as: the program angle in the second stage and above is a constant attack angle, and a flight program is: wherein, θ(t) is a rocket trajectory inclination angle; a cz = constant angle of attack; S4: taking a launch azimuth angle, the program turning angle, a final stage ignition time, and a final stage working time length as launch parameters, and taking a standard orbit height, a standard orbit speed, a local standard trajectory inclination angle, and a standard orbit inclination angle as standard target orbit parameters; S5: obtaining corresponding target orbit parameters by using a rocket initial state and initial launch parameters through a shooting integral trajectory equation; S6: calculating a deviation of the target orbit parameters obtained in step S5 relative to the standard target orbit parameters, and judging whether a terminal time orbit eccentricity deviation is less than 0.001, an orbit height deviation is less than 1 km, and an orbit inclination angle deviation is less than 0.0001° based on the deviation, if all the conditions are met, stopping the calculation and outputting a trajectory; otherwise, performing the next step: S7: respectively performing small amount ±Δfig on the program corner, small amount ±Δt on the final stage firing time 23 and small amount ±ΔT on the final stage working time MZT , obtaining corresponding orbit height R + , orbit speed V + , orbit inclination Θ + , orbit height R - , orbit speed V - and orbit inclination Θ - by the shooting integral orbit equation, calculating the partial derivatives of orbit height, orbit speed and local orbit inclination relative to the program corner, the final stage working time and the final stage firing time; wherein ±Δfig is the program corner change amount, ±Δt 23 is the final stage firing time change amount, and ±ΔT MZT is the final stage working time change amount S8: obtaining an iterative launch parameter by iteratively iterating a current launch parameter through a Newton iteration process, and then taking the iterative launch parameter as the initial launch parameter to perform the step S5 again.

2. The three-stage solid launch vehicle trajectory design method of claim 1, wherein, In the step S6, a calculation formula of the deviation of the target orbit parameters relative to the standard target orbit parameters is as follows: wherein, Standard track height; Standard track speed; Local standard ballistic angle of inclination; Standard orbital inclination; R f To obtain the orbital height in the target orbit elements from the shooting integral equation of trajectory; V f To obtain the orbital velocity in the target orbit elements from the shooting integral equation of trajectory; Θ f To obtain the ballistic inclination angle in the target orbit elements from the shooting integral equation of trajectory i f To obtain the inclination of the orbit among the orbital elements of the target by the shooting integral equation of the trajectory.

3. The three-stage solid launch vehicle trajectory design method of claim 2, wherein, a calculation formula of a partial derivative of an orbit height, an orbit speed, and a local trajectory inclination angle relative to the program turning angle, the final stage working time length, and the final stage ignition time is as follows:

4. The three-stage solid launch vehicle trajectory design method of claim 3, wherein, In the step S8, the current launch parameter is iterated through the Newton iteration process, and the process is as follows: wherein, A0 is a launch azimuth angle; n is an iteration number.

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