CN113761670B - Balanced flight theory and online orbit-in capability assessment method of carrier rocket - Google Patents
Balanced flight theory and online orbit-in capability assessment method of carrier rocket Download PDFInfo
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Abstract
The invention discloses a carrier rocket equilibrium flight theory method, which combines the steps of carrying out flight motion analysis on a rocket under a thrust fault, establishing a dynamic model on the flight mechanics process of continuous maneuvering and orbital transfer of the rocket, judging the flight state of the rocket based on the equilibrium flight theory, and carrying out autonomous guidance control on the rocket, can effectively solve the online autonomous guidance control of the rocket under an engine thrust descent fault mode, gives out an analysis theory, can adapt to rockets of different parameter types and fault modes, has small calculated amount, and is suitable for online application. The invention also discloses an online orbit-in capability assessment method of the carrier rocket, which combines the thrust acceleration time function under the fault mode, judges the flight state of the rocket, estimates the velocity impulse of the current actual fuel level of the rocket and the total velocity increment required by the orbit-in of the rocket, can accurately judge whether the rocket can be saved and provides a feasible guidance scheme aiming at the condition of saving.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a balance flight theory and online orbit-in capability assessment method for a carrier rocket, and particularly relates to a balance flight theory for autonomous control under a rocket thrust fault mode and an online orbit-in capability assessment method based on the balance flight theory.
Background
The systems of the carrier rocket are products of fine design and a large number of tests, have very high reliability, but inevitably encounter various faults in the process of executing tasks according to the Murphy's law, and the fault mode and the occurrence moment are uncertain.
Among the numerous failure modes of a whole rocket, power system failure is most frequently occurring and often the most serious consequence of a launch vehicle. Statistics on existing fault data indicate that: about 60% of the faults in rocket powered flight segments are power system faults; particularly, under the design constraint of the heavy carrier rocket aiming at greatly improving the carrying capacity, a binding mode of a plurality of parallel boosters is generally adopted, so that the probability of power system failure is increased to a certain extent, and the failure of a flight task is directly caused when the probability of power system failure is serious.
A non-fatal engine failure that occurs outside the atmosphere is a typical situation. In 1964, the Tuxing No. 1 rocket was suddenly shut down in advance when the rocket actually flown for 117 seconds, and 1H-1 engine was suddenly shut down in advance. The secondary main engine of the Tuxing No. 5 carrier rocket for launching the Apollo No. 13 spacecraft is shut down 132 seconds in advance due to reasons in 1970, 4 and 11 days. In the flight of the second carrier rocket of the long sign No. five, the thrust of the first-stage engine of the core is instantaneously and greatly reduced in the period of 2 days 7 in 2017. The interplanetary passenger vehicle airship developed by the united states boeing company and the united states national space agency (NASA) on 12 months and 20 days 2019 presents software errors with abnormal mission overhead time. In addition, both the american delta No. 4 launch vehicle and the falcon No. 9 launch vehicle experience failure modes during flight in which one or more engines of the power system fail. These thrust anomaly non-fatal engine failures often have serious consequences of mission failure. Therefore, in recent years, attention has been paid to an intelligent technology of a carrier rocket, and a disposal strategy of a carrier rocket in which a thrust descent fault occurs in an ascending section is one of the entry points.
There are two main approaches to the current investigation of non-fatal engine faults with abnormal thrust:
1. the guidance method comprises an early-stage standard track tracking guidance method, an earth star No. 5 iterative guidance method based on an optimal control theory, a space plane dynamic explicit guidance and a plurality of improved iterative guidance algorithms at present.
2. The real-time optimization method comprises a convex optimization method, a simulated annealing method, a neural network method and the like.
Both of the above methods have certain disadvantages: the problem of the guidance method is that the guidance method is an execution method, the estimation of the track-in capability is insufficient, and the track-in precision is difficult to ensure in some cases; the problem with the optimization method is that convergence, computational efficiency and real-time are difficult to meet the demands of online applications.
The intelligent carrier rocket with intelligent brain has strong demands for autonomous information sensing, rapid fault detection, intelligent decision making, real-time reconstruction and the like. Therefore, it is particularly critical to identify the failure mode and perform the capability assessment at the first time when a failure is encountered, and whether the on-line assessment of the ability to track a thrust system failure is relevant to success or failure of the task.
Disclosure of Invention
The first aim of the invention is to provide a carrier rocket equilibrium flight theoretical method, which comprises the following specific technical scheme:
a method of balanced flight theory for a carrier rocket (in particular a balanced flight theory method for autonomous control in rocket thrust failure mode), comprising the steps of:
step one, performing flight motion analysis of a rocket in a thrust fault mode, identifying faults of a power system of the rocket, obtaining stress conditions of the rocket in radial and circumferential directions, acting effects on the height and speed of the rocket, and obtaining thrust acceleration a in the fault mode c Is a function of time of (2);
step two, establishing a dynamics model of a rocket flight process to obtain a dynamics equation of rocket flight as shown in expression 1):
wherein: beta represents range angle, r represents earth center distance, t represents time, mu represents gravitational coefficient, a r Representing the radial component of thrust acceleration, a θ A circumferential component representing thrust acceleration;
judging the state of the rocket:
if the thrust acceleration a of rocket c Satisfying expression 12), the rocket enters an equilibrium flight state:
wherein: n is the flying angular velocity of the target circular orbit,omega is the range angular velocity, < >>g 0 Is circular track gravitational acceleration->
If the thrust acceleration a of rocket c Satisfying expression 15) but not satisfying expression 12), the rocket enters a quasi-equilibrium flight state;
wherein: Δh is the height margin; v θ Is the circumferential velocity component at the moment of failure;
if the thrust acceleration a of rocket c Failing to satisfy expression 15), the rocket crashes into the atmosphere;
step four, autonomous guidance control is carried out, specifically:
during balanced flight, the optimal guidance law Θ is obtained by expression 3) P (here, thrust acceleration inclination at equilibrium flight), the maneuver orbit time T from elliptic trajectory to circular orbit at equilibrium flight is obtained by expression 6):
in the quasi-equilibrium flight process, the transition time delta T from the quasi-equilibrium flight to the equilibrium flight is obtained by the expression 18), and the optimal guidance law theta is obtained by the expression 21) P (here the optimal local acceleration tilt for quasi-equilibrium flight):
wherein: r is (r) 0 Representing the initial ground center distance for a quasi-equilibrium flight.
In the above technical solution, preferably, in the fourth step:
the radial total acceleration component and the speed component in the balanced flight process are 0, namelyAnd decomposing the thrust acceleration in the circumferential direction and the radial direction, expression 1) becomes expression 2):
the best guidance law expression 3) for balanced flight is obtained from expression 2).
In the above technical solution, preferably, the flight angular velocity n and the range angular velocity ω of the target circular orbit are substituted into expression 2), and the two expressions are synthesized to obtain expression 4):
solving the ordinary differential equation based on expression 4) results in expression 5):
further integration of both sides of expression 5) yields expression 6) to calculate the maneuver-orbit time T from elliptic trajectory to circular orbit of balanced flight.
In the above technical solution, preferably, in the fourth step:
expressing centrifugal acceleration by the circumferential velocity component at the time of failure, expression 1) is converted into expression 16):
after the delta T time is set, the rocket can reach new balance, and the earth center distance is unchanged, then r=r 0 Expression 17) is derived from expression 16):
expanding on expression 17), the second order small amount a is omitted c 2 cos 2 Θ P ·ΔT 2 Resulting in expression 18) calculates the transition time Δt from the quasi-equilibrium flight to the equilibrium flight.
In the above technical scheme, the transition time DeltaT from the quasi-equilibrium flight to the equilibrium flight is preferably minimizedExpression 20) can be obtained to calculate the optimal guidance law for quasi-equilibrium fly.
The invention provides a balanced flight theory method of a carrier rocket, which can meet the requirement of on-line application and the requirements of in-orbit precision, and the specific scheme is as follows: firstly, carrying out flight motion analysis on a rocket under the condition of thrust faults to obtain the stress conditions of the rocket in the radial direction and the circumferential direction; secondly, establishing a dynamics model for a flight mechanics process of continuous maneuvering orbit transfer of the rocket to obtain a dynamics equation of rocket flight; then judging the state of the rocket to obtain the flight state of the rocket (based on balance theory, modes such as balance flight and quasi-balance flight are included); and finally, carrying out autonomous guidance control on the rocket. The scheme of the invention can effectively solve the online autonomous guidance control of the rocket in the engine thrust descending fault mode, gives out an analysis theory, can adapt to rockets of different parameter types and fault modes, has small calculated amount and is suitable for online application.
The second object of the present invention is to provide an on-line orbit entering capability assessment method of a carrier rocket, comprising the following steps:
step one, thrust acceleration a of rocket c Judging to obtain a rocket entering a balanced flight state, a rocket entering a quasi-balanced flight state and a rocket entering an atmosphere crash;
step two, estimating the velocity impulse Deltav of the current rocket actual fuel level through an expression 21); by expression 22) estimating the total velocity delta Δv required for rocket orbit Re ：
Δv＝v idk -Δv 1k -Δv 2k -Δv 3k 21)；
Wherein: v idk The speed generated by the thrust of the rocket under the vacuum non-attractive action is called ideal speed; deltav 1k For the loss of speed caused by gravitational acceleration componentIs gravitational force loss; deltav 2k Speed loss due to drag; deltav 3k Is the speed loss caused by the atmospheric static pressure when the engine works in the atmosphere;thrust acceleration a of rocket in quasi-equilibrium flight process c Average value of (2); />To balance thrust acceleration a of rocket during flight c Average value of (2); Δt is the transition time from the quasi-equilibrium flight condition to the equilibrium flight condition; t is the maneuver orbit time from elliptical trajectory to circular orbit of equilibrium flight;
step three, the current rocket actual fuel level has velocity impulse Deltav and the total velocity increment Deltav required by rocket orbit Re Comparison is performed:
if the current actual fuel level of the rocket has the velocity impulse Deltav which is more than or equal to the total velocity increment Deltav required by the rocket track entering Re Judging that the rocket can be saved, and guiding according to the corresponding guidance law according to the condition that the rocket enters a balanced flight state, the rocket enters a quasi-balanced flight state or the rocket enters an atmosphere crash;
if the current actual fuel level of the rocket has a velocity impulse Deltav smaller than the total velocity increment Deltav required by the rocket to enter the orbit Re And judging that the thrust loss is too large, so that the rescue can not be saved, and giving up the rescue.
The invention provides an online orbit-in capability assessment method of a carrier rocket, which can realize accurate assessment of the online orbit-in capability of the rocket, and the specific scheme is as follows: firstly, identifying faults of a power system of a rocket, and acquiring a time function of thrust acceleration in a fault mode; secondly, estimating the velocity impulse of the current actual fuel level of the rocket and the total velocity increment required by the rocket in orbit; and finally, comparing the velocity impulse of the current actual fuel level of the rocket with the total velocity increment required by the rocket in orbit, and accurately judging whether the rocket can be saved.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a schematic view of a transient ellipse in ballistic flight;
FIG. 2 is a schematic diagram of a mechanical analysis of a rocket in an extra-atmospheric flight phase according to the present invention;
FIG. 3 is a force analysis schematic of a continuous thrust rocket of the present invention;
FIG. 4 (a) is a schematic diagram of a guidance law for balanced flight;
FIG. 4 (b) is a schematic diagram of the guidance law for quasi-equilibrium flight;
FIG. 5 is a schematic diagram of a flight procedure reconstruction based on equilibrium flight theory according to the present invention;
FIG. 6 is a flow chart of the on-line orbital transfer capability assessment of the launch vehicle in this embodiment;
FIG. 7 is a schematic view of analysis of the orbital capability area of a rocket in accordance with the present invention;
FIG. 8 is a graph of guidance laws and fly height over time in accordance with the present invention;
FIG. 9 is a graph of near-site altitude and far-site altitude over time after a rocket of the present invention enters a safe circular orbit.
Detailed Description
Embodiments of the invention are described in detail below with reference to the attached drawings, but the invention can be implemented in a number of different ways, which are defined and covered by the claims.
Example 1:
a carrier rocket balance flight theory method (in particular to a balance flight theory method for autonomous control under a rocket thrust fault mode), namely an autonomous control method under the rocket thrust fault mode, which comprises the following steps:
1. rocket flight motion analysis under a thrust fault mode is performed in the following detail:
according to the theory of launch vehicle ballistics, the rocket trajectory is part of a geocentric elliptical orbit, as shown in fig. 1. Due to different mission missiles, the trajectories of the carrier rocket and the ballistic missile are different, the instantaneous elliptic orbit near-point of the orbit entering point of the carrier rocket is generally above the safety height, and the elliptic orbit near-point of the final stage main engine shutdown point of the ballistic missile is intersected with the earth.
In the out-of-atmosphere flight section before orbit, rocket motion is generally represented as a lifting process of flying height and speed, but in consideration of engineering constraints such as actual thrust-weight ratio of the rocket, the two lifting processes do not require synchronization and are stressed to achieve better efficiency. For example, in the section before the track-in point, a strategy of continuously increasing the speed and smoothly changing the altitude (i.e. the speed increment is mainly in the circumferential direction, and the radial speed is basically constant) is often adopted, and at this time, the motion of the rocket is in a stage of continuously increasing the near point at the far point of the instantaneous elliptical orbit, such as the near point lifting in fig. 1. If the rocket thrust is insufficient at this time, the elevation of the trajectory near-site is not timely, the trajectory cannot be prevented from intersecting with the earth, and according to the elliptic trajectory theory, the trajectory elevation continuously decreases in the subsequent rocket flight, and finally the task failure is caused.
Mechanical analysis is carried out on rocket motion under a thrust fault mode, a local horizontal coordinate system (an origin is a rocket centroid, triaxial is respectively along radial direction, circumferential direction and normal direction of a trajectory plane) is established, rocket stress is concentrated in the trajectory plane outside an atmosphere, and the stress condition of a rocket body in the radial direction and the circumferential direction is shown in fig. 2, wherein: radial forces are the radial components of gravitational, centrifugal and thrust forces, and the resultant force determines the movement of the rocket in the radial, i.e. height direction, wherein centrifugal forces are related to circumferential velocity and orbit height. The circumferential force is a circumferential component of the thrust force, with the effect that the circumferential speed is changed, and at the same time, the change in circumferential speed will directly affect the centrifugal force.
If the thrust value is large enough, the circumferential quick acceleration can be realized on the basis of guaranteeing the radial three-force balance, and the rocket has higher maneuvering orbit transfer efficiency; if the thrust is too small, radial three-force balance cannot be supported, and if the speed cannot be effectively increased in the living height range, the centrifugal force is increased, and finally the rocket can crash.
The magnitude of the engine thrust for the radially balanced portion is a major loss of capacity because there is no conversion to speed increase (as understood by the comparative impulse action); thus, the more the thrust drops when the rocket fails, the longer the flight time, the greater the proportion of capacity loss; it can also be extended that if radial force balance is ensured by the radial component of the thrust, the circumferential component of the thrust accelerates, and the thrust direction is adjusted in real time as the circumferential speed increases, the centrifugal acceleration increases, so that the radial force is balanced all the time, the minimum capacity loss is realized at the acceleration level, and the optimal trajectory adjustment is realized. The flight dynamics mechanism analysis can explain the basic principle that the rocket loses the advantage of the thrust fault task in the out-of-atmosphere flight section before orbit entering, and also provides ideas for the research of fault treatment strategies.
2. The dynamic modeling of rocket balance flight process is as follows:
in the process that the rocket flies out of the atmosphere and runs towards a target orbit, a rocket stress model of continuous thrust is shown in fig. 3, the rocket is subjected to the action of earth attraction and engine thrust, and centrifugal inertia force action is also required to be considered in a local horizontal coordinate system. In FIG. 3, O E Represents the earth center, beta represents the range angle, r represents the earth center distance, a c Representing thrust acceleration (vector), a r Representing the radial component of thrust acceleration, a θ Represents the circumferential component of thrust acceleration, Θ P Representing inclination of thrust acceleration (i.e. thrust acceleration a c The angle with the local horizontal, also called the optimal guidance law), v represents the velocity vector.
The mass change in rocket flight is classified into the change of acceleration, and rocket flight dynamics is obtained in the radial direction and the circumferential direction of a local horizontal coordinate system as shown in expression 1):
wherein: t represents time, and μ represents the coefficient of gravity.
3. Judging the state of the rocket and performing autonomous guidance control, wherein the details are as follows:
thrust acceleration a of rocket c The thrust fault mode is determined according to the thrust fault mode, and the thrust fault mode can be a determined time function or can be measured in real time. The default is typically failure mode determination, and this thrust acceleration is also determined over time, without measurement, which is not a constant, but rather a time-varying amount.
3.1, when the balance flight is satisfied, the radial total acceleration component and the speed component in the flight process are 0, namely Considering the continuous thrust acceleration to determine, the direction is adjustable, decomposing the thrust acceleration and substituting the decomposed thrust acceleration into expression 1) to obtain expression 2):
from expression 2) expression 3) optimal guidance law Θ for solving balanced flight P ：
Angular velocity of flight for circular orbit of targetAnd range angular velocity +.>Brings in expression 2) and combines the two expressions (specifically squaring the left and right sides of the two equations in expression 2, then left and right to right) to give expression 4):
solving the ordinary differential equation based on expression 4) results in expression 5):
further integrating both sides of expression 5) to obtain expression 6) for calculating the maneuver transition time T from elliptical trajectory to circular orbit for balanced flight:
by solving the definite integral expression 6), the maneuvering orbit transferring time from the elliptic trajectory to the circular orbit meeting the balanced flight condition can be obtained, and the flight process of accelerating from the elliptic trajectory to the target circular orbit can be analyzed.
Such as: let the ratio of thrust acceleration to circular track gravitational acceleration be
When ω < n, transforming the denominator of the integral term in expression 6) yields expression 7):
performing transformation derivation on the expression 6) to obtain an expression 8):
wherein: k is the ratio of the gravitational acceleration to the thrust acceleration of the circular orbit,taking the integral intermediate transformation variables τ and α, let ∈ ->α＝τ 2 ，τ 0 The value of t is the value of t. Integrating expression 8) yields expression 9):
wherein: t is time; ellipticF is a first type of incomplete elliptic integral, or can be further developed into expression 10):
the first type of incomplete elliptic integral solution can refer to the prior art, can give a higher-order approximate solution, meets the requirement of quick calculation, or performs calculation by using a numerical integration method. In the case where expression 10) can be solved analytically, ω (t) (i.e., the range angular velocity at time t), t ε [0, T]And therefore the thrust acceleration tilt angle theta P (optimal guidance law) can be quickly solved according to expression 3. Therefore, the equilibrium flight process can be theoretically analyzed, the time and the burnup of the whole process can be rapidly calculated, and the speed loss or the thrust efficiency of the continuous thrust track transfer process can also be calculated.
It should be noted that: the balanced flight conditions represent only temporary safety and not long-term danger relief, and if there is a fuel leak, the circumferential acceleration time is not long enough, the circumferential speed constraint required for the circular orbit is not reached when the fuel is exhausted, and the rocket is still difficult to enter the safety orbit.
In the solving process of expression 10), the condition to be satisfied is expression 11):
when the rocket is in an acceleration section, ω is less than or equal to n, the condition that the balanced flight needs to satisfy can be obtained is expression 12):
according to the balanced flight condition, whether the rocket is in a dangerous state or has self-rescue capability can be judged based on the rocket thrust acceleration level after faults.
3.2, due to the existence of the circumferential component of the thrust acceleration, the circumferential component of the speed will increase, and the centrifugal acceleration will increase continuously, so that the thrust acceleration component required for achieving radial force balance will decrease continuously, and therefore, the circumferential and radial are dynamic processes of mutual coupling and mutual conversion, so that a certain margin exists in the balanced flight conditional expression 12).
If it isThe further descent of the rocket can be restrained by increasing the centrifugal acceleration according to the rocket height level, namely, whether the rocket can be rapidly accelerated in the circumferential direction within the range of slightly reducing the allowable height, which can be judged through time estimation.
The thrust acceleration is completely concentrated in the circumferential direction, and the radial negative acceleration, namely theta, is not considered P Because the thrust acceleration has the best effect on circumferential acceleration at the moment of 0, the radial centrifugal acceleration is accelerated most rapidly, the centrifugal acceleration and the gravitational force are balanced by the transition time delta T, the rocket reaches the survival height at the moment, and the geocentric meridian at the moment is r L ，r L =r- Δh, Δh is the height margin, and can be approximated using expression 13):
wherein: v θ For the circumferential velocity component at the moment of failure，
Then the condition for achieving rocket descent-stopping to ascent is expression 14):
i.e. the sum of centrifugal and thrust accelerations is greater than gravitational acceleration, deltav θ For circumferential speed increase in this process, deltav θ ≈a c ΔT。
If the thrust acceleration a of the rocket c Failing to satisfy expression 15), the rocket crashes into the atmosphere.
3.3 thrust acceleration a of rocket c Satisfying expression 15) but not satisfying expression 12), the rocket enters a quasi-equilibrium flight state.
In fact, during flight, acceleration in the circumferential direction will increase the speed fastest, the centrifugal acceleration increases fastest, but the initial radial negative acceleration value in this case is also the largest, also at altitude; conversely, if the full thrust is applied in the radial direction, the radial negative acceleration is minimal, the height drop is slow, but the centrifugal acceleration cannot be increased. There should be a compromise between the two extremes, namely a limited range of altitude reduction, and a fast realization of balanced flight conditions, which requires an optimal thrust acceleration tilt angle, with minimal burnup if the transition time from quasi-balanced flight to balanced flight is minimized.
Expressed as a circumferential velocity component, expression 1) is converted into expression 16):
after the delta T time is set, the rocket can reach new balance, and r is given by 0 Representing the initial ground center distance of a quasi-equilibrium flight, and the ground center distance (r, also referred to herein as the initial ground center distance of the equilibrium flight) is unchanged, then there is r=r 0 Expression is obtained according to expression 16)
Formula 17):
expanding on expression 17), the second order small amount a is omitted c 2 cos 2 Θ P ·ΔT 2 Resulting in transition time Δt expression 18) from quasi-equilibrium flight to equilibrium flight:
minimizing the transition time DeltaT from quasi-equilibrium to equilibriumObtaining expression 19):
expression 20) can be used to calculate the optimal guidance law Θ in combination with expression 19) P ：
By comparing expression 3) and expression 20), it can be found that the satisfaction is satisfiedBalanced flight status of the conditions and fulfils +.>The guidance laws in the case of the quasi-equilibrium flight state of the condition are shown in fig. 4 (a) and 4 (b). Under the quasi-equilibrium flight condition, the optimal direction of thrust acceleration is not the radial direction or the circumferential direction, but the different effects of the two directions are still considered, so that the shortest flight time to radial force balance can be realized. Since the balanced flight represents the most efficient way of thrust, expression 3) and expression 20) are also the optimal guidance schemes for the extra-atmospheric flight segment prior to rocket orbit.
The scheme of applying the embodiment specifically comprises the following steps:
simulation analysis is carried out on an atmospheric layer external power flight section of a certain two-stage carrier rocket, a fault mode is set to be an engine thrust descending fault of non-fuel leakage, and feasibility is verified according to different fault moments and different engine residual thrust proportions:
1. on-line reconstruction and guidance law reconstruction flight program
Simulation analysis is carried out on an atmospheric layer external power flight section of a certain two-stage carrier rocket, the fault mode is a non-fuel leakage engine thrust descending fault, the fault time is set to be 400s, and the proportion of the residual thrust of the engine is 55%. The on-line reconstruction flight procedure adopts the rapid push calculation method; for a space flight section before orbit entering, the guidance law reconstruction flight program adopts a balanced flight expression 3) or a quasi-balanced flight expression 20) to provide a thrust acceleration inclination angle required by guidance, solves a trajectory differential equation, and performs flight program reconstruction according to the principle and the step of flight program reconstruction by utilizing the analysis theory of balanced flight. Since range angle information is determined mainly from the rocket's own navigation system, the key part of the main class flight procedure is still embodied as the inclination of thrust acceleration.
The calculated thrust acceleration inclination angle and the calculated angle deviation are shown in fig. 5, the angle deviation in fig. 5 is the difference between the on-line reconstruction algorithm and the four-order fixed-step guidance law reconstruction algorithm relative to the five-order variable-step guidance law reconstruction algorithm, the maximum deviation of the obtained thrust acceleration inclination angle in the whole power flight section is not more than 0.5 degrees, but the calculated amount is small due to the existence of an approximate analysis algorithm in the calculation process, so that the on-line reconstruction algorithm has higher precision and small calculated amount, and is suitable for on-line calculation on an arrow.
Example 2:
an online orbit entering capability evaluation method of a carrier rocket based on a balanced flight theory is shown in fig. 6, and comprises three parts:
a first part: during the flying process of the rocket, monitoring whether the rocket is abnormal or not, if not, flying according to a program; if yes, enter the second part:
a second part: judging whether the engine fails, if so, confirming an engine failure mode, performing rocket capability assessment (such as fuel capability), and entering a third part; otherwise, flying according to the program;
third section: the judgment decision is specifically as follows:
the energy is insufficient, saving is abandoned, and the aircraft flies according to the program;
the energy is abundant, the fault does not affect the task, the rescue is not needed, and the flight is carried out according to the program;
the energy has allowance and needs to be saved. The predetermined task can be completed through the reconstruction of the flight program, and the flight program is generated on line; and (5) flying according to a program. The emergency orbit can be entered through flight program reconstruction, and the flight program is generated on line; and (5) flying according to a program.
In the second part:
confirming the engine fault of the rocket and acquiring the thrust acceleration a under the fault mode c . And calculating a time function of the thrust acceleration according to the power system fault mode identification result.
This example is based on part of the disclosure in example 1, namely the thrust acceleration a of the rocket according to the method disclosed in example 1 c To judge to obtain the rocket in equilibrium flight state (if the thrust acceleration a of the rocket c Satisfying expression 12)), the rocket enters a quasi-equilibrium flight state (if the thrust acceleration a of the rocket c Satisfying expression 15) but not satisfying expression 12)) and the rocket crashes into the atmosphere (if the thrust acceleration a of the rocket c Not satisfying expression 15)).
By expression 21) estimates the velocity impulse Δv that the current rocket actual fuel level has:
Δv＝v idk -Δv 1k -Δv 2k -Δv 3k 21)；
wherein: v idk The speed generated by the thrust of the rocket under the vacuum non-attractive action is called ideal speed; deltav 1k A loss of speed due to gravitational acceleration component, referred to as gravitational loss; deltav 2k Speed loss due to drag; deltav 3k Is the speed loss caused by the atmospheric static pressure when the engine works in the atmosphere;
by expression 22) estimating the total velocity delta Δv required for rocket orbit Re ：
Wherein:thrust acceleration a of rocket in quasi-equilibrium flight process c Average value of (2); />To balance thrust acceleration a of rocket during flight c Average value of (2); Δt is the transition time from the quasi-equilibrium flight condition to the equilibrium flight condition; t is the maneuver orbit time from elliptical trajectory to circular orbit of balanced flight. />And->The method can be obtained by adopting a method of averaging after integrating, or can be obtained by adopting other averaging methods, and the method is determined according to actual requirements.
Having a velocity impulse Deltav for the current rocket actual fuel level and a total velocity increment Deltav required for rocket orbit Re Comparison is performed:
if the current actual fuel level of the rocket has the velocity impulse Deltav which is more than or equal to the total velocity increment Deltav required by the rocket track entering Re Judging that the vehicle can be saved and guiding is carried out, specifically: optimum guidance law theta for balanced flight according to the above P And the maneuvering orbit transfer time T from the elliptic trajectory to the circular orbit of the balance flight guides the balance flight; optimum guidance law theta for quasi-equilibrium flight P And guiding the equilibrium flight in alignment with the transition time deltat from the quasi-equilibrium flight to the equilibrium flight.
If the current actual fuel level of the rocket has a velocity impulse Deltav smaller than the total velocity increment Deltav required by the rocket to enter the orbit Re And judging that the thrust loss is too large, so that the rescue can not be saved, and giving up the rescue.
In a specific capability assessment process, the motion process in which different acceleration stages possibly exist is considered, for example, aiming at the primary thrust descending fault of the core, the primary working of the core is insufficient to enter a survival track, and the secondary starting of the core is required to further accelerate and raise the flying speed until entering a circular track. Because the dynamic characteristics of all the sub-stages of the rocket are different, the comprehensive calculation of grading and segmentation is needed.
The scheme of applying the embodiment specifically comprises the following steps:
simulation analysis is carried out on an atmospheric layer external power flight section of a certain two-stage carrier rocket, a fault mode is set to be an engine thrust descending fault of non-fuel leakage, and an in-orbit capability assessment algorithm based on a balanced flight theory is verified on the basis of different fault moments and different engine residual thrust proportions. In the simulation process, a first step is adopted to enter a safe high circular orbit, and a second step is adopted to lift a distant place to enter a large elliptical orbit, wherein the former step mainly considers the application of a balanced flight theory.
1. Rail-mounted capability area analysis based on balanced flight theory
Setting the fault time interval to be 350s to 750s, covering the primary core faults and the secondary core faults, and researching the safety and countermeasures of the rocket system when engine thrust faults with different residual thrust proportions occur at different times.
The derailment capability region can be calculated based on equilibrium flight theory for different engine residual thrust ratios as shown in fig. 7, with the engine residual thrust ratio allowing the most severe condition to be the lower limit of region 2. At least the safe circular orbit can be reached by adopting balanced flight in the area 1; in zone 2, at least a safe circular orbit can be reached with quasi-equilibrium flight; in region 3, the thrust loss ratio is too large, and the capacity is insufficient, so that the device cannot be saved. The figure gives a thrust fault situation and a decision guide in the task process.
Based on a balanced flight theory algorithm, a software platform is further developed, and simulation analysis shows that: the equilibrium flight theory method is correct, has small calculated amount and is suitable for online application. The method has good practicability, and can provide technical theoretical support for autonomous fault handling of the carrier rocket thrust fault mode.
2. Derailment capability assessment contrast for different fault levels
The fault time is set to be 350s, and the residual thrust ratio of the engine is respectively 55% and 40% to simulate. As shown in the graph of the time-dependent change of the guidance law and the flying height, the guidance law is balanced when the residual thrust is 55%, and the guidance law is balanced when the residual thrust is 40%, so that the safety circular orbit can be ensured to be reached.
After entering the safe circular orbit, the orbit maneuver control of the remote-place lifting is executed. The time-dependent curve graphs of the near-site height and the far-site height are shown in fig. 9, when the track-in point is reached, the near-site heights are 343km and 305km respectively for the states of 55% and 40% of the residual thrust, and the far-site heights can reach 21345km and 6169km, so that the track-in capability is stronger when the residual thrust is 55%. And a height guidance strategy is further applied to the 55% state of the residual thrust, so that the near point of the track-in point is kept at 225km, and the height of the far point can be raised to 25500km.
It is emphasized that the orbit entering capability assessment based on the balanced flight theory only needs to calculate the first type of incomplete elliptic integral, and can adopt an approximate formula or a numerical integration method, the calculated amount of which is far smaller than that of iterative guidance and ordinary differential equation set solving, so that the engineering application requirement of an arrow-borne computer on line in real time can be met.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A method of balancing flight theory of a launch vehicle, comprising the steps of:
step one, performing flight motion analysis of a rocket in a thrust fault mode, identifying faults of a power system of the rocket, obtaining stress conditions of the rocket in radial and circumferential directions, acting effects on the height and speed of the rocket, and obtaining thrust acceleration a in the fault mode c Is a function of time of (2);
step two, establishing a dynamics model of a rocket flight process to obtain a dynamics equation expression 1) of rocket flight:
wherein: beta represents range angle, r represents earth center distance, t represents time, mu represents gravitational coefficient, a r Representing the radial component of thrust acceleration, a θ A circumferential component representing thrust acceleration;
judging the state of the rocket:
if the thrust acceleration a of rocket c Satisfying expression 12), the rocket enters an equilibrium flight state:
wherein: n is the flying angular velocity of the target circular orbit,omega is the range angular velocity, < >>g 0 Is circular track gravitational acceleration->
If the thrust acceleration a of rocket c Satisfying expression 15) but not satisfying expression 12), the rocket enters a quasi-equilibrium flight state;
wherein: Δh is the height margin; v θ As the circumferential velocity component at the time of failure,
if the thrust acceleration a of rocket c Failing to satisfy expression 15), the rocket crashes into the atmosphere;
step four, autonomous guidance control is carried out, specifically:
during balanced flight, the optimal guidance law Θ is obtained by expression 3) P The maneuver-orbit time T from elliptic trajectory to circular orbit of balanced flight is obtained by expression 6):
in the quasi-equilibrium flight process, the transition time delta T from the quasi-equilibrium flight to the equilibrium flight is obtained by the expression 18), and the optimal guidance law theta is obtained by the expression 20) P ：
Wherein: r is (r) 0 Representing the initial ground center distance for a quasi-equilibrium flight.
2. The balanced flight theory method according to claim 1, wherein in the fourth step:
the radial total acceleration component and the speed component in the balanced flight process are 0, namelyAnd decomposing the thrust acceleration in the circumferential direction and the radial direction, expression 1) becomes expression 2):
the best guidance law expression 3) for balanced flight is obtained from expression 2).
3. The balanced flight theory method according to claim 2, wherein the flight angular velocity n and the range angular velocity ω of the target circular orbit are substituted into expression 2), and the two expressions are synthesized to obtain expression 4):
solving the ordinary differential equation based on expression 4) results in expression 5):
further integration of both sides of expression 5) yields expression 6) to calculate the maneuver-orbit time T from elliptic trajectory to circular orbit of balanced flight.
4. A balanced flight theory method according to claim 3, wherein in the fourth step:
expressed as a circumferential velocity component, expression 1) is converted into expression 16):
after the delta T time is set, the rocket can reach new balance, and the ground center distance is unchanged, then r=r 0 Expression 17) is derived from expression 16):
expanding on expression 17), the second order small amount a is omitted c 2 cos 2 Θ P ·ΔT 2 The transition time Δt expression 18 from the quasi-equilibrium flight to the equilibrium flight is obtained).
5. The method according to claim 4, wherein the transition time DeltaT from the quasi-equilibrium flight to the equilibrium flight is minimizedExpression 20 of the optimum guidance law for quasi-equilibrium flight can be obtained).
6. An on-line orbit-in capability assessment method for a carrier rocket by using the equilibrium flight theory method as claimed in claim 1, which is characterized by comprising the following steps:
step one, thrust acceleration a of rocket c Judging to obtain a rocket entering a balanced flight state, a rocket entering a quasi-balanced flight state and a rocket entering an atmosphere crash;
step two, estimating the velocity impulse Deltav of the current rocket actual fuel level through an expression 21); by expression 22) estimating the total velocity delta Δv required for rocket orbit Re ：
Δv＝v idk -Δv 1k -Δv 2k -Δv 3k 21)；
Wherein: v idk The speed generated by the thrust of the rocket under the vacuum non-attractive action is called ideal speed; deltav 1k A loss of speed due to gravitational acceleration component, referred to as gravitational loss; deltav 2k Speed loss due to drag; deltav 3k Is the speed loss caused by the atmospheric static pressure when the engine works in the atmosphere;thrust acceleration a of rocket in quasi-equilibrium flight process c Average value of (2); />To balance thrust acceleration a of rocket during flight c Average value of (2);
step three, the current rocket actual fuel level has velocity impulse Deltav and the total velocity increment Deltav required by rocket orbit Re Comparison is performed:
if the current actual fuel level of the rocket has the velocity impulse Deltav which is more than or equal to the total velocity increment Deltav required by the rocket track entering Re Judging that the rocket can be saved, and guiding according to the corresponding guidance law according to the condition that the rocket enters a balanced flight state, the rocket enters a quasi-balanced flight state or the rocket enters an atmosphere crash;
if the current actual fuel level of the rocket has a velocity impulse Deltav smaller than the total velocity increment Deltav required by the rocket to enter the orbit Re And judging that the thrust loss is too large, so that the rescue can not be saved, and giving up the rescue.
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