CN107562999B - Carrier rocket solid engine guidance deviation simulation method - Google Patents
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- 239000007787 solid Substances 0.000 title claims abstract description 76
- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000004088 simulation Methods 0.000 title claims abstract description 14
- 239000003814 drug Substances 0.000 claims abstract description 50
- 238000004364 calculation method Methods 0.000 claims abstract description 14
- 238000000342 Monte Carlo simulation Methods 0.000 claims abstract description 10
- 238000005303 weighing Methods 0.000 claims description 12
- 238000004422 calculation algorithm Methods 0.000 claims description 8
- 229940079593 drug Drugs 0.000 claims description 5
- 230000005540 biological transmission Effects 0.000 claims description 3
- 238000002485 combustion reaction Methods 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims 1
- 238000006243 chemical reaction Methods 0.000 description 2
- 239000004449 solid propellant Substances 0.000 description 2
- 238000007619 statistical method Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
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Abstract
The invention provides a carrier rocket solid engine guidance deviation simulation method, which comprises the following steps: s1: calculating theoretical average specific impulse and theoretical total medicine loading according to rated internal ballistic parameters of the solid engine; s2: calculating the total impact of the solid engine under the state of deviation according to the theoretical average specific impact, the theoretical total medicine loading amount, the average specific impact deviation and the total medicine loading amount deviation; s3: calculating the average second consumption according to the theoretical total medicine loading amount, the deviation of the total medicine loading amount, the rated working time and the deviation of the working time; calculating average thrust according to the total impact, rated working time and working time deviation; s4: and calculating a mass center motion equation of the guidance system by using the average second consumption and the average thrust to simulate and analyze the influence of the deviation of the solid engine on the guidance system. The method is simple in calculation and strong in practicability, and has a strong engineering application value for analyzing the influence of the deviation of the solid engine by Monte Carlo simulation of the carrier rocket guidance system.
Description
Technical Field
The invention relates to the field of carrier rocket guidance control, in particular to a carrier rocket solid engine guidance deviation simulation method.
Background
The solid engine is a chemical rocket engine using a solid propellant. The carrier rocket solid engine generally provides internal ballistic nominal parameters for use by the guidance system, and the deviation of the solid engine is generally provided in the form of an internal on-ballistic deviation and an internal off-ballistic deviation. The guidance system generally adopts a Monte Carlo method to carry out simulation analysis on various deviations, and the form of upper deviation and lower deviation of an inner trajectory only provides two envelope curves, so that the guidance system is inconvenient to carry out Monte Carlo simulation, and the influence of the deviation of the solid engine on the guidance system is difficult to analyze.
Disclosure of Invention
The invention aims to solve the technical problem of providing a simulation method for the guidance deviation of the carrier rocket solid engine, which has simple calculation and strong practicability and has stronger engineering application value for analyzing the influence of the solid engine deviation by Monte Carlo simulation of a carrier rocket guidance system.
In order to solve the problems, the invention provides a carrier rocket solid engine guidance deviation simulation method, which comprises the following steps:
s1: calculating theoretical average specific impulse and theoretical total charge according to rated internal ballistic parameters of the solid engine, wherein the specific algorithm is as follows:
calculating theoretical average specific impulse according to rated internal ballistic parameters of solid engine
The method comprises the following steps:
first, the thrust F of the rated internal trajectory of the solid engine is calculatedG(t), calculated as formula (1):
then, calculating theoretical total medicine loading m according to rated internal ballistic parameters of the solid engineyCalculating as formula (2), and calculating the theoretical average specific impulse according to the total drug loading
The calculation is as formula (3):
wherein,
the second consumption of the solid engine at the T moment is shown, and T is the rated working time of the solid engine;
s2: and calculating the total impact of the solid engine under the state with deviation according to the theoretical average specific impact, the theoretical total medicine loading, the average specific impact deviation and the total medicine loading deviation, wherein the specific algorithm is as follows:
according to the theoretical total medicine loading quantity myTheoretical average specific impulse
Average specific impulse deviation provided by solid engine test run
And the total medicine loading deviation Delta m provided by pouring and weighingyCalculating the total impulse I of the solid engine in a deviation state according to the formula (4):
wherein epsilon1Is the first independent error coefficient, ε2Is a second independent error coefficient;
s3: calculating the average second consumption according to the theoretical total medicine loading amount, the deviation of the total medicine loading amount, the rated working time and the deviation of the working time; calculating the average thrust according to the total impact, the rated working time and the working time deviation, wherein the specific algorithm is as follows:
according to the theoretical total medicine loading quantity myAnd total medicine loading deviation delta m provided by pouring and weighingyRated operation of solid engineThe average second consumption is calculated by the time T and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (5):
wherein epsilon3Is a third independent error coefficient;
according to the theoretical total medicine loading quantity myAnd total medicine loading deviation delta m provided by pouring and weighingyCalculating the average thrust by the rated working time T of the solid engine and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (6):
s4: calculating a centroid motion equation of the guidance system by using the average second consumption and the average thrust to simulate and analyze the influence of the deviation of the solid engine on the guidance system, wherein the specific algorithm is as follows:
using mean thrust
And average second consumption
Setting the first independent error coefficient, the second independent error coefficient and the third independent error coefficient to obey normal distribution: epsilon1～N(0,1)、ε2～N(0,1)、ε3N (0,1), analyzing the influence of the deviation of the solid engine on the guidance system according to the guidance system mass center motion equation and Monte Carlo simulation statistics,
wherein, the guidance system adopts mass center motion equations as formulas (7) and (8):
in the formula,
a rocket mass at time t, wherein m (t) is non-volatilet＝0In order to obtain the takeoff mass of the rocket,
in order to obtain the average second consumption amount calculated in step S3,
is a conversion matrix from an arrow coordinate system to a transmitting inertia coordinate system,
for the mean thrust, δ, calculated in step S3Z、δYFor pitch and yaw angles, R, of solid enginesi(i＝bx、by、bz)For transmitting three components of aerodynamic force, g, in an inertial framei(i＝x、y、z)For launching three components of earth gravity under an inertial coordinate system, Vi(i＝xa、ya、za)For transmitting three components of velocity, x, in an inertial framea、ya、zaThree components for the position under the inertial frame of transmission.
After the technical scheme is adopted, compared with the prior art, the invention has the following beneficial effects:
the total loading amount and the deviation thereof, the working time and the deviation thereof, the average specific impulse and the deviation thereof are used for displaying and representing the average thrust and the average second consumption, so that the influence of the deviation of the solid engine on the system can be conveniently analyzed by guidance Monte Carlo simulation;
the first independent error coefficient, the second independent error coefficient and the third independent error coefficient are set to obey normal distribution, a statistical analysis result of mu +/-3 sigma is given, and the confidence coefficient of a simulation result is improved.
Drawings
Fig. 1 is a schematic flow chart of a simulation method of guidance deviation of a solid-state engine of a launch vehicle according to an embodiment of the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather construed as limited to the embodiments set forth herein.
Referring to FIG. 1, in one embodiment, a method for simulating guidance deviation of a solid state engine of a launch vehicle comprises the following steps:
s1: calculating theoretical average specific impulse and theoretical total medicine loading according to rated internal ballistic parameters of the solid engine;
s2: calculating the total impact of the solid engine under the state of deviation according to the theoretical average specific impact, the theoretical total medicine loading amount, the average specific impact deviation and the total medicine loading amount deviation;
s3: calculating the average second consumption according to the theoretical total medicine loading amount, the deviation of the total medicine loading amount, the rated working time and the deviation of the working time; calculating average thrust according to the total impact, rated working time and working time deviation;
s4: and calculating a mass center motion equation of the guidance system by using the average second consumption and the average thrust to simulate and analyze the influence of the deviation of the solid engine on the guidance system.
Preferably, in step S4, a monte carlo simulation is performed to analyze the influence of the deviation of the solid engine on the guidance system using the average second consumption and the average thrust.
The total loading quantity and the deviation thereof, the working time and the deviation thereof, and the average specific impulse and the deviation thereof are used for displaying and representing the average thrust and the average second consumption, so that the influence of the deviation of the solid engine on the system can be conveniently analyzed by guidance Monte Carlo simulation.
The following is a specific description of the simulation method of the guidance deviation of the solid engine of the launch vehicle, but not limited thereto.
Step S1 is first executed: and calculating the theoretical average specific impulse and the theoretical total medicine loading according to the rated internal ballistic parameters of the solid engine.
Specifically, in step S1, the internal trajectory (internal ballistics) is a part of the trajectory, and the rated internal trajectory parameters of the solid engine are known. Calculating theoretical average specific impulse according to rated internal ballistic parameters of solid engine
The method comprises the following steps:
first, the thrust F of the rated internal trajectory of the solid engine is calculatedG(t), calculated as formula (1):
specifically, in step S1, the theoretical total charge m is calculated from the rated internal ballistic parameter of the solid engineyThe dosage is the amount of the solid propellant, the calculation is shown as a formula (2), and the theoretical average specific impulse is calculated according to the total loading
The calculation is as formula (3):
wherein,
the consumption per second at the T moment of the solid engine is T, and T is the rated working time of the solid engine.
Step S2 is then executed: and calculating the total impact of the solid engine under the state of deviation according to the theoretical average specific impact, the theoretical total medicine loading, the average specific impact deviation and the total medicine loading deviation.
And introducing the average specific impact deviation and the total medicine loading deviation into the deviation simulation, and cooperatively associating the average specific impact deviation and the total medicine loading deviation through the calculation of the total impact.
Specifically, in step S2, the theoretical total drug loading myTheoretical average specific impulse
Average specific impulse deviation provided by solid engine test run
And the total medicine loading deviation Delta m provided by pouring and weighingyCalculating the total impulse I of the solid engine in a deviation state according to the formula (4):
wherein epsilon1Is the first independent error coefficient, ε2Is the second independent error coefficient.
The solid engine test run refers to a test run before the solid engine is actually used, and it is needless to say that the average specific impulse deviation provided by the solid engine test run of the present embodiment is provided when the performance meets the standard. Pouring weighing is the process of weighing and charging propellant, and can be a test process, and a certain deviation exists between the total medicine loading amount provided by the pouring weighing and the charging process, and is used as the deviation of the total medicine loading amount.
Step S3 is then executed: calculating the average second consumption according to the theoretical total medicine loading amount, the deviation of the total medicine loading amount, the rated working time and the deviation of the working time; and calculating the average thrust according to the total impact, the rated working time and the working time deviation.
And introducing the working time deviation into the deviation simulation, and matching and associating the working time deviation, the average specific impulse deviation and the total medicine loading deviation through calculating the average second consumption and the average thrust.
Specifically, in step S3, the theoretical total drug loading myAnd total medicine loading deviation delta m provided by pouring and weighingyCalculating the average second consumption by calculating the rated working time T of the solid engine and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (5):
wherein epsilon3Is the third independent error coefficient.
In step S3, the theoretical total drug loading myAnd total medicine loading deviation delta m provided by pouring and weighingyCalculating the average thrust by the rated working time T of the solid engine and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (6):
step S4 is then executed: and calculating a mass center motion equation of the guidance system by using the average second consumption and the average thrust to simulate and analyze the influence of the deviation of the solid engine on the guidance system.
Specifically, in step S4, the average thrust is used
And average second consumption
Setting the first independent error coefficient, the second independent error coefficient and the third independent error coefficient to obey normal distribution: epsilon1～N(0,1)、ε2～N(0,1)、ε3N (0,1), analyzing the influence of the deviation of the solid engine on the guidance system according to the guidance system mass center motion equation and Monte Carlo simulation statistics,
wherein, the guidance system adopts mass center motion equations as formulas (7) and (8):
in the formula,
a rocket mass at time t, wherein m (t) is non-volatilet＝0In order to obtain the takeoff mass of the rocket,
in order to obtain the average second consumption amount calculated in step S3,
is a conversion matrix from an arrow coordinate system to a transmitting inertia coordinate system,
for the mean thrust, δ, calculated in step S3Z、δYFor pitch and yaw angles, R, of solid enginesi(i＝bx、by、bz)For transmitting three components of aerodynamic force, g, in an inertial framei(i＝x、y、z)For launching three components of earth gravity under an inertial coordinate system, Vi(i＝xa、ya、za)For transmitting three components of velocity, x, in an inertial framea、ya、zaThree components for the position under the inertial frame of transmission.
The mass center motion equation adopted by the guidance system is the existing equation, the input of the equation is the amount with deviation calculated by the embodiment of the invention, and the calculated deviation is substituted into the equation to calculate the influence of the deviation on the guidance system, so that the calculation is simple, the practicability is high, and the engineering application is facilitated.
The first independent error coefficient, the second independent error coefficient and the third independent error coefficient are set to obey normal distribution, a statistical analysis result of mu +/-3 sigma is given, and the confidence coefficient of a simulation result is improved.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the scope of the claims, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention.
Claims (1)
1. A carrier rocket solid engine guidance deviation simulation method is characterized by comprising the following steps:
s1: calculating theoretical average specific impulse and theoretical total charge according to rated internal ballistic parameters of the solid engine, wherein the specific algorithm is as follows:
calculating theoretical average specific impulse according to rated internal ballistic parameters of solid engine
The method comprises the following steps:
first, the solid launch is calculatedThrust F of rated internal trajectory of machineG(t), calculated as formula (1):
then, calculating theoretical total medicine loading m according to rated internal ballistic parameters of the solid engineyCalculating as formula (2), and calculating the theoretical average specific impulse according to the total drug loading
The calculation is as formula (3):
wherein,
the second consumption of the solid engine at the T moment is shown, and T is the rated working time of the solid engine;
s2: and calculating the total impact of the solid engine under the state with deviation according to the theoretical average specific impact, the theoretical total medicine loading, the average specific impact deviation and the total medicine loading deviation, wherein the specific algorithm is as follows:
according to the theoretical total medicine loading quantity myTheoretical average specific impulse
Average specific impulse deviation provided by solid engine test run
And the total medicine loading deviation Delta m provided by pouring and weighingyCalculating the total impulse I of the solid engine in a deviation state according to the formula (4):
wherein epsilon1Is the first independent error coefficient, ε2Is a second independent error coefficient;
s3: calculating the average second consumption according to the theoretical total medicine loading amount, the deviation of the total medicine loading amount, the rated working time and the deviation of the working time; calculating the average thrust according to the total impact, the rated working time and the working time deviation, wherein the specific algorithm is as follows:
according to the theoretical total medicine loading quantity myAnd total medicine loading deviation delta m provided by pouring and weighingyCalculating the average second consumption by calculating the rated working time T of the solid engine and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (5):
wherein epsilon3Is a third independent error coefficient;
according to the theoretical total medicine loading quantity myAnd total medicine loading deviation delta m provided by pouring and weighingyCalculating the average thrust by the rated working time T of the solid engine and the working time deviation Delta T provided by the trial run of the solid engine
The calculation is as formula (6):
s4: calculating a centroid motion equation of the guidance system by using the average second consumption and the average thrust to simulate and analyze the influence of the deviation of the solid engine on the guidance system, wherein the specific algorithm is as follows:
using mean thrust
And average second consumption
Setting the first independent error coefficient, the second independent error coefficient and the third independent error coefficient to obey normal distribution: epsilon1～N(0,1)、ε2～N(0,1)、ε3N (0,1), analyzing the influence of the deviation of the solid engine on the guidance system according to the guidance system mass center motion equation and Monte Carlo simulation statistics,
wherein, the guidance system adopts mass center motion equations as formulas (7) and (8):
in the formula,
a rocket mass at time t, wherein m (t) is non-volatilet＝0In order to obtain the takeoff mass of the rocket,
in order to obtain the average second consumption amount calculated in step S3,
from an arrow coordinate system to a launch inertial coordinate systemThe transformation matrix of (a) is,
for the mean thrust, δ, calculated in step S3Z、δYFor pitch and yaw angles, R, of solid enginesi(i＝bx、by、bz)For transmitting three components of aerodynamic force, g, in an inertial framei(i＝x、y、z)For launching three components of earth gravity under an inertial coordinate system, Vi(i＝xa、ya、za)For transmitting three components of velocity, x, in an inertial framea、ya、zaThree components for the position under the inertial frame of transmission.
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| CN111027222A (en) * | 2019-12-18 | 2020-04-17 | 北京空天技术研究所 | Multi-pulse engine total impact correction method and system for Lambert orbit change of spacecraft |
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| CN111638654B (en) * | 2020-05-12 | 2023-11-10 | 上海宇航系统工程研究所 | Fault-adaptive carrier rocket intelligent control semi-physical simulation method |
| CN112149292B (en) * | 2020-09-13 | 2022-05-31 | 中国运载火箭技术研究院 | Method, device and storage medium for determining engine disturbance torque |
| CN111881614B (en) * | 2020-09-28 | 2020-12-08 | 中国人民解放军国防科技大学 | Solid rocket engine charging characterization method |
| CN112417775B (en) * | 2020-10-30 | 2024-03-26 | 中国运载火箭技术研究院 | Method for calculating ballistic performance in thrust termination and pressure relief process of solid rocket engine |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1524191A1 (en) * | 2003-10-17 | 2005-04-20 | Thales | Landing navigation method and corresponding ground station |
| CN109325288A (en) * | 2018-09-17 | 2019-02-12 | 北京宇航系统工程研究所 | A kind of Solid Launch Vehicle population parameter based on uncertainty optimization determines method and system |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1524191A1 (en) * | 2003-10-17 | 2005-04-20 | Thales | Landing navigation method and corresponding ground station |
| CN109325288A (en) * | 2018-09-17 | 2019-02-12 | 北京宇航系统工程研究所 | A kind of Solid Launch Vehicle population parameter based on uncertainty optimization determines method and system |
Non-Patent Citations (2)
| Title |
|---|
| 固体火箭发动机总冲精度预示与分析;蔡湘芬;《推进技术》;19960430;第17卷(第2期);第27-31页 * |
| 基于蒙特卡罗方法火箭入轨精度分析研究;王立扬 等;《上海航天》;20160525;第33卷;第77-80页 * |
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