CN106371312B - Lift formula based on fuzzy controller reenters prediction-correction method of guidance - Google Patents
Lift formula based on fuzzy controller reenters prediction-correction method of guidance Download PDFInfo
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Abstract
The lift formula based on fuzzy controller that the invention discloses a kind of reenters prediction-correction method of guidance, and for trajectory predictions by the way of numerical integration, correcting algorithm takes fuzzy controller, and the longitudinal movement and transverse movement to aircraft are corrected simultaneously.Firstly, the process of reentering is divided into initial descending branch and quasi- equilibrium glide section according to the characteristic for the process that reenters.Initial descending branch is guided using constant value angle of heel, and the size of angle of heel is determined by Reentry Error item.Into after quasi- equilibrium glide section, the SOT state of termination is predicted, then angle of heel size, angle of attack size and angle of heel overturning opportunity are determined using fuzzy controller, voyage deviation, height tolerance and lateral deviation are eliminated respectively, and by adjusting terminal location, guarantee the course angle for entering terminal area energy region (TAEM).The present invention effectively increases the robustness and flexibility of guidance algorithm, improves the thinking of conventional iterative correction, and correction only needs a trajectory predictions each time, substantially reduces calculation amount.
Description
Technical Field
The invention relates to the technical field of guidance control, in particular to a reusable aircraft reentry prediction-correction guidance method based on a fuzzy controller.
Background
A Reusable Launch Vehicle (RLV) refers to an aircraft that can freely travel between space and the earth, repeatedly Launch multiple times, and achieve horizontal fixed-point landing. The reusable aircraft has a large lift-drag ratio (the lift-drag ratio is generally more than 0.5) and strong maneuverability. Research in RLV in the united states was carried out earlier and has been in the world's lead. The first generation of RLV aircraft is represented by space shuttle, and the birth of the RLV aircraft makes the reusability of the space shuttle become reality from ideal, and has a historic significance. The main models developed by the second generation RLV are an X-33 advanced technology verification machine, an X-34 small-sized sub-orbit flight verification machine, an X-37 secondary orbit entering verification machine and an X-37B orbit test aircraft. The success of the X-37B project represents the great advantages of the RLV technology in the United states and the development direction of future aerospace vehicles. Currently, the united states is working on the development of third generation RLVs in an effort to improve the safety and reliability of RLV aircraft. By 2040, the U.S. fourth generation RLV could take off at any region of the earth, enter orbit in a variety of ways, and be able to return to re-enter to any predetermined destination. In recent years, China also carries out a great deal of research on the aspect and carries out related experiments, and domestic reusable aircrafts are expected to be put into practice.
The reusable aircraft return reentry process is divided into four phases, namely a departure phase, a reentry phase, a terminal energy management phase (TAEM), and a landing phase. The reentry stage is the most complex and difficult stage. At the stage, the speed of the aircraft is reduced to 2-3 Mach from more than twenty Mach, and the process constraints such as heat flow, overload and dynamic pressure and the terminal constraints such as energy, position and course angle need to be met.
Reentry guidance methods for reusable aircraft can be divided into two categories: one is standard trajectory guidance and the other is prediction-correction guidance. The standard trajectory guidance method comprises two parts of off-line standard trajectory design and on-line trajectory tracking, and is successfully applied to aerospace airplanes. The method comprises the steps of firstly designing a resistance acceleration-speed (D-V) profile in a flight corridor, and then designing a track tracking controller to track the D-V profile. In order to adapt to the requirement of the new generation RLV reentry guidance, the space plane reentry guidance method is further developed and mainly embodied in the aspects of flight profile optimization and design, a tracking control rule design method, a profile updating technology and the like. Such as an Evolved Acceleration Guidance method (EAGLE). The most prominent feature of EAGLE is the ability to plan a three-dimensional trajectory, thereby providing the ability to deal with large lateral maneuver problems.
Although the standard trajectory guidance method has great success in practical application, the main defects are that the method cannot get rid of the dependence on the standard trajectory and has insufficient flexibility. Therefore, in recent years, attention has been directed to a prediction-correction guidance method. The prediction-correction guidance method comprises two parts of trajectory prediction and instruction correction. Depending on the prediction mode, the prediction-correction guidance can be divided into analytic prediction-correction guidance and numerical prediction-correction guidance. The analytic prediction-correction guidance predicts the track through an approximate analytic formula, has small calculated amount, can meet the requirement of on-line calculation, but has low guidance precision and poor process constraint treatment. The numerical prediction-correction guidance predicts the track by utilizing the numerical integration of the motion equation, has higher prediction precision, but has large calculation amount, and is not beneficial to engineering realization. As the level of computers has increased, numerical predictive guidance is receiving increasing attention.
Disclosure of Invention
The invention aims to solve the technical problem of providing a reusable aircraft reentry prediction-correction guidance method based on a fuzzy controller aiming at the defects of the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a reusable aircraft reentry prediction-correction guidance method based on a fuzzy controller comprises the following steps: a reusable aircraft reentry prediction-correction guidance method based on a fuzzy controller comprises the following steps:
1) when the aircraft starts to enter again, the size of the roll angle | sigma of the initial descent section is calculated according to the state deviation and the aerodynamic coefficient deviationiniWhile calculating the sign (σ) of the roll angle from the line of sight angle of the aircraft to the target pointini) At σiniUnder the guidance action of the aircraft, the aircraft continuously descends until the end condition of the initial descending section is met
Where δ is the threshold value for entering the equilibrium glide state, which can be set to 0.02, r is the ground center distance, V is the speed of the aircraft, the ground center distance to speed derivative dr/dV-Vsin θ/(D + gsin θ), θ is the speed inclination, D is the resistive acceleration, g is the gravitational acceleration, (dr/dV)QEGCObtaining the corresponding slope of the equilibrium glide trajectory in the height-velocity profile by differentiating the equilibrium glide condition with respect to V;
2) after entering the gliding section, updating the atmospheric density and aerodynamic coefficient error models according to the current state and the measurement result of the accelerometer, and ensuring that the models are consistent with the reality;
3) performing track prediction by taking a current point as a starting point, firstly establishing a model of an attack angle and a roll angle section, then performing numerical integration on a reentry dynamic model by adopting a Longgoku tower numerical integration method and taking energy as an independent variable, finishing integration when the energy of the aircraft reaches a cut-off condition to obtain a terminal state, and calculating a range deviation delta R, a height deviation delta h and a transverse position deviation CR;
4) updating the reentry terminal position according to the predicted terminal course angle, namely, entering the entrance of the TAEM area, ensuring that the aircraft vertically enters the TAEM area,
wherein λ isTAnd phiTTo the latitude and longitude of the landing field, λFAnd phiFLatitude and longitude of TAEM area entrance, RTAEMRadius of the TAEM region, psi is the flight azimuth;
5) correcting the guidance instruction according to the prediction result, and correcting by adopting two fuzzy controllers, wherein the input of the fuzzy controller A is residual energy Eto-goThe range deviation delta R is output as a roll angle correction delta sigma and an attack angle correction delta α, the input of the fuzzy controller B is a transverse position deviation CR, and the output is a change delta E of the roll angle overturning time;
6) after the roll angle correction quantity delta sigma is obtained, the delta sigma is further processed, so that the correction of the current roll angle is completed,
|σc|＝|σc|pre+kσΔtsim
wherein, Δ tgudFor the guidance period, kσBeing the slope of the change in the roll angle, Δ tsimTo simulate the integration step, | σc|preIs the roll angle, | σ, of the previous guidance periodcI is the current roll angle;
7) calculating the constraint boundary of the roll angle corrected in step 6), and if the amplitude of the roll angle exceeds the boundary, taking the boundary value
Wherein,limiting the roll angle for heat flow constraints, σq,maxLimiting the roll angle for dynamic pressure constraints, σn,maxLimiting the roll angle for overload restraint, kmaxDesigned as a constant or piecewise linear function for different aircraft kmaxIs different (e.g. constant 0.95), kmaxThe function of correcting the inclination angle boundary is achieved;
8) when correcting the current roll angle, adjusting the nodes of the roll angle profile model at the same time, namely changing the roll angle profile model of the track prediction:
|σm|＝|σm|pre+kmΔσ
wherein k ismIs an adjustable constant of 0-1, | σmI is a node of the roll angle model, | σm|preFor the last guidance period | σmTaking the value of |; after obtaining the correction amount Δ E of the roll angle turning timing, the following processing is performed
Erev＝Erev,pre+Sign·ΔE
Wherein E isrevEnergy in roll-over of roll angle, Erev,preE obtained for the last guidance periodrev(ii) a When the energy of the aircraft falls to EhIn time, the height deviation is eliminated by adjusting the attack angle
αf＝αf,pre+kh(hf-hF)
Wherein, αfAngle of attack for reentry terminal αf,preα for the last guidance periodfValue, khIs a feedback coefficient (e.g., -2 x 10)-6)，hFFor the required height of the terminal to be reached,is the predicted terminal height.
In the step 1), the initial falling section roll angle | σiniThe | calculation method is as follows:
|σini|＝|σini|0+aΔCl+aΔCd+bΔρ+cΔθ0+dΔV0
wherein, is Δ V0For initial speed deviation, Δ θ0For initial velocity tilt angle deviation, Δ Cl、ΔCdThe deviation of the lift coefficient and the deviation of the drag coefficient are respectively, the Delta rho is the deviation of the atmospheric density, the constants a, b, c and d reflect the influence of each error term on the initial descending section, and the deviation is set through simulation analysis.
Sign (sigma) of the roll angle calculated from the line of sight angle of the aircraft to the target pointini) Is calculated by
sign(σini)＝-sign(ψ-ψLOS)
Wherein psiLOSIs the line of sight angle of the aircraft to the target point.
The control quantity model used in the track prediction is
1) The angle of attack model is
Wherein Ma is the flight Mach number, MafMach number for reentry terminal αfNear maximum lift-to-drag ratio angle of attack, α0Is an adjustable variable, in order to reduce the heat flow, the aircraft enters the atmosphere again at a large angle of attack;
2) the model of the roll angle is
Wherein, | σcI is the magnitude of the roll angle at the current time, | σfI is the roll angle amplitude of the terminal, determined preliminarily according to the state of the end point, Em、|σmI is a design node;
3) in the process of the aircraft, the roll angle is turned twice, the second turning is close enough to the reentry end point (for example, the normalized energy is 0.98), the turning time is adjusted in real time through a correction algorithm, the first turning time is corrected by only adopting the method in the step 9) in the claim 1 before the first turning, the second turning time is kept unchanged, and the second turning time is corrected by adopting the method in the step 9) in the claim 1 after the first turning.
The constraint boundary of the roll angle is
Wherein, K is the influence item of the earth rotation, M is the mass of the aircraft, SrIs the reference area, k, of the aircraftQAs the parameters of the heat flow model,qmax、nmaxmaximum heat flow, dynamic pressure, overload constraints, respectively.
The calculation formula of the range deviation and the transverse position is as follows
Wherein λ is0、φ0To re-enter the longitude, latitude, lambda of the initial pointf、φfThe longitude and latitude of the predicted reentry end point. The lateral position deviation is in the P coordinate system (see reference [1 ]]) The solution is obtained by the following steps of (1),is phiFThe representation in the P-coordinate system is,is phifIn the P coordinate system, REThe radius of the earth.
Compared with the prior art, the invention has the beneficial effects that: the invention designs a prediction-correction guidance algorithm based on a fuzzy controller, which has the advantages that: (1) the idea of the traditional prediction-correction method is improved, only one track prediction is needed for each correction, and the calculated amount is greatly reduced. (2) The method adopts the fuzzy controller to carry out three-dimensional correction on the aircraft motion, and improves the robustness and flexibility of the guidance algorithm.
Drawings
FIG. 1 is a lift reentry process diagram;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3(a) a graph of membership functions for range deviations of an aircraft; FIG. 3(b) a plot of membership functions for the residual energy of the aircraft; FIG. 3(c) a graph of membership functions for the amount of aircraft roll angle adjustment; FIG. 3(d) a graph of membership functions for the aircraft angle of attack adjustments; FIG. 3(e) a plot of membership functions for lateral deviation of the aircraft; FIG. 3(f) is a graph of membership functions for the aircraft rollover timing adjustment;
FIG. 4(a) a chart of aircraft re-entry altitude change; FIG. 4(b) a ground re-entry trajectory diagram of the aircraft; FIG. 4(c) a diagram of aircraft reentry angle of attack variation; FIG. 4(d) a re-entrant roll angle variation diagram for the aircraft; FIG. 4(e) a chart of the heat flow of the aircraft re-entering; FIG. 4(f) a graph of aircraft reentry overload changes;
FIG. 5 is a re-entrant landing profile for an aircraft.
Detailed Description
Assuming that a reusable aircraft returns from space and reenters, the flight state includes altitude h, longitude λ, latitude φ, velocity V, velocity inclination θ and heading angle ψ, and the equation of motion for its reentry process can be expressed as:
wherein, L and D are respectively the lift force and the resistance force of the airship in the reentry process, and the calculation formula is
In equation (1), Cθ、CψThe coriolis acceleration term caused by the rotation of the earth,bulk acceleration term for earth rotation
As shown in fig. 2, for the reentry vehicle in this embodiment, the specific implementation steps of the present invention are as follows:
s1, initial descending section guidance. Calculating the size of the roll angle of the initial descending section according to the deviation of the initial state and the deviation of the aerodynamic coefficient
|σini|＝|σini|0+aΔCL+aΔCD+bΔρ+cΔθ0+dΔV0 (3)
Wherein, | σini|0The deviation amounts are normalized to 3 °, and a, b, c, and d are 12, 10, 12, and 10, respectively. While calculating the sign (sigma) of the roll angle from the line of sight angle of the aircraft to the target pointini) At σiniUnder the guidance action of the aircraft, the aircraft continuously descends until the end condition of the initial descending section is met
And S2, establishing a model of an attack angle and a roll angle.
(S2-a) the angle of attack model is
Wherein, α0Has an initial value of 45 DEG, αfThe initial value of (a) is 15 °.
(S2-b) the model of the roll angle is
Wherein E is normalized energy, Em＝0.8，|σmThe initial value of | is π/4.
(S2-c) roll angle rollover model. In the process of the aircraft, the roll angle is overturned twice, and the initial value of the first overturning time is Erev0.6, the initial value of the second overturn time is Erev＝0.96。
And S3, predicting the track. And after entering the gliding section, updating the atmospheric density and aerodynamic coefficient error models according to the current state and the measurement result of the accelerometer, and ensuring that the models are consistent with the reality. Then, track prediction is carried out by taking the current point as a starting point, a Longgoku tower numerical integration method is adopted based on a control quantity model in S2, the kinetic equation is integrated by taking energy as an independent variable until the energy is reduced to the energy required by TAEM, integration is stopped, a terminal state is obtained, and a voyage deviation delta R, a height deviation delta h and a transverse position deviation CR are calculated.
And S4, correcting the flight parameters according to the predicted terminal state.
(S4-a) updating the re-entry terminal position, i.e., the entrance into the TAEM area, with the predicted terminal heading angle to ensure that the aircraft enters the TAEM area vertically.
Wherein R isTAEMThe radius of the TAEM is taken as 100 km.
(S4-b) correcting the guidance instruction according to the prediction result, wherein the correction algorithm is realized by adopting two fuzzy controllers, and the input of the fuzzy controller A is energy Eto-goThe course deviation delta R is output as a roll angle correction delta sigma and an attack angle correction delta α, the input of the fuzzy controller B is a transverse position deviation CR, the output is a roll angle overturning energy variation delta E, membership function of all variables is shown in an attached diagram 3, and the rule of the fuzzy controller is shown in a table 1.
TABLE 1(a) fuzzy rule Table of roll angle adjustment
TABLE 1(b) fuzzy rule table of angle of attack adjustment
TABLE 1(c) fuzzy rule Table of roll Angle rollover timing adjustment
(S4-b-1) after obtaining the roll angle correction amount Delta sigma, it is further processed to continue the command
Wherein, Δ tgudDetermining the predicted time length according to the track, and taking the predicted time length as 1.5s, delta tsimTake 0.5 s.
(S4-b-2) adjusting the pitch point of the roll angle profile model while correcting the current roll angle, to increase the turndown capability of the aircraft.
|σm|＝|σm|pre+kmΔσ (9)
Wherein k ismIs taken to be 0.5, | σmThe maximum value of | is 85 °.
(S4-b-3) calculating a constraint boundary of the roll angle, and if the magnitude of the roll angle exceeds the boundary, taking the boundary value
Wherein k ismaxIs a linear piecewise function and is determined by simulation analysis.
(S4-b-4) after obtaining the correction amount of the angle of attack Delta α, the command is further processed to continue the operation
Wherein, α0∈[42°,50°]。
(S4-b-5) determination of the roll angle rollover timing. After obtaining the correction amount Δ E of the roll angle turning timing, the following processing is performed
Before the first correction, the first overturning time is corrected by the above formula, and the second overturning time is kept unchanged. After the first correction, the second overturn time is corrected by adopting the formula.
(S4-b-6) when the energy of the aircraft is reduced to EhIn time, the height deviation is eliminated by adjusting the attack angle
And S5, transmitting the corrected guidance instruction to a high-precision kinetic equation, integrating, and completing one guidance period. And judging whether the energy of the aircraft meets the requirements of the TAEM interface, if so, ending the whole simulation process, otherwise, turning to S2 and entering the next guidance period.
To further illustrate the effect of the present invention on reentry guidance of reusable aircraft, a simulation example is presented herein. The mass of the aircraft is 37362.9kg, and the characteristic area is Sr＝149.388m2The initial state is as follows
h0＝121.51km，λ0＝-117.01°，φ0＝-18.225°，
V0＝7621.8m/s，θ0＝-1.4379°，ψ0＝-38.329°；
Reentry terminal requirements
Vf＝926m/s，hf＝30.48km；
Landing site location
λT＝-80.138°，φT＝-28.61°；
The heat flow, dynamic pressure and overload are restricted to
qmax＝14364Pa，nmax＝2.5g0
The types, distributions and sizes of the various errors considered during the simulation are shown in table 1.
TABLE 2 error parameter types and distributions
200 sets of errors were randomly extracted for MonteCarlo numerical target practice simulation. The statistical results of the target practice simulation are shown in table 3, and it can be seen from the data in the table that the guidance accuracy of the height and the speed is high. The results of the targeting simulation are given in fig. 4 and 5.
TABLE 3 Monte-Carlo numerical simulation target practice statistical results
Reference documents:
[1]Y.Xie,L.H.Liu,J.Liu,G.J.Tang,et al.Rapid generation of entrytrajectories with waypoint and no-fly zone constraints[J].Acta Astronautica,2012,77:167-181.
Claims (4)
1. A lift-type reentry prediction-correction guidance method based on a fuzzy controller is characterized by comprising the following steps:
1) when the aircraft starts to enter again, the roll angle amplitude value | sigma of the initial descent section is calculated according to the state deviation and the aerodynamic coefficient deviationiniAnd simultaneously calculating the sign (sigma) of the initial descent segment roll angle according to the line-of-sight angle from the aircraft to the target pointini) At an initial roll angle σiniUnder the guidance action of the aircraft, the aircraft continuously descends until the end condition of the initial descending section is met
Wherein, δ is the threshold value for entering the balanced gliding state, r is the earth center distance, V is the speed of the aircraft, the derivation of the earth center distance to the speed dr/dV is-V sin theta/(D + g sin theta), theta is the speed dip angle, D is the resistance acceleration, g is the gravity acceleration, (dr/dV)QEGCObtaining the corresponding slope of the equilibrium glide trajectory in the height-velocity profile by differentiating the equilibrium glide condition with respect to V;
2) after entering the gliding section, updating the atmospheric density and aerodynamic coefficient error models according to the current state and the measurement result of the accelerometer, and ensuring that the models are consistent with the reality;
3) performing track prediction by taking a current point as a starting point, firstly establishing a model of an attack angle and a roll angle section, then performing numerical integration on a reentry dynamic model by adopting a Longgoku tower numerical integration method and taking energy as an independent variable, finishing integration when the energy of the aircraft reaches a cut-off condition to obtain a terminal state, and calculating a range deviation delta R, a height deviation delta h and a transverse position deviation CR;
4) updating the reentry terminal position according to the predicted terminal course angle, namely, entering an entrance of the TAEM area, and ensuring that the aircraft vertically enters the TAEM area, namely:
wherein λ isTAnd phiTLongitude and latitude, λ, of the landing field, respectivelyFAnd phiFLongitude and latitude, R, of TAEM area entry, respectivelyTAEMRadius of the TAEM region, psi is the flight azimuth;
5) correcting the guidance instruction according to the prediction result, and correcting by adopting two fuzzy controllers, wherein the input of the fuzzy controller A is residual energy Eto-goThe range deviation delta R is output as a roll angle correction delta sigma and an attack angle correctionThe quantity delta α, the input of the fuzzy controller B is the transverse position deviation CR, and the output is the variation delta E of the roll angle overturning opportunity;
6) after obtaining the roll angle correction amount Δ σ, further processing Δ σ to complete the correction of the current roll angle:
|σc|＝|σc|pre+kσΔtsim
wherein, Δ tgudFor the guidance period, kσBeing the slope of the change in the roll angle, Δ tsimTo simulate the integration step, | σc|preIs the roll angle, | σ, of the previous guidance periodcI is the amplitude of the roll angle at the current moment;
7) calculating the constraint boundary of the current roll angle corrected in step 6), and if the amplitude of the roll angle exceeds the boundary, taking the boundary value
Wherein,limiting the roll angle for heat flow constraints, σq,maxLimiting the roll angle for dynamic pressure constraints, σn,maxLimiting the roll angle for overload restraint, kmaxThe method is designed to be a constant value or a piecewise linear function;
8) when correcting the current roll angle, adjusting the nodes of the roll angle profile model at the same time, namely changing the roll angle profile model of the track prediction:
|σm|＝|σm|pre+kmΔσ
wherein k ismIs an adjustable constant of 0-1, | σmI is a node of the roll angle model, | σm|preFor the last guidance weekPeriod | σmTaking the value of |; after obtaining the amount of change Δ E in the roll angle turning timing, the following process is performed
Erev＝Erev,pre+Sign·ΔE
Wherein E isrevEnergy in roll-over of roll angle, Erev,preE obtained for the last guidance periodrev；σcFor the roll angle at the present moment, when the energy of the aircraft falls to EhIn time, the height deviation is eliminated by adjusting the attack angle
Wherein, αfAngle of attack for reentry terminal αf,preα for the last guidance periodfValue, khAs a feedback factor, hFFor the required height of the terminal to be reached,is the predicted terminal height; ehIs the energy of the aircraft at altitude h.
2. The fuzzy controller based lift reentry prediction-correction guidance method of claim 1, wherein in step 1), the initial descent roll angle | σ | (s |) isiniThe | calculation method is as follows:
|σini|＝|σini|0+aΔCL+aΔCD+bΔρ+cΔθ0+dΔV0
wherein, | σini|0To account for the initial roll angle magnitude of the error, Δ V0For initial speed deviation, Δ θ0For initial velocity tilt angle deviation, Δ CL、ΔCDRespectively being a lift coefficient and a resistance systemThe number deviation, delta rho, is the atmospheric density deviation, and the constants a, b, c and d reflect the influence of each error term on the initial descending section and are set through simulation analysis.
3. The fuzzy controller based lift reentry prediction-correction guidance method of claim 1, wherein the line of sight angle of the aircraft to the target point calculates sign (σ) of the initial descent segment roll angleini) Is calculated by
sign(σini)＝-sign(ψ-ψLOS)
Wherein psiLOSIs the line of sight angle of the aircraft to the target point.
4. The fuzzy controller based lift reentry prediction-correction guidance method of claim 1, wherein the constraint boundary of the roll angle is
Wherein, CLAnd CDRespectively lift coefficient and drag coefficient, g0Is the gravitational constant, K is the influence term of the earth' S rotation, M is the mass of the aircraft, SrIs the reference area, k, of the aircraftQAs the parameters of the heat flow model,qmax、nmaxmaximum heat flow, dynamic pressure, overload constraints, respectively.
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