CN116576862A - Method for planning flight path of airship in near space - Google Patents
Method for planning flight path of airship in near space Download PDFInfo
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Abstract
The invention discloses a method for planning tracks of a nearby space airship, which relates to the technical field of aviation traffic, and comprises the steps of firstly, carrying out flight phase division on the tracks of the nearby space airship to obtain different flight state phases; secondly, constructing thermodynamic dynamics coupling models and constraint conditions of the near space airship for each flight state stage; and finally, discretizing an objective function corresponding to the thermodynamic dynamics coupling model of each flight state stage by using a Gaussian pseudo-spectrum method, and solving by using constraint conditions to obtain a flight path planning result of each flight state stage. And introducing a thermodynamic model into model differential equation constraint of the flight path optimization problem to reduce risks and costs possibly brought by a thermodynamic process from the level of pre-flight path planning, thereby achieving the purposes of reducing flight safety risks and reducing energy consumption.
Description
Technical Field
The invention relates to the technical field of aviation traffic, in particular to a method for planning a flight path of an airship in a near space.
Background
The near space generally refers to an airspace 10-20km away from the earth's sea level, which is between the flying altitude of a conventional aircraft and the flying altitude of a spacecraft, and has very important strategic significance. The airship flying in the near space has a larger investigation range and longer dead time compared with a conventional aircraft; meanwhile, compared with a satellite, the satellite has lower interference and higher observation and communication quality because the satellite is positioned below an ionosphere. Therefore, the near space airship has very wide application prospect, and the application of the near space airship is realized based on the track planning of the near space airship, so that the data on the planned route are acquired.
The internal mass of the airship is mostly composed of gas, so that the thermodynamic state change of the gas in the airship due to the internal and external heat exchange can have an effect on the buoyancy, the appearance and other flight characteristics of the airship, thereby affecting the tracks of the airship in the nearby space. The existing research on the aspect of high-altitude airship track planning is generally based on a highly simplified thermodynamic model, and in the research process, the moment that the floating weight adjusting process of the airship is finished is generally assumed to be finished, the adjusting capacity limit of a valve or a blower is ignored, the influence of external radiation on the air in the airship bag is directly calculated, the existence of a skin is ignored, and the like. Although the mathematical forms of the problems are sufficiently brief, so that solutions with certain rationality on the qualitative level can be obtained through iterative calculation, too much improper simplification leads to larger access between thermodynamic models and actual conditions, and therefore the reference value of calculation results in actual flight is greatly reduced.
Meanwhile, in order to maintain the balance of the floating weight under the condition of lower atmospheric density, the airship in the nearby space generally adopts a soft airship configuration, and under the condition, the pressure difference between the air inside the airship and the external atmosphere becomes an important index related to the flight safety. Too high a pressure differential can bring about the risk of explosion of the hull, while too low a pressure differential can fail to maintain the complete shape of the airship, thereby losing buoyancy due to the reduced volume and eventually leading to a crash. Therefore, the flight path planning of the near space airship can change the external atmospheric pressure environment in the flight process of the airship, thereby directly affecting the flight safety.
Therefore, how to accurately plan the flight path of the near space airship, and reduce the risk of flight safety are urgent problems to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a method for planning the flight path of an airship in the near space, which introduces a thermodynamic model into the constraint of a model differential equation of the problem of flight path optimization to reduce the risk and cost possibly brought by the thermodynamic process from the level of the prior flight path planning, thereby achieving the purposes of reducing the flight safety risk and reducing the energy consumption.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for planning a path of an airship in a near space comprises the following steps:
step 1: carrying out flight phase division on the flight path of the near space airship to obtain different flight state phases;
step 2: constructing thermodynamic dynamics coupling models and constraint conditions of the near space airship for each flight state stage;
step 3: and discretizing an objective function corresponding to the thermodynamic dynamics coupling model of each flight state stage by using a Gaussian pseudo-spectrum method, and solving by using constraint conditions to obtain a flight path planning result of each flight state stage.
Preferably, control distribution is performed on the track planning result, and the control quantity in the track planning result is converted into an operation instruction.
Preferably, the flight state phases comprise a conformal ascending phase, a resident flight phase, a conformal descending phase and a return-to-field flight phase
Preferably, in step 2, a kinematic model, a kinetic model, a thermodynamic model and an environmental heat exchange model of the near space airship are constructed;
coupling the thermodynamic model with the airship vertical direction kinetic model and the kinematic model in the kinetic model in the conformal ascending stage and the conformal descending stage to obtain a thermodynamic kinetic coupling model;
and coupling the thermodynamic model with the airship horizontal direction kinetic model and the kinematic model in the kinetic model in the resident air flight stage and the return field flight stage to obtain the thermodynamic kinetic coupling model.
Preferably, the thermodynamic coupling model is expressed in the form of a Bolza problem.
Preferably, the airship kinematic model includes an airship positional kinematic equation and an airship attitude kinematic equation expressed as:
wherein ,representing the airship kinematics equation; x, y and z respectively represent three direction coordinates of an inertial coordinate system; />Representing a transpose of the transformation matrix of the ground coordinate system G and the hull coordinate system B; v denotes the airship heart velocity coordinate in the hull coordinate system B, v= [ u, v, w ]] T U, v, w represent body core velocities in three directions, respectively; c represents cos; s represents sin; psi represents the yaw angle; θ represents a pitch angle;
representing an airship attitude kinematics equation; phi represents a roll angle; the coordinates of the airship angular velocity in the hull coordinate system B are expressed as ω= [ p, q, r] T P, q, r denote the angular velocities in three directions, respectively.
Preferably, the kinetic model is expressed as:
wherein V represents an airspeed vector; f (F) ay ，F ax ，F az Representing external forces acting on the airship under the airflow coordinate system;representing the track deflection angle; gamma represents track dip; m is m 1 ，m 2 ，m 3 Respectively representing mass components in three directions under an airflow coordinate system; w (w) ax ，w ay ，w az Respectively representing wind velocity vectors in three directions in the airflow coordinate system.
Preferably, the near space airship comprises an overpressure balloon, an outer balloon body and an air balloon, helium is filled in the overpressure balloon and the outer balloon body, air is filled in the air balloon, and a thermodynamic model that each gas in each balloon meets is expressed as:
wherein ,representing the total energy; q (Q) ir Indicating infrared radiation heat exchange; q (Q) hc Representing convective heat transfer; he represents helium in the overpressure envelope, he represents helium in the outer envelope, air represents air in the air envelope; />Is the fluid-induced internal energy change, +.>Is the internal energy change caused by acting externally.
Preferably, the selected state quantity of the conformal ascent phase is expressed as:
x＝[t,T F ,T G ,h g ,h g_dot ,m air ] T
wherein t is the rise time; t (T) F ，T G The temperature of the outer skin of the airship and the temperature of the gas in the airship are respectively, namely the temperature of helium in the outer capsule body and the temperature of helium in the overpressure capsule and air in the air capsule; h is a g Is the altitude of the airship; h is a g_dot The change rate of the airship height is the ascending speed of the airship; m is m air Is an air bagTotal mass of medium air;
the selection control amount is expressed as:
u＝[m air_dot ] T
m air_dot representing the rate of change of the total mass of air in the air bag; t represents a transpose;
the constraint is expressed as:
the objective function is expressed as:
J＝t f -t 0 。
preferably, the selected state quantity of the standing-air flight phase and the return-to-field flight phase is expressed as:
wherein t is the time of flight; t (T) F ,T G The temperature of the outer skin of the airship and the temperature of the gas in the airship are respectively; x is x g ,y g Is the coordinate of the airship under an inertial coordinate system; v is the airspeed vector, i.e., the airspeed of the airship in the horizontal plane; t is the total thrust received by the airship;yaw angle for track of airship, +.>Yaw rate is the track of the airship;
the selection control amount is expressed as:
in the formula ,Tdot Is the rate of change of the total thrust;angular acceleration, which is the track deflection angle;
the simplified thermodynamic coupling model is expressed as:
in the formula Ay For aerodynamic drag force, k, of the airship along the y-axis direction under the coordinate system of the airship 2 Is an additional mass coefficient w of the airship in the y-axis direction of a hull coordinate system x ,w y The wind speed on the X and Y axes is the wind speed on the inertial coordinate system;
the resident flight stage comprises two conditions of regional resident flight and mission course flight, and a regional resident objective function and a mission course flight objective function are correspondingly constructed;
the region-resident objective function is expressed as:
where g (·) is a positive correlation function of the distance of the airship to the center of the residence area and the radius of the residence area, Q s_c The total radiation energy received by the solar cell array on the airship; a represents regional residence, b represents maximum energy obtaining, and c represents minimum energy consumption;
the mission course flight objective function is expressed as:
J A ＝t f -t 0
a represents the shortest flight time, B represents the shortest flight route, C represents the maximum energy obtaining, and D represents the lowest energy consumption.
Preferably, the selected state quantity of the conformal descent phase is expressed as:
x＝[t,T F ,T G ,h g ,h g_dot ,m air ,m he_ex ] T ；
the selection control amount is expressed as:
u＝[m air_dot ,m he_ex_dot ] T ；
in the formula ,mhe_ex Helium mass m of outer capsule air_dot The total mass flow of air filled in the air bag; m is m he_ex_dot A mass flow rate of helium gas to the outer bladder;
the simplified model equation for the descent segment of the airship is:
compared with the prior art, the invention discloses a method for planning the flight path of the airship in the near space, which is a flight path optimizing method for the conformal lifting and the high-low horizontal flight stage of the airship, and the optimal track is obtained by establishing a thermodynamic dynamics coupling model of the airship and carrying out multi-constraint optimization solving by matching with related constraints and targets, so that the purposes of reducing the flight safety risk and reducing the energy consumption are achieved. The method models and solves the flight path optimization problem based on a more complete airship thermodynamic model, and can obtain a more detailed planning result with reference value.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for planning the flight path of a nearby space airship provided by the invention;
FIG. 2 is a schematic diagram of air quality and air quality change rate at a conformal ascent stage according to the present invention;
FIG. 3 is a schematic view of the height and the height change rate of the conformal lifting phase provided by the invention;
FIG. 4 is a schematic diagram of the pressure and pressure difference inside and outside the conformal ascent phase provided by the present invention;
FIG. 5 is a schematic diagram of the volume of gas in the bladder during the ascent phase of the present invention;
FIG. 6 is a schematic diagram of the gas and skin temperatures during the ascent phase of the present invention;
FIG. 7 is a graph showing the time-dependent open/close state of the air bag valve according to the present invention;
FIG. 8 is a schematic diagram of a task route planning mode optimization calculation result provided by the invention;
FIG. 9 is a schematic diagram of the results of the optimization calculation of the regional resident mode provided by the invention;
FIG. 10 is a graph of airship altitude rate of change/altitude over time provided by the present invention;
FIG. 11 is a graph showing the air mass change rate/air mass over time provided by the present invention;
FIG. 12 is a graph of the rate of change of helium mass versus time provided by the present invention;
FIG. 13 is a graph showing the pressure/internal and external differential pressure over time provided by the present invention;
FIG. 14 is a graph showing the valve/blower on/off state as a function of time provided by the present invention;
FIG. 15 is a schematic diagram of a result of the optimization calculation of the return field segment provided by the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention discloses a method for planning a flight path of an airship in a near space, and the flow is shown in figure 1.
1) In modeling airship objects, the following assumptions may be made without loss of generality:
plate earth hypothesis: the ground is an infinitely extending plane and ignores the rotation of the earth, the ground coordinate system can be regarded as an inertial coordinate system.
Rigid body assumption: because the outer bag body always needs to meet the shape-preserving requirement, the pneumatic elastic effect of the outer bag body of the airship can be ignored, and the floating center of the airship coincides with the body center.
Ideal gas assumption: the gas in each air bag meets the ideal gas state equation.
Transient heat balance assumption: heat transfer between each skin and gas is accomplished instantaneously, i.e., the skin and gas are considered particles during thermal analysis.
The roll angle of the airship is 0: since the center of buoyancy of the airship is above the center of gravity, a buoyancy moment will be generated to maintain the roll angle of the airship at 0, thus assuming phi=0.
The airship tail control is not considered, and only the airship air bag and the propeller are considered as a controller.
2) The defined coordinate system involved in modeling is as follows:
(1) inertial coordinate system g= { O g x g y g z g }. Its origin O g Fixed at one point on the ground, O g x g The axis is positioned in the ground plane and points to the forward direction, O g y g The axis points to the north in the ground plane, O g z g The axis is perpendicular to the ground and faces away from the earth center, and the three axes form a right hand system, namely a northeast day coordinate system.
(2) Hull coordinate system b= { O b x b y b z b (same control coordinate system in section 4.1). Its origin O b Is positioned at the body center of the airship, and the connecting line of the body center and the mass center of the airship is perpendicular to the longitudinal axis and O b y b The axis points to the bow along the longitudinal axis on the longitudinal symmetry plane of the airship, O b x b The longitudinal symmetry plane of the vertical airship of the shaft points to the right, O b z b The axis-passing body center is directed upwards perpendicular to the Oxy-plane, and forms a right-hand coordinate system with the other two axes.
(3) Air flow coordinate system a= { O a x a y a z a }. Its origin O a Is consistent with the ship body coordinate system, O a y a The axis is consistent with the vector direction of airspeed V (speed of relative air flow) of the airship, O a z a The axis is positioned in the plane of symmetry of the airship and is vertical O a y a The axis is directed upwards, O a x a The axis being perpendicular to O a y a z a The plane and the other two axes form a right hand coordinate system.
3) The angles are defined based on the above coordinate system as follows:
(1) euler angles [ theta, phi ]] T Is determined by a hull coordinate system B and a ground coordinate system G;
yaw angle ψ: o (O) b y b Axis to ground plane (O) g x g y g Plane) projection onto true north (O) g y g Axes), yaw to the left (west) is positive;
pitch angle θ: o (O) b y b Shaft and ground plane (O) g x g y g Plane), the head-up is positive.
Roll angle phi: o (O) b z b Shaft and O pass b y b The included angle between the vertical planes of the axes is positive when rolling right (clockwise).
(2) Angle of airflow [ alpha, beta ]] T Determined by airspeed vector V and hull coordinate system B:
angle of attack α: airspeed vector V at boat symmetry plane O b y b z b Projection onto the longitudinal axis O of the hull b y b Included angle between the projection line and the boat bodyLongitudinal axis O b y b The upper part is positive;
sideslip angle beta: airspeed vector V and boat plane of symmetry O b y b z b The included angle between the two is positive at the right side of the symmetry plane.
(3) Track angleDetermined by an airflow coordinate system A and a ground coordinate system G:
track pitch angle γ: airspeed vector V and ground plane O g x g y g The included angle between the two is positive upwards;
track deflection angle: space velocity vector V is at O g x g y g Projection of plane and O g y g The included angle of the shaft is positive on the left side.
Track roll angle μ: o (O) a z a Shaft and O pass a y a The included angle between the vertical planes of the axes rolls right to be positive.
4) According to the definition of the coordinate system and the related angle, a transformation matrix among three coordinate systems can be obtained:
(1) conversion matrix from ground coordinate system G to hull coordinate system B
Wherein s represents sin, c represents cos, and the same applies below
(2) Conversion matrix from ground coordinate system G to airflow coordinate system A
(3) Conversion matrix from hull coordinate system B to airflow coordinate system A
In the research of airship kinematics, the position and posture of the airship are represented by the coordinates ζ= [ x, y, z ] of the body center position in the inertial coordinate system G] T And Euler angles gamma= [ theta, phi] T Representing the speed and angular velocity of the airship with the coordinate expression v= [ u, v, w ] of its body center velocity in the hull coordinate system B] T And the coordinate expression ω= [ p, q, r ] of the airship angular velocity in the hull coordinate system B] T Description.
5) The airship position kinematic equation is:
the coordinates of the angular velocity of the airship in the inertial coordinate system can be obtained by the attitude angle and the change rate thereof:
in the formula Is the inertial system { x } i ,y i ,z i Unit vector { i } on axis i ,j i ,k i Coordinate expression in inertial system G, +.>Is the coordinate expression of the unit vector j in the inertial system G on the y axis of the hull coordinate system. The expression of the airship angular velocity in the hull coordinate system is obtained by transforming the above expression into the hull coordinate system B:
when cos theta is not equal to 0, the airship attitude kinematic equation is obtained by the above formula
6) Dynamics model
According to assumption 1, ignoring the elastic effect of the airship capsule, regarding it as a rigid body, according to newton's second law, the kinetic equation under the inertial system is:
wherein F is an external force acting on the airship, and comprises buoyancy B, gravity G, aerodynamic force A and thrust T, namely F=B+G+T+A;
the above form under the air flow coordinate system is:
wherein the mass matrix M is the sum of the own mass matrix and the additional mass matrix
The inertial velocity is expressed in the airflow coordinate system as:
wherein wax ,w ay ,w az Wind speed vector expressed in airflow coordinate system:
in the formula we ,w n Wind speeds in the east and north directions of the ground coordinate system are respectively.
The kinetic equation can be obtained in combination:
7) Thermodynamic model
The thermal environment of stratospheric airships consists of an external and an internal environment. Outside the airship, the outer capsule body skin of the airship performs convection heat exchange with the atmosphere, and receives solar radiation, ground air infrared radiation and self external radiation. Inside the airship, radiation heat exchange can be carried out among all the capsules of the airship, and convection heat exchange can occur between the capsule skins and contact gas.
The temperature change of the skin is obtained by the following method
in the formula Qsun For heat exchange of solar radiation, Q ir-ex For heat exchange between the skin and external infrared radiation, Q hc-ex For the convective heat exchange of the skin and the outside,for the infrared radiation heat exchange of the skin and the interior gas, +.>Heat exchange is performed for convection of the skin and the internal gas.
For gas, the gas in the same closed capsule is considered as a whole, namely the temperature and pressure of the gas in each part of the capsule are considered to be the same, including the gas just entering the capsule, and the temperature and pressure of the gas are also considered to be the same as the temperature and pressure of the capsule at once. A total of three gases: helium in the overpressure envelope (corresponding to subscript He), helium in the outer envelope (corresponding to subscript He) and air in the air envelope (corresponding to subscript air), each gas satisfying the thermodynamic equation:
wherein the subscript ir represents infrared radiation heat exchange, hc represents convection heat exchange,is the fluid-induced internal energy change, +.>Is the internal energy change caused by acting externally.
8) Calculating an environmental heat exchange model, wherein the environmental heat exchange model comprises solar radiation heat exchange, infrared radiation heat exchange and convection heat exchange;
1. solar radiation heat exchange
In order to calculate the amount of solar radiation heat exchange, it is necessary to know the intensity and direction of solar radiation at the current location.
(1) Intensity of solar radiation
Considering the periodic variation of the earth's distance in revolution of the earth, the solar radiation intensity at the surface of the earth's atmosphere upper boundary perpendicular to the solar rays can be expressed as:
I sol ＝fI 0 (16)
in the formula I0 The solar constant refers to solar radiation energy obtained in unit area and unit time from the surface perpendicular to sunlight rays at the upper boundary of the earth atmosphere when the solar-earth distance is positioned at the average value; f is a sun-earth distance correction coefficient, and is generally calculated by adopting the following method:
where n is the date number of the day in one year.
(2) Direction of the sun
The "northeast day" coordinates are used in calculating the solar direction.
The direction in which the sun is located is generally expressed by the azimuth angle of the sun and the altitude angle of the sun:
S＝[cosθ s sinψ s cosθ s cosψ s sinθ s ] T (18)
in the formula θs The solar altitude is defined as an included angle between the incident direction of sunlight at a certain point on the earth and the ground plane; psi phi type s The solar azimuth angle is defined as the angle between the projection of the solar direction vector on the horizontal plane and the north-right direction (y-axis), and is clockwise positive.
The calculation of the solar altitude requires three quantities: local latitude, solar declination angle, and solar hour angle.
The declination angle of the sun refers to the included angle between the connecting line of the center of the earth and the center of the sun and the equatorial plane of the earth, and the calculation method is as follows:
where n is the date number of the day in one year.
The calculation formula of the solar time angle is as follows:
in the formula ts The standard time is the current time zone, and the unit is hours; l is the longitude of the current position, L s Longitude corresponding to standard time of the current time zone is given in degrees; e is the time difference between the true solar time and the flat solar time, the unit is minutes, and the calculation method is as follows:
e＝0.0028-1.9857sinD+9.9059sin2D-7.0924cosD-0.6882cos2D (21)
in the formula Called the day angle, n is the date number of the day in one year.
Solar altitude angle theta s The method meets the following conditions:
sinθ s ＝sinφsinδ+cosφcosδcosω (22)
where phi is the current position dimension.
Calculating the solar altitude angle theta from the above s Then, the solar azimuth angle psi can be further calculated s The two satisfy the following relationship:
(3) Solar radiation heat exchange calculation
There are three main ways in which solar radiation affects the skin of an airship: direct solar radiation, solar radiation scattered by the atmosphere, and solar radiation reflected by the ground.
(1) Direct solar radiation
The direct solar radiation intensity can be expressed as:
in the formula I0 For the solar radiation intensity at the outer boundary of the atmosphere on the day calculated above; n is the ordinal number of the current date in one year.
The direct solar radiation power received by the unit surface on the skin is equal to the flux of the radiation intensity vector on the surface, so the direct solar radiation heat receiving quantity in unit time of the ith unit surface can be expressed as:
Q sd,i ＝α sol τ atm,s I d S·n i ·A i (25)
in the formula αsol Is the absorptivity of the skin material to solar radiation; a is that i Is the area of the ith skin cell; τ atm,s The transmittance of the atmosphere to solar radiation is calculated as follows:
τ atm,s ＝0.5(e -0.65m +e -0.095m ) (26)
wherein m is the mass ratio of the atmosphere, and the calculation method is as follows:
in the formula Ph Atmospheric pressure at the current altitude; p (P) 0 Is sea level atmospheric pressure; θ s Is the solar altitude.
(2) Atmospheric scattered radiation
The atmospheric scattered solar radiation intensity can be calculated as follows:
the solar scattered radiation heat reception amount per unit time of the ith skin unit is:
in the formula For the angular coefficient of the unit facing the sky, +.>
(3) Ground reflection of solar radiation
After the direct solar radiation and the scattered solar radiation reach the ground, a part of the radiation is reflected, and the reflected radiation intensity is expressed as follows:
I r ＝ρ[I d sinθ s +I s ] (30)
where ρ is the average reflectivity of the ground to solar radiation.
And then the ground reflection solar radiation heat receiving quantity in the unit time of the ith skin unit is obtained:
/>
in the formula For the angular coefficient of the current cell facing the ground, +.>
2. Infrared radiation heat exchange
The outer surface of the airship skin is subjected to solar radiation, and also subjected to infrared radiation of the atmosphere and the ground, and meanwhile, frequent infrared radiation reflection phenomena exist between the inner surfaces of the skin.
(1) Atmospheric infrared radiation
The skin unit receives atmospheric infrared radiation intensity:
in the formula As defined above, is the angular coefficient of the skin surface to the sky; sigma=5.67×10 -8 W/(m 2 ·K 4 ) Is a stefin-boltzmann constant; t (T) s The effective temperature of the atmosphere at the current altitude; epsilon s The calculation method is as follows:
ε s ＝0.52+0.65×pw 0.5 (33)
wherein pw is the partial pressure of water vapor in the atmosphere, and is calculated by the following method:
(2) Ground infrared radiation
The skin unit receives the ground infrared radiation intensity:
in the formula ,εg Is ground infrared emissivity; t (T) g Is the earth surface temperature; τ atm,ir The calculation method is as follows:
for the surface temperature T g It is assumed to vary periodically with the following law:
T g ＝273.15+33-0.09752×(t-12) 2 (37)
where t is the current time in hours.
(3) Infrared radiation inside the hull
There is also a significant amount of infrared radiation heat exchange between the interior surfaces of the airship skin. Here it is assumed that the skin is an opaque material, ignoring infrared radiation and the transmission of solar radiation.
Let J denote the radiation leaving the skin unit and G denote the radiation reaching the skin unit.
For any skin element i, its infrared radiation emitted inside the airship includes self-infrared radiation and infrared radiation reflecting other skin elements:
in the formula εf Infrared emissivity of the skin unit; t (T) i For the temperature value of the skin unit, X j,i For the angular coefficient of skin element j to skin element i:
/>
wherein lj,i Is the distance between the center points of the two unit surfaces; θ 1 ，θ 2 Is the included angle between the connecting line of the central points of the two unit surfaces and the normal vector of the connecting line.
Solving J according to i The infrared radiation reaching the skin element i can then be expressed as:
finally, the amount of heat exchange of the internal infrared radiation of the skin unit i is expressed as:
Q i,ir,in ＝(G i -J i )A i (41)。
3. convection heat exchange
Convection heat transfer refers to the phenomenon of heat transfer between a fluid and the surface of the solid when the fluid flows through the solid, and convection is mainly divided into natural convection and forced convection, wherein natural convection refers to fluid movement of each part of the fluid due to density difference caused by temperature, and forced convection refers to fluid movement driven by a fan, a pump and the like. In the flying process of the airship, natural convection exists between the internal gas and the skin, and natural convection and forced convection exist between the skin and the external atmosphere.
The dynamic viscosity, the heat conductivity coefficient and the Plantain number of the air and the helium are needed in the convective heat transfer calculation, and the calculation method is as follows:
(1) air-conditioner
Pr air ＝0.804-3.25×10 4 T air (44)
(2) Helium gas
Pr He ＝0.729-1.6×10 -4 T He (47)
The convective heat transfer coefficient h has the expression:
wherein Nu is the number of noose corresponding to the gas; l is the characteristic length and generally refers to a dimension in a direction perpendicular to the heat exchange surface.
(1) Convective heat transfer of the skin to the outside atmosphere
The stratospheric airship is a streamline rotary ellipsoidal airship body, and the forced convection heat exchange of the stratospheric airship and the outside atmosphere can be equivalent to a weighted average of the forced convection of a flat plate and the outer surface of a sphere.
Forced convection heat exchange nussel number Nu of flat plate L The calculation method comprises the following steps:
pr is the Plantt number; re is the external fluent local reynolds number,u is the flow rate; l is the characteristic dimension, which is taken as the short side of the flat plate under the condition of the forced convection of the flat plate, and is regarded as the short axis treatment of the ellipsoid of the airship, and is taken as the diameter of the sphere under the condition of the forced convection of the sphere, and is also regarded as the short axis treatment of the capsule of the airship; v is kinematic viscosity->μ is the dynamic viscosity corresponding to the gas, ρ is the fluid density.
Forced convection number Nu of noose on sphere surface D The calculation method comprises the following steps:
forced convection noose number Nu on airship envelope surface F Taking a weighted average of the above two noose numbers:
Nu F ＝βNu L +(1-β)Nu D (51)
where β is a weighting factor, here taken to be 0.5.
Natural convection nussel number Nu N The calculation method of (2) is as follows:
where Gr is the number of Grashof,g is the gravitational acceleration, beta is the gas volume expansion coefficient, defined as the reciprocal of the calculated number average of the fluid temperature and the wall temperature, i.e.>
Based on the difference between Gr and Re, the total noose numbers for forced and natural convection are expressed as:
(2) Convective heat exchange between skin and internal gas
It is apparent that the convective heat transfer between the skin and the interior gas is dominated by natural convection, and the internal forced convection is ignored.
Kreith gives an expression for the natural convection heat transfer noossel number inside a balloon:
/>
the convective heat transfer calculation method between the inner surface of the skin unit and the gas in the bag is as follows:
the subscripts He, i and air in the formula respectively represent skin units which are in direct contact with helium in the capsule and air in the capsule; h is a He ，h air The calculation method for the convective heat transfer coefficient of helium and air is given above.
(3) Convection heat exchange between air and helium in boat
Helium and air in the airship capsule body are subjected to convective heat transfer mainly through a diaphragm between the main air bag and the auxiliary air bag, and the calculation method comprises the following steps:
Q air,He ＝KA air,He (T air -T He ) (56)
in the formula Aair,He The area of the diaphragm between the main air bag and the auxiliary air bag; k is a heat transfer coefficient and is calculated by the following method:
9) Airship track planning
The mathematical expression of the Bolza problem is as follows:
wherein phi is a Mayer performance index function (terminal); g is Lagrange type performance index function (process); p is a static parameter vector; x (t) is a state vector; u (t) is a control vector.
The flying stage of the high-altitude airship is divided into four stages of conformal ascending, resident air flying, conformal descending and return field flying. The airship in the conformal ascending section lightens the weight and promotes the height by releasing the air in the air bag; in the resident air flight section, the airship flies for a long time at cruising altitude through a propeller on the airship; the airship in the conformal descending section sucks air through a blower on the bag body to increase weight and complete descending; the airship in the return field section returns to the base through horizontal flight. In view of the external environmental characteristics of different flight phases and the difference of important attention in the flight process, the method provided by the invention can be used for independently considering each phase and performing targeted model simplification, and a flight path optimization method is respectively provided.
And performing planning calculation on all four stages including an ascending section, a blank section, a descending section and a return field section. It should be noted that, considering the limitation of the application of the track optimization result in the actual engineering scene, in the ascending section and the descending section, after the optimization calculation result is obtained, a simulation prediction calculation based on the built-in model is performed, and in the simulation process, the ring control decision (the switch decision of the valve or the blower) is performed based on the optimization result, so as to form a list composed of a series of ring control decisions and the corresponding heights thereof, and the list is sent to the on-board computer through the data link and stored, and when in use, the list is determined by the on-board planning partial function through the lookup table of the current height.
1. Ascending section
In the airship conformal ascending stage, the transverse movement does not start power control, and the planning focus is on the longitudinal movement of the airship. Therefore, the model is simplified, dynamics and kinematics models in the horizontal direction of the airship are ignored, and the thermodynamic model of the airship is coupled with dynamics and kinematics models in the vertical direction of the airship to be a planning model. Selecting state quantity:
x＝[t,T F ,T G ,h g ,h g_dot ,m air ] T (59)
wherein T is the rise time, T F ，T G The temperature of the outer skin of the airship and the temperature of the gas (outer capsule helium, overpressure capsule helium and air capsule air) in the airship are respectively h g Is the altitude of the airship, h g_dot For the rate of change of the airship height, i.e. the speed of ascent of the airship, m air Is the total mass of air in the air bag.
Selecting a control amount:
u＝[m air_dot ] T (60)
a simplified model equation of the airship, i.e. dynamic constraints, can be obtained:
the rise optimization objective is that the rise time is the shortest, so the objective function is defined as follows:
J＝t f -t 0 (62)
after inputting certain initial conditions and constraint conditions, discretizing by using a Gaussian pseudo-spectrum method and solving by using a constraint optimization solver to obtain a result shown in figures 2-6.
In the figure, the air quality in the airship ballonet is continuously reduced, and the altitude is stably increased. The long-term maintenance of the pressure difference between the inside and outside of the airship at the minimum safety limit is shown in fig. 4, which illustrates that the main problem faced by the airship in the shape-keeping and rising stage is that the airship loses pressure due to the too high gas release speed, and in fig. 3, the change rate of the air quality in the air bag of the airship under the same time period is not up to the maximum value, and the optimization algorithm is seen to properly reduce the air release rate in order to avoid the pressure loss.
After the planning result is obtained, the control distribution is needed to convert the control quantity, namely the air bag discharging air quality rate, into the operation sequence of opening/closing the valve. The result of the planning is a height value sequence H g ＝「h g1 ,h g2 ,…,h gN ]And corresponding air quality value sequence M air ＝[m air1 ,m air2 ,…,m airN ]Based on the planning result, re-simulation is carried out in a simplified model, and simulation logic is as follows:
(1) If h gi ≤h g ＜h gi+1 And m is airi ＞m airi+1 If the internal and external pressure difference is higher than the lower limit of the safety pressure difference, opening all air bag valves to exhaust;
(2) Otherwise, all air bag valves are closed.
The final valve operation sequence is shown in fig. 7, the change of the valve switch state forms a valve operation list according to the height corresponding to the valve operation, 0 represents closing, 1 represents opening, and the valve operation list is sent to the on-board computer in a certain data form.
2. Empty space section
The stratospheric airship is mainly controlled in the horizontal plane through an electric propeller in the air-laying section, and simultaneously, the stratospheric airship is matched with air bag air suction and exhaust and pressure regulation of the inner bag of overpressure to realize the security control of hyperthermia and overpressure. The focus of the park section track planning is lateral movement as opposed to longitudinal movement as compared to the ascender section. Therefore, considering that the airship is in a stable state at a designated altitude, the net buoyancy of the airship at the space is assumed to be 0, the altitude change rate is also 0, and the attack angle and the track inclination angle are also constant to be 0. Under this assumption, the airship model is simplified, only the horizontal motion is considered, and the vertical and airship roll and pitch attitude changes are ignored. The selection state variables are:
wherein T is the flight time, T F ,T G The temperature of the outer skin of the airship and the temperature of the gas in the airship are respectively x g ,y g Is the coordinate of the airship under the inertial coordinate system, V is the airspeed (in the horizontal plane) of the airship, T is the total thrust exerted by the airship,yaw angle for track of airship, +.>Is the track yaw rate of the airship.
Selecting the control quantity as
in the formula ,Tdot As a rate of change of the total thrust force,angular acceleration, which is the track deflection angle.
The simplified model equation is:
in the formula Ay For aerodynamic drag force, k, of the airship along the y-axis direction under the coordinate system of the airship 2 Is an additional mass coefficient w of the airship in the y-axis direction of a hull coordinate system x ,w y The wind speed on the X and Y axes is the magnitude of the wind speed under the inertial coordinate system.
There are two cases of the task of the empty segment: regional residency and mission airlines.
The optimization targets of the regional residency are: a. regional residence, b. maximum energy gain, c. minimum energy consumption. The corresponding objective functions are respectively:
in the formula g (& gt)) Is a positive correlation function of the distance from the airship to the center of the residence area and the radius of the residence area, Q s_c Is the total radiant energy received by the solar cell array.
The optimization targets of the mission route flight are as follows: A. the flight time is shortest, the flight route is shortest, the energy obtaining is maximum, and the energy consumption is lowest. The corresponding objective functions are respectively:
J A ＝t f -t 0 (69)
and solving the two cases under certain initial conditions and constraint conditions and target combination. Fig. 8 is a solution result of a mission course flight mode, in which six groups of graphs are respectively a horizontal track graph of a planning result, a state quantity change curve of the planning result, a power consumption and solar panel energy obtaining curve, an internal and external differential pressure curve, an internal and external differential temperature curve of the airship, and a final output horizontal track graph after smoothing treatment in consideration of steering capability limitation under the actual flight condition of the airship. Fig. 9 is a plan result obtained by taking a certain circular area as the active range of the regional resident flight in the regional resident mode, which is the same as the mission course flight mode, and six groups of lines in the figure are respectively a plan result horizontal track diagram, a plan result state quantity change curve, an airship power energy consumption and solar panel energy obtaining curve, an inside-outside differential pressure curve, an inside-outside differential temperature curve and a final output horizontal track diagram after smoothing treatment in consideration of the steering capability limitation under the actual flight condition of the airship.
The pressure difference between the inside and the outside of the airship is always kept near the highest safety limit in the planning result of the two cases, which shows that the main problem faced by the airship in the long-term resident air flight stage is the overpressure risk caused by heating. The approach to avoiding this is generally to maintain a higher cruising speed to increase the convective heat dissipation rate.
3. Descending section
The airship conformal descending section is divided into a descending region adjusting section and a regional prediction descending section. The falling area adjusting section is used for giving a proper initial falling position according to a falling simulation result, and the area prediction falling section is used for starting the falling of the airship from the initial position until the falling is completed. The planning content of both stages is a conformal descent process starting from an initial point.
The descending section of the airship is similar to the ascending section, the power control is not started in the horizontal direction, the descending speed and the conformal pressure difference constraint are met mainly by means of air bag inflation and outer bag body deflation, and when the pressure difference is overlarge, part of outer bag body helium gas needs to be released to reduce the pressure in the bag, so that the state quantity of the outer bag body helium gas mass is added compared with the ascending section.
The state quantity is selected as
x＝[t,T F ,T G ,h g ,h g_dot ,m air ,m he_ex ] T (73)
Selecting the control amount as
u＝[m air_dot ,m he_ex_dot ] T (74)
in the formula mair_dot For the total mass flow of air filled in the air bag, m he_ex_dot Mass flow of helium gas is vented to the outer capsule.
The simplified model equation for the descent segment of the airship is:
after inputting certain initial conditions and constraint conditions, discretizing by using a Gaussian pseudo-spectrum method and solving by using a constraint optimization solver to obtain a result as shown in figures 10-13. It can be seen from fig. 13 that the pressure differential across the airship is maintained near the highest safety limit, indicating that the main problem faced by the airship in the descent phase is the overpressure of the hull after the intake of gas. From fig. 11 and 12 it can be seen that the optimization results tend to reduce the risk of overpressure by two methods, namely releasing helium and reducing the air intake rate.
Based on the change condition of the gas quality in the capsule in the planning result of the descent segment, the result shown in fig. 14 is obtained by the simulation prediction calculation process. The airship conformal descending section is divided into a descending region adjusting section and a regional prediction descending section. The falling area adjusting section is used for giving a proper initial falling position according to a falling simulation result, and the area prediction falling section is used for starting the falling of the airship from the initial position until the falling is completed. The calculation under both schemes is therefore identical and will not be repeated here.
4. Return field section
The return field flight of the stratospheric airship is essentially the mission route resident flight under the low-altitude environment. When the descending section of the airship is finished and the altitude tends to be stable, the power of the pneumatic electric propeller is output, so that the control of the flight path, the heading and the flight speed of the platform is realized; meanwhile, the safety control of the day and night pressure of the outer bag body is coupled, and the low-altitude accurate return-field controllable power flight of the platform is realized by controlling the air bag to suck and exhaust for adjustment. Therefore, the mathematical form of the return field planning problem is basically consistent with that of the empty space, and is not repeated here.
After inputting certain initial conditions and constraint conditions, discretizing by using a Gaussian pseudo-spectrum method and solving by using a constraint optimization solver to obtain a result shown in FIG. 15. The conditions of the return field section and the air-resident section are similar, and the long-time irradiation of solar radiation leads to high risk of gas overpressure, so that optimization is concentrated in two aspects: firstly, the flying speed is improved so as to obtain higher convection heat dissipation efficiency; secondly, the airship is close to the attitude with the smallest surface area exposed to solar radiation as much as possible, which is also the reason why the track optimization result does not tend to go straight to the target.
Gauss pseudo-spectrum method (GPM, gauss pseudospectral method) is a point-matching method with high calculation efficiency, and the basic principle is as follows: performing discretization processing on a state variable and a control variable of an optimal control problem on a series of Legendre-Gauss discrete points (LG fitting points), and constructing a Largrange interpolation polynomial by taking the LG fitting points as nodes so as to approximate the state variable and the control variable; deriving the global interpolation polynomial to approximate the time derivative of the state variable, thereby converting the differential equation constraint into a set of algebraic constraints; the terminal state can be obtained by adding a right function to the initial state, and the integral term in the performance index is calculated by Gauss integral. Through the transformation, the original optimal control problem is converted into a nonlinear programming problem with a series of algebraic constraints, and then the corresponding numerical optimal solution is obtained.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. The method for planning the flight path of the airship in the near space is characterized by comprising the following steps of:
step 1: carrying out flight phase division on the flight path of the near space airship to obtain different flight state phases;
step 2: constructing thermodynamic dynamics coupling models and constraint conditions of the near space airship for each flight state stage;
step 3: and discretizing an objective function corresponding to the thermodynamic dynamics coupling model of each flight state stage by using a Gaussian pseudo-spectrum method, and solving by using constraint conditions to obtain a flight path planning result of each flight state stage.
2. The method of claim 1, wherein the flight phase comprises a conformal ascent phase, a airborne flight phase, a conformal descent phase, and a return-to-field flight phase.
3. The method for planning the flight path of the spacecraft of claim 2, wherein in the step 2, a kinematic model, a kinetic model, a thermodynamic model and an environmental heat exchange model of the spacecraft are constructed;
coupling the thermodynamic model with the airship vertical direction kinetic model and the kinematic model in the kinetic model in the conformal ascending stage and the conformal descending stage to obtain a thermodynamic kinetic coupling model;
and coupling the thermodynamic model with the airship horizontal direction kinetic model and the kinematic model in the kinetic model in the resident air flight stage and the return field flight stage to obtain the thermodynamic kinetic coupling model.
4. A method of planning a flight path of an aircraft in space according to claim 1, wherein the thermodynamic coupling model is expressed in the form of a Bolza problem.
5. A method of planning a path of an aircraft in space according to claim 3, wherein the kinematic model comprises an airship positional kinematic equation and an airship attitude kinematic equation expressed as:
wherein ,representing the airship kinematics equation; x, y and z respectively represent three direction coordinates of an inertial coordinate system; />Representing a transpose of the transformation matrix of the ground coordinate system G and the hull coordinate system B; v denotes the airship heart velocity coordinate in the hull coordinate system B, v= [ u, v, w ]] T U, v, w represent body core velocities in three directions, respectively; c represents cos; s represents sin; psi represents the yaw angle; θ represents a pitch angle;
representing an airship attitude kinematics equation; phi represents a roll angle; the coordinates of the airship angular velocity in the hull coordinate system B are expressed as ω= [ p, q, r] T P, q, r denote the angular velocities in three directions, respectively.
6. A method of planning a path of an aircraft in space according to claim 3, wherein the dynamics model is expressed as:
wherein V represents an airspeed vector; f (F) ay ，F ax ，F az Respectively representing external forces acting on the airship in three directions under the airflow coordinate system;representing the track deflection angle; gamma represents track dip; m is m 1 ，m 2 ，m 3 Respectively representing mass components in three directions under an airflow coordinate system; w (w) ax ，w ay ，w az Respectively representing wind velocity vectors in three directions in the airflow coordinate system.
7. A method of path planning for an adjacent space airship according to claim 3, wherein the adjacent space airship comprises an overpressure envelope, an outer envelope and an air envelope, the overpressure envelope and the outer envelope being filled with helium and the air envelope being filled with air, and the thermodynamic model satisfied by each gas in each envelope is expressed as:
wherein ,representing the total energy; q (Q) ir Indicating infrared radiation heat exchange; q (Q) hc Representing convective heat transfer; he represents helium in the overpressure envelope, he represents helium in the outer envelope, air represents air in the air envelope; />Is the fluid-induced internal energy change, +.>Is the internal energy change caused by acting externally.
8. A method of planning a path of an aircraft in space according to claim 3, wherein the selected state quantity x of the conformal ascent phase is expressed as:
x＝[t,T F ,T G ,h g ,h g_dot ,m air ] T
wherein t is the rise time; t (T) F ，T G The temperature of the air in the outer skin of the airship and the airship respectively; h is a g Is the altitude of the airship; h is a g_dot Is the change rate of the airship height; m is m air Is the total mass of air in the air bag;
the selection control amount u is expressed as:
u＝[m air_dot ] T
m air_dot representing the rate of change of the total mass of air in the air bag; t represents a transpose;
the constraint is expressed as:
the objective function is expressed as:
J＝t f -t 0 。
9. a method of planning a flight path of a spacecraft as claimed in claim 3, wherein the selected state quantity x of the stay-in-flight phase and return-to-flight phase is expressed as:
wherein t is the time of flight; t (T) F ,T G The temperature of the outer skin of the airship and the temperature of the gas in the airship are respectively; x is x g ,y g Is the coordinate of the airship under an inertial coordinate system; v is an airspeed vector; t is the total thrust received by the airship;yaw angle for track of airship, +.>Yaw rate is the track of the airship;
the selection control amount u is expressed as:
in the formula ,Tdot Is the rate of change of the total thrust;angular acceleration, which is the track deflection angle;
the simplified thermodynamic coupling model is expressed as:
in the formula Ay For aerodynamic drag force, k, of the airship along the y-axis direction under the coordinate system of the airship 2 Is an additional mass coefficient w of the airship in the y-axis direction of a hull coordinate system x ,w y The wind speed on the X and Y axes is the wind speed on the inertial coordinate system;
the resident flight stage comprises two conditions of regional resident flight and mission course flight, and a regional resident objective function and a mission course flight objective function are correspondingly constructed;
the region-resident objective function is expressed as:
where g (·) is a positive correlation function of the distance of the airship to the center of the residence area and the radius of the residence area, Q s_c The total radiation energy received by the solar cell array on the airship; a represents regional residence, b represents maximum energy obtaining, and c represents minimum energy consumption;
the mission course flight objective function is expressed as:
J A ＝t f -t 0
a represents the shortest flight time, B represents the shortest flight route, C represents the maximum energy obtaining, and D represents the lowest energy consumption.
10. A method of path planning for an aircraft in space according to claim 3, wherein the selected state quantity for the conformal descent phase is expressed as:
x＝[t,T F ,T G ,h g ,h g_dot ,m air ,m he_ex ] T ；
the selection control amount is expressed as:
u＝[m air_dot ,m he_ex_dot ] T ；
in the formula ,mhe_ex Helium mass for the outer capsule; m is m air_dot The total mass flow of air filled in the air bag; m is m he_ex_dot A mass flow rate of helium gas to the outer bladder; t (T) F ，T G The temperature of the air in the outer skin of the airship and the airship respectively; h is a g Is the altitude of the airship; h is a g_dot Is the change rate of the airship height; m is m air Is the total mass of air in the air bag; [] T Representing a transpose;
the simplified model equation for the descent segment of the airship is:
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