CN112231831A - Terminal multi-constraint energy management method under strong coupling condition of solid carrier rocket - Google Patents

Terminal multi-constraint energy management method under strong coupling condition of solid carrier rocket Download PDF

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CN112231831A
CN112231831A CN202011093665.3A CN202011093665A CN112231831A CN 112231831 A CN112231831 A CN 112231831A CN 202011093665 A CN202011093665 A CN 202011093665A CN 112231831 A CN112231831 A CN 112231831A
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张迁
许志
张源
刘家宁
杨垣鑫
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Northwestern Polytechnical University
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Abstract

The invention relates to a terminal multi-constraint energy management method under a strong coupling condition of a solid carrier rocket, which realizes the inhibition of a coupling term by solving the control direction of alternating attitude speed; meanwhile, for a task mode of 'boosting-sliding-boosting' outside the atmosphere, a theoretical relation between sliding ignition time, a required speed vector and the number of terminal orbits is deduced on the basis of the theory, the problem of two-point boundary values of the solid carrier rocket under the condition of fixed arc length is solved, and multi-constraint guidance access of the solid carrier rocket with coupling inhibition capability under the exhaust shutdown mode is realized.

Description

Terminal multi-constraint energy management method under strong coupling condition of solid carrier rocket
Technical Field
The invention belongs to the technical field of aerospace, and relates to a depletion shutdown energy management technology and a multi-constraint guidance technology for a solid carrier rocket to rapidly launch space satellite loads.
Background
In order to improve the mass ratio and reliability, the solid rocket cancels a thrust termination mechanism, so that the solid rocket can only adopt fuel exhaustion shutdown but cannot perform guidance shutdown. Therefore, an energy management method must be designed with the goal of achieving the desired speed vectors to be increased under run-out shutdown conditions. The energy management method takes a speed vector to be accelerated as a base guidance vector, and generates an additional attitude angle and dissipates redundant energy by designing different speed increment control models. Generally, the energy management method does not restrict the change of the position vector, mainly because the additional attitude adjustment angle required after considering the position restriction is obviously increased, and the energy management method is difficult to be practically applied. The prior art research mainly focuses on the planning of a nonlinear model and the iterative format of an algorithm closed loop, but ignores the coupling influence generated by an additional position vector in the speed control process and the optimal channel problem of speed control implementation, so that the dissipation degree adaptation to energy management is poor and the guidance precision is reduced.
Disclosure of Invention
Technical problem to be solved
The method aims to solve the defects that the existing energy management method aims at the problem of multi-constraint guidance of the solid carrier rocket, namely, the solid carrier rocket has to enter a solar synchronous orbit with terminal multi-orbit root constraint in a depletion shutdown mode under the requirement of space load tasks such as rapid launching of a small satellite, and the like, so that the coupling of the energy management method and the guidance method is serious. Aiming at the problem of terminal state coupling caused by energy management, an extended theoretical algorithm suitable for exhausted shutdown guidance is deduced based on a fixed point guidance algorithm, and the suppression of a coupling term is realized by solving an alternating attitude speed control direction; meanwhile, for a task mode of 'boosting-sliding-boosting' outside the atmosphere, a theoretical relation between sliding ignition time, a required speed vector and the number of terminal orbits is deduced on the basis of the theory, the problem of two-point boundary values of the solid carrier rocket under the condition of fixed arc length is solved, and multi-constraint guidance access of the solid carrier rocket with coupling inhibition capability under the exhaust shutdown mode is realized.
Technical scheme
A terminal multi-constraint energy management method under the condition of strong coupling of a solid carrier rocket is characterized by comprising the following steps:
step 1: according to the center-of-earth radius r at the moment of ignitionigVelocity vector vigDetermining the position vector r of the virtual pulse point by the semimajor axis a, the eccentricity e and the track inclination angle i of the target trackimp: according to rigAnd vigTime of engine operation TsEngine specific impulse IspThrust T of engine and second flow of engine
Figure BDA0002722950700000021
Rocket initial total mass m0Rocket current mass m (t), fuel mass msThe virtual pulse point r can be calculated by the following formulaimpWherein r issub.fAnd vsub.fThe ground center distance and the absolute speed W of the rated shutdown time of the extension sliding trackMAnd RMApparent speed increment and apparent position increment generated by the engine respectively; g (r) ═ mu/r3R is the vector of the earth's gravity,
Figure BDA0002722950700000022
is a velocity vector, g, due to gravity0Is sea level gravitational acceleration;
rimp＝rsub.f-(RM/WM)·vsub.f
Figure BDA0002722950700000023
Figure BDA0002722950700000024
Figure BDA0002722950700000025
Figure BDA0002722950700000026
step 2: determining a desired velocity vector vΓΓ: according to the speed vector v of the sliding tracksub.gAnd velocity vector v of target trackorb.gThe required velocity vector v can be calculated from the following equationΓAnd its direction Γ;
Figure BDA0002722950700000027
and step 3: determining the coupling suppression direction epsilon: on-orbit coordinate system P according to required velocity vector direction gammaimp-XgYgZgComponent Γ in (1)x,Γy,ΓzAnd intermediate variables λ and l, the coupling suppression direction ε can be calculated by:
ε＝[εx εy εz]
εx＝-Γz/l
εy＝-Γztanλ/l
εz＝(Γx+Γytanλ)/l
θorb＝arctan(vorb.y/vorb.x)
tanλ＝(vorb.impsinθorb+Δvg)/(vorb.impcosθorb)
Figure BDA0002722950700000033
wherein v isorb.x、vorb.yRespectively the tangential velocity and the normal velocity of the track on the target track, vorb.impThe velocity at the virtual pulse point is the magnitude;
and 4, step 4: determining velocity control model additional attitude angle uem(t): according to the rocket thrust T, the current rocket mass m (T) and the position component rΓ、rεCan determine the additional attitude angle u of the speed control modelem(t)：
Figure BDA0002722950700000034
Wherein, WMThe magnitude of the total apparent speed increase produced for the engine;
and 5: determining coupling term parameters m and n: according to the selected speed control model uem(t)＝UVIC(t), the coupling terms m and n can be calculated, where vΓfFor the speed increment, r, produced by the engine after the speed control model is usedΓ(tf)＝rΓf；rε(tf)＝rεfFor position increment, r, produced by the engine after the speed control model is usedimpIs the size of the centroid radial at the virtual pulse point, g (r)imp) The gravity of the earth at the virtual pulse point;
m＝rεfεz；n＝-rεfεz·Δvg/rimp
Δvg＝g(rimp)·(rΓf/vΓf)
Figure BDA0002722950700000035
step 6: determining coupling-under-influence virtual pulse point position vector r'impAnd a velocity vector v'imp: calculating the position vector r of the virtual pulse point according to the step 1impVelocity vector v at virtual pulse point on the sliding tracksub.impSpeed increment v generated by the engine after the speed control model is adoptedΓfCoupling terms m and n and the tracking coordinate system Pimp-XgYgZgComponent of z direction
Figure BDA0002722950700000036
Can calculate r'impAnd v'imp：
Figure BDA0002722950700000041
And 7: determining the difference Δ v between the desired velocity vectorsΓ: according to coupling influence lower virtual pulse point position vector r'impAnd a velocity vector v'impTo obtain
Figure BDA0002722950700000042
The difference Δ v between the required velocity vectors can be calculatedΓ：
ΔvΓ＝v′Γ-vΓ
Wherein v isΓ＝vorb.g-vsub.g；
And 8: determining a guidance instruction: if Δ vΓIf | < esp, outputting guidance instruction xbAnd ending the iteration; otherwise, let vΓ＝v′Γ，rimp＝r′impAnd turning to step 2 for loop iteration:
xb＝sinuem(t)·ε+cosuem(t)·Γ
wherein u isemFor additional pose angles, esp is the precision of the difference between the given required velocity vectors;
the ignition time, the speed control model and the iterative calculation process of the alternating attitude direction of the guidance algorithm are all in the unpowered sliding stage of the carrier rocket, and the boosting stage after the engine is ignited generates a guidance instruction according to the speed control model planned in advance.
Esp in step 8 takes 0.1.
Advantageous effects
The invention provides a terminal multi-constraint energy management method under the condition of strong coupling of a solid carrier rocket, which realizes the adaptability of speed control by controlling the maximum attitude adjusting angle according to different load masses. And the speed control plane is calculated by adopting a fixed point guidance coupling suppression algorithm under the condition of different load qualities due to additional influences of different degrees generated in the speed control process, the track height deviation reaches the hundred-meter magnitude, the maximum speed control deviation is 0.514m/s, the result can meet the terminal speed and position constraint conditions, and the suppression of the coupling term in speed control is realized.
For the track ground center distance constraint, the accuracy in the coupling suppression plane reaches 50m magnitude and is not influenced by the initial track inclination angle, and the coupling term has strong suppression capability. In addition, for the track-entering velocity vector constraint, under the condition that the residual velocity of 550m/s needs to be dissipated in velocity control, the control precision of the velocity magnitude reaches the magnitude of 10m/s, and the control precision of the velocity magnitude is higher in a track vertical plane and a coupling suppression plane; and the control precision of the speed inclination angle is higher in the track plane and the coupling suppression plane. And finally, for track inclination angle constraint, the precision in a coupling suppression plane reaches 0.01 degree.
The extended fixed-point guidance theory is analyzed and discussed aiming at the coupling terms, so that the deviation of parameters such as terminal earth center distance, absolute speed and track inclination angle caused by coupling is effectively inhibited. The fixed point guidance coupling suppression method can suppress coupling terms generated in the energy management process, and the coupling suppression plane decomposes the additional position quantity into quantities irrelevant to the terminal state constraint (such as the true near point angle of the track-in point, the right ascension of the rising intersection point and the like). Therefore, according to the fixed-point guidance coupling suppression method, the solving of the base guidance vector and the control of the exhausted shutdown speed are combined together, and the problem of multiple constraints of the terminal under the exhausted shutdown condition is solved.
Drawings
FIG. 1 velocity control Process additive position Change Profile
FIG. 2 is a schematic diagram of a velocity control plane formed by desired velocity vectors
FIG. 3 is a diagram showing the relationship between vectors of the fixed point guidance principle
FIG. 4 is a schematic diagram showing the relationship between vectors in a velocity control coordinate system
FIG. 5 logic diagram of velocity control coupled fixed point guidance method
FIG. 6 is a simulation curve of the fixed point guidance coupling suppression method for different load masses: (a) a change curve of the earth center distance; (b) an absolute velocity profile; (c) a local ballistic dip curve; (d) a track inclination curve; (e) a pitch angle command curve; (f) a yaw angle command curve;
FIG. 7 different speed control processes simulate various state quantity change curve clusters: (a) a change curve of the earth center distance; (b) an absolute velocity profile; (c) a local ballistic dip curve; (d) a track inclination curve; (e) a pitch angle command curve; (f) a yaw angle command curve.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
1. basic principle of energy management coupling expansion method
In order to realize the required speed vector to be increased under the exhausted shutdown condition, the change of the position vector is not restricted, and the required additional attitude adjusting angle is obviously increased after the position restriction is considered, so that the practical application is difficult. As shown in fig. 1, the speed position increment generated by the engine after the speed control model is adopted is as follows:
vΓ(tf)＝vΓf；vε(tf)＝0；rΓ(tf)＝rΓf；rε(tf)＝rεf (1)
1.1 coupling effects due to energy management
In an energy management speed control coordinate system OpAnd- Γ ε η, the vector direction to be accelerated is Γ, the ε axis may be in either the orbital plane or the orbital homeotropic plane, as shown in FIG. 2. According to the fixed point guidance principle, the terminal state of the carrier rocket is as follows:
Figure BDA0002722950700000061
Figure BDA0002722950700000062
as shown in fig. 3, the physical meaning of each vector relationship in the fixed point guidance principle is: r issub.f、vsub.fThe center distance and the absolute speed of the rated shutdown time of the extension sliding track are represented; by rorb.f、vorb.fRepresenting the actual flight trajectory terminal centroid distance and absolute velocity.
There is a rocket moment variation of
ΔH＝mf·rorb.f×vorb.f-m0·r0×v0 (4)
Substituting the terminal state expression (2) and the expression (3) into a rocket moment of momentum variation expression delta H to obtain:
ΔH＝mf(rsub.f+rΓfΓ)×(vsub.f+vΓfΓ)+mfrεf·ε×(vsub.f+vΓfΓ)-m0r0×v0 (5)
after simplification and combination, the momentum moment variable quantity under the speed control model is obtained through arrangement:
ΔH＝mfrimp×(vsub.imp+vΓf·Γ)-m0r0×v0+Hem (6)
in the formula HemThe coupling term representing the change in the moment of momentum is the change in the moment of momentum caused by the position increment generated by the velocity control process, and is expressed as:
Hem＝mfrεf·ε×(vsub.f+vΓf·Γ) (7)
accordingly, the center-to-center distance of the equivalent pulse point is rimp＝rsub.f-(rΓf/vΓf)·vsub.f. Coupling term H brought about by speed controlemThe damage changes the original equivalent pulse vector relation, so that the constraint of the number of terminal tracks cannot be met. Furthermore, the magnitude of the additional position quantity is relevant for the design of the speed control model, and the degree of coupling influence is in fact determined only by the speed control direction epsilon once the adopted speed control model is determined.
1.2 determination of energy management coupling parameters
For analyzing the influence of the velocity control direction epsilon, the orbit coordinate system P at the equivalent pulse pointimp-XgYgZgIn, define XgAxis, YgAxis and ZgUnit vectors of axes are 1 respectivelyx,1yAnd 1z. As shown in fig. 4, the sub-expressions of the velocity vector directions Γ and ∈ are:
Figure BDA0002722950700000071
coupling term H of momentum moment change according to the vector relation of equation (8)emThe expression is as follows:
Figure BDA0002722950700000072
in the formula,. DELTA.vg＝g(rimp)·(rΓf/vΓf). Substituting formula (8) into (9) yields:
Figure BDA0002722950700000073
to minimize the influence of the coupling term, the speed control direction ε is set to be on the current track plane Pimp-XgYgThe inner projection (the distance between the centers of approach points is changed) is suppressed, and the vector projection in the track plane is parallel, namely:
Figure BDA0002722950700000074
coupling term H of the change of moment of momentum according to the vector relation of equation (11)emThe expression is simplified as follows:
Figure BDA0002722950700000075
and (3) adopting an undetermined coefficient method to express the formula (12) as an expression containing undetermined parameters m and n:
Figure BDA0002722950700000076
comparing equation (13) and equation (12), the solution is:
m＝rεfεz；n＝-rεfεz·Δvg/rimp (14)
at this time, the equivalent pulse point r'impAnd equivalent rail speed v'impComprises the following steps:
Figure BDA0002722950700000081
2. determination of coupling rejection velocity control direction
In order to solve the velocity vector relationship and the velocity control direction epsilon, the orbit coordinate system P at the equivalent pulse pointimp-XgYgZgAnd the vector relation of each coordinate axis is as follows:
Xg||v′imp；Yg||r′imp；Zg＝Xg×Yg (16)
the velocity vector v of the sliding track as shown in fig. 2sub.gAnd velocity vector v of target trackorb.gAt Pimp-XgYgZgThe components in are represented as:
vsub.g＝[vsub.xcosΔA vsub.y vsub.xsinΔA]T (17)
vorb.g＝[vorb.x vorb.y 0]T (18)
according to the theoretical relation between the state quantity and the number of the tracks, the track tangential velocity vxNormal velocity v to the trackyRespectively as follows:
Figure BDA0002722950700000082
the number of tracks in the P-th track is obtained according to the formula (19) based on the number of tracks in the glide track and the number of tracks in the target trackimpVelocity v ofsub.x，vorb.x，vsub.y，vorb.yValues, where the azimuthal deviation is expressed as:
Figure BDA0002722950700000083
up to this point, the velocity vector to be accelerated and its direction are calculated according to equation (17) and equation (18):
Figure BDA0002722950700000084
since the vector direction Γ and the vector direction ∈ are orthogonal, in combination with the minimization equation (11) of the momentum moment coupling term, a system of equations results:
Figure BDA0002722950700000085
solving equation (22) yields the expression for the vector direction ε:
Figure BDA0002722950700000091
wherein tan λ ═ vorb.impsinθorb+Δvg)/(vorb.impcosθorb)；θorb＝arctan(vorb.y/vorb.x) (ii) a The specific expression of the variable l is:
Figure BDA0002722950700000092
under the coupling influence of the speed control model, the equivalent pulse point is not in the current track plane, but can be considered as the intersection point P of the track planeimpTranslation along the z-axis, i.e.:
Figure BDA0002722950700000093
the ignition time after considering the effect of the speed control coupling is:
tig＝t0-imp+Ts-rΓf/vΓf (26)
in summary, according to the fixed-point guidance theory and the expansion form thereof, the base guidance vector Γ, the rocket ignition time and the alternating attitude direction epsilon are respectively calculated by the formula (21), the formula (26) and the formula (23). In particular, in the coplanar tracks, ΓzWith 0, speed control along the normal to the track plane (parallel to the z-axis) is the way to achieve the least coupling effect.
The fixed-point guidance expansion theory proves that the base guidance is still applicable under the influence of speed control coupling, and the analytical expressions of ignition time, required speed vectors and alternating attitude directions are obtained. Taking the minimum additional angular velocity control model as an example, the maximum attitude adjusting angle is obtained according to the total apparent velocity modulus of the engine and the velocity required by guidance, and the additional position quantity is obtained through numerical integration. The calculation flow of the coupling suppression speed control is shown in fig. 5, and the specific steps are as follows:
(1) determining an equivalent pulse point r according to the initial state quantity and the target track parameters a, e, iimp: according to the center-of-earth radius r at the moment of ignitionigVelocity vector vigTime of engine operation TsEngine specific impulse IspThrust T of engine, second flow m of engine and initial total mass m of rocket0Rocket current mass m (t), fuel mass msThe equivalent pulse point r can be calculated by the following formulaimpWherein r issub.fAnd vsub.fThe ground center distance and the absolute speed W of the rated shutdown time of the extension sliding trackMAnd RMApparent speed increment and apparent position increment generated by the engine respectively; g (r) ═ mu/r3R is the vector of the earth's gravity,
Figure BDA0002722950700000101
is a velocity vector, g, due to gravity0Is sea level gravitational acceleration;
rimp＝rsub.f-(RM/WM)·vsub.f
Figure BDA0002722950700000102
Figure BDA0002722950700000103
Figure BDA0002722950700000104
Figure BDA0002722950700000105
(2) determining a desired velocity vector vΓΓ: according to the speed vector v of the sliding tracksub.gAnd velocity vector v of target trackorb.gThe required velocity vector v can be calculated from the following equationΓAnd its direction Γ;
Figure BDA0002722950700000106
(3) determining the coupling suppression direction epsilon: on-orbit coordinate system P according to required velocity vector direction gammaimp-XgYgZgComponent Γ in (1)x,Γy,ΓzAnd intermediate variables λ and l, the coupling suppression direction ε being calculated by the formulaorb.x、vorb.yRespectively the tangential velocity and the normal velocity of the track on the target track, vorb.impThe velocity at the virtual pulse point is the magnitude;
εx＝-Γz/l
εy＝-Γztanλ/l
εz＝(Γx+Γytanλ)/l
θorb＝arctan(vorb.y/vorb.x)
tanλ＝(vorb.impsinθorb+Δvg)/(vorb.impcosθorb)
Figure BDA0002722950700000108
(4) determining velocity control model additional attitude angle uem(t): according to the rocket thrust T, the current rocket mass m (T) and the position component rΓ、rεCan determine the additional attitude angle u of the speed control modelem(t) wherein WMThe magnitude of the total apparent speed increase produced for the engine;
Figure BDA0002722950700000114
(5) determining coupling term parameters m and n: according to the selected speed control model uem(t)＝UVIC(t), the coupling terms m and n can be calculated, where vΓfFor the speed increment, r, produced by the engine after the speed control model is usedΓ(tf)＝rΓf；rε(tf)＝rεfFor position increment, r, produced by the engine after the speed control model is usedimpIs the size of the centroid radial at the virtual pulse point, g (r)imp) The gravity of the earth at the virtual pulse point;
m＝rεfεz；n＝-rεfεz·Δvg/rimp
Δvg＝g(rimp)·(rΓf/vΓf)
Figure BDA0002722950700000111
(6) determining a coupling under influence equivalent pulse point position vector r'impAnd a velocity vector v'imp: calculating a virtual pulse point position vector r according to (a)impVelocity vector v at virtual pulse point on the sliding tracksub.impSpeed increment v generated by the engine after the speed control model is adoptedΓfCoupling terms m and n and the tracking coordinate system Pimp-XgYgZgComponent of z direction
Figure BDA0002722950700000112
Can calculate r'impAnd v'imp；
Figure BDA0002722950700000113
(7) Determining the difference Δ v between the desired velocity vectorsΓ: according to coupling influence lower equivalent pulse point position vector r'impAnd a velocity vector v'impTo obtain
Figure BDA0002722950700000115
The difference Δ v between the required velocity vectors can be calculatedΓWherein v isΓ＝vorb.g-vsub.g；
ΔvΓ＝v′Γ-vΓ
(8) Determining a guidance instruction: if Δ vΓIf | < esp, outputting guidance instruction xbAnd ending the iteration, wherein uemAdjusting the posture angle additionally; otherwise, let vΓ＝v′Γ，rimp＝r′impAnd (5) turning to the step (2) for loop iteration.
xb＝sinuem·ε+cosuem·Γ
Where esp is the accuracy of the difference between the desired velocity vectors given, which can typically be 0.1.
The ignition time, the speed control model and the iterative calculation process of the alternating attitude direction of the guidance algorithm are all in the unpowered sliding stage of the carrier rocket, and the boosting stage after the engine is ignited generates a guidance instruction according to the speed control model planned in advance.
The invention takes the implementation example that the exhausted shutdown solid carrier rocket enters the sun synchronous orbit. The specific parameters are as follows:
1) target orbit: 500km sun synchronous orbit.
2) And (4) terminal constraint: the constraint conditions of the terminal flight state are as follows:
hf＝500(km)，vf＝7616.8(m/s)，θf＝0(°)，if＝98(°) (31)
3) parameter and deviation configuration: quality of the rail entering load: the carrier rocket takes 200kg as the maximum load, and the load is reduced by 50kg in sequence until no load; initial deviation of track inclination angle: Δ i is [0,3,6,9,12] ° five states.
By adopting the guidance method, the following results are obtained by testing:
(1) load quality adaptability simulation result
Deviation of an actual flight trajectory, adjustment of a terminal task and change of satellite load mass all require that the speed control method has certain adaptability to the flight task. Considering that the carrier rocket takes 200kg as the maximum load, the load of 50kg is reduced in sequence until no load is taken as the condition for simulation. The solid carrier rockets with different load masses generate residual velocity modulus by means of depletion shutdown, the multi-constraint requirement of the terminal is realized through a velocity control model (taking an alternating attitude velocity control model as an example), a simulation curve is shown in fig. 6, and the simulation terminal deviation result is shown in table 1.
According to different load qualities, the adaptability of speed control is realized by controlling the maximum attitude adjusting angle. And the speed control plane is calculated by adopting a fixed point guidance coupling suppression algorithm under the condition of different load qualities due to additional influences of different degrees generated in the speed control process, the track height deviation reaches the hundred-meter magnitude, the maximum speed control deviation is 0.514m/s, the result can meet the terminal speed and position constraint conditions, and the suppression of the coupling term in speed control is realized. Meanwhile, the speed control plane is determined by the speed vector in the inertial space, so that the pitch angle command and the yaw angle command are in a mutual coupling relation.
TABLE 1 statistics of results of fixed-point guidance coupling suppression methods on different load masses
Figure BDA0002722950700000122
Figure BDA0002722950700000131
(2) Out-of-plane orbit adaptability simulation
According to expression (23) of the coupling suppression direction, the influence of the coupling term is not only related to the degree of speed control but also influenced by the track dihedral angle. Therefore, taking the minimum additional angular velocity control model as an example, the velocity control degree η is 20%, and the initial track inclination angle deviation Δ i is set to [0,3,6,9,12], respectively]Five states for different speed control planes (P in the track plane)imp-XgYgPerpendicular plane P of the railimp-XgZgAnd a coupling suppression plane Op- Γ epsilon) was verified by simulation, and the simulation result is shown in fig. 7.
In contrast track plane Pimp-XgYgPerpendicular plane P of the railimp-XgZgAnd a coupling suppression plane OpThe coupling effect of three different in-plane velocity controls on the terminal state of Γ ∈ can lead to the following results:
1) because the minimum additional angular velocity control model has strong control capability on the velocity vector, the velocity magnitude graph 7(b) and the velocity dip angle graph 7(c) reach terminal constraint values in each plane;
2) for the additional position quantity generated in the process of the minimum additional angular velocity control model, the deviation between the track height and the track inclination angle is obviously increased in the track surface, and the influence on the track vertical surface is relatively small;
3) when the tracks are coplanar, the vertical plane of the tracks is basically coincident with the coupling suppression plane, and only the coupling suppression plane O is formed as the degree of the different planes of the tracks is increasedpthe-Gamma epsilon can meet the constraint requirements of each terminal, and the simulation comparison result is shown in Table 2.
TABLE 1 results statistics of velocity control coupling effects in different planes
Figure BDA0002722950700000132
Figure BDA0002722950700000141
For track center-to-earth constraint, P in the track planeimp-XgYgThe influence is most obvious, and the maximum deviation value reaches 2.4 km; track vertical plane Pimp-XgZgThe maximum value of the deviation is 4.58km, and each deviation is increased along with the increase of the initial track inclination angle; coupling suppression plane OpThe precision in the gamma epsilon reaches 50m magnitude and is not influenced by the initial track inclination angle, and the coupling term has strong inhibition capability. In addition, for the track-entering velocity vector constraint, under the condition that the velocity control degree eta is 20 percent (the residual velocity of 550m/s needs to be dissipated), the control precision of the velocity magnitude reaches the magnitude of 10m/s, and the velocity vector constraint is on the vertical plane P of the trackimp-XgZgAnd a coupling suppression plane OpWithin- Γ epsilon, the velocity magnitude is controlled with greater precision, while within the track plane Pimp-XgYgAnd a coupling suppression plane OpWithin- Γ epsilon, the control precision of the velocity dip angle is higher. This shows that although the velocity vector constraint is taken into account when designing the minimum additional angular velocity control model, the coupling suppression plane OpThe- Γ epsilon approach is still more advantageous in suppressing errors. Finally, for orbital inclination angle constraints, P is in the orbital planeimp-XgYgChanges the position of the track-in point in the track plane, and the vertical plane P of the trackimp-XgZgChanging the track entry point to the direction of the track normal influences the rising point right ascension of the track entry point; although the influence principles of the two planes are different, the two planes have influence on the track inclination angle of the track at the track entry point, and the P in the track planeimp-XgYgThe maximum deviation reaches 2.2354 DEG, and the vertical plane P of the trackimp-XgZgMaximum of 0.0144 DEG, coupling suppression plane OpThe precision of-Gamma epsilon reaches the order of 0.01 deg.

Claims (2)

1. A terminal multi-constraint energy management method under the condition of strong coupling of a solid carrier rocket is characterized by comprising the following steps:
step 1: according to the center-of-earth radius r at the moment of ignitionigVelocity vector vigDetermining the position vector r of the virtual pulse point by the semimajor axis a, the eccentricity e and the track inclination angle i of the target trackimp: according to rigAnd vigTime of engine operation TsEngine specific impulse IspThrust T of engine and second flow of engine
Figure FDA0002722950690000011
Rocket initial total mass m0Rocket current mass m (t), fuel mass msThe virtual pulse point r can be calculated by the following formulaimpWherein r issub.fAnd vsub.fThe ground center distance and the absolute speed W of the rated shutdown time of the extension sliding trackMAnd RMApparent speed increment and apparent position increment generated by the engine respectively; g (r) ═ mu/r3R is the vector of the earth's gravity,
Figure FDA0002722950690000012
is a velocity vector, g, due to gravity0Is sea level gravitational acceleration;
rimp＝rsub.f-(RM/WM)·vsub.f
Figure FDA0002722950690000013
Figure FDA0002722950690000014
Figure FDA0002722950690000015
Figure FDA0002722950690000016
step 2: determining a desired velocity vector vΓΓ: according to the speed vector v of the sliding tracksub.gAnd velocity vector v of target trackorb.gThe required velocity vector v can be calculated from the following equationΓAnd its direction Γ;
Figure FDA0002722950690000017
and step 3: determining the coupling suppression direction epsilon: on-orbit coordinate system P according to required velocity vector direction gammaimp-XgYgZgComponent Γ in (1)x,Γy,ΓzAnd intermediate variables λ and l, the coupling suppression direction ε can be calculated by:
ε＝[εx εy εz]
εx＝-Γz/l
εy＝-Γztanλ/l
εz＝(Γx+Γytanλ)/l
θorb＝arctan(vorb.y/vorb.x)
tanλ＝(vorb.imp sinθorb+Δvg)/(vorb.imp cosθorb)
Figure FDA0002722950690000021
wherein v isorb.x、vorb.yRespectively the tangential velocity and the normal velocity of the track on the target track, vorb.impThe velocity at the virtual pulse point is the magnitude;
and 4, step 4: determining velocity control model additional attitude angle uem(t): according to the rocket thrust T, the current rocket mass m (T) and the position component rΓ、rεCan determine the additional attitude angle u of the speed control modelem(t)：
Figure FDA0002722950690000022
Wherein, WMThe magnitude of the total apparent speed increase produced for the engine;
and 5: determining coupling term parameters m and n: according to the selected speed control model uem(t)＝UVIC(t), the coupling terms m and n can be calculated, where vΓfFor the speed increment, r, produced by the engine after the speed control model is usedΓ(tf)＝rΓf；rε(tf)＝rεfFor position increment, r, produced by the engine after the speed control model is usedimpIs the size of the centroid radial at the virtual pulse point, g (r)imp) The gravity of the earth at the virtual pulse point;
m＝rεfεz；n＝-rεfεz·Δvg/rimp
Δvg＝g(rimp)·(rΓf/vΓf)
Figure FDA0002722950690000023
step 6: determining coupling-under-influence virtual pulse point position vector r'impAnd a velocity vector v'imp: calculating the position vector r of the virtual pulse point according to the step 1impVelocity vector v at virtual pulse point on the sliding tracksub.impSpeed increment v generated by the engine after the speed control model is adoptedΓfCoupling terms m and n and the tracking coordinate system Pimp-XgYgZgComponent of z direction
Figure FDA0002722950690000025
Can calculate r'impAnd v'imp：
Figure FDA0002722950690000024
And 7: determining the difference Δ v between the desired velocity vectorsΓ: according to coupling influence lower virtual pulse point position vector r'impAnd a velocity vector v'impTo obtain
Figure FDA0002722950690000031
The difference Δ v between the required velocity vectors can be calculatedΓ：
ΔvΓ＝v′Γ-vΓ
Wherein v isΓ＝vorb.g-vsub.g；
And 8: determining a guidance instruction: if Δ vΓIf | < esp, outputting guidance instruction xbAnd ending the iteration; otherwise, let vΓ＝v′Γ，rimp＝r′impAnd turning to step 2 for loop iteration:
xb＝sinuem(t)·ε+cosuem(t)·Γ
wherein u isemFor additional pose angles, esp is the precision of the difference between the given required velocity vectors;
the ignition time, the speed control model and the iterative calculation process of the alternating attitude direction of the guidance algorithm are all in the unpowered sliding stage of the carrier rocket, and the boosting stage after the engine is ignited generates a guidance instruction according to the speed control model planned in advance.
2. The method for multi-constraint energy management of the terminal under the condition of strong coupling of the solid launch vehicle according to claim 1, wherein esp in step 8 is 0.1.
CN202011093665.3A 2020-10-14 2020-10-14 Terminal multi-constraint energy management method under strong coupling condition of solid carrier rocket Pending CN112231831A (en)

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