CN112947573A - Reentry guidance method for hypersonic aircraft under terminal time constraint - Google Patents

Reentry guidance method for hypersonic aircraft under terminal time constraint Download PDF

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CN112947573A
CN112947573A CN202110278512.4A CN202110278512A CN112947573A CN 112947573 A CN112947573 A CN 112947573A CN 202110278512 A CN202110278512 A CN 202110278512A CN 112947573 A CN112947573 A CN 112947573A
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CN112947573B (en
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梁子璇
崔平远
朱圣英
徐瑞
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a reentry guidance method of a hypersonic aircraft under terminal time constraint, which mainly solves the problem of terminal time constraint of a cooperative attack task of multiple hypersonic aircraft. The implementation method of the invention comprises the following steps: designing a parameterized U-shaped direction angle deviation corridor for controlling the course angle of the aircraft and the terminal time; predicting reentry terminal time by adopting a dynamic model containing an attack angle and a roll angle control section compensation and a fourth-order Adams integral method, and obtaining a time difference; and the time difference is eliminated by adjusting the boundary width coefficient of the U-shaped corridor on line, so that the time control of the reentry terminal of the hypersonic aircraft is realized. The guidance method disclosed by the invention can better meet the terminal time constraint through the transverse-lateral tilt angle reversal logic under the condition of not influencing the tracking precision of longitudinal states such as height, speed and the like, and provides an effective solution for the cooperative attack guidance problem of the hypersonic aircraft.

Description

Reentry guidance method for hypersonic aircraft under terminal time constraint
Technical Field
The invention relates to a reentry guidance method, in particular to a reentry guidance method of a hypersonic aircraft under terminal time constraint, and belongs to the field of aircraft guidance control.
Background
The hypersonic reentry aircraft generally flies in a near space with the height of 20-100 kilometers, the reentry speed can reach more than 20 Mach, and the hypersonic reentry aircraft has the characteristics of long range, high speed, strong maneuverability and the like and can be used for long-distance rapid striking. However, the development of the remote detection technology and the deployment of the advanced defense system limit the penetration probability of hypersonic velocity to the aircraft to a certain extent, so that the strategic deterrence force is influenced. In order to improve the penetration probability, an effective attack mode must be adopted, and the cooperative attack of multiple aircrafts is an effective way for improving the penetration capability. Due to the long range and large maneuvering range of the reentry aircrafts, the aircrafts may be separated by thousands of kilometers, and the intercommunication is difficult. Thus, a feasible cooperative attack scenario is: and the terminal time of each aircraft is controlled on line through an advanced re-entry guidance method, so that all the aircraft arrive at the target point at the same time at the expected moment.
The existing reentry guidance method mainly aims at a single aircraft, and mainly considers path constraints such as heat flux density, dynamic pressure and overload and terminal constraints such as height, speed and to-be-flown range during design. And if the flight to be flown is taken as a reentry section ending condition, the terminal restricts the state quantities such as the required altitude, the speed, the course angle and the like to be equal to respective expected values. For the multi-aircraft cooperative attack task, the conventional terminal constraint is required to be met, the time is also required to be controllable, and the reentry guidance problem is further complicated due to the increased terminal time constraint. Therefore, in order to complete the cooperative attack task of the hypersonic re-entry aircraft, a re-entry guidance method under the constraint of terminal time needs to be researched on the basis of the conventional re-entry guidance problem.
Disclosure of Invention
The invention aims to provide a reentry guidance method of a hypersonic aerocraft under terminal time constraint aiming at the problem that the existing reentry guidance technology cannot meet the terminal time constraint of a cooperative attack task, and further meets the terminal time constraint on the basis of ensuring conventional terminal constraints such as height, speed, flight range to be flown, course angle and the like. The guidance method disclosed by the invention can provide an effective solution for the problem of guidance of hypersonic aircraft cooperative attack.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a reentry guidance method of a hypersonic aircraft under terminal time constraint, which designs a parameterized U-shaped direction angle deviation corridor used for controlling the course angle of the hypersonic aircraft and the terminal time; predicting reentry terminal time by adopting a dynamic model containing an attack angle and a roll angle control section compensation and a fourth-order Adams integral method, and obtaining a time difference; and the boundary width coefficient of the U-shaped corridor is adjusted on line, so that the time difference is eliminated, and the time control of the hypersonic aircraft re-entering the terminal is realized.
The invention discloses a reentry guidance method of a hypersonic aircraft under terminal time constraint, which comprises the following steps:
step one, aiming at terminal direction angle constraint and terminal time constraint, a parameterized U-shaped direction angle deviation corridor is designed, and based on the relation between the aircraft roll angle and the boundary of the U-shaped corridor, the reversal logic of the roll angle of the hypersonic aircraft is established.
The specific implementation method of the first step is as follows:
first, the heading angle deviation is defined as the aircraft heading angle psi and the target boresight angle psiLOSDeviation between
Figure BDA0002974678790000021
On the spherical surface, the calculation formula of the visual angle of the aircraft to the target is
Figure BDA0002974678790000022
Wherein theta and phi are the longitude and latitude of the aircraft, respectivelyTPhi and phiTThe longitude and latitude of the target point are respectively.
Then, using a fractional order function, the U-shaped directional angular deviation corridor C (v) which decreases with decreasing aircraft speed v is designed as follows
C(v)＝Cf+K(v-v1)1/4-K(vf-v1)1/4 (3)
Where K is the boundary width coefficient, vfFor a desired re-entry terminal velocity, v1Is less than vfA certain speed, v1＝0.8vf。CfFor the corridor at vfThe value of (c) is as follows. So that the terminal azimuth does not exceed the maximum allowable deviation delta psifThen, there are:
Cf＝ηΔψf (4)
wherein the coefficient eta takes a value between 0 and 1.
The inversion logic for obtaining the aircraft roll angle σ based on the designed heading angle deviation corridor is as follows
Figure BDA0002974678790000023
Wherein σpIs the roll angle command at the previous time.
And step two, in the reentry flight process, predicting the flight trajectory and the flight time by using a four-order Adams numerical integration method by combining a hypersonic reentry aircraft kinetic equation, a control section compensation method and the U-shaped direction angle deviation corridor designed in the step one, and terminating integration when the aircraft enters a terminal area to obtain a terminal time predicted value.
The concrete implementation method of the second step is as follows:
during integration, hypersonic reentry vehicle dynamic equation considering earth rotation is adopted
Figure BDA0002974678790000031
Wherein r is the distance from the geocenter to the mass center of the aircraft, gamma is the trajectory inclination angle, L is the lift acceleration, D is the resistance acceleration, g is the gravity acceleration, F1、F2And F3Is the relevant term of the rotational angular velocity of the earth.
In order to eliminate the influence of transverse lateral maneuver on the longitudinal state quantities such as height and speed, the roll angle and attack angle curves adopted during the track integration need to be compensated and corrected, i.e. compensation values are superposed on the basis of nominal values
Figure BDA0002974678790000032
Wherein α is the angle of attack; alpha is alpharefAnd σrefRespectively, nominal values of the attack angle and the roll angle, corresponding to the nominal track; delta alpha and Delta sigma are respectively compensation values of an attack angle and a roll angle, and are obtained according to the longitudinal state deviation
Figure BDA0002974678790000033
Wherein, K2×3To follow a flight course stogoA time-varying feedback coefficient matrix, wherein Δ r is a state deviation of a geocentric distance, Δ γ is a state deviation of a ballistic inclination angle, and Δ v is a state deviation of a velocity; the flight distance to be flown is calculated according to a two-point distance formula on the spherical surface
stogo＝REarccos[cosφcosφTcos(θ-θT)+sinφsinφT] (9)
Wherein R isEThe radius of the earth.
And (3) combining the kinetic equation of the formula (6) and the control profile of the formula (7-8), and completing numerical integration of the reentry flight trajectory by using a fourth-order Adams integration method. The integration process takes the aircraft entering a terminal area as a termination condition, and the flight range s to be flown from the aircraft to a target pointtogoWhen the radius is smaller than the radius of the terminal area, the integration is terminated, and the predicted value t of the terminal time is outputp。
Step three, calculating the difference between the terminal time predicted value obtained in the step two and the terminal time expected value, and if the time difference is within an allowable range, giving a tilting angle reversal instruction under the terminal time constraint by a U-shaped direction angle deviation corridor; otherwise, adjusting the boundary width coefficient K of the corridor on line according to the time difference, so that the time difference can be controlled within an allowable range, and then giving a tilting angle reversal instruction by the new U-shaped direction angle deviation corridor.
The concrete implementation method of the third step is as follows:
calculating the predicted value t of the terminal timepAnd the expected value tfThe difference, i.e., the time difference Δ t, and whether the following conditions are satisfied
|Δt|≤Δtmax (10)
Wherein, Δ tmaxThe maximum terminal time error allowed. If the predicted value t ispAnd the expected value tfIf the difference satisfies the equation (10), the roll angle reversal command is directly given by the equation (5), otherwise, the boundary width coefficient K of the U-shaped corridor needs to be adjusted.
Let the initial boundary width coefficient be K(1)Corresponding terminal time difference is Deltat(1)Then the boundary width coefficient after the first adjustment is as follows
Figure BDA0002974678790000041
Where δ is a small amount.
To obtain K(2)And then, the expected value of the terminal time is calculated again in the step two, and whether the time difference is within the allowable range or not is judged. If not, the subsequent adjustment adopts an iteration method. For the ith adjustment (i ≧ 2), the corresponding boundary width coefficient is
Figure BDA0002974678790000042
And (3) obtaining a boundary width coefficient meeting the formula (10) by using an iteration method given by the formula (12), finally giving a roll angle reversal command by the formula (5), and obtaining a corresponding reentry guidance command by combining a longitudinal trajectory tracking law.
Advantageous effects
1. The hypersonic aircraft reentry guidance method under the terminal time constraint, disclosed by the invention, brings the terminal time constraint into a transverse lateral guidance task, designs a simple U-shaped direction angle deviation corridor, meets the terminal time constraint by adjusting the boundary width coefficient of the corridor, realizes effective control of reentry terminal time under the condition of not influencing the tracking precision of longitudinal states such as height, speed and the like, can solve the problem of terminal time constraint in a cooperative attack task, is easy to realize, and has a better engineering application prospect.
2. According to the hypersonic aircraft reentry guidance method under the terminal time constraint, when the terminal time is predicted, the attack angle and the roll angle control section containing compensation are adopted, so that the accuracy of flight path and terminal time prediction is improved, and the control precision of the terminal time is further improved.
Drawings
FIG. 1 is a flow chart of steps of a reentry guidance method of a hypersonic aerocraft under the constraint of terminal time, which is disclosed by the invention;
fig. 2 is a U-shaped directional angle deviation corridor corresponding to the boundary width coefficient K-6;
FIG. 3 is a reentry trajectory ground projection curve under terminal time constraints;
FIG. 4 is a plot of the angular deviation of the direction and U-shaped corridor under the terminal time constraint;
fig. 5 is a roll angle curve under a terminal time constraint.
Detailed Description
For a better understanding of the objects and advantages of the invention, reference is made to the following description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention.
In order to verify the feasibility of the method, a reentry guidance method simulation under the terminal time constraint is performed by taking a reentry task of a CAV-H aircraft as an example. Initial height of aircraft is h060km, speed v06400m/s, longitude θ 00, latitude phi 00; terminal height of aircraft is hf30km, velocity vf2000m/s, maximum azimuth angle deviation delta psi f5 °; longitude of the target point is thetaT59 deg. and latitude phi T30 °; the expected re-entry terminal time is 1600s, and the maximum terminal time error allowed by the cooperative attack is delta tmax＝1s。
As shown in fig. 1, the method for guidance of reentry of a hypersonic aircraft under the terminal time constraint disclosed in this embodiment specifically includes the following steps:
step one, aiming at terminal direction angle constraint and terminal time constraint, a parameterized U-shaped direction angle deviation corridor is designed, and based on the relation between the aircraft roll angle and the boundary of the U-shaped corridor, the reversal logic of the roll angle of the hypersonic aircraft is established.
First, the heading angle deviation is defined as the aircraft heading angle psi and the target boresight angle psiLOSDeviation between
Figure BDA0002974678790000051
On the spherical surface, the calculation formula of the visual angle of the aircraft to the target is
Figure BDA0002974678790000052
Then, using a fractional order function, the U-shaped directional angular deviation corridor C (v) which decreases with decreasing aircraft speed v is designed as follows
C(v)＝Cf+K(v-v1)1/4-K(vf-v1)1/4 (15)
Where K is the boundary width coefficient, vfFor a desired re-entry terminal velocity, v1Is less than vfA certain speed of, can be v1＝0.8vf。CfFor the corridor at vfThe value of (c) is as follows. So that the terminal azimuth does not exceed the maximum allowable deviation delta psifIs designed as
Cf＝ηΔψf (16)
Wherein the coefficient takes on a value between 0 and 1.
The obtained U-shaped corridor is shown in fig. 2, taking K as 6 and η as 0.8.
The inversion logic for obtaining the aircraft roll angle σ based on the designed heading angle deviation corridor is as follows
Figure BDA0002974678790000061
Wherein σpIs the roll angle command at the previous time.
And step two, in the reentry flight process, predicting the flight trajectory and the flight time by using a four-order Adams numerical integration method by combining a hypersonic reentry aircraft kinetic equation, a control section compensation method and the U-shaped direction angle deviation corridor designed in the step one, and terminating integration when the aircraft enters a terminal area to obtain a terminal time predicted value.
During integration, hypersonic reentry vehicle dynamic equation considering earth rotation is adopted
Figure BDA0002974678790000062
Wherein r is the distance from the geocenter to the mass center of the aircraft, gamma is the trajectory inclination angle, L is the lift acceleration, D is the resistance acceleration, and g is the gravity acceleration; f1、F2And F3For the related term of the rotational angular velocity omega of the earth, the expression is as follows
Figure BDA0002974678790000063
In order to eliminate the influence of transverse lateral maneuver on the longitudinal state quantities such as height and speed, the roll angle and attack angle curves adopted during the track integration need to be compensated and corrected, i.e. compensation values are superposed on the basis of nominal values
Figure BDA0002974678790000064
Wherein α is the angle of attack; alpha is alpharefAnd σrefRespectively, nominal values of the attack angle and the roll angle, corresponding to the nominal track; delta alpha and Delta sigma are respectively compensation values of an attack angle and a roll angle, and are obtained according to the longitudinal state deviation
Figure BDA0002974678790000065
Wherein, K2×3To follow a flight course stogoA time-varying feedback coefficient matrix, wherein Δ r is a state deviation of a geocentric distance, Δ γ is a state deviation of a ballistic inclination angle, and Δ v is a state deviation of a velocity; the flight distance to be flown is calculated according to a two-point distance formula on the spherical surface
stogo＝REarccos[cosφcosφTcos(θ-θT)+sinφsinφT] (22)
Wherein the radius of the earth RE＝6378.14km。
And (3) combining the kinetic equation of the formula (18) and the control profile of the formula (20-21), and completing the numerical integration of the reentry flight trajectory by using a fourth-order Adams integration method. The integration process takes the aircraft entering a terminal area as a termination condition, and the flight range s to be flown from the aircraft to a target pointtogoWhen the radius of the terminal area is less than 100km, the integral is terminated, and a predicted value t of the terminal time is outputp. When K is 6, the value t is predictedp＝1565.6s。
Step three, calculating the difference between the terminal time predicted value obtained in the step two and the terminal time expected value, and if the time difference is within an allowable range, giving a tilting angle reversal instruction under the terminal time constraint by a U-shaped direction angle deviation corridor; otherwise, adjusting the boundary width coefficient K of the corridor on line according to the time difference, so that the time difference can be controlled within an allowable range, and then giving a tilting angle reversal instruction by the new U-shaped direction angle deviation corridor.
Calculating the predicted value t of the terminal timepAnd the expected value tfThe time difference Δ t was found to be-34.4 s. Judging whether the following conditions are satisfied
|Δt|≤Δtmax (23)
If the above condition is satisfied, the roll angle reversal command is given by equation (17) as it is. And the boundary width coefficient K of the U-shaped corridor needs to be adjusted because the boundary width coefficient K does not meet the requirement.
Let the initial boundary width coefficient be K(1)Corresponding terminal time difference is Deltat(1)Then the boundary width coefficient after the first adjustment is as follows
Figure BDA0002974678790000071
Wherein, the value of delta is 0.5.
To obtain K(2)After 6.5, step two is executed again, and the expected value of the terminal time is 1571.6 s. The time difference is still not within the allowable range, and then the adjustment is carried out by adopting an iteration method. For the ith adjustment (i ≧ 2), the corresponding boundary width coefficient is
Figure BDA0002974678790000072
The iterative method given by the formula (25) can be used for obtaining the boundary width coefficient meeting the formula (23), finally, the formula (17) gives a roll angle reversal command, and a corresponding reentry guidance command can be obtained by combining with a longitudinal trajectory tracking law.
Under the guidance method, the ground projection curve of the reentry flight trajectory is shown in FIG. 3, the time when the reentry flight trajectory reaches the target point is 1599.8s, the time error is-0.2 s, and the terminal time constraint requirement of the cooperative attack task is met. The directional angle deviation and the U-shaped corridor boundary during flight are shown in fig. 4, and it can be seen that the directional angle deviation is well controlled within the upper and lower boundaries of the corridor. The roll angle curve of the aircraft is shown in fig. 5, which is totally called 4 reversals. The result shows that the designed U-shaped corridor and the adjusting method thereof can effectively control the time of the reentry terminal, so that the formed reentry guidance method can be used for the cooperative attack task of the hypersonic aircraft.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. The reentry guidance method of the hypersonic aircraft under the terminal time constraint is characterized by comprising the following steps: the method comprises the following steps:
step one, aiming at terminal direction angle constraint and terminal time constraint, designing a parameterized U-shaped direction angle deviation corridor, and establishing reversal logic of the roll angle of the hypersonic aircraft based on the relation between the roll angle of the aircraft and the boundary of the U-shaped corridor;
the specific implementation method of the first step is as follows:
first, the heading angle deviation is defined as the aircraft heading angle psi and the target boresight angle psiLOSDeviation between
Figure FDA0002974678780000011
On the spherical surface, the calculation formula of the visual angle of the aircraft to the target is
Figure FDA0002974678780000012
Wherein theta and phi are the longitude and latitude of the aircraft, respectivelyTPhi and phiTRespectively the longitude and latitude of the target point;
then, using a fractional order function, the U-shaped directional angular deviation corridor C (v) which decreases with decreasing aircraft speed v is designed as follows
C(v)＝Cf+K(v-v1)1/4-K(vf-v1)1/4 (3)
Where K is the boundary width coefficient, vfFor a desired re-entry terminal velocity, v1Is less than vfA certain speed, v1＝0.8vf；CfFor the corridor at vfTaking the value of (A); so that the terminal azimuth does not exceed the maximum allowable deviation delta psifThen, there are:
Cf＝ηΔψf (4)
wherein the coefficient eta takes the value from 0 to 1;
the inversion logic for obtaining the aircraft roll angle σ based on the designed heading angle deviation corridor is as follows
Figure FDA0002974678780000013
Wherein σpThe roll angle command at the previous moment;
in the reentry flight process, predicting flight trajectory and flight time by using a four-order Adams numerical integration method by combining a hypersonic reentry aircraft kinetic equation, a control section compensation method and the U-shaped direction angle deviation corridor designed in the step one, and terminating integration when the aircraft enters a terminal area to obtain a terminal time predicted value;
the concrete implementation method of the second step is as follows:
during integration, hypersonic reentry vehicle dynamic equation considering earth rotation is adopted
Figure FDA0002974678780000021
Wherein r is the distance from the geocenter to the mass center of the aircraft, gamma is the trajectory inclination angle, L is the lift acceleration, D is the resistance acceleration, g is the gravity acceleration, F1、F2And F3Is the relative term of the rotational angular velocity of the earth;
in order to eliminate the influence of transverse lateral maneuver on longitudinal state quantity, the roll angle and attack angle curves adopted during the track integration need to be compensated and corrected, i.e. compensation values are superposed on the basis of nominal values
Figure FDA0002974678780000022
Wherein α is the angle of attack; alpha is alpharefAnd σrefRespectively, nominal values of the attack angle and the roll angle, corresponding to the nominal track; delta alpha and Delta sigma are respectively compensation values of attack angle and roll angle, and are deviated according to longitudinal stateDifference is obtained
Figure FDA0002974678780000023
Wherein, K2×3To follow a flight course stogoA time-varying feedback coefficient matrix, wherein Δ r is a state deviation of a geocentric distance, Δ γ is a state deviation of a ballistic inclination angle, and Δ v is a state deviation of a velocity; the flight distance to be flown is calculated according to a two-point distance formula on the spherical surface
stogo＝REarccos[cosφcosφTcos(θ-θT)+sinφsinφT] (9)
Wherein R isEIs the radius of the earth;
combining the kinetic equation of the formula (6) and the control profile of the formula (7-8), and completing numerical integration of the reentry flight trajectory by using a fourth-order Adams integration method; the integration process takes the aircraft entering a terminal area as a termination condition, and the flight range s to be flown from the aircraft to a target pointtogoWhen the radius is smaller than the radius of the terminal area, the integration is terminated, and the predicted value t of the terminal time is outputp；
Step three, calculating the difference between the terminal time predicted value obtained in the step two and the terminal time expected value, and if the time difference is within an allowable range, giving a tilting angle reversal instruction under the terminal time constraint by a U-shaped direction angle deviation corridor; otherwise, adjusting the boundary width coefficient K of the corridor on line according to the time difference to enable the time difference to be controlled within an allowable range, and then giving a tilting angle reversal instruction by the new U-shaped direction angle deviation corridor;
the concrete implementation method of the third step is as follows:
calculating the predicted value t of the terminal timepAnd the expected value tfThe difference, i.e., the time difference Δ t, and whether the following conditions are satisfied
|Δt|≤Δtmax(10) Wherein, Δ tmaxIs the maximum terminal time error allowed; if the time difference delta t satisfies the formula (10), directly giving a tilting angle reversal command by the formula (5), otherwise, adjusting the boundary width coefficient K of the U-shaped corridor;
let the initial boundary width coefficient be K(1)Corresponding terminal time difference is Deltat(1)Then the boundary width coefficient after the first adjustment is as follows
Figure FDA0002974678780000031
Wherein δ is a minor amount;
to obtain K(2)Then, the expected value of the terminal time is calculated again in the step two, and whether the time difference is within the allowable range or not is judged; if the condition is not met, then the subsequent adjustment adopts an iteration method; for the ith adjustment (i ≧ 2), the corresponding boundary width coefficient is
Figure FDA0002974678780000032
And (3) obtaining a boundary width coefficient meeting the formula (10) by using an iteration method given by the formula (12), finally giving a roll angle reversal command by the formula (5), and obtaining a corresponding reentry guidance command by combining a longitudinal trajectory tracking law.
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