CN113960926B - Self-adaptive adjustment method for pneumatic capturing guidance parameter boundary - Google Patents
Self-adaptive adjustment method for pneumatic capturing guidance parameter boundary Download PDFInfo
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Abstract
The invention discloses a self-adaptive adjustment method for a pneumatic capture guidance parameter boundary, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: on the premise of giving a pneumatic capturing maneuver mode, establishing a pneumatic capturing maneuver optimal control problem model. And through maximum principle analysis, the tilting angle section structure corresponding to the optimal aerodynamic capture maneuver is provided, and a control parameter section is provided for the guidance loop, so that the optimality of guidance is ensured. Based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, the universality and the robustness of the optimal pneumatic capture guidance are realized by establishing a self-adaptive adjustment method of the pneumatic capture guidance parameter boundary, and the low fuel consumption performance of the guidance process is synchronously improved. The invention has the following advantages: (1) strong robustness and high repeatability; (2) The flexibility is high, and the method is suitable for various planetary pneumatic capturing tasks; (3) The method has good mobility, and the control parameter boundary does not need to be manually given in advance.
Description
Technical Field
The invention relates to a control parameter boundary self-adaptive adjusting method for improving pneumatic capturing guidance performance, in particular to a method suitable for planetary detection single pneumatic capturing optimal guidance, and belongs to the technical field of aerospace.
Background
The capture braking is the first step in the implementation of planetary detection tasks such as mars and the like, and is also an important maneuvering process of an underground detection task reflector into the earth orbit. Since conventional thrust brake capture requires a large amount of fuel consumption, reducing capture brake burnup is a central technical challenge of urgent concern in this field. The pneumatic capture braking is considered to significantly reduce the use of aircraft burnup and thus becomes an important leading edge technique for capture braking. The reliability and performance of the guidance algorithm is critical in determining success or failure of the task and in implementing the performance during pneumatic capture. In initial research, the design of the guidance algorithm takes the control parameter as a constant profile, and the capture process of the target track is realized by calculating the value of the control parameter in each guidance link. However, later-stage researches show that the capturing guidance precision under the constant profile is lower and the performance index is poorer, so that the Lu et al researches show that the optimum pneumatic capturing profile structure greatly improves the pneumatic capturing performance. However, control parameter boundary dependence still exists at present, and the control parameter boundary dependence has limitations on different system parameters and different task modes, and is difficult to adaptively expand and migrate. Therefore, the adaptive adjustment method for the pneumatic capturing guidance parameter boundary provided by the patent not only can overcome the influence of the parameter boundary on the application of the guidance algorithm in different pneumatic capturing tasks, but also can improve the performance of the guidance algorithm to a certain extent, thereby having greater potential application value.
Among the developed methods for aerodynamic capture guidance, prior art [1] (see: lafleur, J M, the Conditional Equivalence of Δ V Minimization and Apoapsis Targeting in Numerical Predictor-Corrector Aerocapture Guidance [ R ]. NASA TM-2011-216156,Johnson Space Center,Houston,TX,Aug.2011.) gives an aerodynamic capture guidance algorithm with constant roll angle as a control quantity, which, although advantageous in terms of robustness and adaptation, has a lower performance due to a non-optimal structure of the profile, and a larger approach maneuver after aerodynamic capture.
The prior art [2] (see: lu P, cerimele C J, tigges MA, et al, optimal Aerocapture Guidance [ J ]. Journal of Guidance, control, and Dynamics,2015,38 (4): 553-565.) developed an optimal aerodynamic capture guidance algorithm, the authors designed an aerodynamic capture guidance method with optimal performance for the first time based on an optimal profile, but the algorithm stability and robustness was dependent on engineering data of roll angle boundaries in a certain aerodynamic capture scene, thus greatly limiting algorithm migration and parameter adaptability
Disclosure of Invention
The invention discloses a self-adaptive adjusting method for a pneumatic capturing guidance parameter boundary, which aims to solve the technical problems that: the self-adaptive adjusting method of the pneumatic capturing guidance parameter boundary is established on the basis of designing the control parameter boundary capable of being self-adaptively adjusted and establishing a parameter boundary self-adaptive adjusting law, and the self-adaptive and low-fuel consumption performance of the pneumatic capturing guidance is improved by self-adaptively adjusting the control parameter boundary through the self-adaptive adjusting method. The invention has the following advantages: (1) strong robustness and high repeatability; (2) The flexibility is high, and the method is suitable for various planetary pneumatic capturing tasks; (3) The method has good mobility, and the control parameter boundary does not need to be manually given in advance.
The invention aims at realizing the following technical scheme:
the invention discloses a self-adaptive adjustment method for a pneumatic capture guidance parameter boundary, which establishes a pneumatic capture maneuvering optimal control problem model on the premise of giving a pneumatic capture maneuvering mode. And through maximum principle analysis, the tilting angle section structure corresponding to the optimal aerodynamic capture maneuver is provided, and a control parameter section is provided for the guidance loop, so that the optimality of guidance is ensured. Based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, the universality and the robustness of the optimal pneumatic capture guidance are realized by establishing a self-adaptive adjustment method of the pneumatic capture guidance parameter boundary, and the low fuel consumption performance of the guidance process is synchronously improved.
The invention discloses a self-adaptive adjustment method for a pneumatic capture guidance parameter boundary, which comprises the following steps:
step one: on the premise of giving a pneumatic capturing maneuver mode, establishing a pneumatic capturing maneuver optimal control problem model.
Step 1.1: and giving out the pneumatic capturing maneuver mode and meeting the terminal constraint and performance index of the corresponding pneumatic capturing maneuver mode. The pneumatic capturing maneuver mode is a single pulse pneumatic capturing maneuver mode or a double pulse pneumatic capturing maneuver mode.
In the pneumatic capturing process, the aircraft needs to apply a speed pulse at an arch point after flying through an atmosphere outside kepler orbit, so that the whole pneumatic capturing process can be completed. The pulse applied at the post-atmospheric camber is an in-orbit maneuver. The pulse maneuver required for pneumatic capture corresponds to a single pulse pneumatic capture maneuver mode or a double pulse pneumatic capture maneuver mode.
The single pulse pneumatic capturing maneuvering mode is that the instantaneous orbit telecentric point after the aircraft is out of the atmosphere is overlapped with one arch point of the target orbit, and at the moment, pulse maneuvering delta V applied to the telecentric point is only needed once in the whole process, so that the orbit near-center point after maneuvering is identical with the near-center point of the target orbit.
The double pulse pneumatic capturing maneuvering mode is that the instantaneous orbit telecentric point after the aircraft is out of the atmosphere and the two arch points of the target orbit are not coincident, and at the moment, the aircraft is required to apply a first maneuvering DeltaV at the telecentric point of the orbit after the aircraft is out of the atmosphere 1 So that the near-center point of the orbit coincides with the near-center point of the target orbit after the first maneuver, and then applying a second maneuver DeltaV when the aircraft is traveling to the near-center point 2 The purpose of this maneuver is to bring the aircraft into the target orbit.
For single pulse pneumatic capture, the vector diameter of the position of the telecentric point of the elliptical orbit of the aircraft out of the atmosphere after pneumatic capture is required to be equal to the vector diameter of the position of the telecentric point of the target orbit, namely
r a ＝r T,a (1)
Wherein r is a Is the vector diameter of the telecentric point position of the track after pneumatic capturing, and r T,a The vector diameter of the telecentric point of the target track. For single pulse pneumatic capture, the speed pulse is the size of the in-orbit pulse DeltaV, and a calculation formula can be directly deduced according to the Kepler orbit energy, namely
Wherein μ is a constant of planetary attraction, a T Is a semi-long axis of a target track, a is pneumaticThe semilong axis of the post-capture track.
For double pulse pneumatic capture, strict out-of-air-track telecentric point position constraints are not required, and there is no terminal equation constraint as in equation (1). The calculation formula of the total speed increment of the two pulse pneumatic capturing is deduced according to the Kepler orbit energy formula, and is
Wherein r is T,p The vector diameter is the position vector diameter of the near-center point of the target track.
The formula (1) is the terminal constraint of single-pulse pneumatic capturing, and the formulas (2) and (3) are the performance indexes of single-pulse pneumatic capturing maneuver and double-pulse pneumatic capturing maneuver respectively.
Step 1.2: and establishing an optimal control problem model for pneumatic capturing maneuver, and taking the optimal control problem as an open loop process of single guidance.
The aerodynamic capture optimal control problem model is a model foundation for constructing a guidance loop, and comprises dynamics, terminal constraint and performance indexes.
The aerodynamic capture dynamics model is a polar coordinate system model, and the corresponding state variables are position vector diameter r, speed V, longitude theta, latitude phi, track angle gamma and course angle phi respectively. The only control parameter in the dynamic model is the roll angle σ, which will also be the control parameter to be designed in the guidance link.
The terminal constraint of the pneumatic capturing maneuver exists only in the single-pulse pneumatic capturing mode, the expression of the terminal constraint is shown in the formula (1), and the terminal constraint is also a basic equation for constructing a single-pulse pneumatic capturing closed-loop guidance equation.
The performance index of pneumatic capturing is the pulse maneuver size no matter the single pulse pneumatic capturing maneuver or the double pulse pneumatic capturing maneuver. The single pulse pneumatic capture guidance equation is considered to be constructed through the terminal constraint equation, so that the performance index cannot appear in the design of a guidance loop. However, for the double-pulse pneumatic capturing process, because there is no terminal constraint, a single-target unconstrained optimization problem of the guidance loop needs to be built based on the performance index (3), namely, an optimal control problem model of pneumatic capturing maneuver is built, and the optimal control problem is used as an open loop process of single guidance.
Step two: and through maximum principle analysis, the tilting angle section structure corresponding to the optimal aerodynamic capture maneuver is provided, and a control parameter section is provided for the guidance loop, so that the optimality of guidance is ensured.
Considering that the performance index contains only non-integral terms composed of terminal state quantities, namely the performance index belongs to the Mayer type, the performance index-related terms are not contained in the Hamilton equation of longitudinal dynamics. I.e. Hamilton equation h=λ T x L Where the state variable given longitudinal dynamics is x L ＝[r,V,γ] T Furthermore, λ= [ λ ] r ,λ V ,λ γ ] T Is the corresponding collaborative state vector of longitudinal dynamics variable. Based on the principle of maximum value, the tilting angle sigma corresponding to the optimal pneumatic capturing maneuver is known as
From equation (4), it can be seen that the cosine of the control variable roll angle σ takes a linear form in the Hamilton equation. Considering that the range constraint of the roll angle sigma is (0 DEG, 180 DEG) during atmospheric flight, so sigma and cos sigma exhibit a monotonic relationship, the optimal roll angle sigma * Has a bang-bang control structure, i.e. in [ sigma ] min ,σ max ]A jump will occur between them, wherein the jump time t s Is an important parameter in the design process of the guidance loop.
Step three: based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, the universality and the robustness of the optimal pneumatic capture guidance are realized by establishing a self-adaptive adjustment method of the pneumatic capture guidance parameter boundary, and the low fuel consumption performance of the guidance process is synchronously improved.
Based on bang-bang structure of optimal roll angle, during aerodynamic capture maneuver, the aircraft flies at minimum roll angle firstThe row, this segment is referred to herein as the P1 segment. Then at jump time t s The point is switched to the maximum roll angle flight, which is called the P2 segment. Although the roll angle corresponding to segment P1 is a constant value sigma min But is the most critical stage for the whole guidance link, in this stage, the roll angle boundary value of the P2 section is only involved in the solution process of a single guidance open loop, and the boundary value of the P2 section is the key that affects the guidance robustness and performance at present. When the aircraft enters the P2 section, the guidance process only considers the value of the roll angle and does not relate to the boundary, so that the robustness and the mobility of guidance are not affected as in the existing guidance logic.
In order to improve the robustness and the optimality of the guidance algorithm under the condition of meeting the constraint of the target track inclination angle, an adaptive inclination angle upper boundary adjustment link is additionally added in the guidance ring section P1. That is, at the beginning, the upper boundary sigma of the roll angle is selected max Then gradually changing sigma in each subsequent guidance link max The change amount is delta sigma, and the changed criterion is whether the current guidance link is successful or not and meets the constraint requirement. The upper boundary of the tilting angle input by the current guidance link is sigma u The next guidance link actually uses sigma max Is that
The guidance failure corresponding to the parameter boundary self-adaptive regulation law (5) is different from the characteristic reflected by the two pneumatic capturing modes. For the single pulse mode, it corresponds to t s And (3) the guidance process at the current moment is continued after the boundary adjustment at the tilting angle without solution. Whereas the double pulse mode corresponds to the total velocity pulse DeltaV 12 Compared with the previous guidance link, the abrupt increase condition occurs.
The adaptive calculation formula of the corresponding control parameter roll angle is formula (5) for adaptively adjusting the guidance parameters, and in each guidance loop process, the value of the maximum boundary of the roll angle is calculated according to formula (5), so that the problem of guidance failure corresponding to formula (5) is solved, the universality and the robustness of optimal pneumatic capturing guidance are realized, and the low-fuel consumption performance of the guidance process is synchronously improved.
The beneficial effects are that:
1. the invention discloses a self-adaptive adjustment method for a pneumatic capture guidance parameter boundary, which is characterized in that a strategy of self-adaptive adjustment of an upper boundary along with constraint and performance indexes of control parameters is designed, a parameter boundary self-adaptive adjustment law is established, and the self-adaptive adjustment method for the pneumatic capture guidance parameter boundary established on the basis is used for self-adaptively adjusting the control parameter boundary, so that the optimal pneumatic capture guidance is prevented from being dependent on manually setting boundary parameters, the self-adaptive and algorithm migration performance is remarkably achieved, and the low fuel consumption performance of the guidance process is synchronously improved.
2. According to the self-adaptive adjustment method for the pneumatic capture guidance parameter boundary, disclosed by the invention, the solvable judgment of the guidance loop is added into the judgment condition of the self-adaptive adjustment of the parameter boundary, the potential risk that the guidance is failed due to the artificial given parameter boundary is overcome through the self-adaptive adjustment law of the parameter boundary, and the feasibility of each guidance loop is ensured through the adjustment of the self-adaptive parameter boundary, so that the robustness is strong and the advantage is obvious.
3. The invention discloses a self-adaptive adjustment method for the boundary of the pneumatic capturing guidance parameters, which is characterized in that the parameter boundary adjustment in the guidance design is only aimed at the boundary of a tilting angle, so that the parameter boundary adjustment is not influenced by the parameters of a target planetary system, the target orbit and the parameters of an aircraft for pneumatic capturing, the pneumatic capturing environment is not strictly limited and restrained, and the atmospheric entering state and the parameters of the aircraft are arbitrarily given, so that the application range of the pneumatic capturing guidance is wide.
Drawings
FIG. 1 is a schematic representation of the single and double pulse pneumatic capture modes of step 1 of the present invention;
FIG. 2 is a schematic view of the structure of the aerodynamic capture maneuver of the optimal roll angle in step 2 of the present invention;
FIG. 3 is a flow chart of the guidance parameter boundary adaptive adjustment algorithm applied to segment P1 in step 4 of the present invention.
FIG. 4 is a flow chart of a method of adaptive adjustment of aerodynamic capture guidance parameter boundaries in accordance with the present invention;
FIG. 5 is a simulated section of roll angle obtained by comparison with different guidance algorithms in this embodiment;
fig. 6 is a graph showing the dispersion of aerodynamic performance indicators of aerodynamic capture under different guidance algorithms based on monte carlo targeting in this embodiment, wherein fig. 6 a) is a graph showing the dispersion of aerodynamic performance indicators of aerodynamic capture of a single pulse, and fig. 6 b) is a graph showing the dispersion of aerodynamic performance indicators of aerodynamic capture of a double pulse.
Detailed Description
For a better illustration of the objects and advantages of the present invention, a detailed explanation of the invention is provided below by simulation and comparative analysis of the pneumatic capture guidance problem.
Example 1:
as shown in fig. 4, the adaptive adjustment method for the boundary of the pneumatic capturing guidance parameter disclosed in this embodiment specifically includes the following implementation steps:
step one: on the premise of giving a pneumatic capturing maneuver mode, establishing a pneumatic capturing maneuver optimal control problem model.
Step 1.1: and giving out the pneumatic capturing maneuver mode and meeting the terminal constraint and performance index of the corresponding pneumatic capturing maneuver mode. The pneumatic capturing maneuver mode is a single pulse pneumatic capturing maneuver mode or a double pulse pneumatic capturing maneuver mode.
In the pneumatic capturing process, the aircraft needs to apply a speed pulse at an arch point after flying through an atmosphere outside kepler orbit, so that the whole pneumatic capturing process can be completed. The pulse applied at the post-atmospheric camber is an in-orbit maneuver. The pulse maneuver required for pneumatic capture corresponds to a single pulse pneumatic capture maneuver mode or a double pulse pneumatic capture maneuver mode.
The single pulse pneumatic capturing maneuvering mode is that the instantaneous orbit telecentric point after the aircraft is out of the atmosphere is overlapped with one arch point of the target orbit, and at the moment, pulse maneuvering delta V applied to the telecentric point is only needed once in the whole process, so that the orbit near-center point after maneuvering is identical with the near-center point of the target orbit.
Double pulse pneumatic capturing maneuver modeThe instantaneous orbit telecentric point after the aircraft is out of the atmosphere and the two arch points of the target orbit are not coincident, and at the moment, the aircraft is required to apply a first maneuver DeltaV at the telecentric point of the orbit after the aircraft is out of the atmosphere 1 So that the near-center point of the orbit coincides with the near-center point of the target orbit after the first maneuver, and then applying a second maneuver DeltaV when the aircraft is traveling to the near-center point 2 The purpose of this maneuver is to bring the aircraft into the target orbit.
For single pulse pneumatic capture, the vector diameter of the position of the telecentric point of the elliptical orbit of the aircraft out of the atmosphere after pneumatic capture is required to be equal to the vector diameter of the position of the telecentric point of the target orbit, namely
r a ＝r T,a (1)
Wherein r is a Is the vector diameter of the telecentric point position of the track after pneumatic capturing, and r T,a The vector diameter of the telecentric point of the target track. For single pulse pneumatic capture, the speed pulse is the size of the in-orbit pulse DeltaV, and a calculation formula can be directly deduced according to the Kepler orbit energy, namely
Wherein μ is a constant of planetary attraction, a T For the target orbit semi-major axis, a is the semi-major axis of the orbit after pneumatic capture.
For double pulse pneumatic capture, strict out-of-air-track telecentric point position constraints are not required, and there is no terminal equation constraint as in equation (1). The calculation formula of the total speed increment of the two pulse pneumatic capturing is deduced according to the Kepler orbit energy formula, and is
Wherein r is T,p The vector diameter is the position vector diameter of the near-center point of the target track.
A schematic of the single and double pulse pneumatic capture modes is shown in fig. 1. The formula (1) is the terminal constraint of single-pulse pneumatic capturing, and the formulas (2) and (3) are the performance indexes of single-pulse pneumatic capturing maneuver and double-pulse pneumatic capturing maneuver respectively.
Step 1.2: and establishing an optimal control problem model for pneumatic capturing maneuver, and taking the optimal control problem as an open loop process of single guidance.
The aerodynamic capture optimal control problem model is a model foundation for constructing a guidance loop, and comprises dynamics, terminal constraint and performance indexes.
The aerodynamic capture dynamics model is a polar coordinate system model, and the corresponding state variables are position vector diameter r, speed V, longitude theta, latitude phi, track angle gamma and course angle phi respectively. The only control parameter in the dynamic model is the roll angle σ, which will also be the control parameter to be designed in the guidance link.
The terminal constraint of the pneumatic capturing maneuver exists only in the single-pulse pneumatic capturing mode, the expression of the terminal constraint is shown in the formula (1), and the terminal constraint is also a basic equation for constructing a single-pulse pneumatic capturing closed-loop guidance equation.
The performance index of pneumatic capturing is the pulse maneuver size no matter the single pulse pneumatic capturing maneuver or the double pulse pneumatic capturing maneuver. The single pulse pneumatic capture guidance equation is considered to be constructed through the terminal constraint equation, so that the performance index cannot appear in the design of a guidance loop. However, for the double-pulse pneumatic capturing process, because there is no terminal constraint, a single-target unconstrained optimization problem of the guidance loop needs to be built based on the performance index (3), namely, an optimal control problem model of pneumatic capturing maneuver is built, and the optimal control problem is used as an open loop process of single guidance.
Step two: and through maximum principle analysis, the tilting angle section structure corresponding to the optimal aerodynamic capture maneuver is provided, and a control parameter section is provided for the guidance loop, so that the optimality of guidance is ensured.
Considering that the performance index contains only non-integral terms composed of terminal state quantities, namely the performance index belongs to the Mayer type, the performance index-related terms are not contained in the Hamilton equation of longitudinal dynamics. I.e. Hamilton equation h=λ T x L Given here the longitudinal directionState variable of orientation dynamics is x L ＝[r,V,γ] T Furthermore, λ= [ λ ] r ,λ V ,λ γ ] T Is the corresponding collaborative state vector of longitudinal dynamics variable. Based on the principle of maximum value, the tilting angle sigma corresponding to the optimal pneumatic capturing maneuver is known as
From equation (4), it can be seen that the cosine of the control variable roll angle σ takes a linear form in the Hamilton equation. Considering that the range constraint of the roll angle sigma is (0 DEG, 180 DEG) during atmospheric flight, so sigma and cos sigma exhibit a monotonic relationship, the optimal roll angle sigma * Has a bang-bang control structure, i.e. in [ sigma ] min ,σ max ]A jump will occur between them, wherein the jump time t s Is an important parameter in the design process of the guidance loop. A schematic diagram of the optimal cross-sectional structure of the roll angle is shown in fig. 2.
Step three: based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, the universality and the robustness of the optimal pneumatic capture guidance are realized by establishing a self-adaptive adjustment method of the pneumatic capture guidance parameter boundary, and the low fuel consumption performance of the guidance process is synchronously improved.
Based on the bang-bang configuration of optimal roll angle, the aircraft first flies at the minimum roll angle during the aerodynamic capture maneuver, this segment is referred to herein as segment P1. Then at jump time t s The point is switched to the maximum roll angle flight, which is called the P2 segment. Although the roll angle corresponding to segment P1 is a constant value sigma min But is the most critical stage for the whole guidance link, in this stage, the roll angle boundary value of the P2 section is only involved in the solution process of a single guidance open loop, and the boundary value of the P2 section is the key that affects the guidance robustness and performance at present. When the aircraft enters the P2 section, the guidance process only considers the value of the roll angle and does not relate to the boundary, so that the robustness and the mobility of guidance are not affected as in the existing guidance logic.
To meet the objectThe robustness and the optimality of a guidance algorithm are improved under the constraint of the track inclination angle, and a self-adaptive upper boundary adjustment link of the inclination angle is additionally added in the manufacturing of the guide ring joint P1. That is, at the beginning, the upper boundary sigma of the roll angle is selected max Then gradually changing sigma in each subsequent guidance link max The change amount is delta sigma, and the changed criterion is whether the current guidance link is successful or not and meets the constraint requirement. The upper boundary of the tilting angle input by the current guidance link is sigma u The next guidance link actually uses sigma max Is that
The guidance failure corresponding to the parameter boundary self-adaptive regulation law (5) is different from the characteristic reflected by the two pneumatic capturing modes. For the single pulse mode, it corresponds to t s And (3) the guidance process at the current moment is continued after the boundary adjustment at the tilting angle without solution. Whereas the double pulse mode corresponds to the total velocity pulse DeltaV 12 Compared with the previous guidance link, the abrupt increase condition occurs. The flow of the guidance parameter boundary adaptive adjustment algorithm applied to the P1 segment is shown in fig. 3.
The adaptive calculation formula of the corresponding control parameter roll angle is formula (5) for adaptively adjusting the guidance parameters, and in each guidance loop process, the value of the maximum boundary of the roll angle is calculated according to formula (5), so that the problem of guidance failure corresponding to formula (5) is solved, the universality and the robustness of optimal pneumatic capturing guidance are realized, and the low-fuel consumption performance of the guidance process is synchronously improved.
Based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, a self-adaptive adjustment method of the pneumatic capturing guidance parameter boundary is established, so that universality and robustness of optimal pneumatic capturing guidance are realized, and low fuel consumption performance of the guidance process is synchronously improved.
Step four: and (3) constructing a single-pulse or double-pulse pneumatic capture optimal closed-loop guidance method based on the control parameter boundary adaptively regulated by the self-adaptive regulation method of the pneumatic capture guidance parameter boundary established in the step (III), and improving the self-adaptability and the performance of pneumatic capture guidance by the optimal closed-loop guidance method.
According to the tilting angle profile structure provided in the second step, the only variable parameter in the pneumatic capturing process is jump time t s . Therefore, the single-pulse or double-pulse pneumatic capturing optimal closed loop guidance method uses the jumping time t s As a single variable of the guided closed loop design. Taking the difference of two pneumatic capturing modes into consideration simultaneously, acquiring the jumping moment t in the optimal closed loop guidance process s And in a different manner. For monopulse pneumatic capture, each guidance link solves a univariate nonlinear equation (1) based on the Brent method to obtain t s The method comprises the steps of carrying out a first treatment on the surface of the For double pulse pneumatic capture, each guidance link is based on the Golden Section method by applying the performance index DeltaV of the formula (3) 12 Optimizing to obtain t s 。
The optimal closed loop guidance method is described as: first, guidance begins as the aircraft enters the atmosphere. In each guidance circuit, when the aircraft is in the P1 stage, the terminal constraint (1) and the optimized performance index (3) are calculated for the single pulse pneumatic capture and the double pulse pneumatic capture respectively to obtain t s Meanwhile, in the P1 section flight process, in the single guidance loop calculation, the self-adaptive adjustment strategy of the upper boundary of the control parameter is applied by adopting a calculation formula given by the formula (5) in the third step, so that the autonomous parameter boundary adjustment is realized. After the aircraft enters the P2 section, a single variable of each guidance loop design becomes a constant roll angle sigma until the aircraft flies out of the atmosphere, and the aerodynamic capture maneuver process is completed.
Based on the optimal closed loop guidance method, different initial entrance angle states are selected to represent different atmosphere entrance conditions, and the dispersion of performance indexes of the pneumatic capture guidance algorithm in different states is obtained through Monte Carlo targeting random errors, so that the robustness and the performance of the adaptive adjustment method of the pneumatic capture guidance parameter boundary are analyzed.
To verify the feasibility of the method, take the example of a monthly return to the pneumatic capture task, take the gravitational constant μ= 398600km 3 /s 2 . Furthermore, the aircraft mass is 10387kg, nominal reference area of the aircraft of 19.86m 2 . The pneumatic capturing target track is a round track which is 200km near the ground, and the target track inclination angle i T Take 90 °. In addition, the lower boundary of the tilting angle amplitude is sigma min =15°, upper boundary of roll angle amplitude σ max =165°, in the guidance link, the roll angle change Δσ takes 5 °.
Furthermore, the state given the atmospheric entry point is: initial position r 0 =121.9 km, initial longitude θ 0 = 242.75deg, initial latitude φ 0 -46.67deg, initial velocity V 0 = 11.055km/s, initial heading angle ψ 0 -1.6979deg, initial track angle γ 0 Take-5.91 deg. In addition, in the process of preparation, the deviation meets the standard normal distribution, and the 3 sigma value is 25% of the nominal value.
In order to compare and analyze the advantages of the parameter boundary self-adaptive adjustment algorithm provided by the patent applied to the guidance process, the guidance methods of self-adaptive control parameter boundary adjustment and fixed parameter boundary are distinguished by names, namely, a single-pulse pneumatic capturing guidance of parameter boundary self-adaptive adjustment is taken as a mode A1, and a double-pulse pneumatic capturing guidance of parameter boundary self-adaptive adjustment is taken as a mode A2; the single pulse aerodynamic capture guidance of the fixed parameter boundary is mode B1 and the double pulse aerodynamic capture guidance of the fixed parameter boundary is mode B2.
Fig. 5 shows a roll angle (control amount) profile of the guidance process in the four modes, and it can be seen from the figure that the parameter boundary adaptive adjustment algorithm provided by the present patent makes the corresponding atmospheric flight time of the guidance algorithm (i.e. modes A1 and A2) longer, and the upper boundary of the roll angle is larger. And simultaneously, the boundary value of the roll angle always fluctuates in a small range in order to restrain the performance loss possibly caused by random errors.
Table 1 comparison of effects of aerodynamic capture guidance in four modes
The statistics results of total track-in speed pulses and tilting angle jump time corresponding to four modes are shown in table 1, and it can be seen from the table that the parameter boundary self-adaptive adjustment algorithm provided by the present invention makes the required speed pulse consumption in the guidance process obviously smaller than the pulse consumption corresponding to the guidance algorithm under the fixed parameter boundary, and the saved speed pulse quantity is about 30%.
In order to analyze the advantages of the parameter boundary self-adaptive adjustment method under different entrance angle conditions, the velocity pulse distribution corresponding to the four modes under the different entrance angle conditions is given through Monte Carlo simulation. The number of monte carlo simulations was n=3000, during which a 3 sigma random error of 25% was applied, respectively. The lateral control of the guidance process is the same as above. Fig. 6 (a) and 6 (b) show velocity pulse dispersion diagrams corresponding to single pulse pneumatic capturing and double pulse pneumatic capturing, respectively.
As can be seen from FIG. 6, compared with the fixed parameter boundary, the parameter boundary self-adaptive adjustment method provided by the patent has obvious improvement in the aspect of speed pulse consumption no matter for single pulse pneumatic capture or double pulse pneumatic capture, and can save about 30m/s at maximum. The advantages of the pneumatic capture guidance algorithm in improving the performance of the pneumatic capture guidance algorithm are obviously verified.
While the foregoing has been provided for the purpose of illustrating the general principles of the invention, it will be understood that the foregoing disclosure is only illustrative of the principles of the invention and is not intended to limit the scope of the invention, but is to be construed as limited to the specific principles of the invention.
Claims (3)
1. An adaptive adjustment method for pneumatically capturing guidance parameter boundaries is characterized by comprising the following steps: comprises the following steps of the method,
step one: on the premise of giving a pneumatic capturing maneuver mode, establishing a pneumatic capturing maneuver optimal control problem model;
the first implementation method of the step is that,
step 1.1: giving out a pneumatic capturing maneuver mode and meeting terminal constraint and performance indexes of the corresponding pneumatic capturing maneuver mode; the pneumatic capturing maneuver mode is a single-pulse pneumatic capturing maneuver mode or a double-pulse pneumatic capturing maneuver mode;
in the pneumatic capturing process, the aircraft needs to apply a speed pulse at an arch point after flying through an atmosphere outside kepler orbit, so that the whole pneumatic capturing process can be completed; the pulse applied by the arch point after the air is discharged is a rail-entering maneuver; the pulse maneuver required by the pneumatic capture corresponds to a single pulse pneumatic capture maneuver mode or a double pulse pneumatic capture maneuver mode;
the single pulse pneumatic capturing maneuvering mode is that an instantaneous orbit telecentric point of an aircraft after the aircraft is out of the atmosphere is overlapped with an arch point of a target orbit, and at the moment, pulse maneuvering delta V applied to the telecentric point is only needed once in the whole process, so that the heights of a orbit near-center point after maneuvering and a target orbit are the same;
the double pulse pneumatic capturing maneuvering mode is that the instantaneous orbit telecentric point after the aircraft is out of the atmosphere and the two arch points of the target orbit are not coincident, and at the moment, the aircraft is required to apply a first maneuvering DeltaV at the telecentric point of the orbit after the aircraft is out of the atmosphere 1 So that the near-center point of the orbit coincides with the near-center point of the target orbit after the first maneuver, and then applying a second maneuver DeltaV when the aircraft is traveling to the near-center point 2 The aim of this maneuver is to bring the aircraft into the target orbit;
for single pulse pneumatic capture, the vector diameter of the position of the telecentric point of the elliptical orbit of the aircraft out of the atmosphere after pneumatic capture is required to be equal to the vector diameter of the position of the telecentric point of the target orbit, namely
r a ＝r T,a (1)
Wherein r is a Is the vector diameter of the telecentric point position of the track after pneumatic capturing, and r T,a The vector diameter of the telecentric point position of the target track; for single pulse pneumatic capture, the magnitude of the speed pulse motor DeltaV applied to the telecentric point can be directly deduced into a calculation formula according to Kepler orbit energy, namely
Wherein μ is a constant of planetary attraction, a T A is the semi-long axis of the target track, a is the semi-long axis of the track after pneumatic capturing;
for double-pulse pneumatic capture, strict telecentric point position constraint of an out-of-air track is not required, and terminal equation constraint as shown in formula (1) does not exist; the calculation formula of the total speed increment of the two pulse pneumatic capturing is deduced according to the Kepler orbit energy formula, and is
Wherein r is T,p The vector diameter of the near-center point position of the target track;
the formula (1) is the terminal constraint of single-pulse pneumatic capturing, and the formulas (2) and (3) are the performance indexes of single-pulse pneumatic capturing maneuver and double-pulse pneumatic capturing maneuver respectively;
step 1.2: establishing an optimal control problem model of pneumatic capturing maneuver, and taking the optimal control problem as an open loop process of single guidance;
the aerodynamic capture optimal control problem model is a model foundation for constructing a guidance loop, and comprises dynamics, terminal constraint and performance indexes;
the aerodynamic capture dynamics model is a polar coordinate system model, and the corresponding state variables are position vector diameter r, speed V, longitude theta, latitude phi, track angle gamma and course angle psi respectively; in addition, the only control parameter in the dynamic model is the roll angle sigma, and the parameter is also used as the control parameter to be designed in the guidance link;
the terminal constraint of the pneumatic capturing maneuver exists only in a single-pulse pneumatic capturing mode, the expression of the terminal constraint is shown in a formula (1), and the terminal constraint is also a basic equation constructed by a single-pulse pneumatic capturing closed-loop guidance equation;
the performance index of pneumatic capturing is the pulse maneuver size no matter the single pulse pneumatic capturing maneuver or the double pulse pneumatic capturing maneuver; the single-pulse pneumatic capture guidance equation is considered to be constructed through a terminal constraint equation, so that performance indexes cannot appear in the design of a guidance loop; however, for the double-pulse pneumatic capturing process, because no terminal constraint exists, a single-target unconstrained optimization problem of a guidance loop needs to be established based on the performance index (3), namely, an optimal control problem model of pneumatic capturing maneuver is established, and the optimal control problem is used as an open loop process of single guidance;
step two: the optimal tilting angle section structure corresponding to the optimal pneumatic capturing maneuver is provided through maximum principle analysis, and a control parameter section is provided for a guidance loop, so that the optimality of guidance is ensured;
the implementation method of the second step is that,
considering that the performance index only comprises non-integral terms composed of terminal state quantity, namely the performance index belongs to the Mayer type, the Hamilton equation of the longitudinal dynamics does not comprise terms related to the performance index; i.e. Hamilton equation h=λ T x L Where the state variable given longitudinal dynamics is x L ＝[r,V,γ] T Furthermore, λ= [ λ ] r ,λ V ,λ γ ] T A collaborative state vector corresponding to the longitudinal dynamics variable; based on the principle of maximum value, the tilting angle sigma corresponding to the optimal pneumatic capturing maneuver is known as
As can be seen from equation (4), the cosine of the control variable roll angle σ takes a linear form in the Hamilton equation; considering that the range constraint of the roll angle sigma is (0 DEG, 180 DEG) during atmospheric flight, so sigma and cos sigma exhibit a monotonic relationship, the optimal roll angle sigma * Has a bang-bang control structure, i.e. in [ sigma ] min ,σ max ]A jump will occur between them, wherein the jump time t s Important parameters in the design process of the guidance loop;
step three: based on the strategy that the tilting angle boundary is gradually changed along with the guidance process, the universality and the robustness of the optimal pneumatic capture guidance are realized by establishing a self-adaptive adjustment method of the pneumatic capture guidance parameter boundary, and the low fuel consumption performance of the guidance process is synchronously improved.
2. An adaptive adjustment method for aerodynamic capture guidance parameter boundaries as defined in claim 1, wherein: based on the bang-bang configuration of the optimal roll angle, the aircraft first flies at the minimum roll angle during the aerodynamic capture maneuver, this segment is referred to herein as the P1 segment; then at jump time t s The position is switched to the maximum roll angle flight, and the section is called a P2 section; although the roll angle corresponding to segment P1 is a constant value sigma min But is the most critical stage for the whole guidance link, in the stage, the roll angle boundary value of the P2 section is only involved in the solving process of a single guidance open loop, and the boundary value of the P2 section is the key for influencing the guidance robustness and performance at present; when the aircraft enters the P2 section, the guidance process only considers the value of the roll angle and does not relate to the boundary, so that the robustness and the mobility of guidance are not affected as in the existing guidance logic.
3. A method of adaptive adjustment of aerodynamic capture guidance parameter boundaries as defined in claim 2, wherein: the specific implementation method of the third step is that,
in order to improve the robustness and the optimality of a guidance algorithm under the condition of meeting the constraint of a target track inclination angle, an adaptive inclination angle upper boundary adjustment link is additionally added in the guidance ring section P1; that is, at the beginning, the upper boundary sigma of the roll angle is selected max Then gradually changing sigma in each subsequent guidance link max The change amount is delta sigma, and the changed criterion is whether the current guidance link is successful or not and meets the constraint requirement; the upper boundary of the tilting angle input by the current guidance link is sigma u The next guidance link actually uses sigma max Is that
Wherein, the ginseng isThe guidance failure corresponding to the number boundary self-adaptive regulation law (5) is different for the characteristics reflected by the two pneumatic capturing modes; for the single pulse mode, it corresponds to t s The guidance process at the current moment is continuously implemented after the boundary adjustment of the upper side angle without solution; whereas the double pulse mode corresponds to the total velocity pulse DeltaV 12 Compared with the previous guidance link, the abrupt increase condition occurs;
the adaptive calculation formula of the corresponding control parameter roll angle is formula (5) for adaptively adjusting the guidance parameters, and in each guidance loop process, the value of the maximum boundary of the roll angle is calculated according to formula (5), so that the problem of guidance failure corresponding to formula (5) is solved, the universality and the robustness of optimal pneumatic capturing guidance are realized, and the low-fuel consumption performance of the guidance process is synchronously improved.
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