CN110908407A - Improved prediction guidance method for RLV reentry heat flow rate tracking - Google Patents

Improved prediction guidance method for RLV reentry heat flow rate tracking Download PDF

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CN110908407A
CN110908407A CN201911124407.4A CN201911124407A CN110908407A CN 110908407 A CN110908407 A CN 110908407A CN 201911124407 A CN201911124407 A CN 201911124407A CN 110908407 A CN110908407 A CN 110908407A
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flow rate
heat flow
aircraft
guidance
roll angle
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CN110908407B (en
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林海兵
都延丽
刘武
唐明明
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses an improved prediction guidance method for RLV (reusable launch vehicle) reentry heat flow rate tracking, and relates to the technical field of flight guidance. The invention improves the longitudinal guidance law and the transverse guidance law in the prediction correction guidance, and mainly comprises the following aspects: when designing a longitudinal guidance law, firstly determining the maximum value of the heat flow rate at the current moment, and then introducing a heat flow rate tracking compensation term into the longitudinal guidance law design to correct the inclination angle amplitude; in the design process of the transverse guidance law, the transverse guidance logic designed by the improved artificial potential field method can effectively process geographical constraints, and the transverse guidance logic after the reusable vehicle flies through the no-fly zone is determined by a track azimuth angle error corridor. The invention can not only ensure the landing point precision of the aircraft, but also meet the process constraint and the geographical constraint in the flight process.

Description

Improved prediction guidance method for RLV reentry heat flow rate tracking
Technical Field
The invention relates to the technical field of flight guidance, in particular to an improved prediction guidance method for RLV reentry heat flow rate tracking.
Background
The Reusable Launch Vehicle (RLV) not only can be used as a civil vehicle for freely going to and from the sky, but also has the capability of global rapid attack. After the time of space shuttle was over, the success of falcon number 9 and x-37 greatly encouraged people to develop a hot tide for reusable vehicles. Therefore, extensive research has been conducted on the construction, materials, guidance, control, etc. systems of reusable vehicles in major countries of the world.
However, the reusable vehicle has the problems of complex flight environment, multiple tasks, and harsh constraints during reentry, which present new requirements and challenges for the design of guidance laws. Currently, the re-entry guidance law can be basically classified into a nominal trajectory guidance method and a predictive correction guidance method. The design of the nominal track guidance law comprises a nominal track design part and a nominal track tracking part, wherein the nominal track is designed to meet the requirements of flight tasks and the constraint requirements of heat flow, dynamic pressure, overload and the like. The nominal track guidance needs to be planned off line, and the defect of poor flexibility of the method can be overcome by prediction correction guidance.
The prediction correction algorithm can predict the deviation of the drop point through an integral iteration link according to the current aircraft state, and further generate a guidance instruction meeting the drop point precision. Aiming at the problems of path constraints such as waypoints, no-fly zones and the like in the reentry process of a reusable carrier, the prediction correction method mainly controls whether the deviation of the course angle is within the range of an error corridor, if the deviation of the course angle exceeds the boundary of the corridor, the sign of the roll angle is reversed, and then the aircraft is ensured to pass through the preset waypoints or avoid the no-fly zone. The longitudinal guidance obtains parameters needed in the roll angle amplitude model through the prediction of the falling point, and hard constraints such as heat flow, overload and the like are introduced into an algorithm as compensation terms in the iteration process.
However, the future reentry aircraft has the requirements of more complex tasks, more strict requirements on loads and the like, and in order to meet the requirements of future flight tasks, it is necessary to design a corresponding prediction correction guidance law for the heat flow tracking of the reentry aircraft.
Disclosure of Invention
The invention provides an improved prediction guidance method for RLV reentry heat flow rate tracking, which is characterized in that a heat flow rate tracking compensation and an improved artificial potential field method of a reentry aircraft are incorporated into the design of a prediction correction guidance law, so that the aircraft can not only ensure the requirement of the landing precision, but also meet the requirements of path constraint and geographical constraint.
In order to achieve the purpose, the invention adopts the following technical scheme:
an improved prediction guidance method for RLV reentry heat flow rate tracking introduces heat flow rate tracking compensation to longitudinal guidance and introduces a no-fly zone avoidance method to transverse guidance on the basis of the existing improved prediction correction guidance method.
The prediction correction algorithm works in the glide section of the aircraft, and the improved prediction guidance method for RLV reentry heat flow rate tracking is operated under the condition of obtaining the initial value of the vertex of the quadratic function of the roll angle parameterized model, and comprises the following specific steps:
s1, in each guidance period, the prediction correction algorithm obtains the vertex value of the quadratic function in the roll angle parameterized model according to the drop point error correction, and then the roll angle amplitude value in the current flight state is obtained through calculation by using the roll angle parameterized model.
And S2, correcting the roll angle amplitude obtained in the flight process by using the heat flow rate tracking feedback compensation idea.
S3, designing a transverse guidance law by adopting an improved artificial potential field method, and determining a roll angle symbol to realize the avoidance of a no-fly zone. And after the aircraft flies through the no-fly zone, using a traditional flight path azimuth error corridor to avoid the situation that the inclination angle frequently deflects when the aircraft approaches the target, and circularly executing S1-S3 until the flight mission of the glide section is finished.
Further, in S2, the compensation algorithm for the heat flow rate tracking feedback compensation determines the maximum value of the tracking heat flow rate at the current time by an S function whose abscissa is determined by a function of the ratio of the lift and drag estimated using the evanescent memory filter to the respective nominal conditions.
Further, the S1 includes:
establishing a dimensionless three-degree-of-freedom dynamic model taking energy as an independent variable:
Figure BDA0002275649140000031
wherein, R, theta and phi are respectively the dimensionless distance from the centroid of the aircraft to the geocentric, the longitude and latitude of the infrasatellite point of the aircraft, gamma is the track inclination angle, psi is the track direction angle, s is the residual longitudinal range, L and D are respectively the dimensionless lift force and the resistance of the aircraft, V is the dimensionless speed under the airflow coordinate system, omega is the normalized rotation angular velocity of the earth, the roll angle sigma is the control quantity of the guidance system in the flight process, and the positive and negative of sigma is determined by the transverse guidance logic;
defining an energy equation for the aircraft as:
Figure BDA0002275649140000041
the roll angle parameterized model quadratic function based on the energy e is:
|σ(e)|＝X(e-Y)2+Z (7)
where Z is the value found by the predictive correction search and X, Y are functional forms of Z, as shown below
Figure BDA0002275649140000042
Wherein e isfEnergy of the aircraft end point, σfAmplitude of roll angle of the aircraft terminal point, e0Energy, σ, of the current point at the beginning of the guidance algorithm for predictive correction0Correcting the roll angle amplitude of the current point when the guidance algorithm is predicted; thus, the amplitude | σ | of the roll angle in the flight process is obtained.
Further, the S2 includes:
establishing a heat flow rate equation:
Figure BDA0002275649140000043
wherein k isqIs the heat flow rate model coefficient, ρ is the atmospheric density,
Figure BDA0002275649140000044
at the maximum heat flow rate boundary, V is the flight speed; the product of the atmospheric density and velocity in the equation is denoted as ρ VnWhen heat flow rate tracking is achieved, ρ VnIs a constant. Where n is 6.3, which is twice the upper bound of the velocity in the heat flow rate equation, ρ VnThe derivation can be:
Figure BDA0002275649140000051
the velocity formula with time t as the independent variable before unnormalization neglecting the effect of earth rotation is shown below
Figure BDA0002275649140000052
Therefore, the sine value sin gamma of the reference track inclination angle can be obtained by substituting equation (15) into equation (10)refIs described in (1).
Because the predictive correction algorithm is done with normalization, under quasi-equilibrium glide conditions, the velocity after normalization is approximately
Figure BDA0002275649140000053
Wherein D1＝D/(mg0)；
The output roll angle magnitude command is derived according to the following equation:
Figure BDA0002275649140000054
wherein σcmdFor the output amplitude command value, σbaseIs a magnitude instruction determined by a roll angle parameterized model;
because R ═ R0+h，r0Is the mean radius of the earth, h is the altitude of the aircraft, so when r0When the time is not changed, the user can select the time,
Figure BDA0002275649140000055
k0is a gain adjustment coefficient, L isDimensionless lift of the aircraft;
to realize the heat flow rate tracking compensation, the sine value of the reference track inclination angle is obtained, and the sine value is indirectly corrected by correcting the resistance acceleration, wherein the correction formula is as follows:
Figure BDA0002275649140000056
in the formula, D0Is the resistance acceleration value at the current moment, Delta D is the gain quantity, kpIn order to be a proportional parameter,
Figure BDA0002275649140000057
and
Figure BDA0002275649140000058
respectively are the normalized values of the heat flow rate and the heat flow rate error at the current moment, and D is the dimensionless resistance of the aircraft;
the ratios of lift and drag, normalized to L and D at their respective nominal values, are denoted as kLAnd kDThen, the S function is designed to obtain the maximum reference value of the heat flow rate, and the value of the abscissa is x ═ a (k)D-1)+b(1-kL) Wherein a and b are adjustment coefficients;
the S function is shown below
Figure BDA0002275649140000061
In the formula, KiI is 1,2 and 3 are design parameters,
Figure BDA0002275649140000062
for reference value, the current value obtained
Figure BDA00022756491400000610
Numerical value replacement
Figure BDA0002275649140000064
In
Figure BDA0002275649140000065
The numerical value of (c).
Further, the S3 includes:
aiming at the problem of geographical constraint (no-fly zone) in the flight process, establishing a potential field function of repulsion and attraction of an artificial potential field method:
Figure BDA0002275649140000066
Figure BDA0002275649140000067
wherein theta is the longitude of the intersatellite point of the aircraft at the current position, phi is the latitude of the intersatellite point of the aircraft at the current position,
Figure BDA0002275649140000068
for the ith waypoint gravitational potential field function,
Figure BDA0002275649140000069
is a function of the repulsive potential field of the jth no-fly region, m∞,mrep,kattFor the parameter to be designed, p ═ θ, pNj＝(θNj,φNj) Respectively the current position of the aircraft and the circle center position theta of the jth no-fly zoneNjLongitude, phi, as the center of the circleNjThe latitude of the circle center. p is a radical ofwiIs the ith waypoint, i.e., the desired drop point, RNjRadius of no-fly zone, sNjDistance of the current aircraft from the center of the circle, ξNjIs the angle representation corresponding to the radius of the no-fly circle, rhoNjThe influence range of the jth no-fly zone.
Differentiating the potential field function to obtain the size of the attractive force and the repulsive force, and after defining the direction of the attractive force and the repulsive force and the boundary of the track direction angle, designing the roll angle overturning logic as follows:
Figure BDA0002275649140000071
wherein,σpthe roll angle at the previous moment is taken,
Figure BDA0002275649140000072
and
Figure BDA0002275649140000073
the distribution is the upper and lower boundaries when the roll angle is reversed;
after the aircraft flies through all the no-fly zones, the transverse guidance logic is switched to the traditional mode of determining the inclination angle symbol by a track azimuth error corridor;
according to the inclination angle amplitude and the sign thereof obtained at the current moment, carrying out iterative integration on a dimensionless three-degree-of-freedom dynamic model taking energy as an independent variable until the current energy is less than the preset energy value of a terminal point, and observing whether the residual flight meets the following equation or not:
Figure BDA0002275649140000074
where z is the distance between the current drop point and the desired drop point, efIs the energy of the aircraft terminal point,
Figure BDA0002275649140000075
is the terminal landing field radius.
If the formula (29) is satisfied, stopping the predictive guidance algorithm to obtain a vertex value Z of the roll angle parameterized model; if not, updating the vertex Z value in the quadratic function of the roll angle parameterized model in the S1 by using a truncation root-finding method, and circularly executing S1-S3 until the residual voyage meets the terminal error requirement or the number of root-finding iterations reaches a preset maximum value.
The invention has the beneficial effects that:
the method introduces the active heat flow rate compensation into the longitudinal guidance law design of the prediction correction algorithm, so that the aircraft can meet the constraint requirement and consume as much energy as possible in the heat flow rate influence section; meanwhile, a method for improving the artificial potential field and a control strategy of mixed lateral logic are introduced into transverse guidance, so that the aircraft can avoid a no-fly zone, and the problem of too frequent overturn when the aircraft approaches a target point can be reduced. The improved prediction correction algorithm not only meets the task requirements in the control process, but also ensures the landing point precision of the aircraft.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a graph of the results of 50 heat flow rate traces;
FIG. 3 is a graph of the overload variation for 50 times;
FIG. 4 is a graph of 50 ground track changes;
FIG. 5 is a schematic diagram of a conventional lateral guidance logic.
Detailed Description
In order that those skilled in the art will better understand the technical solutions of the present invention, the present invention will be further described in detail with reference to the following detailed description.
An embodiment of the present invention provides an improved predictive guidance method for RLV reentry heat flow rate tracking, as shown in FIG. 1, where the reusable vehicle with a medium lift-drag ratio is Horus-2B, the maximum aircraft heat flow rate is typically 450 kilowatts per square meter, the maximum overload is about 4g, and the initial and end states of the reentry segment are shown in Table 1.
Figure BDA0002275649140000081
TABLE 1
In the table, the units of aircraft altitude are kilometers, speed are meters per second, and the remaining angles are degrees. The six state quantities respectively represent the flying height, the latitude and longitude of the subsatellite point, the speed of the aircraft, the track inclination angle and the track azimuth angle.
Table 2 shows the coefficient of variation k of the aerodynamic parameterlAnd kdFour combinations of variations wherein CL＝(1+kl)CL，CD＝(1+kd)CD. The subscript max represents the maximum value of the variable.
Variables of Simulation 1 Simulation 2 Simulation 3 Simulation 4
klmax 0.1 0.1 -0.1 -0.1
kdmax 0.1 -0.1 0.1 -0.1
TABLE 2
To compare the effectiveness of the proposed method, a total of 50 simulations were performed. 1. The conditions in table 2 were alternately subjected to Monte-Carlo simulations 25 times; 2. the simulation is also performed for 25 times under the condition of the distribution of the coefficient gauss, and the absolute value of the disturbance boundary of the pneumatic parameter is 0.1. The boundaries under the gaussian distribution of the remaining variable perturbations in the Monte-Carlo simulation results are shown in the table below.
Status of state H0 θ0 φ0 V γ0 ψ0 m
Deviation of ±1 ±0.5 ±0.5 ±15 ±0.05 ±0.5 ±100
The units for the variables are in accordance with Table 1, and the units for the masses m are in kilograms.
According to the guidance flow of fig. 1, the simulation experiment was performed according to the following procedure.
Step 1, obtaining tilt angle [ sigma ] through longitudinal guidance law
And predicting and correcting a drop point, and then correcting the amplitude model of the roll angle through a drop point error of a terminal until a roll angle amplitude parameterized model quadratic function vertex value meeting the drop point precision is obtained or the upper limit of the number of times of the truncation iteration is reached. In this algorithm, normalization is required because the order of the state variables differ greatly. Furthermore, the energy e changes monotonically during flight, and the energy expression is as follows:
Figure BDA0002275649140000101
after neglecting the influence of the earth rotation angular rate, the energy e is calculated with respect to dimensionless time
Figure BDA0002275649140000102
Of (a) is given, wherein r0The radius of the earth, g0For the acceleration of gravity at sea level, the following equation is obtained:
Figure BDA0002275649140000103
therefore, the equation of the dimensionless three-degree-of-freedom mechanical model with respect to the energy e can be obtained as follows:
Figure BDA0002275649140000104
Figure BDA0002275649140000105
wherein R, theta, phi are dimensionless distances from the centroid to the centroid, longitude and latitude of the aircraft sub-satellite points, gamma is the track inclination angle, psi is the track heading angle, s is the remaining longitudinal range, V is the dimensionless speed in the air current coordinate system, the normalized autorotation angular velocity of the earth is omega, the roll angle sigma is the control quantity during flight, the positive and negative of which are determined by transverse guidance logic, the value of the other control quantity attack angle α is shown in the following table,
e 0.549 0.815 0.925 0.956 0.974 0.992
α 40° 40° 36° 31° 26° 15°
in order to judge the landing point precision of the terminal, the actual value of the range s to be flown is calculated according to the spherical triangle theory and is as follows:
s＝arccos(sinφsinφf+cosφcosφfcos(θf-θ)) (5)
wherein (theta, phi) is the current longitude and latitude of the aircraft, (thetaf,φf) Is the longitude and latitude of the target point.
L and D are dimensionless lift force and drag force of the aircraft respectively, and the normalized expression is as follows:
Figure BDA0002275649140000111
wherein q is the dynamic pressure of the current position, S is the reference area, m is the mass of the aircraft, g0Acceleration of gravity at sea level, CL,CDLift and drag aerodynamic parameters, respectively.
The quadratic function of the roll angle amplitude parameterized model of the prediction correction algorithm is given as:
|σ(e)|＝X(e-Y)2+Z (7)
wherein Z is a value obtained by prediction correction search, and X and Y are function expressions of Z.
Specific expressions of X and Y are shown below
Figure BDA0002275649140000112
In the formula, efEnergy of the aircraft end point, σfAmplitude of roll angle of the aircraft terminal point, e0Energy, σ, of the current point in order to perform a predictive correction guidance algorithm0Correction of the roll angle amplitude of the current point in the guidance algorithm for prediction, efAnd σfThe terminal roll angle amplitude is set to 60 degrees in the simulation process according to the terminal condition calculation and the pre-definition calculation respectively.
Step 2, introducing compensation amount in longitudinal guidance law design
The heat flow rate equation is shown below in terms of,
Figure BDA0002275649140000113
wherein k isq91089918.35 are the heat flow rate model coefficients, ρ is the atmospheric density,
Figure BDA0002275649140000114
v is the normalized velocity for the maximum heat flow rate boundary. As can be seen from the observation of the formula (9) (. rho.V)nThe tracking of the heat flow rate can be achieved at a constant value, n is twice the velocity superscript in equation (9),in this example n is 6.3, let ρ VnDerived by derivation
Figure BDA0002275649140000121
Figure BDA0002275649140000122
Wherein, the expression of the atmospheric density ρ is as follows,
Figure BDA0002275649140000123
where ρ is01.225 for reference atmospheric density, e for natural constant, fitting coefficients are as follows:
Figure BDA0002275649140000124
however, although the fitting atmospheric density has high accuracy, a simple exponential atmospheric model is used in equation (11), which is specifically expressed as follows:
Figure BDA0002275649140000125
ρ11.225, and Hs7050m, both end up with similar atmospheric density, h1In meters, and formula (13) in kilometers for medium and high levels. Note that the dimensional atmospheric density of the predictive correction algorithm is converted to a derivative of the dimensionless height, and the ratio of the converted derivative of equation (14) to the atmospheric density is more suitable for the operation in the compensation term.
The velocity formula before normalization with time t as the argument is shown below,
Figure BDA0002275649140000126
the sine value sin gamma of the reference track inclination angle can be obtained in the formula (10) after the formula (15) is subjected to non-dimensionalizationrefIs described in (1).
The output roll angle command is then derived according to the following equation:
Figure BDA0002275649140000131
wherein σcmdTo the output instruction value, σbaseIs a value obtained by the formula (7), k0And 20 is a gain adjustment coefficient, and L is the dimensionless lift force of the aircraft.
And 3, correcting the expression of the sine value of the reference track inclination angle in the heat flow rate compensation algorithm according to the step 2, wherein under the condition of known speed, the current heat flow rate value is tracked, and the required correction is carried out on the resistance angular speed value, so that the expression of the sine value of the reference track inclination angle is indirectly corrected.
Figure BDA0002275649140000132
Wherein D is0Is the resistance acceleration value at the current moment, Delta D is the gain quantity, kpIs a proportional parameter, the value is 3,
Figure BDA0002275649140000133
and
Figure BDA0002275649140000134
normalized values for the heat flow rate and the heat flow rate error, respectively, at the current moment, D is the dimensionless resistance of the aircraft. In order to satisfy that the flight has enough energy to reach the target point, the maximum heat flow rate value is obtained by using a sigmod function in an adaptive mode, and the expression is as follows:
Figure BDA0002275649140000135
wherein,
Figure BDA0002275649140000136
is a reference value, and takes the value of 400000, KiI is 1,2,3 is a design parameterAnd (4) counting. And K1Value of 60000, K2Value of 80, K3Values of 30000, i.e.:
Figure BDA0002275649140000137
wherein the variable x is obtained by the following formula
x＝0.9(kD-1)+0.1(1-kL) (19)
Wherein k isDAnd kLIs the ratio of the filtered value of the evanescent memory filter to the nominal value in equation (5), wherein the evanescent memory filter is designed as follows.
Xn+1＝Xn+(1-β)(X*-Xn) (20)
XnAnd Xn+1Past and current filtered values, X is the measured value, β is a gain in the range 0 to 1, in an embodiment 0.9.
Step 4, designing a transverse guidance law
In order to avoid the problem of the no-fly zone in the flight process, an Artificial Potential Field Method (APFM) is used to convert the original no-fly zone problem into a problem of solving a reference course angle direction, so that the potential Field functions of repulsion and attraction are designed as follows:
Figure BDA0002275649140000141
Figure BDA0002275649140000142
wherein theta is the longitude of the intersatellite point of the aircraft at the current position, phi is the latitude of the intersatellite point of the aircraft at the current position,
Figure BDA0002275649140000143
for the ith waypoint gravitational potential field function,
Figure BDA0002275649140000144
is a function of the repulsive potential field of the jth no-fly region, m∞,mrep,kattFor the parameter to be designed, p ═ θ, pNj＝(θNj,φNj) Respectively the current position of the aircraft and the circle center position theta of the jth no-fly zoneNjLongitude, phi, as the center of the circleNjLatitude of the centre, pwiIs the ith waypoint (desired drop point). RNjRadius of no-fly zone, sNjξ distance from the center of the circle for the current aircraftNjIs the angle representation corresponding to the radius of the no-fly circle. In this embodiment, since the RLV has limited lateral maneuvering, i and j are both equal to 1, i.e., in this embodiment, there is only one no-fly zone and one waypoint, which is the terminal landing point, and the parameter is m∞＝1000,mrep＝50,katt＝20，pN1＝[-70°,-3°]，RN1＝300km，ξN1Is the angle value corresponding to the radius under the no-fly zone, and rhoNj＝7RNj。
The functional expression of repulsion and lift after the derivation of the formulas (21) and (22) is as follows
Figure BDA0002275649140000151
Figure BDA0002275649140000152
Wherein, FattAnd FrepRespectively attractive and repulsive forces, pwg＝(θwg,φwg) Is the target point, i.e. the end point, θwgIs the longitude, phi, of the target pointwgThe latitude of the target point.
Figure BDA0002275649140000153
N ' when the aircraft falls within the no-fly zone circle for the aircraft's line of sight angle to the target point 'repIs a reference direction of repulsion of the aircraft, which may be
Figure BDA0002275649140000154
As a reference, when the aircraft isN 'when passing through the north of the no-fly circle'repThe angle of the 1/4 circumference should be subtracted and, similarly, the angle of the 1/4 circumference should be added when the aircraft passes on the other side of the no-fly circle.
Figure BDA0002275649140000155
Is expressed as follows
Figure BDA0002275649140000156
The repulsive force in the formula (24) is expressed as follows,
Figure BDA0002275649140000157
where the subscript N1 indicates that in embodiments only one no-fly zone is considered,
Figure BDA0002275649140000158
when calculating (2), replacing the corresponding point in the formula (25) with the center coordinates of the no-fly zone, if the north side flies around, subtracting the angle of 1/4 circles, and adding the value to the other side, finally, the direction of the resultant can be obtained.
Then the course angle flip logic is designed as follows:
Figure BDA0002275649140000161
wherein σpThe roll angle at the previous moment is taken,
Figure BDA0002275649140000162
and
Figure BDA0002275649140000163
for the upper and lower boundaries when the roll angle is reversed, the expression is as follows
Figure BDA0002275649140000164
When the north side of the aircraft is around the flight, in equation (27)
Figure BDA0002275649140000165
Is determined by the second expression in the expression (28). Psi ═ psi*±Δψ'thIs a boundary of a reference heading angle, psi 'is a direction of gravitational and repulsive forces,. DELTA.. psi'thThe setting is 8, and the setting is,
Figure BDA0002275649140000166
the included angle between the tangent line at the north side of the no-fly zone and the true north is shown. When the south side of the aircraft is around the aircraft, in formula (27)
Figure BDA0002275649140000167
Determined by the first formula in formula (28).
Figure BDA0002275649140000168
The included angle between the south tangent line and the north tangent line of the no-fly zone.
Second, the lateral guidance logic is switched. Switching the lateral guidance logic to determine the roll angle sign with a course angle error corridor, such as fig. 5, after the aircraft has flown through all no-fly zones, can reduce the problem of flipping too often when the aircraft is approaching the target while ensuring landing accuracy.
Step 5, according to the currently obtained roll angle amplitude and the sign thereof, carrying out iterative integration on the dynamic model until the dynamic model reaches a termination condition (namely a terminal energy predefined value), and observing whether the residual range meets the following equation or not
Figure BDA0002275649140000169
Where z is the distance between the current landing point and the desired landing point, typically the terminal landing field radius
Figure BDA00022756491400001610
Set to 0, then equation (29) represents the distance between the current drop point and the desired drop point. If not, updating the vertex Z value of the quadratic function of the roll angle amplitude parameterized model in the step 1 by using a truncation root-finding method, and repeatingAnd 1-4, until the residual voyage meets the requirement of terminal error or the number of root searching iterations reaches a preset maximum value.
The three figures 2-4 illustrate the effect of the designed method. The significant effect of the method proposed by the present invention on the predictive correction guidance algorithm for heat flow rate tracking can be seen from fig. 2, and fig. 3 shows that although the method proposed by the present invention improves the heat flow rate, the excess energy is also consumed in the overload section. Fig. 4 shows that the method has a good forbidden flight zone avoiding effect.
The invention has the beneficial effects that:
the invention introduces the active heat flow rate compensation into the longitudinal guidance law design of the prediction correction algorithm, so that the heat flow rate meets the requirement of maximum constraint; meanwhile, an improved artificial potential field method and a mixed lateral logic control strategy are introduced into transverse guidance, so that the aircraft can avoid a no-fly zone, and the problem that the aircraft overturns too frequently when approaching a target point can be reduced. The improved prediction correction guidance of the invention not only meets the task requirements in the control process, but also ensures the landing point precision of the aircraft.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. An improved prediction guidance method for RLV (reusable launch vehicle) reentry heat flow rate tracking is characterized in that on the basis of the existing prediction correction guidance method, heat flow rate tracking compensation is introduced into longitudinal guidance, and a no-fly zone avoidance method is introduced into transverse guidance;
the improved prediction guidance method for RLV reentry heat flow rate tracking specifically comprises the following steps:
s1, in each guidance period, obtaining a vertex value of a secondary function of the roll angle parameterized model according to the drop point error correction by a prediction correction algorithm, and then obtaining a roll angle amplitude value in the current flight state by using the roll angle parameterized model;
s2, correcting the roll angle amplitude obtained in the flight process by using the heat flow rate tracking feedback compensation idea;
s3, designing a transverse guidance law by adopting an improved artificial potential field method, determining a roll angle symbol to realize avoidance of a no-fly zone, using a traditional flight path direction angle error corridor to avoid the situation that the roll angle frequently deflects when the aircraft approaches a target after the aircraft flies through the no-fly zone, and circularly executing S1-S3 until the flight mission of the reentry glide section is finished.
2. The improved guidance method of RLV reentry heat flow rate tracking of claim 1 wherein in S2, the compensation algorithm of heat flow rate tracking feedback compensation determines the maximum value of the tracking heat flow rate at the current time by an S function whose abscissa is determined by a function of the ratio of the lift and drag estimated using an apogee filter to the respective nominal case.
3. The improved guidance method for RLV reentry heat flow rate tracking of claim 1 wherein said S1 comprises:
establishing a dimensionless three-degree-of-freedom dynamic model taking energy as an independent variable:
Figure FDA0002275649130000021
wherein, R, theta and phi are respectively the dimensionless distance from the centroid of the aircraft to the geocenter and the longitude and latitude of the infrasatellite point of the aircraft, gamma is a flight path inclination angle, psi is a flight path direction angle, s is the rest longitudinal path, L and D are respectively the dimensionless lift force and the resistance of the aircraft, V is the dimensionless speed under an airflow coordinate system, omega is the normalized rotation angular velocity of the earth, an inclination angle sigma is the control quantity of a guidance system in the flight process, and the positive and negative of sigma is determined by transverse guidance logic;
defining an energy equation for the aircraft as:
Figure FDA0002275649130000022
the roll angle parameterized model quadratic function based on the energy e is:
|σ(e)|＝X(e-Y)2+Z (7)
where Z is the value found by the predictive correction search and X, Y are functional forms of Z, as shown below
Figure FDA0002275649130000023
Wherein e isfEnergy of the aircraft end point, σfAmplitude of roll angle of the aircraft terminal point, e0Energy, σ, of the current point at the beginning of the guidance algorithm for predictive correction0Correcting the roll angle amplitude of the current point at the beginning of the guidance algorithm for prediction; thus, the amplitude | σ | of the roll angle in the flight process is obtained.
4. The improved guidance method for RLV reentry heat flow rate tracking of claim 1 wherein said S2 comprises:
establishing a heat flow rate equation:
Figure FDA0002275649130000031
wherein k isqIs the heat flow rate model coefficient, ρ is the atmospheric density,
Figure FDA0002275649130000032
at the maximum heat flow rate boundary, V is the flight speed; the product of the atmospheric density and velocity in the equation is denoted as ρ VnWhen heat flow rate tracking is achieved, ρ VnIs a constant, where n is 6.3, will be ρ VnThe derivation can be:
Figure FDA0002275649130000033
the velocity formula with time t as the argument before the unnormalization neglecting the effect of earth rotation is as follows:
Figure FDA0002275649130000034
therefore, substituting equation (15) into equation (10) can obtain the sine value sin γ of the reference track inclination anglerefThe expression of (1);
under quasi-equilibrium glide conditions, the velocity after normalization is approximately
Figure FDA0002275649130000035
Wherein D1＝D/(mg0)；
The output roll angle magnitude command is derived according to the following equation:
Figure FDA0002275649130000036
wherein σcmdFor the output amplitude command value, σbaseIs a magnitude instruction determined by a roll angle parameterized model;
because R ═ R0+h，r0Is the mean radius of the earth, h is the altitude of the aircraft, so when r0When the time is not changed, the user can select the time,
Figure FDA0002275649130000041
k0is a gain adjustment coefficient, and L is the dimensionless lift force of the aircraft;
the sine value of the reference track inclination angle is corrected indirectly by correcting the resistance acceleration, and the correction formula is as follows:
Figure FDA0002275649130000042
in the formula, D0Is the resistance acceleration value at the current moment, Delta D is the gain quantity, kpIn order to be a proportional parameter,
Figure FDA0002275649130000043
and
Figure FDA0002275649130000044
respectively are the normalized values of the heat flow rate and the heat flow rate error at the current moment, and D is the dimensionless resistance of the aircraft;
the ratios of lift and drag, normalized for L and D at their respective nominal values, are denoted as kLAnd kDDesigning S function to obtain maximum reference value of heat flow rate, and x ═ a (k) on abscissaD-1)+b(1-kL) Wherein a and b are adjustment coefficients;
the S function is as follows:
Figure FDA0002275649130000045
in the formula, KiI is 1,2 and 3 are design parameters,
Figure FDA0002275649130000046
is a reference value, which is preset; the maximum heat flow rate boundary obtained currently
Figure FDA0002275649130000047
Numerical value replacement
Figure FDA0002275649130000048
In
Figure FDA0002275649130000049
The numerical value of (c).
5. The improved guidance method for RLV reentry heat flow rate tracking of claim 1 wherein said S3 comprises:
establishing a potential field function of repulsion and attraction of an artificial potential field method:
Figure 1
wherein theta is the longitude of the intersatellite point of the aircraft at the current position, phi is the latitude of the intersatellite point of the aircraft at the current position,
Figure FDA0002275649130000052
for the ith waypoint gravitational potential field function,
Figure FDA0002275649130000053
is a function of the repulsive potential field of the jth no-fly region, m∞,mrep,kattFor the parameter to be designed, p ═ θ, pNj＝(θNj,φNj) Respectively the current position of the aircraft and the circle center position theta of the jth no-fly zoneNjLongitude, phi, as the center of the circleNjThe latitude of the circle center. p is a radical ofwiIs the ith waypoint, i.e., the desired drop point, RNjRadius of no-fly zone, sNjDistance of the current aircraft from the center of the circle, ξNjIs the angle representation corresponding to the radius of the no-fly circle, rhoNjRepresenting the influence range of the no-fly zone;
differentiating the repulsive force of the artificial potential field method and the potential field function of the attractive force to obtain the size of the attractive force and the repulsive force, and after defining the direction of the attractive force and the repulsive force and the boundary of a track azimuth angle, designing the overturning logic of the inclination angle as follows:
Figure FDA0002275649130000054
where σ is the roll angle, σpThe roll angle at the previous moment is taken,
Figure FDA0002275649130000055
and
Figure FDA0002275649130000056
respectively as the upper and lower boundaries when the roll angle is reversed;
after the aircraft flies through all the no-fly zones, switching the transverse guidance logic to the traditional mode of determining the inclination angle symbol by a flight path direction angle error corridor;
performing iterative integration on a dimensionless three-degree-of-freedom dynamic model taking energy as an independent variable according to the inclination angle amplitude and the sign obtained at the current moment until the current energy is smaller than a preset energy value of a terminal point, and observing whether the remaining voyage meets the following equation or not:
Figure FDA0002275649130000061
where z is the distance between the current drop point and the desired drop point range, efIs the energy of the aircraft terminal point,
Figure FDA0002275649130000062
is the terminal landing field radius;
if equation (29) is satisfied, stopping predictive guidance, if not, updating a vertex Z value in the roll angle parameterized model quadratic function in the S1 by using a truncation root method, and circularly executing S1-S3 until the residual voyage meets a terminal error requirement or the number of root searching iterations reaches a preset maximum value.
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