CN113671974A - Turning approach accurate guidance method for return section of cross-domain aircraft - Google Patents
Turning approach accurate guidance method for return section of cross-domain aircraft Download PDFInfo
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Abstract
The invention discloses a turning approach accurate guidance method for a return section of a cross-domain aircraft, and belongs to the technical field of aerospace. The invention comprises the following steps: establishing turning approach dynamics of an aircraft energy management area, and giving starting and ending state constraints of the turning approach process of the aircraft; segmenting the turning approach flight trajectory according to the flight trajectory characteristics of the aircraft, and deducing to obtain turning trajectory characteristic parameters and trajectory connection conditions of each segment; deriving an open-loop control law of the initial turning section through an arc trajectory constraint equation based on the arc trajectory characteristics of the initial turning section, giving a range proportional attack angle control law based on the linear flight trajectory characteristics of the linear capturing section, and deriving the open-loop control law of the runway alignment section through the arc trajectory constraint equation based on the arc trajectory characteristics of the runway alignment section; and constructing a cross-domain aircraft turning approach closed loop prediction correction guidance frame which takes the turning radius of the runway alignment section as a guidance parameter and takes the terminal approach energy as a correction target, and giving a cross-domain aircraft turning approach track.
Description
Technical Field
The invention relates to a turning approach accurate guidance method for a cross-domain aircraft return section, in particular to an accurate guidance method suitable for a near-ground cross-domain wave-rider aircraft to turn and align to a return runway, and belongs to the technical field of aerospace.
Background
The cross-aerospace-domain aircraft is a trend of future development of space on-orbit service and space-ground round-trip systems, and becomes a main target of development of the world aerospace-space integrated aircraft due to huge potential application value. In the overall design of a cross-domain aircraft, the reliability of a return section is a decisive factor for ensuring the safe return flight of the aircraft, and the alignment of a turning approach to a landing runway is an important link in the return section. The turning approach of the cross-domain aircraft is divided into a direct approach and an indirect approach. When the energy of the aircraft is small, direct approach is generally adopted in order to realize large-range turning under limited energy, and when the energy of the aircraft is redundant, approach by indirectly crossing a runway is required in order to guarantee low-speed approach before landing. However, at present, a turning approach strategy which simultaneously satisfies two approach modes is not available. Obviously, the two approach modes depend on the track energy of the aircraft before turning approach, and the adaptive adjustment of the matched turning approach maneuver guidance strategy is needed because the residual energy of the aircraft in the returning process cannot be preset in advance. Aiming at the problems, the turning approach strategy provided by the patent not only can adapt to turning approach modes under different residual energies, but also can match the unified turning approach strategy requirements under different aircraft system parameters on the premise of analyzing the guidance law in a segmented manner.
In the developed guidance method for the approach turn of the aircraft return segment, the prior art [1] (see Lan X J, Liu L, Wang Y J. on line trajectory planning and guidance for reusable launch vehicles in the tertiary area [ J ]. Acta Astronautica,2016,118: 237-.
In the prior art [2] (see work, lift reentry aircraft reentry guidance and terminal energy management research [ D ]. harbin industrial university, 2011.), a turning alignment guidance method based on nominal approach trajectory information is provided, and although the method is better in precision and reliability, the method does not have universality and multitask mode adaptability due to the dependence on the nominal trajectory information.
Disclosure of Invention
The invention discloses a method for accurately guiding turning approach of a cross-domain aircraft return section, which aims to solve the technical problems that: by designing and deducing an analytic guidance law of the aircraft turning approach, the cross-domain aircraft turning approach is realized, wherein the aircraft turning approach comprises a direct approach and an indirect approach, and the invention can realize uniform and accurate guidance of the direct approach and the indirect approach. The invention has the following advantages: (1) the robustness is strong, and the repeatability is high; (2) the flexibility is high, and the method is suitable for various approach states; (3) the lift-drag ratio of the aircraft is not strictly limited and restricted; (4) the application range of the target approach track energy is wide.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a method for accurately guiding a turning approach of a cross-domain aircraft at a return section, which is used for establishing turning approach dynamics of an aircraft energy management area and giving starting and ending state constraints of the turning approach process of the aircraft. And segmenting the turning approach flight trajectory according to the flight trajectory characteristics of the aircraft, and deducing to obtain turning trajectory characteristic parameters and trajectory connection conditions of each segment. According to the segmented track, based on the circular arc track characteristic of the initial turning section, the open-loop control law of the initial turning section is deduced through a circular arc track constraint equation, based on the linear flight track characteristic of the linear capturing section, the proportional attack angle control law of the course is given, and based on the circular arc track characteristic of the runway alignment section, the open-loop control law of the runway alignment section is deduced through the circular arc track constraint equation. And constructing a cross-domain aircraft turning approach closed loop prediction correction guidance frame which takes the turning radius of the runway alignment section as a guidance parameter and takes the terminal approach energy as a correction target, so that a cross-domain aircraft turning approach track is given based on the guidance frame.
The invention discloses a method for accurately guiding a turning approach of a return section of a cross-domain aircraft, which comprises the following steps:
the method comprises the following steps: and establishing a turning approach dynamics model of the aircraft energy management area.
And selecting the central point of the aircraft landing runway as an origin to establish a ground inertia coordinate system. The x-axis direction is chosen to be the direction from the origin of coordinates along the runway toward the approach direction of the aircraft, and the y-axis is perpendicular to the x-axis in the horizontal plane and toward the right side of the approach direction of the aircraft, while the altitude h, the flight path angle γ, and the flight heading angle ψ are also considered in the dynamics equations. The corresponding kinetic equation is expressed as
Where μ represents the gravitational constant of the earth and V is the aircraft velocity. In order to facilitate the design of a subsequent guidance algorithm framework, a flight path energy parameter e is directly used as an independent variable, and the expression e is mu/r-V2And/2, wherein r is the size of the position radial, and the speed V can be directly obtained. Lift acceleration L and drag acceleration D of
Wherein S is the reference area of the aircraft, ρ is the dimensional earth atmospheric density, m is the mass of the aircraft, CLAnd CDThe lift coefficient and the drag coefficient are respectively, the parameters are generally functions of an attack angle alpha, and the attack angle is generally used as a control angle for adjusting flight path energy, so that the parameters are one of objects for open-loop guidance law design in a subsequent guidance law design process.
In addition, sigma is a roll angle, is a control angle of the aircraft in the approach turning process, and is also one of objects designed by an open-loop guidance law in the subsequent guidance law design process. Therefore, the control quantities in the subsequent open-loop guidance law design include the angle of attack α and the roll angle σ.
When the aircraft makes a turning approach, the initial state is usually given in real time according to the measurement system, so the initial stateThe state constraint is x (e)0)＝[x0,y0,h0,γ0,ψ0]T. To ensure that the aircraft can land safely on approach, the trajectory energy is generally sufficient at the moment the aircraft arrives at the alignment runway, so the end state constraint can be expressed as e (t) andf)＝ef. At the same time, since the position and direction of the aircraft aiming at the runway are also fixed, the tip position and heading angle, i.e. x, must be fixedf0, the aircraft is positioned on the runway straight line; psifAnd 0, indicating that the aircraft approaches towards the runway.
Step two: and segmenting the turning approach flight trajectory according to the flight trajectory characteristics of the aircraft, and deducing to obtain turning trajectory characteristic parameters and trajectory connection conditions of each segment. The subsection comprises an initial turning section, a linear capturing section and a runway aligning section.
And 2.1, segmenting the turning approach flight path according to the flight path characteristics of the aircraft.
According to the mode of the aircraft turning approach, considering the characteristics of the turning approach, the flight path in the whole process is divided into three sections, namely an initial turning section, a straight line capturing section and a runway aligning section.
And 2.2, establishing characteristic parameters of the initial turning section based on the flight track characteristics of the initial turning section.
In order to simplify the design complexity of the turning approach track, the starting point TEP of the initial turning section is the initial position of the aircraft starting approach, and the xy plane track of the initial turning is a circular arc. Recording the coordinate of the circle center of the track of the initial turning section as (x1, y1) and the radius of the initial turning section as RS1, at this time, according to the geometrical relationship of the initial turning section, the coordinate value of the circle center of the initial turning section is
Wherein, the coefficient matrix K is a coordinate conversion matrix which converts the original coordinate system into a coordinate system with the x-axis pointing to the center of a circle, and the expression is
The value of the radius RS1 of the initial turning circle is generally set according to the trajectory residual energy. The characteristic parameters also include the center of a turning circle (x1, y1), which is expressed as a function of RS 1.
And 2.3, establishing characteristic parameters of the runway alignment section according to the runway position and the initial state requirement in the landing process.
According to the terminal state constraint given in step one, the position and direction of the aircraft aiming at the runway are fixed, so that when the aircraft arrives at the runway aiming position ALI, the position of the aircraft is fixed as the terminal constraint, namely the terminal position is
Therefore, the center coordinates (x2, y2) of the runway alignment section can be intuitively obtained as
Wherein +/-represents that the aircraft is in a direct approach or an indirect approach, and the turning approach guidance strategy designed in the third subsequent step is generally used for the two approach modes.
The value of the radius RS2 of the runway alignment circle significantly affects the trajectory energy at the moment of runway alignment and will therefore be designed as a guidance parameter. In addition, the characteristic parameters also comprise the centers (x2, y2) of the runway alignment circles, and the expression of the characteristic parameters is shown as formula (6).
And 2.4, establishing characteristic parameters of the straight line capturing section.
The key parameter of the straight line capturing section is to determine the tangent points of the track of the section, namely an entry point A and an end point B, with the initial turning section and the runway alignment section, and the corresponding position coordinates are (xA, yA) and (xB, yB) respectively. In the straight line capturing segment, the characteristic parameters are used for calculating the position coordinates of the points A and B, so that a foundation is laid for the design of a subsequent guidance law. In order to calculate the two position coordinates, a constraint equation is established. First, points A and B satisfy the constraint equation of a circle, i.e.
(xA-x1)2+(yA-y1)2＝RS12 (7)
(xB-x2)2+(yB-y2)2＝RS22 (8)
Meanwhile, the AB line segment is on the common tangent line of the initial turning circle and the runway alignment circle, so that the requirement of the method is also met
Wherein k ═ 1 indicates whether the aircraft is an indirect approach or a direct approach, and if "-1", the aircraft is a direct approach, and if "+ 1", the aircraft is an indirect approach.
Respectively substituting the formula (9) into the formulae (7) and (8) to obtain the compound
Wherein the content of the first and second substances,
according to the formula (10), the value of yB is calculated as
Wherein the content of the first and second substances,
combined vertical type (9) and (11) are
The key parameters of the straight line capturing segment are the corresponding position coordinates (xA, yA) and (xB, yB) of the entry point A and the end point B, and the expression of the key parameters is equivalent to the function of the guidance parameters RS 2.
And 2.5, establishing track connection conditions in the whole turning approach process.
Step 2.4 provides characteristic parameters of the linear capturing section, namely tangent point position coordinates of the track of the linear capturing section and the initial turning section and the runway aligning section, namely position coordinates (xA, yA) and (xB, yB) corresponding to the entry point A and the end point B. The connection condition of the initial turning section and the linear capturing section is represented by the coordinates of the point A, and when the aircraft runs to the point A along the initial turning section, the aircraft enters the linear capturing section; and the connection condition of the linear capturing section and the runway alignment section is represented by a point B coordinate, and when the aircraft runs to the point B along the linear capturing section, the aircraft enters the runway alignment section.
Step three: deriving an open-loop control law of the initial turning section through an arc trajectory constraint equation based on the arc trajectory characteristic of the initial turning section, and giving a control law analytical expression of the initial turning section; based on the linear flight path characteristics of the linear capturing section, a range proportional attack angle control law is given, and the linear path energy attenuation process of any initial and final constraint can be realized; based on the arc track characteristics of the runway alignment section, the open-loop control law of the runway alignment section is deduced through an arc track constraint equation, and an analytic expression of the control law of the runway alignment section can be given.
Step 3.1: and deriving a roll angle sigma control law of the initial turning section and the runway alignment section.
For the initial turning section, since the flight trajectory is a circle on the xy plane, the following constraint relationship is satisfied
(x-x1)2+(y-y1)2＝RS12 (15)
The derivation is carried out on the formula (15) and simplified to obtain
2(x-x1)cosψ+2(y-y1)sinψ＝0 (16)
Meanwhile, the derivative is obtained again, and the dynamic equation (1) is combined to simplify the roll angle open-loop control law sigma of the initial turning section1Is composed of
Similarly, for the course alignment segment, the roll angle open-loop control law σ2Is composed of
And 3.2, giving an attack angle alpha control law of the linear capturing section.
In the initial turn and runway alignment sections, the angle of attack profile is typically constant, since it is considered how the aircraft turns. Whereas in the straight line capture section, the primary task of the aircraft is to reduce energy, and therefore, the angle of attack needs to be designed to meet the requirements. Meanwhile, in order to ensure that the three sections of attack angle profiles are continuous, the attack angle value of the initial moment of the linear capturing section needs to be ensured to be equal to the attack angle value alpha of the initial turning section0The angle of attack at the end of the linear capture segment is equal to the angle of attack alpha of the alignment segmentfTherefore, a range-based proportional attack angle control law is designed for the straight line capturing section. The overall angle of attack open-loop control law is as follows
Wherein s represents voyage, s0AIs the initial turn course, sABIs the total course of the straight line capturing section, scBIs the total range, s, from the current position to point BBfIs the course alignment segment voyage.
Step four: constructing a guidance parameter by taking the turning radius RS2 of the alignment section of the runway as a guidance parameter and taking the terminal approach energy efAnd correcting the guidance framework for the cross-domain aircraft turning approach closed-loop prediction of the correction target.
In step one, an initial state x (e) is given0)＝[x0,y0,h0,γ0,ψ0]TAnd an end energy constraint e (t)f)＝efThe problem to be solved is how to obtain the terminal track energy under the ideal constraint condition by iteratively calculating the guidance parameters on the premise of giving the initial state. Through the derivation of the second step and the third step, the radius RS1 of the initial turning circle track and the runway alignment position x are givenfMeanwhile, the characteristic parameters y1, (xA, yA), (xB, yB) of the whole flight path and the open-loop control laws of all stages in the flight process are constructed into a function of the turning circle radius RS2 of the runway alignment section. Therefore, the terminal track energy e can be used by taking RS2 as a guidance parameterfAnd constructing a cross-domain aircraft turning approach closed-loop prediction correction guidance frame for correcting the target.
The generation of the guidance track comprises a prediction link and a correction link, wherein in the prediction link, according to the alignment requirement of a terminal runway, the termination condition of numerical recursion prediction can be set as
y＝0 and-k·y-＞0 (20)
Wherein, y-The value of y before the instant of the terminal is shown, and k is defined in step two, namely k is +/-1 to indicate whether the aircraft is in an indirect approach or a direct approach, if the aircraft is in a negative 1 state, the aircraft is in a direct approach, and if the aircraft is in a positive 1 state, the aircraft is in an indirect approach.
For the calibration procedure, the target constraint equation is
Φ＝e(tf)-ef＝0 (21)
Therefore, a univariate implicit equation needs to be solved. Considering that the iterative convergence of the univariate correction equation is high, the Newton iteration method with simple algorithm structure is selected to solve the correction equation in each guidance link. The iterative process is
In the above formula, the first and second carbon atoms are,
by finite difference approximation. Because the iteration equation (22) has a single solution, the algorithm of the iteration process has strong robustness. Meanwhile, in the prediction correction guidance process, the turning circle radius RS2 of the runway alignment section is used as a guidance parameter, so that the method is not influenced by aircraft parameters and an approach state, and the algorithm flexibility is high. Iterative solution is carried out by the formula (22) to obtain a guidance parameter value meeting the terminal energy constraint under the allowable precision epsilon, namely the guidance parameter value is
RS2*＝{RS2(k+1)||Φ(RS2(k+1))≤ε＜|Φ(RS2(k))|} (23)
Step five: and C, a cross-domain aircraft turning approach closed loop prediction correction guidance frame constructed based on the step four is provided, and a cross-domain aircraft turning approach track is given.
Giving an initial state x (e) based on step one0)＝[x0,y0,h0,γ0,ψ0]TAnd terminal constraint e (t)f)＝ef、xf＝0、ψfEstablishing characteristic parameters y1, (xA, yA), (xB, yB) of the flight trajectory of each stage through the second step, constructing an open-loop control law of each stage in the flight process as a function of the turning circle radius RS2 of the runway alignment section, analyzing the open-loop control law by using an initial turning section, a straight line capturing section and the runway alignment section obtained in the third step to enable the aircraft to fly according to a preset characteristic trajectory, and finally, using the tail end approach energy e in the fourth stepfGiving out a runway alignment section turning radius RS2 meeting terminal energy constraint for a cross-domain aircraft turning approach closed loop prediction correction guidance framework for correcting a target, and substituting the turning radius RS2 into an open loop control law in the third step and an open loop control law in the second stepAnd connecting conditions in three stages, and obtaining a turning approach flight track of the cross-region aircraft meeting the terminal energy constraint and the runway alignment position through numerical integration.
Has the advantages that:
1. the invention discloses a turning approach accurate guidance method for a cross-domain aircraft return section, which is characterized in that a flight track is segmented into an initial turning section, a straight line capturing section and a runway aligning section, and a roll angle control law and an attack angle control law are deduced based on track characteristics of each section, so that the coupling of longitudinal flight and lateral flight in turning approach flight is simplified, and further, a guidance system is simple in structure and high in efficiency.
2. The invention discloses a method for accurately guiding the turning approach of a return section of a cross-domain aircraft, which is characterized in that the initial state only determines the radius of the track of the initial turning section and is irrelevant to the radius RS2 of the alignment circle of a runway, so that the initial state does not directly influence the guidance process, the initial state of the turning approach of the aircraft is not limited, and the flexibility is high.
3. According to the method for accurately guiding the turning approach of the return section of the cross-domain aircraft, the section of the turning approach track is designed only according to the geometrical characteristics of the flight track, so that the configuration of the turning approach track is not influenced by the pneumatic parameters of the aircraft, and the application range is wide.
4. According to the method for accurately guiding the turning approach of the cross-domain aircraft return section, the design of the turning approach track only needs to consider the direction of the aircraft relative to the runway and is not influenced by a specific approach mode, so that a guidance frame has universality on the approach process of the aircraft, and the repeatability is high.
Drawings
FIG. 1 is a schematic view of the direct approach and the indirect approach of an aircraft in step 2 of the present invention;
FIG. 2 is a flow chart of a method for accurately guiding the turning approach of a cross-domain aircraft return section in the invention;
FIG. 3 is a flight trajectory of a direct approach of the aircraft in the present embodiment;
fig. 4 is a flight trajectory of the indirect approach of the aircraft in the present embodiment.
Detailed Description
To better illustrate the objects and advantages of the present invention, the present invention is explained in detail below by a simulation analysis of a cross-domain aircraft turn approach guidance problem.
Example 1:
as shown in fig. 2, the method for accurately guiding the turning approach of the return section of the cross-domain aircraft disclosed by the embodiment of the invention comprises the following steps:
the method comprises the following steps: and establishing turning approach dynamics of an aircraft energy management area.
And selecting the central point of the aircraft landing runway as an origin to establish a ground inertia coordinate system. The x-axis direction is chosen to be the direction from the origin of coordinates along the runway toward the approach direction of the aircraft, and the y-axis is perpendicular to the x-axis in the horizontal plane and toward the right side of the approach direction of the aircraft, while the altitude h, the flight path angle γ, and the flight heading angle ψ are also considered in the dynamics equations. The corresponding kinetic equation is expressed as:
where μ represents the gravitational constant of the earth and V is the aircraft velocity. In order to facilitate the design of a subsequent guidance algorithm framework, a flight path energy parameter e is directly used as an independent variable, and the expression e is mu/r-V2And/2, wherein r is the size of the position radial, and the speed V can be directly obtained. The lift acceleration L and the drag acceleration D are:
wherein S is the reference area of the aircraft, ρ is the dimensional earth atmospheric density, m is the mass of the aircraft, CLAnd CDLift coefficient and drag coefficient respectively, the parameters are generally functions of attack angle alpha, and the attack angle is generally used as a control angle for adjusting flight path energy, so that the parameters are open-loop guidance and guidance in the subsequent guidance law design processOne of the objects of the law design.
In addition, sigma is a roll angle, is a control angle of the aircraft in the approach turning process, and is also one of objects designed by an open-loop guidance law in the subsequent guidance law design process. Therefore, the control quantities in the subsequent open-loop guidance law design include the angle of attack α and the roll angle σ.
When the aircraft makes a turning approach, the initial state is usually given in real time according to a measurement system, so that the initial state is constrained to be x (e)0)＝[x0,y0,h0,γ0,ψ0]T. To ensure that the aircraft can land safely on approach, the trajectory energy is generally sufficient at the moment the aircraft arrives at the alignment runway, so the end state constraint can be expressed as e (t) andf)＝ef. At the same time, since the position and direction of the aircraft aiming at the runway are also fixed, the tip position and heading angle, i.e. x, must be fixedf0, the aircraft is positioned on the runway straight line; psifAnd 0, indicating that the aircraft approaches towards the runway.
Step two: and segmenting the turning approach flight trajectory according to the flight trajectory characteristics of the aircraft, and deducing to obtain turning trajectory characteristic parameters and trajectory connection conditions of each segment. The subsection comprises an initial turning section, a linear capturing section and a runway aligning section.
And 2.1, segmenting the turning approach flight path according to the flight path characteristics of the aircraft.
According to the mode of the aircraft turning approach, considering the characteristics of the turning approach, the flight path in the whole process is divided into three sections, namely an initial turning section, a straight line capturing section and a runway aligning section.
And 2.2, establishing characteristic parameters of the initial turning section based on the flight track characteristics of the initial turning section.
In order to simplify the design complexity of the turning approach track, the starting point TEP of the initial turning section is the initial position of the aircraft starting approach, and the xy plane track of the initial turning is a circular arc. Recording the coordinate of the circle center of the track of the initial turning section as (x1, y1) and the radius of the initial turning section as RS1, at this time, according to the geometrical relationship of the initial turning section, the coordinate value of the circle center of the initial turning section is
Wherein, the coefficient matrix K is a coordinate conversion matrix which converts the original coordinate system into a coordinate system with the x-axis pointing to the center of a circle, and the expression is
The value of the radius RS1 of the initial turning circle is generally set according to the trajectory residual energy. The characteristic parameters also include the center of a turning circle (x1, y1), which is expressed as a function of RS 1.
And 2.3, establishing characteristic parameters of the runway alignment section according to the runway position and the initial state requirement in the landing process.
According to the terminal state constraint given in step one, the position and direction of the aircraft aiming at the runway are fixed, so that when the aircraft arrives at the runway aiming position ALI, the position of the aircraft is fixed as the terminal constraint, namely the terminal position is
Therefore, the center coordinates (x2, y2) of the runway alignment section can be intuitively obtained as
Wherein +/-represents that the aircraft is in a direct approach or an indirect approach, and the turning approach guidance strategy designed in the third subsequent step is generally used for the two approach modes.
The value of the radius RS2 of the runway alignment circle significantly affects the trajectory energy at the moment of runway alignment and will therefore be designed as a guidance parameter. In addition, the characteristic parameters also comprise the centers (x2, y2) of the runway alignment circles, and the expression of the characteristic parameters is shown as formula (6).
And 2.4, establishing characteristic parameters of the straight line capturing section.
The key parameter of the straight line capturing section is to determine the tangent points of the track of the section, namely an entry point A and an end point B, with the initial turning section and the runway alignment section, and the corresponding position coordinates are (xA, yA) and (xB, yB) respectively. In the straight line capturing segment, the characteristic parameters are used for calculating the position coordinates of the points A and B, so that a foundation is laid for the design of a subsequent guidance law. In order to calculate the two position coordinates, a constraint equation is established. First, points A and B satisfy the constraint equation of a circle, i.e.
(xA-x1)2+(yA-y1)2＝RS12 (7)
(xB-x2)2+(yB-y2)2＝RS22 (8)
Meanwhile, the AB line segment is on the common tangent line of the initial turning circle and the runway alignment circle, so that the requirement of the method is also met
Wherein k ═ 1 indicates whether the aircraft is an indirect approach or a direct approach, and if "-1", the aircraft is a direct approach, and if "+ 1", the aircraft is an indirect approach.
Respectively substituting the formula (9) into the formulae (7) and (8) to obtain the compound
Wherein the content of the first and second substances,
according to the formula (10), the value of yB is calculated as
Wherein the content of the first and second substances,
combined vertical type (9) and (11) are
The key parameters of the straight line capturing segment are the corresponding position coordinates (xA, yA) and (xB, yB) of the entry point A and the end point B, and the expression of the key parameters is equivalent to the function of the guidance parameters RS 2.
And 2.5, establishing track connection conditions in the whole turning approach process.
Step 2.4 provides characteristic parameters of the linear capturing section, namely tangent point position coordinates of the track of the linear capturing section and the initial turning section and the runway aligning section, namely position coordinates (xA, yA) and (xB, yB) corresponding to the entry point A and the end point B. The connection condition of the initial turning section and the linear capturing section is represented by the coordinates of the point A, and when the aircraft runs to the point A along the initial turning section, the aircraft enters the linear capturing section; and the connection condition of the linear capturing section and the runway alignment section is represented by a point B coordinate, and when the aircraft runs to the point B along the linear capturing section, the aircraft enters the runway alignment section.
Step three: deriving an open-loop control law of the initial turning section through an arc trajectory constraint equation based on the arc trajectory characteristic of the initial turning section, and giving a control law analytical expression of the initial turning section; based on the linear flight path characteristics of the linear capturing section, a range proportional attack angle control law is given, and the linear path energy attenuation process of any initial and final constraint can be realized; based on the arc track characteristics of the runway alignment section, the open-loop control law of the runway alignment section is deduced through an arc track constraint equation, and an analytic expression of the control law of the runway alignment section can be given.
Step 3.1: and deriving a roll angle sigma control law of the initial turning section and the runway alignment section.
For the initial turning section, since the flight trajectory is a circle on the xy plane, the following constraint relationship is satisfied
(x-x1)2+(y-y1)2＝RS12 (15)
The derivation is carried out on the formula (15) and simplified to obtain
2(x-x1)cosψ+2(y-y1)sinψ＝0 (16)
Meanwhile, the derivative is obtained again, and the dynamic equation (1) is combined to simplify the roll angle open-loop control law sigma of the initial turning section1Is composed of
Similarly, for the course alignment segment, the roll angle open-loop control law σ2Is composed of
And 3.2, giving an attack angle alpha control law of the linear capturing section.
In the initial turn and runway alignment sections, the angle of attack profile is typically constant, since it is considered how the aircraft turns. Whereas in the straight line capture section, the primary task of the aircraft is to reduce energy, and therefore, the angle of attack needs to be designed to meet the requirements. Meanwhile, in order to ensure that the three sections of attack angle profiles are continuous, the attack angle value of the initial moment of the linear capturing section needs to be ensured to be equal to the attack angle value alpha of the initial turning section0And the straight line captures the segment terminal timeThe angle of attack value of (a) is equal to the angle of attack value alpha of the track alignment sectionfTherefore, a range-based proportional attack angle control law is designed for the straight line capturing section. The overall angle of attack open-loop control law is therefore as follows:
wherein s represents voyage, s0AIs the initial turn course, sABIs the total course of the straight line capturing section, scBIs the total range, s, from the current position to point BBfIs the course alignment segment voyage.
Step four: constructing a guidance parameter by taking the turning radius RS2 of the alignment section of the runway as a guidance parameter and taking the terminal approach energy efAnd correcting the guidance framework for the cross-domain aircraft turning approach closed-loop prediction of the correction target.
In step one, an initial state x (e) is given0)＝[x0,y0,h0,γ0,ψ0]TAnd an end energy constraint e (t)f)＝efThe problem to be solved by the patent is how to obtain the terminal track energy under the ideal constraint condition by iteratively calculating the guidance parameters on the premise of giving the initial state. Through the derivation of the second step and the third step, the radius RS1 of the initial turning circle track and the runway alignment position x are givenfMeanwhile, the characteristic parameters y1, (xA, yA), (xB, yB) of the whole flight path and the open-loop control laws of all stages in the flight process are constructed into a function of the turning circle radius RS2 of the runway alignment section. Therefore, the terminal track energy e can be used by taking RS2 as a guidance parameterfAnd constructing a cross-domain aircraft turning approach closed-loop prediction correction guidance frame for correcting the target.
The generation of the guidance track comprises a prediction link and a correction link, wherein in the prediction link, according to the alignment requirement of a terminal runway, the termination condition of numerical recursion prediction can be set as
y＝0 and -k·y-＞0 (20)
Wherein, y-Representing the value of y before the instant of the terminal, k being defined in step twoThat is, k ± 1 indicates whether the aircraft is an indirect approach or a direct approach, and is a direct approach if "-1" and an indirect approach if "+ 1".
For the calibration procedure, the target constraint equation is
Φ＝e(tf)-ef＝0 (21)
Therefore, a univariate implicit equation needs to be solved. Considering that the iterative convergence of the univariate correction equation is high, the Newton iteration method with simple algorithm structure is selected to solve the correction equation in each guidance link. The iterative process is
In the above formula, the first and second carbon atoms are,
by finite difference approximation. Because the iteration equation (22) has a single solution, the algorithm of the iteration process has strong robustness. Meanwhile, in the prediction correction guidance process, the turning circle radius RS2 of the runway alignment section is used as a guidance parameter, so that the method is not influenced by aircraft parameters and an approach state, and the algorithm flexibility is high. Iterative solution is carried out by the formula (22) to obtain a guidance parameter value meeting the terminal energy constraint under the allowable precision epsilon, namely the guidance parameter value is
RS2*＝{RS2(k+1)||Φ(RS2(k+1))|≤ε＜|Φ(RS2(k))|} (23)
Step five: and giving a turning approach track of the cross-domain aircraft.
Giving an initial state x (e) based on step one0)＝[x0,y0,h0,γ0,ψ0]TAnd terminal constraint e (t)f)＝ef、xf＝0、ψfAnd (0), establishing characteristic parameters y1, (xA, yA) and (xB, yB) of the flight trajectory of each stage through the step two, constructing the open-loop control law of each stage in the flight process into a function of the turning circle radius RS2 of the runway alignment section, and capturing the initial turning section and the straight line obtained in the step threeAnalyzing an open-loop control law of segment and runway alignment segment, enabling the aircraft to fly according to a preset characteristic track, and finally passing through the tail-end approach energy e in the step fourfAnd (3) for correcting the target cross-domain aircraft turning approach closed loop prediction correction guidance framework, giving out a runway alignment section turning radius RS2 meeting the terminal energy constraint, substituting the turning radius RS2 into an open-loop control law in the third step and the connection conditions of the three stages in the second step, and obtaining a cross-domain aircraft turning approach flight trajectory meeting the terminal energy constraint and the runway alignment position through numerical integration.
To verify the feasibility of the method, an initial state x is chosen0＝52450m，y0＝-54087m，h0＝28km，γ0＝-6.7°，V0＝914.2m/s，ψ0124.6. Selecting a target runway alignment position xf-8021m, target trajectory energy constraint of ef＝62.45km2/s2. The parametric model of the aircraft is exemplified by an X-33 aircraft. The radius RS1 of the initial turning section is taken as 50km, and the attack angle alpha of the initial turning section is taken0Angle of attack alpha of the aligned section of the runway, 20 degf＝5°。
Giving initial parameters of the turning approach through the first step, dividing the approach track based on the second step, and then obtaining the turning approach track of the cross-domain aircraft meeting the terminal energy constraint through the third step and the fourth step. In order to verify the adaptability and stability advantages of the method under different constraint conditions, simulation analysis of direct approach and indirect approach is given below respectively.
Table 1 shows the relevant parameters of the turn approach trajectory under direct approach and indirect approach conditions.
TABLE 1 direct approach and Indirect approach trajectory parameters
| Approach mode | RS2,km | Total time, s | Terminal height, km | Terminal velocity, m/s |
| Direct approach | 15.6123 | 431.4 | 3.72 | 103.9 |
| Indirect approach | 9.7414 | 436.6 | 3.72 | 104.11 |
As is apparent from the results of table 1, the main difference between direct approach and indirect approach is the radius of the runway alignment circle, and direct approach requires energy attenuation through a larger runway alignment circle because the energy attenuation is faster than indirect approach. Fig. 2 shows the flight trajectory for a direct approach and fig. 3 shows the flight trajectory for an indirect approach. The universality and the reliability of the turning approach guidance method can be shown from the lateral surface by two turning approach modes.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A turning approach accurate guidance method for a return section of a cross-domain aircraft is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: establishing a turning approach dynamics model of an aircraft energy management area;
step two: segmenting the turning approach flight trajectory according to the flight trajectory characteristics of the aircraft, and deducing to obtain turning trajectory characteristic parameters and trajectory connection conditions of each segment; the segments are respectively an initial turning segment, a linear capturing segment and a runway aligning segment;
step three: deriving an open-loop control law of the initial turning section through an arc trajectory constraint equation based on the arc trajectory characteristic of the initial turning section, and giving a control law analytical expression of the initial turning section; based on the linear flight path characteristics of the linear capturing section, a range proportional attack angle control law is given, and the linear path energy attenuation process of any initial and final constraint can be realized; deriving an open-loop control law of the runway alignment section through an arc trajectory constraint equation based on the arc trajectory characteristics of the runway alignment section, and giving a control law analytical expression of the runway alignment section;
step four: constructing a guidance parameter by taking the turning radius RS2 of the alignment section of the runway as a guidance parameter and taking the terminal approach energy efA closed loop prediction correction guidance frame for the turning approach of the cross-domain aircraft of the correction target;
step five: and C, a cross-domain aircraft turning approach closed loop prediction correction guidance frame constructed based on the step four is provided, and a cross-domain aircraft turning approach track is given.
2. The method for accurately guiding the turning approach of the return section of the cross-domain aircraft as claimed in claim 1, is characterized in that: the first implementation method comprises the following steps of,
selecting a central point of an aircraft landing runway as an origin to establish a ground inertia coordinate system; selecting the direction of an x axis as a direction which is from a coordinate origin to the approach direction of the aircraft along the runway, wherein a y axis is vertical to the x axis in the horizontal plane and faces to the right side of the approach direction of the aircraft, and simultaneously, the altitude h, the flight path angle gamma and the flight heading angle psi of the aircraft are also considered in the kinetic equation; the corresponding kinetic equation is expressed as
Where μ represents the gravitational constant of the earth and V is the aircraft velocity; in order to facilitate the design of a subsequent guidance algorithm framework, a flight path energy parameter e is directly used as an independent variable, and the expression e is mu/r-V2The r is the size of the position vector, and the speed V can be directly obtained; lift acceleration L and drag acceleration D of
Wherein S is the reference area of the aircraft, ρ is the dimensional earth atmospheric density, m is the mass of the aircraft, CLAnd CDThe parameters are respectively a lift coefficient and a drag coefficient, generally the parameters are functions of an attack angle alpha, and the attack angle is generally used as a control angle for adjusting flight track energy, so that the parameters are one of objects designed by an open-loop guidance law in the subsequent guidance law design process;
in addition, sigma is a roll angle, is a control angle of the aircraft in the approach turning process, and is also one of objects designed by an open-loop guidance law in the subsequent guidance law design process; therefore, the control variables in the subsequent open-loop guidance law design include an attack angle α and a roll angle σ;
when the aircraft makes a turning approach, the initial state is usually given in real time according to a measurement system, so that the initial state is constrained to be x (e)0)＝[x0,y0,h0,γ0,ψ0]T(ii) a To ensure that the aircraft can land safely on approach, the trajectory energy is generally sufficient at the moment the aircraft arrives at the alignment runway, so the end state constraint can be expressed as e (t) andf)＝ef(ii) a At the same time, since the position and direction of the aircraft aiming at the runway are also fixed, the tip position and heading angle, i.e. x, must be fixedf0 denotes flyThe walking device is positioned on the straight line of the runway; psifAnd 0, indicating that the aircraft approaches towards the runway.
3. The method for accurately guiding the turning approach of the return section of the cross-domain aircraft as claimed in claim 2, is characterized in that: the second step is realized by the method that,
step 2.1, segmenting the turning approach flight track according to the flight track characteristics of the aircraft;
according to the turning approach mode of the aircraft, considering the characteristics of the turning approach, dividing the flight path in the whole process into three sections, namely an initial turning section, a straight line capturing section and a runway aligning section;
step 2.2, establishing characteristic parameters of the initial turning section based on the flight track characteristics of the initial turning section;
in order to simplify the design complexity of the turning approach track, the starting point TEP of the initial turning section is the initial position of the aircraft starting to approach, and the xy plane track of the initial turning is a circular arc; recording the coordinate of the circle center of the track of the initial turning section as (x1, y1) and the radius of the initial turning section as RS1, at this time, according to the geometrical relationship of the initial turning section, the coordinate value of the circle center of the initial turning section is
Wherein, the coefficient matrix K is a coordinate conversion matrix which converts the original coordinate system into a coordinate system with the x-axis pointing to the center of a circle, and the expression is
The value of the radius RS1 of the initial turning circle is generally set according to the trajectory residual energy; in addition, the characteristic parameters also comprise the centers (x1, y1) of the turning circles, and the expression of the centers is a function of RS 1;
step 2.3, establishing characteristic parameters of the runway alignment section according to the runway position and the initial state requirement in the landing process;
according to the terminal state constraint given in step one, the position and direction of the aircraft aiming at the runway are fixed, so that when the aircraft arrives at the runway aiming position ALI, the position of the aircraft is fixed as the terminal constraint, namely the terminal position is
Therefore, the center coordinates (x2, y2) of the runway alignment section can be intuitively obtained as
Wherein +/-indicates that the aircraft is in a direct approach or an indirect approach, and the turning approach guidance strategy designed in the third subsequent step is generally used for the two approach modes;
the value of the radius RS2 of the runway alignment circle significantly influences the track energy at the runway alignment time, and therefore the value is designed as a guidance parameter; in addition, the characteristic parameters also comprise the centers (x2, y2) of the runway alignment circles, and the expression of the characteristic parameters is shown as formula (6);
step 2.4, establishing characteristic parameters of a straight line capturing section;
the key parameters of the straight line capturing section are that the tangent points of the section of track, the initial turning section and the runway aligning section, namely an entry point A and an end point B, need to be determined, and the corresponding position coordinates are (xA, yA) and (xB, yB) respectively; in the straight line capturing section, the characteristic parameters are used for calculating the position coordinates of the points A and B, so that a foundation is provided for the design of a subsequent guidance law; in order to calculate the two position coordinates, a constraint equation needs to be established; first, points A and B satisfy the constraint equation of a circle, i.e.
(xA-x1)2+(yA-y1)2＝RS12 (7)
(xB-x2)2+(yB-y2)2＝RS22 (8)
Meanwhile, the AB line segment is on the common tangent line of the initial turning circle and the runway alignment circle, so that the requirement of the method is also met
Wherein, k ═ 1 represents whether the aircraft is an indirect approach or a direct approach, if "-1", the aircraft is a direct approach, and if "+ 1", the aircraft is an indirect approach;
respectively substituting the formula (9) into the formulae (7) and (8) to obtain the compound
Wherein the content of the first and second substances,
according to the formula (10), the value of yB is calculated as
Wherein the content of the first and second substances,
combined vertical type (9) and (11) are
The key parameters of the straight line capturing segment are position coordinates (xA, yA) and (xB, yB) corresponding to the entry point A and the end point B, and the expression of the key parameters is equivalent to a function of the guidance parameter RS 2;
step 2.5, establishing track connection conditions of the whole turning approach process;
step 2.4, giving characteristic parameters of the linear capturing section, namely tangent point position coordinates of the track of the linear capturing section and the initial turning section and the runway aligning section, namely position coordinates (xA, yA) and (xB, yB) corresponding to the entry point A and the end point B; the connection condition of the initial turning section and the linear capturing section is represented by the coordinates of the point A, and when the aircraft runs to the point A along the initial turning section, the aircraft enters the linear capturing section; and the connection condition of the linear capturing section and the runway alignment section is represented by a point B coordinate, and when the aircraft runs to the point B along the linear capturing section, the aircraft enters the runway alignment section.
4. The method for accurately guiding the turning approach of the return section of the cross-domain aircraft as claimed in claim 3, wherein: the third step is to realize the method as follows,
step 3.1: deducing a roll angle sigma control law of an initial turning section and a runway alignment section;
for the initial turning section, since the flight trajectory is a circle on the xy plane, the following constraint relationship is satisfied
(x-x1)2+(y-y1)2＝RS12 (15)
The derivation is carried out on the formula (15) and simplified to obtain
2(x-x1)cosψ+2(y-y1)sinψ＝0 (16)
Meanwhile, the derivative is obtained again, and the dynamic equation (1) is combined to simplify the roll angle open-loop control law sigma of the initial turning section1Is composed of
Similarly, for the course alignment segment, the roll angle open-loop control law σ2Is composed of
Step 3.2, giving an attack angle alpha control law of the linear capturing section;
in the initial turn section and runway alignment section, the angle of attack profile is typically constant, since it is considered how the aircraft turns; in the straight line capture section, the main work of the aircraft is to reduce energy, so the angle of attack needs to be designed to meet the requirements; meanwhile, in order to ensure that the three sections of attack angle profiles are continuous, the attack angle value of the initial moment of the linear capturing section needs to be ensured to be equal to the attack angle value alpha of the initial turning section0The angle of attack at the end of the linear capture segment is equal to the angle of attack alpha of the alignment segmentfTherefore, a proportional attack angle control law based on voyage is designed for the straight line capturing section; the overall angle of attack open-loop control law is as follows
Wherein s represents voyage, s0AIs the initial turn course, sABIs the total course of the straight line capturing section, scBIs the total range, s, from the current position to point BBfIs the course alignment segment voyage.
5. The method for accurately guiding the turning approach of the return section of the cross-domain aircraft as claimed in claim 4, wherein: the implementation method of the fourth step is that,
in step one, an initial state x (e) is given0)＝[x0,y0,h0,γ0,ψ0]TAnd an end energy constraint e (t)f)＝efThe problem to be solved is how to obtain the terminal track energy under the ideal constraint condition by iteratively calculating the guidance parameters on the premise of giving an initial state; through the derivation of the second step and the third step, the radius RS1 of the initial turning circle track and the runway alignment position x are givenfMeanwhile, the whole flight path characteristic parameters y1, (xA, yA), (xB, yB) and the open-loop control laws of all stages in the flight process are constructed into a function of the turning circle radius RS2 of the runway alignment section; therefore, the terminal track energy e can be used by taking RS2 as a guidance parameterfConstructing a cross-domain aircraft turning approach closed-loop prediction correction guidance frame for a correction target;
the generation of the guidance track comprises a prediction link and a correction link, wherein in the prediction link, according to the alignment requirement of a terminal runway, the termination condition of numerical recursion prediction can be set as
y＝0 and -k·y-＞0 (20)
Wherein, y-The value of y before the terminal instant is shown, and k is defined in step two, namely k is +/-1 and represents whether the aircraft is in an indirect approach or a direct approach, if the aircraft is in a negative 1 state, the aircraft is in a direct approach, and if the aircraft is in a positive 1 state, the aircraft is in an indirect approach;
for the calibration procedure, the target constraint equation is
Φ＝e(tf)-ef＝0 (21)
Therefore, a univariate implicit equation needs to be solved; considering that the iterative convergence of the univariate correction equation is high, a Newton iteration method with a simple algorithm structure is selected to solve the correction equation in each guidance link; the iterative process is
In the above formula, the first and second carbon atoms are,
by finite difference approximation; the iteration equation (22) has a single solution, so the algorithm robustness of the iteration process is strong; at the same time due toIn the process of predicting and correcting guidance, the turning circle radius RS2 of the runway alignment section is used as a guidance parameter, so that the influence of aircraft parameters and an approach state is avoided, and the algorithm flexibility is high; iterative solution is carried out by the formula (22) to obtain a guidance parameter value meeting the terminal energy constraint under the allowable precision epsilon, namely the guidance parameter value is
RS2*＝{RS2(k+1)||Φ(RS2(k+1))|≤ε＜|Φ(RS2(k))|} (23)
6. The method for accurately guiding the turning approach of the return section of the cross-domain aircraft as claimed in claim 5, wherein: the fifth step is to realize that the method is that,
giving an initial state x (e) based on step one0)＝[x0,y0,h0,γ0,ψ0]TAnd terminal constraint e (t)f)＝ef、xf＝0、ψfEstablishing characteristic parameters y1, (xA, yA), (xB, yB) of the flight trajectory of each stage through the second step, constructing an open-loop control law of each stage in the flight process as a function of the turning circle radius RS2 of the runway alignment section, analyzing the open-loop control law by using an initial turning section, a straight line capturing section and the runway alignment section obtained in the third step to enable the aircraft to fly according to a preset characteristic trajectory, and finally, using the tail end approach energy e in the fourth stepfAnd (3) for correcting the target cross-domain aircraft turning approach closed loop prediction correction guidance framework, giving out a runway alignment section turning radius RS2 meeting the terminal energy constraint, substituting the turning radius RS2 into an open-loop control law in the third step and the connection conditions of the three stages in the second step, and obtaining a cross-domain aircraft turning approach flight trajectory meeting the terminal energy constraint and the runway alignment position through numerical integration.
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