CN114967749B - Maneuvering trajectory design method for low-cost altimeter - Google Patents

Maneuvering trajectory design method for low-cost altimeter Download PDF

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CN114967749B
CN114967749B CN202210672684.4A CN202210672684A CN114967749B CN 114967749 B CN114967749 B CN 114967749B CN 202210672684 A CN202210672684 A CN 202210672684A CN 114967749 B CN114967749 B CN 114967749B
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height profile
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CN114967749A (en
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王珣子
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Beijing Zhongke Feihong Technology Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses an optimal maneuvering trajectory design method for a low-cost altimeter, which mainly comprises a height section design module, a height section calculation module and a height section application module. The height profile design module is connected with the height profile calculation module and used for constructing a functional relation about height-residual voyage and extracting key design variables. The height profile calculation module is connected with the height profile design module, the height profile application module and the low-cost air pressure type altimeter and used for obtaining polynomial coefficients related to the height profile by solving an equation set according to given initial conditions, terminal conditions and design parameters so as to determine the final form of the height profile. And the height profile application module is connected with the height profile calculation module and is used for generating real-time normal overload according to the current motion state and the height profile design result. Different from the conventional thought of 'ballistic design-altitude measurement-ballistic correction', the method can provide altitude direction speed, acceleration, jerk and higher derivative information for the altimeter, compensate altitude measurement equipment from a ballistic planning layer, and realize the optimal balance between the control precision of the aircraft and the production and use cost.

Description

Maneuvering trajectory design method for low-cost altimeter
Technical Field
The invention belongs to the field of overall design of aircrafts, and relates to an online trajectory planning method suitable for a low-cost air pressure type altimeter.
Background
The invention solves the key contradiction problem between high control precision and low cost of the aircraft by taking low-cost multi-airspace combat missile weapons as background and aiming at the characteristics of large flight airspace, high altitude change, high response speed and the like.
For high-altitude large-span flight, real-time altitude measurement is usually realized by adopting an air pressure type altimeter, and corresponding measurement information is used as feedback of a trajectory control system, so that online guidance and mission planning are realized. The air pressure type altimeter can give the flying height of the aircraft in real time according to the atmospheric environment, is the most direct and effective means for on-missile on-line height measurement, is extremely important for ballistic, guidance, navigation and control systems of the aircraft, and has wide application in the fields of aerospace, war industry, civil use and the like. The pneumatic altimeter can adapt to a large flight airspace and an altitude change rate, but the inherent defect of the pneumatic altimeter in measurement precision needs to be compensated through technical means.
At present, the precision compensation schemes for the low-cost air pressure type altimeter mainly include the following:
the first scheme comprises the following steps: the system is made up by means of high-precision measuring instruments, high-precision inertial measurement units, GPS/Beidou navigator and other equipment. The above compensation means are generally not desirable for low cost aircraft.
Scheme II: the altitude-air pressure nonlinear solver is used, but is influenced by an unsteady and nonlinear relation between the altitude and the atmospheric environment, so that the high-precision control requirement of the aircraft cannot be met.
The existing ballistic control method based on the low-cost air pressure type altimeter has the following defects:
the first disadvantage is that: the height information measurement accuracy and the real-time property are poor. The low-cost air pressure type altimeter is slightly insufficient in the atmospheric environment measurement sensing precision, cannot adapt to the rapid and large-scale change of the aircraft in height, and cannot provide accurate information input for a high-speed flight trajectory mode of strong maneuvering.
The second disadvantage is that: the cost of improving the accuracy of the height measurement information is high. The inherent deficiency of the low-cost altimeter in the measurement precision is usually made up by means of high-precision measuring instruments, high-precision inertial measurement units, GPS/Beidou navigator and other equipment; these compensation means can greatly increase the manufacturing and use costs of the height measuring system, and are not economical.
The third defect: the altitude-atmosphere functional relationship is poorly adapted. The sea pressure correction method is a common air pressure altimeter compensation correction method at present, and the function fitting method is a common means for realizing rapid altitude calculation and correcting measurement data according to an air pressure sensor. However, the relationship between altitude and air pressure is not constant, and cannot be determined analytically, or cannot be expressed comprehensively by using a general fitting method, especially when the aircraft flies at high speed and the altitude changes dramatically.
The defect four is as follows: too strong design constraints affect ballistic design flexibility. In order to use a low-cost air pressure type altimeter, a large number of constraint conditions such as an altitude interval, an altitude change rate, an altitude direction acceleration and the like are generally required to be applied in the design process of a missile weapon system; these constraints greatly limit the feasible range of ballistic design and do not satisfy the requirements of highly dynamic combat modes on ballistic guidance systems.
The traditional altimeter precision compensation mode has the problems of high cost, complex structure, increased total weight, weak interference resistance and the like, and is difficult to meet the low-cost operational use mode. The invention provides an online trajectory planning method suitable for a low-cost altimeter. Different from the conventional thought of ballistic design-altitude measurement-ballistic correction, the method can provide information of speed, acceleration, jerk and higher derivative in the altitude direction for the air pressure type altimeter, compensate altitude measurement equipment from a ballistic planning layer, and realize the optimal balance between the control precision of the aircraft and the production and use cost.
Disclosure of Invention
The invention aims to provide an online trajectory planning method suitable for a low-cost altimeter, which has better anti-interference effect, applicability and efficiency and does not need to rely on an additional high-cost measuring device.
The purpose of the invention is realized by the following technical scheme:
(1) Design altitude-remaining range flight profile
The fly height is designed as a function of the remaining range:
Figure 969341DEST_PATH_IMAGE001
wherein the content of the first and second substances,nis of the order of a polynomial,a i in order to obtain the coefficients to be calculated,Kis a correction coefficient. The invention is to getn=5。
(2) Generating altimeter feedback information
And calculating the speed, the acceleration, the jerk and the high-order derivative in the height direction according to the formula.
(3) Generating flight control information
And calculating the first/second derivative of the altitude to the residual voyage according to the aircraft dynamics equation, and then solving the overload control.
(4) Trajectory iteration method considering terminal constraint and altimeter use constraint
Is provided withF(R L ) Determining flight profile for a fifth order polynomialF(R L ) In (1)And thus there are 6 unknowns to solve for. These unknowns are solved by constructing 6 equations.
1) Two boundary condition equations can be obtained according to the current height and the terminal height.
2) According to the current flight path angle and the terminal flight path angle, two boundary condition equations can be obtained.
3) Let 1/3 and 2/3 of the remaining voyage (respectively noted as
Figure DEST_PATH_IMAGE002
And
Figure 542274DEST_PATH_IMAGE003
) Respectively height value ofh 1 Andh 2 then, there are:
Figure DEST_PATH_IMAGE004
the six equations form an equation set, givenh 1 Andh 2 thereafter, a polynomial can be obtained by solving the system of equationsF(R L ) Coefficient (2) of (1). The design variables are defined as:
Figure 712224DEST_PATH_IMAGE005
(5) Height profile on-line correction method
Calculating normal overload according to the real-time motion state and the section design result of the aircraft, and carrying out recursion to the next motion state after the aircraft is brought into a trajectory control system; and cruising the steps until the residual range is zero.
According to the technical scheme, the invention can provide the speed, the acceleration, the jerk and higher derivative information in the height direction for the air pressure type altimeter, the altitude measurement equipment is compensated from the ballistic planning layer, and the optimal balance between the control precision of the aircraft and the production and use cost can be realized; with only two parameters involved: (h 1 , h 2 ) The ballistic trajectory design can be completed by only solving one equation set, the overall calculation amount is low, the online ballistic trajectory reconstruction based on the height measurement information is facilitated, and the method is superior to the traditional scheme in the aspects of information source and efficiency.
Drawings
In order to clearly illustrate the technical solution of the present invention, the following description will be made with reference to the accompanying drawings. For a person skilled in the art, without inventive effort, further figures can also be obtained from these figures.
Fig. 1 is a schematic diagram of a feedback control strategy based on an altitude-remaining flight profile according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a design result of flight profiles with different altitudes and remaining flight according to an embodiment of the present invention.
Fig. 3 is a diagram illustrating a result of designing a height variation rate curve according to an embodiment of the present invention.
Fig. 4 is a diagram illustrating a design result of a height direction acceleration curve according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a design result of a normal overload control curve according to an embodiment of the present invention.
Fig. 6 is a diagram illustrating the design result of the ballistic inclination angle change rate curve according to the embodiment of the present invention.
Fig. 2 to 6 employ the same initial conditions and terminal conditions, but different profile design parameters. For those skilled in the art, the initial conditions, the final conditions and the profile design parameters (in the formula) can be changed without creative efforth 1 Andh 2 ) Other figures may also be obtained.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings in the technology of the invention; the described embodiments are not all embodiments of the invention. Based on the embodiments of the present invention, those skilled in the art can obtain other embodiments without creative efforts, which belong to the protection scope of the present invention.
The embodiment of the invention provides a maneuvering trajectory design method for a low-cost altimeter, which can provide altitude direction speed, acceleration, jerk and higher derivative information for the low-cost altimeter, compensate altitude measurement equipment from a trajectory planning layer, and realize optimal balance between aircraft control precision and production and use cost. The method mainly comprises the following steps: the device comprises a height profile design module, a height profile calculation module and a height profile application module; wherein:
(1) The height profile design module is connected with the height profile calculation module and used for constructing a function relation about height-residual voyage and extracting key design variables;
if the aircraft moves at a constant speed, the kinetic equation is as follows:
Figure DEST_PATH_IMAGE006
wherein the content of the first and second substances,Vin order to be the magnitude of the speed,γin order to form the inclination angle of the trajectory,hin order to achieve the flying height,N y in order to normally control the overload, the overload is controlled,a e which is the radius of the earth, is,gthe acceleration of the gravity of the earth is the magnitude,R L the remaining voyage (the voyage from the current point to the target point).
The flying height is designed as a function of the remaining range, see formula.
(2) The height profile calculation module is connected with the height profile design module, the height profile application module and the low-cost air pressure type altimeter and used for obtaining polynomial coefficients related to the height profile by solving an equation set according to given initial conditions, terminal conditions and design parameters so as to determine the final form of the height profile;
determining flight profile solving functionF(R L ) Coefficient (b) in (c). Due to the fact thatF(R L ) For a polynomial of the fifth order, there are 6 unknowns to solve for, and 6 equations to construct.
1) From the current altitude and the terminal altitude, two equations can be derived:
Figure 638592DEST_PATH_IMAGE007
2) According to the current flight path angle and the terminal flight path angle, two equations can be obtained:
Figure DEST_PATH_IMAGE008
3) The expansion can be given as:
Figure 846107DEST_PATH_IMAGE009
definition of
Figure DEST_PATH_IMAGE010
Then there is
Figure 199728DEST_PATH_IMAGE011
Wherein:
Figure DEST_PATH_IMAGE012
Figure 122553DEST_PATH_IMAGE013
in summary, only two parameters need to be given for determining the flight profile, i.e. in the formulah 1 Andh 2 。
(3) And the height profile application module is connected with the height profile calculation module and is used for generating real-time normal overload according to the current motion state and the height profile design result.
According to the aircraft dynamics equation, the first and second derivatives of altitude versus remaining range can be expressed as:
Figure DEST_PATH_IMAGE014
according to the kinetic equation, the following can be obtained:
Figure 711667DEST_PATH_IMAGE015
the overload can thus be controlled as:
Figure DEST_PATH_IMAGE016
as shown in fig. 1, the entire height profile update process is detailed as follows:
1) Normal overload is calculated according to the formula and is brought into a trajectory control system;
2) According to a kinetic equation, recursion is carried out to obtain the flight state at the next moment;
3) Re-determining the coefficients according to the formula and the terminal constraint according to the real-time motion state and the terminal constraint;
4) And (5) returning to the step 1 until the residual voyage is zero.
According to the scheme, the obtained partial embodiment is shown in figures 2-6.
FIG. 2 shows the design height profile with the remaining range as the independent variable, under different design parameters (h 1 , h 2 ) The altitude of the aircraft varies with the remaining range. It can be seen that the ballistic design results meet the initial height (15 km) and the terminal height (10 km) and meet the range constraint (177.4 km) under different design parameters.
FIG. 3 shows the design height profile with the remaining range as the independent variable, under different design parameters (h 1 , h 2 ) The history of the altitude change of the aircraft with the remaining voyage. It can be seen that the rate of change of altitude of the aircraft is continuous and very smooth, with the rate of change also being continuous and smooth, at different design parameters, which is advantageous for both the measurement and the calculation of low cost altimeters.
FIG. 4 shows the design of the height profile with the remaining range as an independent variable in different settingsThe parameters are measured by (h 1 , h 2 ) The second derivative of the change in altitude of the aircraft with time (acceleration in the altitude direction) is the history of the change with the remaining course. It can be seen that under different design parameters, the acceleration of the aircraft in the height direction is continuous and very smooth, and the change rate of the acceleration is also continuous and smooth, which is very beneficial to the measurement and calculation of the low-cost altimeter, and meanwhile, the height profile design method provided by the invention can provide high-order derivatives in the height direction, and can provide more reliable height information for a height measurement system.
FIG. 5 shows the design height profile with the remaining range as the independent variable, under different design parameters: (h 1 , h 2 ) The normal control overload of the aircraft follows the course of the remaining voyage. It can be seen that the control overload of the aircraft is continuous and very smooth under different design parameters, and the change rate of the control overload is continuous and smooth, which is beneficial to the control system to realize flight control, and simultaneously, the intensity of the overload change is reduced, and the interference of external load on the height measuring device is also beneficial to be reduced.
FIG. 6 shows the design height profile with the remaining range as the independent variable, under different design parameters (A and B)h 1 , h 2 ) The change course of the trajectory inclination angle of the aircraft along with the remaining voyage. It can be seen that under different design parameters, the ballistic design results all satisfy the initial height (0 °) and the terminal height (-10 °), and satisfy the course constraint (177.4 km); at the same time, the trajectory inclination of the aircraft is continuous and very smooth, and the change rate is also continuous and smooth, which is also reflected in the normal overload.
The invention has the following advantages:
(1) High-order derivative information such as speed, acceleration, jerk and the like in the altitude direction can be rapidly output according to the current remaining range, and the high-order derivative information is used for compensating the deficiency of the low-cost altimeter in the measurement information;
(2) The height profile meeting the use constraint of the low-precision altimeter is generated on line, the overall height variation trend is smooth, and the high-order derivative of the height meets the continuity and the conductibility;
(3) And online trajectory correction on the height channel is realized, and trajectory reconstruction can be completed only through two design variables.
The above description is only one of the embodiments of the present invention, and the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the present invention, and the present invention shall be subject to the protection scope of the appended claims.

Claims (1)

1. A maneuvering trajectory design method facing a low-cost altimeter is characterized in that altitude direction speed, acceleration, jerk and higher derivative information can be provided for the low-cost altimeter, altitude measurement equipment is compensated from a trajectory planning layer, and optimal balance between aircraft control precision and production and use cost can be achieved;
the method mainly comprises the following steps: the device comprises a height profile design module, a height profile calculation module and a height profile application module;
wherein:
1) The height profile design module is connected with the height profile calculation module and used for constructing a function relation about height-residual voyage and extracting key design variables;
if the aircraft moves at a constant speed, the kinetic equation is as follows:
Figure FDA0004080320600000011
wherein V is the velocity, gamma is the trajectory inclination, h is the flight altitude, N y For normal control of overload, a e Is the radius of the earth, g is the magnitude of the acceleration of the earth's gravitational force, R L The remaining voyage is taken;
the fly height is designed as a function of the remaining range:
Figure FDA0004080320600000012
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004080320600000013
wherein n is a polynomial order, a i The coefficient to be solved is K, and the K is a correction coefficient;
calculating the speed, the acceleration, the jerk and the high-order derivative in the height direction according to the function of the remaining flight;
calculating first/second derivatives of the altitude to the remaining voyage according to an aircraft dynamics equation, and then solving for overload control;
2) The height profile calculation module is connected with the height profile design module, the height profile application module and the low-cost air pressure type altimeter and used for obtaining polynomial coefficients related to the height profile by solving an equation set according to given initial conditions, terminal conditions and design parameters so as to determine the final form of the height profile;
let F (R) L ) Determining the flight profile for a fifth order polynomial L ) The coefficient of (1);
from the current altitude and the terminal altitude, two equations can be derived:
Figure FDA0004080320600000014
according to the current flight path angle and the terminal flight path angle, two equations can be obtained:
Figure FDA0004080320600000021
setting the height values h of 1/3 and 2/3 of the remaining voyage respectively 1 And h 2 ，
Are respectively recorded as
R L1 ＝R L0 -(R L0 -R Lf ) 3, and
R L2 ＝R Lf -(R L0 -R Lf ) And/3, then:
Figure FDA0004080320600000022
the equations form an equation set, and after h1 and h2 are given, coefficients in a polynomial F (RL) can be obtained by solving the equation set, and design variables are defined as follows:
U h ＝[h 1 ,h 2 ] T ；
3) And the height profile application module is connected with the height profile calculation module and is used for generating real-time normal overload according to the current motion state and the height profile design result.
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