CN114611209A - Aircraft centroid balance oil supply strategy analysis method based on backtracking algorithm - Google Patents

Aircraft centroid balance oil supply strategy analysis method based on backtracking algorithm Download PDF

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CN114611209A
CN114611209A CN202210222558.9A CN202210222558A CN114611209A CN 114611209 A CN114611209 A CN 114611209A CN 202210222558 A CN202210222558 A CN 202210222558A CN 114611209 A CN114611209 A CN 114611209A
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王孟
黄欣
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Nantong University
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Abstract

The invention provides an aircraft mass center balance oil supply strategy analysis method based on a backtracking algorithm, belongs to the technical field of space flight, and solves the problem that the aircraft is not controlled by considering mass center balance in the flight process. The technical scheme is as follows: comprises the following steps: s1: designing an aircraft system centroid positioning model; s2: on the basis of an aircraft system centroid positioning model, the influence of different oil supply strategies on the aircraft centroid balance is researched by utilizing the backtracking algorithm principle analysis. The invention has the beneficial effects that: the analysis method for the aircraft mass center balance oil supply strategy can automatically adjust the oil supply strategy according to the type and the flight state of the oil supply oil tank, so that the aircraft keeps mass center balance in the flight process, and further, the stable flight of the aircraft can be effectively ensured, and the aircraft flies along a set flight line.

Description

Aircraft centroid balance oil supply strategy analysis method based on backtracking algorithm
Technical Field
The invention relates to the technical field of space flight, in particular to an aircraft mass center balance oil supply strategy analysis method based on a backtracking algorithm.
Background
The oil-driven unmanned aerial vehicle is provided with a plurality of oil tanks, and in the flight process, the oil tanks jointly supply oil to meet the flight task requirement and the engine working requirement. The fuel oil system plays an important role in an aircraft system, the main function of the fuel oil system is to store fuel oil and supply the fuel oil to an engine, however, the aircraft has a great defect in the process of executing a flight task, the fuel oil of each oil tank changes the position of the center of mass in the flight process, and the aircraft is difficult to keep the center of mass balance, so that the aircraft cannot normally fly or stably land, and is easy to crash, serious trauma is brought to the aircraft, and harm is also generated to people and objects on the ground, so that how to strengthen the control on the aircraft is realized, and the condition that the aircraft normally flies or stably lands along a set air route is the direction of research.
With the rapid development of science and technology and the wide application of unmanned aircrafts, the requirements on the aircrafts are higher and higher. An important task for controlling the aircraft is to make oil supply strategies for the oil tanks, which requires consideration of various factors related to the flight of the aircraft and planning of an optimal oil supply strategy through appropriate algorithms and models. Therefore, there is a need to develop and improve existing aircraft fueling strategy analysis methods.
Disclosure of Invention
The invention aims to solve the problem that the influence of oil supply of an oil tank on the mass center of an aircraft system in the flying process of the aircraft is not considered in the prior art, and provides an aircraft mass center balance oil supply strategy analysis method based on a backtracking algorithm.
The invention is realized by the following measures: an aircraft center of mass balance oil supply strategy analysis method based on a backtracking algorithm comprises the following steps:
s1: constructing a mass center positioning equation set of residual fuel oil in the fuel supply oil tank by using the oil supply speed of the oil tank and the pitching angle of the aircraft, and designing an aircraft system mass center positioning model which reflects the mass center position of the fuel supply oil tank of the aircraft through the geometric shape and the flight state of the fuel oil section of the oil tank;
s2: on the basis of an aircraft system centroid positioning model, the influence of different oil supply strategies on the aircraft centroid balance is researched by utilizing the backtracking algorithm principle analysis.
The step S1 includes the following specific steps:
step 1.1: calculating the real-time oil mass of an oil supply tank of the aircraft:
Figure BDA0003538044910000011
Figure BDA0003538044910000012
Figure BDA0003538044910000021
i＝1，3，4，6；
wherein No. 1 and No. 6 spare oil tanks are used for supplying oil to No. 2 and No. 5 main oil tanks respectively, and Vi(0) Is the original fuel volume, V, of tank ii(t) is the real-time fuel quantity of fuel tank i, vi(t) is the oil supply speed of the oil tank i, rho is the fuel density, and delta t is unit time;
step 1.2: calculating the real-time area A of the fuel section in the tanki(t)：
Figure BDA0003538044910000022
Wherein b isiThe width of the inner part of the oil tank i;
step 1.3: comparing the size relation between the real-time fuel section area and the critical area and the degree of a pitch angle theta, and judging the geometric shape of the real-time fuel section:
when theta is 0, the geometrical shape of the fuel section in the critical section of the fuel tank is rectangular;
when 0 < Ai(t)＜v1When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right-angled triangle;
when v is1＜Ai(t)＜v2When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right trapezoid;
when v is2＜Ai(t)＜v3The geometric shape of the fuel oil section in the critical section of the fuel tank is a pentagon, and three corners in the pentagon are right angles;
wherein v is1、v2、v3Respectively, the critical cross-sectional area of the tank when tilted at an angle (as shown in fig. 7-9).
Step 1.4: judging the flight state of the aircraft:
when the pitch angle theta is equal to 0, the aircraft flies straight;
when the pitch angle theta is less than 0, the aircraft flies in an elevation angle;
when the pitch angle theta is larger than 0, the aircraft flies at a depression angle;
step 1.5: converting position coordinates under different coordinate systems:
Figure BDA0003538044910000023
wherein, (x'K，z′K) Is the coordinate of point K in the aircraft coordinate system, (x)K，zK) Is the coordinate of point K in the inertial frame and θ is the pitch angle of the aircraft.
Step 1.6: determining a residual fuel mass center positioning model in the fuel tank as follows:
when the cross section of the fuel oil is rectangular, the center of mass of the aircraft is the center of the quadrangular prism;
when the cross section of the fuel oil is in the shape of a right triangle, the mass center position of the aircraft is the center position of a triangular prism;
when the cross section of the fuel oil is pentagonal, the center of mass of the aircraft is the center of the pentagonal prism;
step 1.7: determining a centroid localization model for the aircraft system as:
Figure BDA0003538044910000024
wherein m isiFor the mass of fuel remaining in the fuel supply tank, M is the net mass of the aircraftI.e. the total mass of the aircraft when not carrying fuel,
Figure BDA0003538044910000031
is the centroid position of the remaining fuel in the fuel tank i,
Figure BDA0003538044910000032
is the real-time centroid position of the aircraft system.
The step S2 includes the following specific steps:
step 2.1: calculating an ideal centroid position of the aircraft system based on a centroid localization model of the aircraft system and a planned fuel consumption speed of an aircraft engine;
step 2.2: the upper limit of the oil supply speed of an oil tank of the aircraft is assumed as follows:
0＜vi≤Ui，i＝1，2，…，6；
wherein v isiFor the supply speed of the aircraft tank i, UiThe upper limit of the oil supply speed of the aircraft oil tank i is constant;
step 2.3: assuming that the aircraft is in flight, the duration of one oil supply per tank is not less than 60 seconds:
Figure BDA0003538044910000033
i＝1，2，…，6；
where T is the fuel consumption time of the engine during the flight of the aircraft, vi(t) is the supply speed of the tank i;
step 2.4: due to the structural limitation of the aircraft, at most 2 fuel tanks can supply oil to the engine at the same time, and at most 3 fuel tanks can supply oil at the same time. When any two of the oil tanks 2, 3, 4, 5 supply oil to the engine, the third oil supply oil tank can only be any one of the oil tank 1 and the oil tank 6:
Figure BDA0003538044910000034
Figure BDA0003538044910000035
step 2.5: during the process of executing the task, the total oil quantity of the combined oil supply of the oil tanks at least meets the planned oil consumption of the engine. If the oil supply quantity of the oil tank system is larger than the planned oil consumption quantity of the engine at a certain time, the redundant fuel oil is discharged out of the aircraft through other devices. If the oil supply amount of the oil tank system is smaller than the planned oil consumption amount of the engine at a certain time, the engine cannot normally operate, and the aircraft fails to execute tasks. The oil supply quantity of each oil tank of the aircraft and the planned oil consumption quantity of the engine meet the following requirements:
u2(t)+u3(t)+u4(t)+u5(t)≥u(t)；
wherein ui(t) is the amount of oil supplied to the oil tank i, and
Figure BDA0003538044910000036
u (t) is the planned fuel consumption of the aircraft engine, and
Figure BDA0003538044910000037
step 2.6: screening alternative oil tanks by using a backtracking algorithm principle:
when a certain node is searched, if no alternative oil tank exists, returning to the previous node, deleting the preferred oil tank in the alternative oil tank, and reselecting the oil tank; if the alternative oil tanks exist, adding a first oil tank in the alternative oil tanks into a pre-oil-supply oil tank, and sequencing the oil-supply oil tanks;
step 2.7: defining the variation trend of the center of mass of the residual fuel oil when the weight of each fuel tank is reduced:
in the X-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the positive direction of the X axis are No. 3, No. 5 and No. 6 oil tanks, and the oil tanks with the centers of mass moving along the negative direction of the X axis are No. 1, No. 2 and No. 4 oil tanks; in the Y-axis direction, when the mass of the oil tank is reduced, the oil tanks with the mass centers moving along the positive direction of the Y axis are No. 2, No. 5 and No. 6 oil tanks, and the oil tanks moving along the negative direction of the Y axis are No. 1, No. 3 and No. 4 oil tanks; in the Z-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the positive Z-axis direction are No. 3 and No. 4 oil tanks, and the oil tanks with the centers of mass moving along the negative Z-axis direction are No. 1, No. 2, No. 5 and No. 6 oil tanks;
step 2.8: judging whether the currently opened oil tank in the pre-oil-supply oil tank meets the change of the mass center:
if the three directions all meet the variation trend of the center of mass, the selection of the pre-supplied oil tank is unchanged;
if two pre-supplied oil tanks exist and one of the three directions does not meet the condition, adding the corresponding oil tank into the alternative oil tank according to the variation trend of the mass center when the weight of each oil tank is reduced;
if three pre-supplied oil tanks exist, abandoning the alternative oil tanks and storing the oil tanks as a feasible solution, namely a feasible oil supply strategy;
if two pre-supply oil tanks exist, and the oil tank 1 and the oil tank 6 are not selected, the oil tank 1 or the oil tank 6 can be selected as a 3 rd pre-supply oil tank in the alternative oil tank in the next step;
in other cases, the moving trend of the real-time mass center close to the ideal mass center on the X, Y, Z axis is judged according to the positions of the real-time mass center and the ideal mass center, and the pre-fuel oil tank is selected from the alternative oil tanks according to the moving direction;
step 2.9: judging whether the real-time oil quantity of the oil tank meets the volume upper limit and the volume lower limit or not:
0.02≤Vi(t)≤aibici；
wherein Vi(t) volume of remaining fuel in tank i, aiIs the length of the inside of the fuel tank i, biWidth of the interior of the tank i, ciIs the height inside the tank i. The lower limit of the volume of the fuel in the fuel tank of the aircraft is 0.02m3After a certain fuel tank starts to supply fuel, the volume of the residual fuel in the fuel tank is less than 0.02m3The oil supply is finished;
step 2.10: and (3) judging the error of the Euclidean distance between the real-time mass center position and the ideal mass center position of the aircraft system:
Figure BDA0003538044910000041
wherein
Figure BDA0003538044910000042
Is the real-time centroid position of the aircraft system,
Figure BDA0003538044910000043
to be an ideal centroid location based on the projected fueling rate of the aircraft,
Figure BDA0003538044910000044
is the Euclidean distance between the real-time centroid position and the ideal centroid position. If the error is larger than the minimum optimization error, the pre-supplied oil tank is reselected, otherwise, the pre-supplied oil tank is not selected, and the oil supply strategy is saved.
Compared with the prior art, the invention has the beneficial effects that: according to the aircraft mass center balance oil supply strategy analysis method based on the backtracking algorithm, the influence of oil supply of an oil tank on the mass center of an aircraft system in the flight process of the aircraft is considered, so that the flight process of the aircraft is more consistent with the actual navigation condition, the pre-oil supply oil tank is screened by applying the backtracking algorithm, the oil supply strategy with the minimum error between the determined real-time mass center and the ideal mass center position plays an obvious promoting role in the stable flight of the aircraft, the aircraft can fly according to a set route, the risk of crash can be reduced, the accurate positioning of the mass center of the aircraft system and the accurate control of the aircraft can be completed on the basis of the existing resources of the aircraft.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is an overall flow chart of an aircraft centroid balancing oil supply strategy analysis method based on a backtracking algorithm according to the present invention;
FIG. 2 is a schematic diagram of oil supply to an aircraft oil tank according to an analysis method of an aircraft centroid balancing oil supply strategy based on a backtracking algorithm;
FIG. 3 is a schematic diagram of the change of the attitude of an oil tank of the aircraft centroid balance oil supply strategy analysis method based on the backtracking algorithm;
FIG. 4 is a schematic diagram of a rectangular fuel oil cross section in straight flight of the aircraft based on the aircraft centroid balance fuel supply strategy analysis method of the backtracking algorithm;
FIG. 5 is a schematic diagram of three shapes of fuel sections of an aircraft in elevation flight according to the aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm;
FIG. 6 is a schematic diagram of three shapes of fuel sections of an aircraft during a depression angle flight according to an aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm;
FIG. 7 shows a fuel critical area v of a fuel tank of an aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm1A schematic diagram;
FIG. 8 shows a critical area v of fuel in a fuel tank of an aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm2A schematic view;
FIG. 9 shows a fuel critical area v of a fuel tank of an aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm3A schematic view;
FIG. 10 is a schematic diagram of the transformation between the aircraft coordinate system and the inertial coordinate system of the aircraft centroid balance oil supply strategy analysis method based on the backtracking algorithm according to the present invention;
FIG. 11 is a schematic diagram of a rectangular fuel section in the straight flight of an aircraft based on the aircraft centroid balance fuel supply strategy analysis method of the backtracking algorithm of the present invention;
FIG. 12 is a schematic diagram of a fuel oil cross section in a right triangle shape during the aircraft elevation flight according to the aircraft centroid balance fuel supply strategy analysis method based on the backtracking algorithm;
FIG. 13 is a schematic diagram of a fuel oil cross section in a right triangle shape during aircraft nose-down angle flight according to the aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm provided by the invention;
FIG. 14 is a schematic diagram of a fuel cross section of a right trapezoid in the aircraft elevation flight according to the aircraft centroid balance fuel supply strategy analysis method based on the backtracking algorithm;
FIG. 15 is a schematic diagram of a fuel cross section in a right trapezoid shape during aircraft nose-down angle flight according to the aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm;
FIG. 16 is a schematic diagram of a pentagon fuel cross section in the aircraft elevation flight according to the aircraft centroid balance fuel supply strategy analysis method based on the backtracking algorithm provided by the invention;
FIG. 17 is a schematic diagram of a pentagon fuel cross section during aircraft depression angle flight according to the aircraft centroid balance fuel supply strategy analysis method based on a backtracking algorithm provided by the invention;
FIG. 18 is a pitch angle of an aircraft centroid balance oil supply strategy analysis method based on a backtracking algorithm provided by the invention
Figure BDA0003538044910000061
A cross-sectional view of the fuel system;
FIG. 19 is a pitch angle of an aircraft centroid balance oil supply strategy analysis method based on a backtracking algorithm according to the present invention
Figure BDA0003538044910000062
A cross-sectional view of the fuel system;
FIG. 20 is a graph of the coordinate change of the center of mass position of an aircraft system of an aircraft center of mass balanced fueling strategy analysis method based on a backtracking algorithm in accordance with the present invention;
FIG. 21 is a graph of the change of the centroid position of an aircraft system of an aircraft centroid balancing oil supply strategy analysis method based on a backtracking algorithm in accordance with the present invention;
FIG. 22 is a graph showing the oil supply speed of 6 oil tanks during the straight flight of the aircraft according to the method for analyzing the aircraft centroid balanced oil supply strategy based on the backtracking algorithm;
FIG. 23 is a graph comparing actual fuel supply speed of an oil tank and planned fuel consumption speed of an engine during straight flight of an aircraft according to the aircraft center-of-mass balance fuel supply strategy analysis method based on a backtracking algorithm;
fig. 24 is a comparison graph of the coordinates of the real-time centroid and the ideal centroid position when the aircraft flies straight according to the aircraft centroid balance oil supply strategy analysis method based on the backtracking algorithm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Example 1
Referring to fig. 1 to 24, the technical scheme provided by the invention is that an aircraft centroid balance oil supply strategy analysis method based on a backtracking algorithm firstly calculates the real-time oil quantity of an aircraft oil supply tank:
Figure BDA0003538044910000063
Figure BDA0003538044910000064
Figure BDA0003538044910000065
i＝1，3，4，6；
wherein No. 1 and No. 6 spare oil tanks are used for supplying oil to No. 2 and No. 5 main oil tanks respectively, and Vi(0) Is the original fuel volume, V, of tank ii(t) is the real-time fuel quantity of fuel tank i, vi(t) is the oil supply speed of the oil tank i, rho is the fuel oil density, and delta t is unit time;
calculating the real-time area A of the fuel section in the tanki(t)：
Figure BDA0003538044910000071
Wherein b isiThe width of the inner part of the oil tank i;
comparing the size relation between the real-time fuel section area and the critical area and the degree of a pitch angle theta, and judging the geometric shape of the real-time fuel section:
when theta is 0, the geometrical shape of the fuel section in the critical section of the fuel tank is rectangular;
when 0 < Ai(t)＜v1When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right-angled triangle;
when v is1＜Ai(t)＜v2When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right trapezoid;
when v is2＜Ai(t)＜v3The geometric shape of the fuel oil section in the critical section of the fuel tank is a pentagon, and three corners in the pentagon are right angles;
wherein v is1、v2、v3Respectively, the critical cross-sectional area of the tank when tilted at an angle (as shown in fig. 7-9).
Judging the flight state of the aircraft:
when the pitch angle theta is equal to 0, the aircraft flies straight;
when the pitch angle theta is less than 0, the aircraft flies in an elevation angle;
when the pitch angle theta is larger than 0, the aircraft flies at a depression angle;
converting position coordinates under different coordinate systems:
Figure BDA0003538044910000072
wherein, (x'K，z′K) Is the coordinate of point K in the aircraft coordinate system, (x)K，zK) Is the coordinate of point K in the inertial frame and θ is the pitch angle of the aircraft.
The model for determining the center of mass of the residual fuel in the fuel tank is as follows:
when the cross section of the fuel oil is rectangular, the center of mass of the aircraft is the center of the quadrangular prism;
when the cross section of the fuel oil is in the shape of a right triangle, the mass center position of the aircraft is the center position of a triangular prism;
when the cross section of the fuel oil is pentagonal, the center of mass of the aircraft is the center of the pentagonal prism;
determining a centroid localization model for the aircraft system as:
Figure BDA0003538044910000073
wherein m isiM is the net mass of the aircraft, i.e. the total mass of the aircraft when not carrying fuel,
Figure BDA0003538044910000074
is the centroid position of the remaining fuel in the fuel tank i,
Figure BDA0003538044910000075
is the real-time centroid position of the aircraft system.
Calculating an ideal centroid position of the aircraft system based on a centroid localization model of the aircraft system and a planned fuel consumption speed of an aircraft engine;
the upper limit of the oil supply speed of an oil tank of the aircraft is assumed as follows:
0＜vi≤Ui，i＝1，2，…，6；
wherein v isiFor the supply speed of the aircraft tank i, UiThe upper limit of the oil supply speed of the aircraft oil tank i is a constant;
assuming that the aircraft is in flight, the duration of one oil supply per tank is not less than 60 seconds:
Figure BDA0003538044910000081
i＝1，2，…，6；
where T is the fuel consumption time of the engine during the flight of the aircraft, vi(t) is the supply speed of the oil tank i;
due to the structural limitation of the aircraft, at most 2 fuel tanks can supply oil to the engine at the same time, and at most 3 fuel tanks can supply oil at the same time. When any two of the oil tanks 2, 3, 4, 5 supply oil to the engine, the third oil supply oil tank can only be any one of the oil tank 1 and the oil tank 6:
Figure BDA0003538044910000082
Figure BDA0003538044910000083
during the process of executing the task, the total oil quantity of the combined oil supply of the oil tanks at least meets the planned oil consumption of the engine. If the oil supply quantity of the oil tank system is larger than the planned oil consumption quantity of the engine at a certain time, the redundant fuel oil is discharged out of the aircraft through other devices. If the oil supply amount of the oil tank system is smaller than the planned oil consumption amount of the engine at a certain time, the engine cannot normally operate, and the aircraft fails to execute tasks. The oil supply quantity of each oil tank of the aircraft and the planned oil consumption quantity of the engine meet the following requirements:
u2(t)+u3(t)+u4(t)+u5(t)≥u(t)；
wherein u isi(t) is the amount of oil supplied to the oil tank i, and
Figure BDA0003538044910000084
u (t) is the planned fuel consumption of the aircraft engine, and
Figure BDA0003538044910000085
screening alternative oil tanks by using a backtracking algorithm principle:
when a certain node is searched, if no alternative oil tank exists, returning to the previous node, deleting the preferred oil tank in the alternative oil tank, and reselecting the oil tank; if the alternative oil tanks exist, adding a first oil tank in the alternative oil tanks into a pre-oil-supply oil tank, and sequencing the oil-supply oil tanks;
defining the variation trend of the center of mass of the residual fuel oil when the weight of each fuel tank is reduced:
in the X-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the positive direction of the X-axis are No. 3, No. 5 and No. 6 oil tanks, and the oil tanks with the centers of mass moving along the negative direction of the X-axis are No. 1, No. 2 and No. 4 oil tanks; in the Y-axis direction, when the mass of the oil tank is reduced, the oil tanks with the mass centers moving along the positive direction of the Y axis are No. 2, No. 5 and No. 6 oil tanks, and the oil tanks moving along the negative direction of the Y axis are No. 1, No. 3 and No. 4 oil tanks; in the Z-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the positive Z-axis direction are No. 3 and No. 4 oil tanks, and the oil tanks with the centers of mass moving along the negative Z-axis direction are No. 1, No. 2, No. 5 and No. 6 oil tanks;
judging whether the currently opened oil tank in the pre-oil-supply oil tank meets the change of the mass center:
if the three directions all meet the variation trend of the center of mass, the selection of the pre-supplied oil tank is unchanged;
if two pre-supplied oil tanks exist and one of the three directions does not meet the condition, adding the corresponding oil tank into the alternative oil tank according to the variation trend of the mass center when the weight of each oil tank is reduced;
if three pre-supplied oil tanks exist, abandoning the alternative oil tanks and storing the oil tanks as a feasible solution, namely a feasible oil supply strategy;
if two pre-supply oil tanks exist, and the oil tank 1 and the oil tank 6 are not selected, the oil tank 1 or the oil tank 6 can be selected as a 3 rd pre-supply oil tank in the alternative oil tank in the next step;
in other cases, the moving trend of the real-time mass center close to the ideal mass center on the X, Y, Z axis is judged according to the positions of the real-time mass center and the ideal mass center, and the pre-supplied oil tank is selected from the alternative oil tanks according to the moving direction;
judging whether the real-time oil quantity of the oil tank meets the volume upper limit and the volume lower limit:
0.02≤Vi(t)≤aibici；
wherein Vi(t) is the residue in the oil tank iVolume of fuel, aiIs the length of the inside of the fuel tank i, biWidth of the interior of the tank i, ciIs the height inside the tank i. The lower limit of the volume of the fuel in the fuel tank of the aircraft is 0.02m3After a certain fuel tank starts to supply fuel, the volume of the residual fuel in the fuel tank is less than 0.02m3The oil supply is finished;
and (3) judging the error of the Euclidean distance between the real-time mass center position and the ideal mass center position of the aircraft system:
Figure BDA0003538044910000091
wherein
Figure BDA0003538044910000092
Is the real-time centroid position of the aircraft system,
Figure BDA0003538044910000093
to be an ideal centroid location based on the projected fueling rate of the aircraft,
Figure BDA0003538044910000094
is the Euclidean distance between the real-time centroid position and the ideal centroid position. If the error is larger than the minimum optimization error, the pre-supply oil tank is reselected, otherwise, the selection of the pre-supply oil tank is unchanged, and the oil supply strategy is saved.
In order to verify the effect of the invention, MATLAB is applied to carry out numerical simulation verification.
FIG. 18 is a cross-sectional view of the fuel system of the present invention in an aircraft in elevation flight. As shown in fig. 18, pitch angle
Figure BDA0003538044910000095
In the process, the fuel level in the fuel tank is inclined, so that the center of mass is shifted.
FIG. 19 is a cross-sectional view of the fuel system of the present invention in an aircraft in elevation flight. As shown in fig. 19, pitch angle
Figure BDA0003538044910000096
And the liquid level of fuel in the fuel tank is more inclined, and the position of the mass center is more deviated.
FIG. 20 is a diagram showing the coordinate variation of the center of mass of the system during the flight of the aircraft according to the present invention.
FIG. 21 is a three-dimensional variation curve of the system centroid position during the flight of the aircraft according to the present invention.
Fig. 22 shows an oil supply strategy for minimizing the error between the real-time centroid and the ideal centroid position when the aircraft flies straight, wherein in the starting time of oil supply, the oil tanks No. 2, 1, 4, 3 and 5 start to supply oil successively, while the oil tank No. 6 does not supply oil all the time.
FIG. 23 is a graph comparing the actual fueling rate of the fuel tank and the planned fueling rate of the engine for a straight flight of an aircraft according to the present invention, as shown in FIG. 23, under the fueling strategy of FIG. 22, the actual fueling rate of the fuel tank of the aircraft is substantially equal to the planned fueling rate of the engine, fuel is wasted less, and the total amount of actual fueling meets the fuel consumption requirements of the engine and the mission requirements of the aircraft.
FIG. 24 is a comparison of coordinates of a real-time centroid and an ideal centroid position when the aircraft flies straight, and the coordinates of the real-time centroid and the ideal centroid position are completely coincident in the X-axis direction within 95-3000 s; in the Y-axis direction, the position coordinate of the real-time centroid and the position coordinate value of the ideal centroid are basically equal in the period of 95-4300 s, the difference value between the real-time centroid and the ideal centroid is large after 4300s, and the real-time centroid and the ideal centroid are basically equal in the Z-axis direction. Thus, under the fueling strategy of fig. 22, the average position error of the real-time centroid of the aircraft from the ideal centroid is 0.251886 m.
The numerical simulation result can be obtained.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. An aircraft center of mass balance oil supply strategy analysis method based on a backtracking algorithm is characterized by comprising the following steps of:
s1: constructing a mass center positioning equation set of residual fuel oil in the fuel supply oil tank by using the oil supply speed of the oil tank and the pitching angle of the aircraft, and designing an aircraft system mass center positioning model which reflects the mass center position of the fuel supply oil tank of the aircraft through the geometric shape and the flight state of the fuel oil section of the oil tank;
s2: on the basis of an aircraft system centroid positioning model, the influence of different oil supply strategies on the aircraft centroid balance is researched by utilizing the backtracking algorithm principle analysis.
2. The retrospective algorithm-based aircraft center-of-mass balanced fuel supply strategy analysis method according to claim 1, wherein the step S1 specifically comprises the following steps:
step 1.1: calculating the real-time oil mass of an oil supply tank of the aircraft:
Figure FDA0003538044900000011
Figure FDA0003538044900000012
Figure FDA0003538044900000013
wherein No. 1 and No. 6 spare oil tanks are used for supplying oil to No. 2 and No. 5 main oil tanks respectively, and Vi(0) Is the original fuel volume, V, of tank ii(t) is the real-time oil quantity of the oil tank i, vi(t) is the oil supply speed of the oil tank i, rho is the fuel density, and delta t is unit time;
step 1.2: calculating the real-time area A of the fuel section in the tanki(t)：
Figure FDA0003538044900000014
Wherein, Vi(t) real-time fuel quantity of fuel tank i, biThe width of the inner part of the oil tank i;
step 1.3: comparing the size relation between the real-time fuel section area and the critical area and the degree of a pitch angle theta, and judging the geometric shape of the real-time fuel section:
when theta is 0, the geometrical shape of the fuel section in the critical section of the fuel tank is rectangular;
when 0 < Ai(t)＜v1When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right-angled triangle;
when v is1＜Ai(t)＜v2When the fuel tank is used, the geometric shape of the fuel oil section in the critical section of the fuel tank is a right trapezoid;
when v is2＜Ai(t)＜v3The geometric shape of the fuel oil section in the critical section of the fuel tank is a pentagon, and three corners in the pentagon are right angles;
wherein v is1、v2、v3The areas of the critical sections of the oil tanks when the oil tanks incline at a certain angle are respectively;
step 1.4: judging the flight state of the aircraft:
when the pitch angle theta is equal to 0, the aircraft flies straightly;
when the pitch angle theta is less than 0, the aircraft flies in an elevation angle;
when the pitch angle theta is larger than 0, the aircraft flies at a depression angle;
step 1.5: converting position coordinates under different coordinate systems:
Figure FDA0003538044900000021
wherein, (x'K，z′K) Is the coordinate of point K in the aircraft coordinate system, (x)K，zK) The coordinate of the point K in an inertial coordinate system is shown, and theta is the pitch angle of the aircraft;
step 1.6: determining a residual fuel mass center positioning model in the fuel tank as follows:
when the cross section of the fuel oil is rectangular, the center of mass of the aircraft is the center of the quadrangular prism;
when the cross section of the fuel oil is in the shape of a right triangle, the mass center position of the aircraft is the center position of a triangular prism;
when the cross section of the fuel oil is pentagonal, the center of mass of the aircraft is the center of the pentagonal prism;
step 1.7: determining a centroid localization model for the aircraft system as:
Figure FDA0003538044900000022
wherein m isiM is the net mass of the aircraft, i.e. the total mass of the aircraft when not carrying fuel,
Figure FDA0003538044900000023
is the centroid position of the remaining fuel in the fuel tank i,
Figure FDA0003538044900000024
is the real-time centroid position of the aircraft system.
3. The retrospective algorithm-based aircraft center-of-mass balanced fuel supply strategy analysis method according to claim 1 or 2, wherein the step S2 specifically comprises the following steps:
step 2.1: calculating an ideal centroid position of the aircraft system based on a centroid localization model of the aircraft system and a planned fuel consumption speed of an aircraft engine;
step 2.2: the upper limit of the oil supply speed of an oil tank of the aircraft is assumed as follows:
0＜vi≤Ui，i＝1，2，…，6；
wherein v isiFor the supply speed of the aircraft tank i, UiThe upper limit of the oil supply speed of the aircraft oil tank i is constant;
step 2.3: assuming that the aircraft is in flight, the duration of one oil supply per tank is not less than 60 seconds:
Figure FDA0003538044900000025
where T is the fuel consumption time of the engine during the flight of the aircraft, vi(t) is the supply speed of the oil tank i;
step 2.4: due to the structural limitation of the aircraft, at most 2 oil tanks can supply oil to the engine at the same time, and at most 3 oil tanks can supply oil at the same time; when any two of the oil tanks 2, 3, 4, 5 supply oil to the engine, the third oil supply oil tank can only be any one of the oil tank 1 and the oil tank 6:
Figure FDA0003538044900000026
Figure FDA0003538044900000027
step 2.5: the aircraft is at the executive task in-process, and the total oil mass that each oil tank jointly supplied oil satisfies the plan oil consumption of engine at least, if the oil feeding of a certain moment oil tank system is greater than the plan oil consumption of engine, unnecessary fuel class passes through other devices and discharges the aircraft, if the oil feeding of a certain moment oil tank system is less than the plan oil consumption of engine, then the unable normal operating of engine and then lead to the aircraft to carry out the task failure, and the oil feeding of each oil tank of aircraft and the plan oil consumption of engine satisfy:
u2(t)+u3(t)+u4(t)+u5(t)≥u(t)；
wherein u isi(t) is the amount of oil supplied to the oil tank i, and
Figure FDA0003538044900000031
u (t) is the planned fuel consumption of the aircraft engines, and
Figure FDA0003538044900000032
step 2.6: screening alternative oil tanks by using a backtracking algorithm principle:
when a certain node is searched, if no alternative oil tank exists, returning to the previous node, deleting the preferred oil tank in the alternative oil tank, and reselecting the oil tank; if the alternative oil tanks exist, adding a first oil tank in the alternative oil tanks into a pre-oil-supply oil tank, and sequencing the oil-supply oil tanks;
step 2.7: defining the variation trend of the center of mass of the residual fuel oil when the weight of each fuel tank is reduced:
in the X-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the positive direction of the X axis are No. 3, No. 5 and No. 6 oil tanks, and the oil tanks with the centers of mass moving along the negative direction of the X axis are No. 1, No. 2 and No. 4 oil tanks; in the Y-axis direction, when the mass of the oil tank is reduced, the oil tanks with the mass centers moving along the positive direction of the Y axis are No. 2, No. 5 and No. 6 oil tanks, and the oil tanks moving along the negative direction of the Y axis are No. 1, No. 3 and No. 4 oil tanks; in the Z-axis direction, when the mass of the oil tank is reduced, the oil tanks with the centers of mass moving along the Z-axis positive direction comprise No. 3 and No. 4 oil tanks, and the oil tanks with the centers of mass moving along the Z-axis negative direction comprise No. 1, No. 2, No. 5 and No. 6 oil tanks;
step 2.8: judging whether the currently opened oil tank in the pre-oil-supply oil tank meets the change of the mass center:
if the three directions all meet the variation trend of the center of mass, the selection of the pre-supplied oil tank is unchanged;
if two pre-supplied oil tanks exist and one of the three directions does not meet the condition, adding the corresponding oil tank into the alternative oil tank according to the variation trend of the mass center when the weight of each oil tank is reduced;
if three pre-supplied oil tanks exist, abandoning the alternative oil tanks and storing the oil tanks as a feasible solution, namely a feasible oil supply strategy;
if two pre-supply oil tanks exist, and the oil tank 1 and the oil tank 6 are not selected, the oil tank 1 or the oil tank 6 can be selected as a 3 rd pre-supply oil tank in the alternative oil tank in the next step;
in other cases, the moving trend of the real-time mass center close to the ideal mass center on the X, Y, Z axis is judged according to the positions of the real-time mass center and the ideal mass center, and the pre-supplied oil tank is selected from the alternative oil tanks according to the moving direction;
step 2.9: judging whether the real-time oil quantity of the oil tank meets the volume upper limit and the volume lower limit:
0.02≤Vi(t)≤aibici；
wherein Vi(t) volume of remaining fuel in tank i, aiIs the length of the inside of the fuel tank i, biWidth of the interior of the tank i, ciThe lower limit of the volume of fuel in the fuel tank of an aircraft, which is the height of the interior of the tank i, is 0.02m3After a certain fuel tank starts to supply fuel, the volume of the residual fuel in the fuel tank is less than 0.02m3The oil supply is finished;
step 2.10: and (3) judging the error of the Euclidean distance between the real-time mass center position and the ideal mass center position of the aircraft system:
Figure FDA0003538044900000041
wherein
Figure FDA0003538044900000042
Is the real-time centroid position of the aircraft system,
Figure FDA0003538044900000043
to be an ideal centroid location based on the projected fueling rate of the aircraft,
Figure FDA0003538044900000044
and (4) selecting the pre-oil supply oil tank again for the Euclidean distance between the real-time centroid position and the ideal centroid position if the error is larger than the minimum optimization error, otherwise, keeping the oil supply strategy if the selection of the pre-oil supply oil tank is unchanged.
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