CN113761670A - Balance flight theory and online orbit entering capability evaluation method of carrier rocket - Google Patents

Balance flight theory and online orbit entering capability evaluation method of carrier rocket Download PDF

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CN113761670A
CN113761670A CN202111241081.0A CN202111241081A CN113761670A CN 113761670 A CN113761670 A CN 113761670A CN 202111241081 A CN202111241081 A CN 202111241081A CN 113761670 A CN113761670 A CN 113761670A
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金华
孟云鹤
陈琪锋
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Shenzhen 303 Defense Technology Co ltd
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Abstract

The invention discloses a balance flight theoretical method of a carrier rocket, which combines the analysis of flight motion of the rocket under thrust failure, the establishment of a dynamic model of the flight mechanical process of continuous maneuvering orbital transfer of the rocket, the judgment of the flight state of the rocket based on the balance flight theory and the autonomous guidance control of the rocket, can effectively solve the online autonomous guidance control of the rocket under the engine thrust descent failure mode, provides an analytic theory, is suitable for rockets with different parameter types and failure modes, has small calculated amount and is suitable for online application. The invention also discloses an online orbit entering capability evaluation method of the carrier rocket, which can accurately judge whether the rocket can be rescued and provide a feasible guidance scheme aiming at the condition that the rocket can be rescued by combining the acquisition of the thrust acceleration time function under the failure mode, the judgment of the flight state of the rocket, the estimation of the speed impulse of the actual fuel level of the rocket at present and the total speed increment required by the rocket to enter the orbit.

Description

Balance flight theory and online orbit entering capability evaluation method of carrier rocket
Technical Field
The invention relates to the technical field of space flight and aviation, relates to a balance flight theory of a carrier rocket and an online orbit entering capability evaluation method, and particularly relates to a balance flight theory for autonomous control in a rocket thrust failure mode and an online orbit entering capability evaluation method based on the balance flight theory.
Background
Each system of the carrier rocket is a product of fine design and a large number of tests, has very high reliability, but various faults are still inevitably encountered in the process of executing tasks according to Murphy's law, and the fault mode and the occurrence time are uncertain.
Among the numerous failure modes of the whole rocket, the failure of the power system is the most frequent occurrence of the carrier rocket and the most serious result is often achieved. Statistics on existing fault data show that: about 60% of faults in the rocket power flight section are faults of a power system; particularly, under the design constraint of greatly improving the carrying capacity of a heavy carrier rocket, a binding mode of multiple parallel thrusters is usually adopted, so that the probability of the power system failure is increased to a certain extent, and the flight mission is directly failed in serious cases.
Non-fatal engine failures that occur outside the atmosphere are a typical case. In 1964, when the Tustar No. 1 rocket actually flies for 117 seconds, 1H-1 engine is suddenly shut down in advance. On 11 th 4 th 1970, the secondary main engine of the carrier rocket, Saturn No. 5, launched the Apollo 13 spacecraft, was shut down 132 seconds earlier for this reason. In 7/2/2017, the thrust of the core first-stage engine is instantaneously and greatly reduced in the flight of a long-mark fifth-size remote second carrier rocket. In 2019, 12 and 20, software errors of abnormal task time consumption occur in an interstellar passenger ship developed by the united states boeing company and the national space administration (NASA). In addition, both the united states delta 4 launch vehicle and the falcon 9 launch vehicle experience failure modes during flight in which one or more engines of the powertrain fail. These thrust anomaly non-fatal engine failures often have serious consequences for mission failure. Therefore, in recent years, attention is paid to intelligent technology of the launch vehicle, and a handling strategy for the launch vehicle to have a thrust descent fault in an ascending section is also one of the entry points.
There are two main approaches to the current study of non-fatal engine failures with thrust anomalies:
the guidance method comprises an early-stage standard-track tracking guidance method, an iterative guidance method based on an optimal control theory of Tustar No. 5, power explicit guidance of a space plane and a plurality of improved iterative guidance algorithms.
And secondly, real-time optimization methods comprise a convex optimization method, a simulated annealing method, a neural network method and the like.
Both of the above methods have certain disadvantages: the guidance method has the problems that the guidance method is an execution method, the estimation of the track entering capability is insufficient, and the track entering precision is difficult to ensure sometimes; the optimization method has the problem that the convergence, the calculation efficiency and the real-time performance are difficult to meet the requirements of online application.
The intelligent carrier rocket with the intelligent brain has strong requirements on autonomous information perception, rapid fault detection, intelligent decision making, real-time reconstruction and the like. Therefore, it is particularly critical to identify the failure mode and perform capability evaluation at the first time when a failure is encountered, and for a thrust system failure, whether the track entering capability is qualified on line or not is evaluated.
Disclosure of Invention
The invention aims to provide a balance flight theoretical method of a carrier rocket, which has the following specific technical scheme:
a balance flight theoretical method of a carrier rocket (specifically a balance flight theoretical method for autonomous control under a rocket thrust failure mode) comprises the following steps:
step one, carrying out flight motion analysis of the rocket in a thrust failure mode and identifying the power system failure of the rocket, obtaining the radial and circumferential stress conditions of the rocket and the effect on the height and speed of the rocket, and obtaining the thrust acceleration a in the failure modecA function of time of;
step two, establishing a dynamic model of the rocket flight process, and obtaining a rocket flight dynamic equation as an expression 1):
Figure BDA0003319565460000021
wherein: beta represents the range angle, r represents the earth center distance, t represents time, mu represents the gravity coefficient of the earth, arRepresenting the radial component of thrust acceleration, aθA circumferential component representing thrust acceleration;
step three, judging the state of the rocket:
if the thrust acceleration a of the rocketcExpression 12 is satisfied), the rocket enters a balanced flight state:
Figure BDA0003319565460000022
wherein: n is the flight angular velocity of the target circular orbit,
Figure BDA0003319565460000023
omega is the angular velocity of the range,
Figure BDA0003319565460000024
g0is the acceleration of the gravity of the circular orbit,
Figure BDA0003319565460000025
if the thrust acceleration a of the rocketcExpression 15) is satisfied but expression 12 is not satisfied), the rocket enters a quasi-balanced flight state;
Figure BDA0003319565460000031
wherein: Δ h is the height margin; v. ofθIs the circumferential velocity component at the moment of failure;
if the thrust acceleration a of the rocketcExpression 15 is not satisfied), the rocket enters the atmosphere to crash;
step four, performing autonomous guidance control, specifically:
in the balanced flight process, the optimal guidance law theta is obtained through the expression 3)P(here, thrust acceleration inclination angle at the time of balanced flight), the maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of balanced flight is obtained by expression 6):
Figure BDA0003319565460000032
Figure BDA0003319565460000033
in the quasi-equilibrium flight process, the transition time delta T from quasi-equilibrium flight to equilibrium flight is obtained through an expression 18), and the optimal guidance law theta is obtained through an expression 21)P(here, the optimal local acceleration tilt angle for quasi-balanced flight):
Figure BDA0003319565460000034
Figure BDA0003319565460000035
wherein: r is0Indicating the initial ground offset for quasi-equilibrium flight.
Preferably, in the above technical solution, in the fourth step:
the total radial acceleration component and the velocity component are both 0 in the balanced flight process, i.e.
Figure BDA0003319565460000041
And the thrust acceleration is resolved in the circumferential direction and the radial direction, expression 1) becomes expression 2):
Figure BDA0003319565460000042
optimal guidance law expression 3) for balanced flight is obtained by expression 2).
Preferably, in the above technical solution, the flight angular velocity n and the range angular velocity ω of the target circular orbit are substituted into the expression 2), and the two expressions are synthesized to obtain the expression 4):
Figure BDA0003319565460000043
solving an ordinary differential equation based on expression 4) to obtain expression 5):
Figure BDA0003319565460000044
further integrating both sides of expression 5) to obtain expression 6) to calculate the maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of the equilibrium flight.
Preferably, in the above technical solution, in the fourth step:
representing the centrifugal acceleration by the circumferential velocity component at the time of failure, expression 1) is transformed into expression 16):
Figure BDA0003319565460000045
after the delta T time, the rocket can reach new balance and the ground center distanceWhen not changed, then r is equal to r0Expression 17 is derived from expression 16):
Figure BDA0003319565460000051
for expression 17), the second order small quantity a is omittedc 2 cos2ΘP·ΔT2Expression 18) is obtained to calculate the transition time Δ T from the quasi-equilibrium flight to the equilibrium flight.
In the above technical solution, it is preferable that the shortest transition time Δ T from quasi-equilibrium flight to equilibrium flight is obtained
Figure BDA0003319565460000052
Expression 20) can be obtained to calculate the optimal guidance law in quasi-balanced flight.
The invention provides a balance flight theoretical method of a carrier rocket, which can meet the requirements of orbit entering precision and on-line application, and the specific scheme is as follows: firstly, carrying out flight motion analysis on the rocket under the thrust fault to obtain the radial and circumferential stress conditions of the rocket; secondly, establishing a dynamic model for the flight mechanics process of the rocket continuous maneuvering orbital transfer to obtain a dynamic equation of rocket flight; then judging the state of the rocket to obtain the flight state of the rocket (based on a balance theory, including modes such as balance flight, quasi-balance flight and the like); and finally, performing autonomous guidance control on the rocket. The scheme of the invention can effectively solve the problem of online autonomous guidance control of the rocket in the engine thrust descent fault mode, provides an analytic theory, can adapt to rockets with different parameter types and fault modes, has small calculated amount and is suitable for online application.
The second purpose of the invention is to provide an online orbit entering capability evaluation method of a carrier rocket, which comprises the following steps:
step one, thrust acceleration a of rocketcJudging to obtain a state that the rocket enters a balanced flight, a state that the rocket enters a quasi-balanced flight and a crash that the rocket enters the atmosphere;
step two, estimating the velocity impulse delta v of the actual fuel level of the current rocket through an expression 21); through expression 22) estimating total velocity increment delta v required by rocket in-orbitRe：
Δv＝vidk-Δv1k-Δv2k-Δv3k 21)；
Figure BDA0003319565460000053
Wherein: v. ofidkThe speed generated by the thrust of the rocket under the action of vacuum gravity-free force is called as ideal speed; Δ v1kThe velocity loss caused by the gravitational acceleration component, called gravitational loss; Δ v2kLoss of speed due to drag; Δ v3kThe speed loss caused by the atmospheric static pressure when the engine is operating in the atmosphere;
Figure BDA0003319565460000054
quasi-balance of thrust acceleration a of rocket in flightcAverage value of (d);
Figure BDA0003319565460000061
for balancing the thrust acceleration a of the rocket during flightcAverage value of (d); Δ T is the transition time from the quasi-equilibrium flight condition to the equilibrium flight condition; t is the maneuvering orbital transfer time from the elliptical trajectory to the circular orbit of the balanced flight;
step three, carrying out velocity impulse delta v of the current rocket actual fuel level and total velocity increment delta v required by rocket orbit enteringReAnd (3) comparison:
if the current actual fuel level of the rocket has a velocity impulse delta v which is more than or equal to the total velocity increment delta v required by the rocket in-orbitReJudging that rescue can be achieved, and conducting guidance according to a corresponding guidance law when the rocket enters a balanced flight state, the rocket enters a quasi-balanced flight state or the rocket enters the atmosphere for crash;
if the current actual fuel level of the rocket has a velocity impulse delta v smaller than the total velocity increment delta v required by the rocket to enter the orbitReIf the thrust loss is too large, the rescue cannot be carried out, and the rescue is abandoned.
The invention provides an online orbit entering capability evaluation method of a carrier rocket, which can realize accurate evaluation of the online orbit entering capability of the rocket, and the specific scheme is as follows: firstly, identifying the power system fault of the rocket, and acquiring a time function of thrust acceleration under a fault mode; secondly, estimating the speed impulse of the actual fuel level of the current rocket and the total speed increment required by the rocket during the orbit entering; and finally, comparing the speed impulse of the current actual fuel level of the rocket with the total speed increment required by the rocket during orbit entering, and accurately judging whether the rocket can be saved.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit 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 the mechanical analysis of a rocket in flight outside the atmosphere according to the present invention;
FIG. 3 is a schematic view of a force analysis of a continuous thrust rocket according to the present invention;
FIG. 4(a) is a guidance law diagram for balanced flight;
FIG. 4(b) is a guidance law diagram for quasi-equilibrium flight;
FIG. 5 is a schematic view of the present invention based on the reconstruction of the flight procedure in equilibrium flight theory;
FIG. 6 is a flow chart of evaluation of the online capability of carrier rocket in this embodiment;
FIG. 7 is a schematic view of a regional analysis of the rocket orbital capability of the present invention;
FIG. 8 is a graph of the time variation of the guidance law and flight altitude of the present invention;
FIG. 9 is a graph of the change in altitude over time of the perigee and apogee after the rocket of the present invention enters a safe circular orbit.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Example 1:
a balance flight theoretical method of a carrier rocket (specifically a balance flight theoretical method for autonomous control under a rocket thrust failure mode), namely an autonomous control method under the rocket thrust failure mode, specifically comprises the following steps:
1. the details of the analysis of the rocket flight motion under the thrust failure mode are as follows:
according to the theory of projectile ballistics of the carrier rocket, the rocket trajectory is a portion of an elliptical orbit of the geocenter, as shown in figure 1. Due to different mission missions, the trajectories of a carrier rocket and a ballistic missile are also different, the instantaneous elliptical orbit near point of the carrier rocket orbit point is generally above the safe height, and the elliptical orbit near points of the last-stage main engine shutdown point of the ballistic missile intersect with the earth.
In the air layer flight section before the orbit, the rocket motion is generally expressed as the lifting process of the flight height and the speed, but in consideration of the engineering constraints such as the actual thrust-weight ratio of the rocket and the like, the two lifting processes do not require synchronization but are emphasized to achieve better efficiency. For example, in the section before the point of entry, a strategy of continuously increasing the speed and making the altitude change more stable is often adopted (i.e., the speed increment is mainly reflected in the circumferential direction, and the radial speed is basically kept constant), and at this time, the motion of the rocket is in the stage of the far point of the instantaneous elliptical orbit and continuously increasing the near point, such as the near point lifting in fig. 1. If the rocket has insufficient thrust, the height of the trajectory near the place cannot be timely lifted, the intersection of the trajectory and the earth cannot be avoided, and according to the elliptic trajectory theory, the height of the trajectory in subsequent rocket flight continuously drops, and finally the task fails.
The rocket motion under the thrust failure mode is subjected to mechanical analysis, a local horizontal coordinate system (the original point is the rocket center of mass, and the three axes are respectively in the radial direction, the circumferential direction and the ballistic surface normal direction) is established, the rocket stress is concentrated in the ballistic plane outside the atmosphere, and the stress conditions of the rocket body in the radial direction and the circumferential direction are shown in figure 2, wherein: the radial force is the radial component of the gravity, the centrifugal force and the thrust, and the resultant force determines the motion of the rocket in the radial direction, namely the height direction, wherein the centrifugal force is related to the circumferential speed and the orbit height. The circumferential force is the circumferential component of the thrust, the effect is to change the circumferential velocity, and at the same time, the circumferential velocity change will directly affect the centrifugal force.
If the thrust value is large enough, the rapid acceleration in the circumferential direction can be realized on the basis of ensuring the radial three-force balance, and the rocket has higher maneuvering orbital transfer efficiency; if the thrust is too small, the radial three-force balance cannot be supported, and at the moment, if the speed cannot be effectively increased in the living height range, the centrifugal force is improved, and finally the rocket can be crashed.
The magnitude of the engine thrust for the radial balance portion is a major loss of capacity because it is not translated into a speed increment (understandable against impulse effects); therefore, the more the thrust is reduced when the rocket fails, the longer the flight time is, and the larger the ratio of the capacity loss is; it can be extended from this that if the radial component of the thrust is used to ensure the radial force balance, the circumferential component of the thrust is accelerated, and the thrust direction is adjusted in real time as the circumferential velocity increases and the centrifugal acceleration increases, so that the radial force is always balanced, the minimum capacity loss is realized at the acceleration level, and the optimal ballistic adjustment is also realized. The flight dynamics mechanism analysis not only can explain the basic principle that thrust fault mission loss occurs in the air layer flight section of the rocket before the rocket enters the orbit, but also provides an idea for fault disposal strategy research.
2. The dynamic modeling of the rocket balance flight process specifically comprises the following steps:
in the process that the rocket flies out of the atmospheric layer and runs towards the target orbit, a rocket stress model of continuous thrust is shown in fig. 3, the rocket is under the action of the gravity of the earth and the thrust of an engine, and the action of centrifugal inertia force needs to be considered in a local horizontal coordinate system. In FIG. 3, OEDenotes the geocentric, beta denotes the range angle, r denotes the geocentric distance, acIndicating thrust acceleration (vector), arRepresenting the radial component of thrust acceleration, aθRepresenting the circumferential component of thrust acceleration, ΘPIndicating thrust acceleration inclination (i.e. thrust acceleration a)cAngle to the local horizontal, also called best guidance law), v represents the velocity vector.
The mass change in rocket flight is attributed to the change of acceleration, and the rocket flight dynamics are obtained in the radial direction and the circumferential direction of a local horizontal coordinate system as shown in an expression 1):
Figure BDA0003319565460000081
wherein: t represents time, and μ represents an earth gravity coefficient.
3. Judging the state of the rocket and carrying out autonomous guidance control, wherein the details are as follows:
thrust acceleration a of rocketcThe determination is determined according to the thrust fault mode, can be a determined time function, and can also be measured in real time. This thrust acceleration is also determined over time, which is generally determined by default as a failure mode, and is not a constant, but rather a time-varying quantity, without measurement.
3.1, when the balance flight is satisfied, the radial total acceleration component and the velocity component in the flight process are both 0, namely
Figure BDA0003319565460000091
Figure BDA0003319565460000092
Considering the determination of the magnitude of the continuous thrust acceleration, the direction is adjustable, and the thrust acceleration is decomposed and substituted into an expression 1) to obtain an expression 2):
Figure BDA0003319565460000093
obtaining an expression 3) from an expression 2) to solve the optimal guidance law theta of the balanced flightP：
Figure BDA0003319565460000094
The flight angular velocity of the target circular orbit
Figure BDA0003319565460000095
And range angular velocity
Figure BDA0003319565460000096
Substituting expression 2), and combining the two equations (specifically, squaring the left and right sides of the two equations in expression 2), and then adding the left and right sides to obtain expression 4):
Figure BDA0003319565460000097
solving an ordinary differential equation based on expression 4) to obtain expression 5):
Figure BDA0003319565460000098
further integrating the two sides of the expression 5) to obtain an expression 6) for calculating the maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of the balanced flight:
Figure BDA0003319565460000099
by solving the quantitative integral expression 6), the maneuvering orbital transfer time from the elliptical trajectory to the circular orbit meeting the balanced flight condition can be obtained, and the flight process from the acceleration of the elliptical trajectory to the target circular orbit can be analyzed.
Such as: the ratio of the thrust acceleration to the gravitational acceleration of the circular orbit is set as
Figure BDA0003319565460000101
When ω < n, transforming denominator of integral term in expression 6) to obtain expression 7):
Figure BDA0003319565460000102
transforming expression 6) to obtain expression 8):
Figure BDA0003319565460000103
wherein: k is the ratio of the gravitational acceleration and the thrust acceleration of the circular orbit,
Figure BDA0003319565460000104
taking integral intermediate transformation variables tau and alpha, order
Figure BDA0003319565460000105
α＝τ2，τ0Is taken as the value of t at the moment t. Integrating expression 8) to obtain expression 9):
Figure BDA0003319565460000106
wherein: t is time; EllipticF is a first type of incomplete elliptic integral, or can be further expanded into expression 10):
Figure BDA0003319565460000107
the solution of the first type of incomplete elliptic integral can refer to the prior art, can provide a high-order approximate solution to meet the requirement of quick calculation, or can carry out calculation by using a numerical integration method. In the case of the expression 10) can be solved analytically, ω (T) (i.e. the range angular velocity at time T) is obtained actually, and T ∈ [0, T ∈ [ T ] []As a function of, and thus the thrust acceleration tilt angle thetaP(optimal guidance law) according to expression 3) can be solved quickly. Therefore, the balance flight process can be theoretically analyzed, and the time and the fuel consumption of the whole process can be fastThe speed calculation, the speed loss or thrust efficiency of the continuous thrust orbital transfer process can also be calculated.
It should be noted that: the balanced flight state only represents temporary safety and does not represent long-term danger relief, if a fuel leakage condition exists, the circumferential acceleration time is not long enough, the circumferential speed constraint required by a circular orbit can not be reached when fuel is exhausted, and the rocket still has difficulty in entering the safe orbit.
In the solving process of expression 10), the condition to be satisfied is expression 11):
Figure BDA0003319565460000111
when the rocket is in an acceleration section, and omega is less than or equal to n, the condition required to be met by balanced flight can be obtained as expression 12):
Figure BDA0003319565460000112
according to the balanced flight condition, whether the rocket is in a dangerous state or not or whether the rocket has self-rescue capability or not can be judged based on the thrust acceleration level of the rocket after the fault.
3.2, because of the existence of the thrust acceleration circumferential component, the circumferential velocity component will be increased, bringing the effect that the centrifugal acceleration will be increased continuously, thereby reducing the thrust acceleration component required for achieving the radial force balance continuously, so the circumferential direction and the radial direction are dynamic processes of mutual coupling and mutual conversion, and therefore the balanced flight condition expression 12) still has a certain margin.
If it is not
Figure BDA0003319565460000113
The centrifugal acceleration can be increased according to the height level of the rocket, namely whether the rocket can be accelerated rapidly along the circumferential direction within the range of slightly reducing the allowable height, so that the further descending of the rocket is restrained, and the judgment can be carried out through time estimation.
The thrust acceleration is completely concentrated in the circumferential direction, and the radial negative acceleration, namely theta, is not consideredPWhen the thrust acceleration is 0, the effect of the thrust acceleration on the circumferential acceleration is the best, so the radial centrifugal acceleration is accelerated fastest, the centrifugal acceleration and the gravity are balanced through the transition time delta T, the rocket reaches the survival altitude, and the geocentric vector is rL，rLR- Δ h, Δ h is a height margin, and can be approximated using expression 13):
Figure BDA0003319565460000114
wherein: v. ofθIs the circumferential velocity component at the moment of failure,
Figure BDA0003319565460000115
then the condition for achieving rocket landing to rise is expression 14):
Figure BDA0003319565460000121
i.e. the sum of centrifugal acceleration and thrust acceleration is greater than gravitational acceleration, avθFor the circumferential velocity increase in this process, Δ vθ≈acΔT。
If the thrust acceleration a of the rocketcExpression 15 is not satisfied), the rocket enters the atmosphere to crash.
Figure BDA0003319565460000122
3.3 thrust acceleration a if rocketcSatisfying expression 15) but not satisfying expression 12), the rocket enters a quasi-equilibrium flight state.
In fact, during the flight, the acceleration in the circumferential direction will make the speed increase fastest, the centrifugal acceleration increase fastest, but the initial radial negative acceleration value in this case is also the largest, and is also fast under the altitude; conversely, if the entire thrust is applied in the radial direction, the negative acceleration in the radial direction is minimal, the height decrease is slow, but the centrifugal acceleration cannot be increased. Between the two extremes mentioned there is a compromise between a limited range of altitude reduction and a fast implementation of the equilibrium flight regime, which requires optimization of the thrust acceleration tilt angle and minimum burn-up if the transition time from quasi-equilibrium flight to equilibrium flight is minimized.
Expressing the centrifugal acceleration by the circumferential velocity component, expression 1) is transformed into expression 16):
Figure BDA0003319565460000123
after the time of delta T, the rocket can reach new balance to make r0Representing the initial ground center distance of quasi-equilibrium flight, and the ground center distance (r, also referred to herein as equilibrium flight initial ground center distance) is not changed, then r ═ r0Expressed according to expression 16)
Formula 17):
Figure BDA0003319565460000124
for expression 17), the second order small quantity a is omittedc 2cos2ΘP·ΔT2Obtaining a transition time Δ T expression 18 from quasi-equilibrium flight to equilibrium flight):
Figure BDA0003319565460000131
the shortest transition time Delta T from quasi-equilibrium flight to equilibrium flight is
Figure BDA0003319565460000132
Yielding expression 19):
Figure BDA0003319565460000133
in conjunction with expression 19), expression 20) may be employed to calculate the optimal guidance law ΘP：
Figure BDA0003319565460000134
By comparing expression 3) with expression 20), it can be found that satisfaction is satisfied
Figure BDA0003319565460000135
Balanced flight conditions of the condition, and satisfaction
Figure BDA0003319565460000136
The guidance law in the case of the quasi-equilibrium flight state of the condition is shown in fig. 4(a) and 4 (b). Under the quasi-equilibrium flight condition, the optimal direction of the thrust acceleration is not along the radial direction or the circumferential direction, but the different actions of the two directions are still considered, so that the shortest flight time of the radial force equilibrium can be realized. Since the balanced flight mode represents the most effective utilization mode of the thrust, the expressions 3) and 20) are also the optimal guidance schemes for the extraatmospheric flight section before the rocket enters the orbit.
The scheme of the embodiment is specifically applied as follows:
simulation analysis is carried out on a power flight section outside an atmosphere of a certain type of two-stage carrier rocket, a failure mode is set as a non-fuel leakage engine thrust descending failure, and feasibility is verified according to different failure moments and different engine residual thrust ratios:
1. on-line reconstruction and guidance law reconstruction flight program
Simulation analysis is carried out on a power flight section outside an atmosphere of a certain type of two-stage carrier rocket, the failure mode is a non-fuel leakage engine thrust reduction failure, the failure time is set to be 400s, and the residual thrust proportion of the engine is 55%. The online reconstruction flight program adopts the rapid recursion calculation method; for the space flight segment before the orbit entering, a 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, a ballistic differential equation is solved, and the flight program is reconstructed by utilizing an analytical theory of balanced flight according to the principle and the steps of flight program reconstruction. Since the range angle information is mainly from the rocket's own navigation system and is determined, the key part of the main classification flight procedure is still reflected in the dip angle of thrust acceleration.
The calculated thrust acceleration inclination angle and the angle deviation are shown in fig. 5, the angle deviation in fig. 5 is that the maximum deviation of the on-line reconstruction algorithm and the four-order fixed-step-length guidance law reconstruction algorithm is not more than 0.5 degrees in the whole power flight section relative to the five-order variable-step-length guidance law reconstruction algorithm, but the total calculated amount is small due to the fact that the approximate analysis algorithm exists in the calculating process, and therefore the on-line reconstruction algorithm is high in precision and small in calculated amount and is suitable for on-line calculation on arrows.
Example 2:
a method for evaluating the online orbit entering capability of a carrier rocket based on a balanced flight theory is disclosed, and the specific flow is shown in figure 6, which comprises three parts:
a first part: monitoring whether the rocket is abnormal or not in the flying process, and if not, flying according to the program; if yes, entering a second part:
a second part: judging whether the engine has a fault, if so, confirming the fault mode of the engine, carrying out rocket capacity evaluation (such as fuel capacity), and entering a third part; otherwise, flying according to the program;
and a third part: and (3) judging and deciding, specifically:
giving up rescue when the energy is insufficient, and flying according to the program;
the energy is abundant, the fault does not affect the task, and the flight is carried out according to the program without saving;
the energy has surplus 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; flying according to the program. Through flight program reconstruction, the emergency orbit can be entered, and the flight program is generated on line; flying according to the program.
In the second section:
confirming the engine fault of the rocket and acquiring the thrust acceleration a under the fault modec. Calculating the time of the thrust acceleration according to the fault mode identification result of the power systemAn inter function.
The embodiment is implemented on the basis of part of the content in embodiment 1, that is, the thrust acceleration a of the rocket is obtained according to the method disclosed in embodiment 1cJudging to obtain the state that the rocket enters the balanced flight (if the thrust acceleration a of the rocket is adopted)cSatisfies expression 12)), the rocket enters a quasi-equilibrium flight state (if the thrust acceleration a of the rocket is increased)cSatisfies expression 15) but does not satisfy expression 12)) and a crash of the rocket into the atmosphere (if the thrust acceleration a of the rocket iscExpression 15 is not satisfied)).
Estimating the velocity impulse Δ v that the current rocket actual fuel level has by expression 21):
Δv＝vidk-Δv1k-Δv2k-Δv3k 21)；
wherein: v. ofidkThe speed generated by the thrust of the rocket under the action of vacuum gravity-free force is called as ideal speed; Δ v1kThe velocity loss caused by the gravitational acceleration component, called gravitational loss; Δ v2kLoss of speed due to drag; Δ v3kThe speed loss caused by the atmospheric static pressure when the engine is operating in the atmosphere;
through expression 22) estimating total velocity increment delta v required by rocket in-orbitRe：
Figure BDA0003319565460000151
Wherein:
Figure BDA0003319565460000152
quasi-balance of thrust acceleration a of rocket in flightcAverage value of (d);
Figure BDA0003319565460000153
for balancing the thrust acceleration a of the rocket during flightcAverage value of (d); Δ T is the transition time from the quasi-equilibrium flight condition to the equilibrium flight condition; t is the maneuver orbital transfer time from the elliptical trajectory to the circular orbit of the equilibrium flight.
Figure BDA0003319565460000154
And
Figure BDA0003319565460000155
the average value can be obtained by averaging after integration, or other averaging methods can be used, and the average value is determined according to actual requirements.
The velocity impulse Deltav of the current rocket actual fuel level and the total velocity increment Deltav required by rocket to enter into orbitReAnd (3) comparison:
if the current actual fuel level of the rocket has a velocity impulse delta v which is more than or equal to the total velocity increment delta v required by the rocket in-orbitReAnd judging to be rescued and carrying out guidance, specifically comprising the following steps: according to the optimal guidance law theta of the balanced flightPAnd the maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of the balanced flight guides the balanced flight; according to the optimal guidance law theta of quasi-equilibrium flightPAnd guiding the quasi-equilibrium flight from the transition time delta T of the quasi-equilibrium flight to the equilibrium flight.
If the current actual fuel level of the rocket has a velocity impulse delta v smaller than the total velocity increment delta v required by the rocket to enter the orbitReIf the thrust loss is too large, the rescue cannot be carried out, and the rescue is abandoned.
In a specific capacity evaluation process, a motion process with different acceleration stages is considered, for example, for a core first-stage thrust descent fault, the core first-stage thrust descent fault is not enough to enter a survival orbit after the core first-stage thrust descent fault works, and the flying speed is further accelerated and increased after the core second-stage starting is needed until the core second-stage thrust descent fault enters a circular orbit. Because the dynamic characteristics of each sub-stage of the rocket are different, the classification and the segmentation comprehensive calculation are needed.
The scheme of the embodiment is specifically applied as follows:
simulation analysis is carried out on a power flight section outside an atmosphere of a certain type of two-stage carrier rocket, a failure mode is set to be a non-fuel leakage engine thrust descent failure, and an orbit entering capability evaluation algorithm based on a balanced flight theory is verified according to different failure moments and different engine residual thrust proportions. In the simulation process, the idea of entering a safe height circular orbit in the first step and entering a large elliptical orbit in the second step by lifting a remote place is adopted, wherein the balance flight theory is mainly considered and applied in the previous step.
1. Rail-entering capability area analysis based on balance flight theory
Setting a fault time interval to be 350 s-750 s, covering first-stage core faults and second-stage 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.
For different engine residual thrust ratios, the area of the capability of entering the rail can be calculated based on the balance flight theory as shown in fig. 7, and the allowable most severe state of the engine residual thrust ratio is the lower limit of the area 2. In the area 1, at least a safe circular orbit can be reached by adopting balanced flight; in zone 2, at least a safe circular orbit can be reached by adopting quasi-balanced flight; the region 3 indicates that the thrust loss ratio is too large, the capability is insufficient, and the saving is impossible. The figure shows thrust fault situations and decision guidance during the mission.
Based on a balance flight theory algorithm, a software platform is further developed, and simulation analysis shows that: the balance flight theory method is correct, small in calculation amount and suitable for online application. The method has good practicability, and can provide technical theoretical support for autonomous fault disposal of the thrust fault mode of the carrier rocket.
2. Comparison of evaluation of trackability for different fault levels
The fault time is set to be 350s, and the engine residual thrust proportion is respectively 55% and 40% to carry out simulation. The guide law and the time-varying curve diagram of the flight altitude are shown in fig. 8, the guide law is balanced when the residual thrust is 55%, and the guide law is quasi-balanced when the residual thrust is 40%, so that the guide law and the flight altitude can both be guaranteed to reach the safe circular orbit.
After entering the safe circular orbit, the orbit maneuvering control of the far-field lifting is executed. As shown in fig. 9, when the near point height and the far point height change with time reach the track entering point, the near point height is 343km and 305km respectively, and the far point height can reach 21345km and 6169km respectively for the states of 55% and 40% of residual thrust, so that the track entering capability is stronger when the residual thrust is 55%. And further applying an altitude guidance strategy to the state of 55% of residual thrust to keep the near site of the track entry point at 225km, and then raising the altitude of the far site to 25500 km.
The method is characterized in that the orbit entering capability evaluation based on the balance flight theory only needs to calculate the first type of incomplete elliptic integral, an approximate formula or a numerical integration method can be adopted, the calculation amount is far less than that of iterative guidance and ordinary differential equation solving, and the on-line and real-time engineering application requirements of an rocket-borne computer can be met.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement 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 balance flight theory method of a carrier rocket is characterized by comprising the following steps:
step one, carrying out flight motion analysis of the rocket in a thrust failure mode and identifying the power system failure of the rocket, obtaining the radial and circumferential stress conditions of the rocket and the effect on the height and speed of the rocket, and obtaining the thrust acceleration a in the failure modecA function of time of;
step two, establishing a dynamic model of the rocket flight process to obtain a dynamic equation expression 1 of rocket flight:
Figure FDA0003319565450000011
wherein: beta represents the range angle, r represents the earth center distance, t represents time, mu represents the gravity coefficient of the earth, arRepresenting the radial component of thrust acceleration, aθA circumferential component representing thrust acceleration;
step three, judging the state of the rocket:
if the thrust acceleration a of the rocketcExpression 12 is satisfied), the rocket enters a balanced flight state:
Figure FDA0003319565450000012
wherein: n is the flight angular velocity of the target circular orbit,
Figure FDA0003319565450000013
omega is the angular velocity of the range,
Figure FDA0003319565450000014
g0is the acceleration of the gravity of the circular orbit,
Figure FDA0003319565450000015
if the thrust acceleration a of the rocketcExpression 15) is satisfied but expression 12 is not satisfied), the rocket enters a quasi-balanced flight state;
Figure FDA0003319565450000016
wherein: Δ h is the height margin; v. ofθIs the circumferential velocity component at the moment of failure,
Figure FDA0003319565450000017
if the thrust acceleration a of the rocketcExpression 15 is not satisfied), the rocket enters the atmosphere to crash;
step four, performing autonomous guidance control, specifically:
in the balanced flight process, the optimal guidance law theta is obtained through the expression 3)PThe maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of the equilibrium flight is obtained by expression 6):
Figure FDA0003319565450000021
Figure FDA0003319565450000022
in the quasi-equilibrium flight process, the transition time delta T from quasi-equilibrium flight to equilibrium flight is obtained through an expression 18), and the optimal guidance law theta is obtained through an expression 21)P：
Figure FDA0003319565450000023
Figure FDA0003319565450000024
Wherein: r is0Indicating the initial ground offset for quasi-equilibrium flight.
2. The balanced flight theory method according to claim 1, wherein in the fourth step:
the total radial acceleration component and the velocity component are both 0 in the balanced flight process, i.e.
Figure FDA0003319565450000025
And the thrust acceleration is resolved in the circumferential direction and the radial direction, expression 1) becomes expression 2):
Figure FDA0003319565450000026
optimal guidance law expression 3) for balanced flight is obtained by expression 2).
3. The balanced flight theory method according to claim 2, characterized in that 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):
Figure FDA0003319565450000031
solving an ordinary differential equation based on expression 4) to obtain expression 5):
Figure FDA0003319565450000032
further integrating both sides of expression 5) to obtain expression 6) to calculate the maneuvering orbital transfer time T from the elliptical trajectory to the circular orbit of the equilibrium flight.
4. The balanced flight theory method according to claim 3, wherein in the fourth step:
expressing the centrifugal acceleration by the circumferential velocity component, expression 1) is transformed into expression 16):
Figure FDA0003319565450000033
after the time of delta T, the rocket can reach new balance, and the earth center distance is not changed, so that r is r0Expression 17 is derived from expression 16):
Figure FDA0003319565450000034
for expression 17), the second order small quantity a is omittedc 2cos2ΘP·ΔT2The expression 18) of the transition time Δ T from the quasi-equilibrium flight to the equilibrium flight is obtained.
5. The balanced flight theory method of claim 4, wherein the slave is enabledThe shortest transition time delta T for the quasi-equilibrium flight to reach the equilibrium flight is
Figure FDA0003319565450000035
Expression 21 for the optimal guidance law for quasi-equilibrium flight can be obtained).
6. An online orbit-entering capability evaluation method of a carrier rocket is characterized by comprising the following steps:
step one, thrust acceleration a of rocketcJudging to obtain a state that the rocket enters a balanced flight, a state that the rocket enters a quasi-balanced flight and a crash that the rocket enters the atmosphere;
step two, estimating the velocity impulse delta v of the actual fuel level of the current rocket through an expression 21); through expression 22) estimating total velocity increment delta v required by rocket in-orbitRe：
Δv＝vidk-Δv1k-Δv2k-Δv3k 21)；
Figure FDA0003319565450000041
Wherein: v. ofidkThe speed generated by the thrust of the rocket under the action of vacuum gravity-free force is called as ideal speed; Δ v1kThe velocity loss caused by the gravitational acceleration component, called gravitational loss; Δ v2kLoss of speed due to drag; Δ v3kThe speed loss caused by the atmospheric static pressure when the engine is operating in the atmosphere;
Figure FDA0003319565450000042
quasi-balance of thrust acceleration a of rocket in flightcAverage value of (d);
Figure FDA0003319565450000043
for balancing the thrust acceleration a of the rocket during flightcAverage value of (d);
step three,The velocity impulse Deltav of the current rocket actual fuel level and the total velocity increment Deltav required by rocket to enter into orbitReAnd (3) comparison:
if the current actual fuel level of the rocket has a velocity impulse delta v which is more than or equal to the total velocity increment delta v required by the rocket in-orbitReJudging that rescue can be achieved, and conducting guidance according to a corresponding guidance law when the rocket enters a balanced flight state, the rocket enters a quasi-balanced flight state or the rocket enters the atmosphere for crash;
if the current actual fuel level of the rocket has a velocity impulse delta v smaller than the total velocity increment delta v required by the rocket to enter the orbitReIf the thrust loss is too large, the rescue cannot be carried out, and the rescue is abandoned.
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