CN113503777A - Carrier rocket boosting section guidance method and device based on trajectory analytic solution - Google Patents
Carrier rocket boosting section guidance method and device based on trajectory analytic solution Download PDFInfo
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Abstract
The invention provides a carrier rocket boosting section guidance method and device based on trajectory analytic solution, wherein a boosting section trajectory stepwise solving model of a carrier rocket is established, then the boosting section trajectory stepwise solving model is based on the boosting section trajectory stepwise solving model, the trajectory analytic solution of the boosting section is obtained by using a regular perturbation theory under the condition that the attack angle of the carrier rocket is zero, the analytic solution of the boosting section is further based on the boosting section trajectory stepwise solving model and the analytic solution of the boosting section trajectory under the condition that the attack angle of the carrier rocket is zero, and the trajectory analytic solution of the boosting section is obtained by using the regular perturbation method under the condition that the attack angle of the carrier rocket is not zero; and finally, solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analysis solution and a predetermined guidance strategy. According to the method, the trajectory analytical solution of the carrier rocket in the boosting section is solved, and the analytical solution model of the optimal guidance instruction is established based on the analytical solution, so that numerical integral prediction is avoided, the guidance efficiency is improved, and the practicability is high.
Description
Technical Field
The invention relates to the technical field of aerospace technology and weapons, in particular to a carrier rocket boosting section guidance method and device based on trajectory analytic solution.
Background
The current carrier rocket boosting section trajectory can be generally divided into a program flight section in the atmosphere and a guidance flight section outside the atmosphere, wherein the program flight section adopts an open-loop control instruction set according to time or speed and is not generally subjected to feedback adjustment; and the guidance flight section adopts perturbation guidance or iterative guidance to carry out closed-loop correction. The current closed-loop guidance method in the atmosphere generally adopts an optimal control theory to carry out modeling, and adopts a numerical optimization algorithm to carry out solving, such as a modified shooting method, a matching method, a minimum value algorithm and the like. However, the method has the disadvantages of large calculation amount, low efficiency and low practicability in the implementation process.
Disclosure of Invention
In view of the above, the present invention provides a method and an apparatus for guiding a launch vehicle boosting section based on trajectory analysis solution, so as to improve the guiding efficiency and the practicability.
In a first aspect, an embodiment of the present invention provides a carrier rocket assisted section guidance method based on trajectory analytic solution, including: establishing a boosting section trajectory step-by-step solving model of the carrier rocket; based on a boosting section trajectory step-by-step solving model, solving a trajectory analytic solution of the boosting section by using a regular perturbation theory under the condition that the attack angle of the carrier rocket is zero; based on a boosting section trajectory step-by-step solving model and an analytic solution of a boosting section trajectory under the condition that the attack angle of the carrier rocket is zero, solving the trajectory analytic solution of the boosting section by using a regular perturbation method under the condition that the attack angle of the carrier rocket is not zero; and solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analysis solution and a predetermined guidance strategy.
With reference to the first aspect, an embodiment of the present invention provides a first possible implementation manner of the first aspect, where the step of establishing a stepped solution model of a thrusting section trajectory of a launch vehicle includes: based on a predetermined dynamic model of a boosting section of the carrier rocket, establishing a dynamic model of a trajectory of the boosting section under the condition that an attack angle of the carrier rocket is zero; based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is not zero; and determining the kinetic model and the incremental kinetic model of the boosting section trajectory as a boosting section trajectory step-by-step solving model.
With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention provides a second possible implementation manner of the first aspect, where, based on a boost-section ballistic step-by-step solution model, a step of solving a ballistic analytic solution of a boost section by using a regular perturbation theory when an angle of attack of a launch vehicle is zero includes: on the basis of a dynamic model of a boosting section trajectory under the condition that an attack angle of a carrier rocket is zero, establishing a first regular perturbation model by using a regular perturbation theory; generating a zero-order differential equation of a zero-attack-angle trajectory and a first-order differential equation of the zero-attack-angle trajectory based on the first regular perturbation model; obtaining a zero-order term analytic solution of the zero-attack-angle trajectory based on a zero-order term differential equation of the zero-attack-angle trajectory; obtaining a first-order analytic solution of the zero attack angle trajectory based on a first-order differential equation of the zero attack angle trajectory; generating an approximate trajectory analytic solution of a boosting section under the condition that the attack angle of the carrier rocket is zero based on a zero-order analytic solution of a zero attack angle trajectory and a first-order analytic solution of the zero attack angle trajectory; and determining the approximate trajectory analytic solution as the trajectory analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is zero.
With reference to the second possible implementation manner of the first aspect, an embodiment of the present invention provides a fourth possible implementation manner of the first aspect, where, based on the step-by-step solution model for the trajectory of the booster section and the analytic solution for the trajectory of the booster section when the angle of attack of the carrier rocket is zero, the step of solving the analytic solution for the trajectory of the booster section by using a regular perturbation method when the angle of attack of the carrier rocket is not zero includes: on the basis of an incremental dynamic model of a boosting section trajectory under the condition that the attack angle of a carrier rocket is not zero, establishing a second regular perturbation model by using a regular perturbation theory; generating a zero-order differential equation of the ballistic increment and a first-order differential equation of the ballistic increment based on the second regular perturbation model; obtaining a zero-order analytic solution of the ballistic increment based on a zero-order item differential equation of the ballistic increment; obtaining a first-order analytic solution of the ballistic increment based on a first-order item differential equation of the ballistic increment; generating an approximate analysis solution of the ballistic increment based on a zeroth-order analysis solution of the ballistic increment and a first-order analysis solution of the ballistic increment; and determining the sum of the ballistic analytic solutions of the boosting section as the ballistic analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is not zero and the approximate analytic solution of the ballistic increment and the attack angle of the carrier rocket are zero.
With reference to the first aspect, an embodiment of the present invention provides a fourth possible implementation manner of the first aspect, where the step of obtaining an optimal guidance instruction of the launch vehicle in the boosting section according to the ballistic analytic solution and the predetermined guidance strategy includes: obtaining a relational expression between the terminal state and an attack angle curve based on a ballistic analytical solution; establishing a correction model of the terminal state deviation based on the relational expression; approximating the performance index of a predetermined carrier rocket in a boosting section by using a Chebyshev interpolation polynomial to obtain a discrete performance index; establishing an analytical solving model of optimal guidance correction based on a correction model of terminal state deviation and discrete performance indexes; and solving the optimal guidance instruction based on the analysis solving model of the optimal guidance correction and the predetermined guidance strategy.
In a second aspect, an embodiment of the present invention further provides a boosting segment guidance device based on a ballistic analytic solution, including: the model establishing module is used for establishing a boosting section trajectory step-by-step solving model of the carrier rocket; the first solving module is used for solving a ballistic analysis solution of the boosting section under the condition that the attack angle of the carrier rocket is zero by utilizing a regular perturbation theory based on a boosting section ballistic step-by-step solving model; the second solving module is used for solving an analytic solution of the boosting section trajectory based on a boosting section trajectory step-by-step solving model and under the condition that the attack angle of the carrier rocket is zero, and solving the analytic solution of the trajectory of the boosting section by using a regular perturbation method under the condition that the attack angle of the carrier rocket is not zero; and the optimal guidance module is used for solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analytic solution and the predetermined guidance strategy.
With reference to the second aspect, an embodiment of the present invention provides a first possible implementation manner of the second aspect, where the model building module is further configured to: based on a predetermined dynamic model of a boosting section of the carrier rocket, establishing a dynamic model of a trajectory of the boosting section under the condition that an attack angle of the carrier rocket is zero; based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is not zero; and determining the kinetic model and the incremental kinetic model of the boosting section trajectory as a boosting section trajectory step-by-step solving model.
In a third aspect, an embodiment of the present invention further provides an electronic device, including a processor and a memory, where the memory stores machine-executable instructions capable of being executed by the processor, and the processor executes the machine-executable instructions to implement the foregoing method.
In a fourth aspect, embodiments of the present invention also provide a machine-readable storage medium storing machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the above-described method.
The embodiment of the invention has the following beneficial effects:
the embodiment of the invention provides a carrier rocket boosting section guidance method and device based on trajectory analytic solution, wherein a boosting section trajectory step solving model of a carrier rocket is established firstly, then the boosting section trajectory step solving model is based on the boosting section trajectory step solving model, the trajectory analytic solution of the boosting section is obtained by utilizing the regular perturbation theory under the condition that the attack angle of the carrier rocket is zero, the analytic solution of the boosting section trajectory is further based on the boosting section trajectory step solving model and the analytic solution of the boosting section trajectory under the condition that the attack angle of the carrier rocket is zero, and the trajectory analytic solution of the boosting section is obtained by utilizing the regular perturbation method under the condition that the attack angle of the carrier rocket is not zero; and finally, solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analysis solution and a predetermined guidance strategy. According to the method, the trajectory analytic solution of the carrier rocket in the boosting section is solved, and the analytic solution model of the optimal guidance instruction is established based on the analytic solution, so that numerical integral prediction is avoided, the guidance efficiency is improved, and the practicability is high.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a flowchart of a launch vehicle boosting section guidance method based on a ballistic analytic solution according to an embodiment of the present invention;
FIG. 2 is a function provided by an embodiment of the present invention
Comparing the graph with the fitting interpolation polynomial;
FIG. 3 is a function provided by an embodiment of the present invention
Comparing the graph with the fitting interpolation polynomial;
FIG. 4 is a graph of height Vs ballistic dip for four different terminal constraints provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of the calculation time of each guidance period under the constraint of four different terminals according to the embodiment of the present invention;
FIG. 6 is a schematic diagram of the calculated time of the guidance cycle provided by the embodiment of the invention;
fig. 7 is a schematic structural diagram of a device for guiding a launch vehicle boosting section based on a ballistic analytic solution according to an embodiment of the present invention;
fig. 8 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The current boosting section trajectory can be generally divided into a program flight section in the atmosphere and a guidance flight section outside the atmosphere, wherein the program flight section adopts an open-loop control instruction set according to time or speed and is not generally subjected to feedback adjustment; and the guidance flight section adopts perturbation guidance or iterative guidance to carry out closed-loop correction. However, for a booster-glide hypersonic aircraft, the higher the altitude in the boost section, the greater the maximum heat flux density in the pull-up section. This requires the booster stage to lower the terminal height so that most or all of the booster stage trajectory is within the atmosphere.
The current closed-loop guidance method in the atmosphere generally adopts an optimal control theory to carry out modeling, and adopts a numerical optimization algorithm to carry out solving, such as a modified shooting method, a matching method, a minimum value algorithm and the like. However, the above methods have problems of large calculation amount, difficulty in on-line application, and the like.
Based on the above, the method, the device and the electronic equipment for guidance of the boost section based on the trajectory analytic solution provided by the embodiment of the invention can be applied to various aircraft boost section guidance scenes.
For the understanding of the embodiment, firstly, a detailed description is given to a launch vehicle boosting section guidance method based on trajectory analytic solution disclosed in the embodiment of the invention,
the embodiment of the invention provides a carrier rocket boosting section guidance method based on ballistic analytic solution, which comprises the following steps as shown in figure 1:
and S100, establishing a boosting section trajectory step-by-step solving model of the carrier rocket.
Under the general condition, firstly, based on a predetermined dynamic model of a boosting section of a carrier rocket, establishing a dynamic model of a trajectory of the boosting section under the condition that an attack angle of the carrier rocket is zero; then, based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is not zero; and finally, determining the kinetic model and the incremental kinetic model of the boosting section trajectory as a boosting section trajectory step-by-step solving model.
And S102, solving a ballistic analysis solution of the boosting section under the condition that the attack angle of the carrier rocket is zero by utilizing a regular perturbation theory based on a boosting section ballistic step-by-step solving model.
In a specific implementation process, a first regular perturbation model is established by utilizing a regular perturbation theory based on a dynamical model of a boosting section trajectory under the condition that an attack angle of a carrier rocket is zero; then generating a zero-order differential equation of a zero-attack-angle trajectory and a first-order differential equation of the zero-attack-angle trajectory based on the first regular perturbation model; then obtaining a zero-order term analytic solution of the zero-attack-angle trajectory based on a zero-order term differential equation of the zero-attack-angle trajectory; obtaining a first-order analytic solution of the zero attack angle trajectory based on a first-order differential equation of the zero attack angle trajectory; generating an approximate trajectory analysis solution of a boosting section under the condition that the attack angle of the carrier rocket is zero based on a zero-order analysis solution of a zero attack angle trajectory and a first-order analysis solution of the zero attack angle trajectory; and finally determining the approximate trajectory analytic solution as the trajectory analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is zero
And S104, solving an analytic solution of the trajectory of the boosting section under the condition that the attack angle of the carrier rocket is zero based on the stepwise solution model of the trajectory of the boosting section, and solving the analytic solution of the trajectory of the boosting section under the condition that the attack angle of the carrier rocket is not zero by using a regular perturbation method.
During specific implementation, firstly, on the basis of the condition that the attack angle of a carrier rocket is not zero, a second regular perturbation model is established by utilizing a regular perturbation theory on the basis of an incremental dynamic model of a boosting section trajectory; then generating a zero-order differential equation of the ballistic increment and a first-order differential equation of the ballistic increment based on a second regular perturbation model; obtaining a zero-order analytic solution of the ballistic increment based on a zero-order item differential equation of the ballistic increment; obtaining a first-order analytic solution of the ballistic increment based on a first-order differential equation of the ballistic increment; generating an approximate analysis solution of the ballistic increment based on the zeroth-order analysis solution of the ballistic increment and the first-order analysis solution of the ballistic increment; and finally, determining the sum of the ballistic analytic solutions of the boosting section to be the ballistic analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is not zero and the approximate analytic solution of the ballistic increment and the attack angle of the carrier rocket are zero.
And S106, solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analysis solution and a predetermined guidance strategy.
In a specific implementation process, firstly, obtaining a relational expression between a terminal state and an attack angle curve based on a trajectory analytic solution; then, based on the relational expression, establishing a correction model of the terminal state deviation; approximating the performance index of the carrier rocket in the boosting section through Chebyshev interpolation polynomial to obtain a discrete performance index; then, based on a correction model of the terminal state deviation and discrete performance indexes, establishing an analytic solving model of optimal guidance correction; finally, solving the optimal guidance instruction based on the analytic solving model of the optimal guidance correction and the predetermined guidance strategy
The embodiment of the invention provides a carrier rocket boosting section guidance method based on trajectory analytic solution, which comprises the steps of firstly establishing a boosting section trajectory stepwise solving model of a carrier rocket, then solving the trajectory analytic solution of a boosting section by using a regular perturbation theory under the condition that the attack angle of the carrier rocket is zero based on the boosting section trajectory stepwise solving model, further solving the analytic solution of the boosting section trajectory under the condition that the attack angle of the carrier rocket is zero based on the boosting section trajectory stepwise solving model, and solving the trajectory analytic solution of the boosting section by using the regular perturbation method under the condition that the attack angle of the carrier rocket is not zero; and finally, solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analysis solution and a predetermined guidance strategy. According to the method, the trajectory analytic solution of the carrier rocket in the boosting section is solved, and the analytic solution model of the optimal guidance instruction is established based on the analytic solution, so that numerical integral prediction is avoided, the guidance efficiency is improved, and the practicability is high.
Aiming at the problem of guidance of a boosting section of a hypersonic aircraft, the invention provides another boosting section guidance method based on trajectory analytic solution, and the method is realized on the basis of the method shown in figure 1. According to the method, firstly, an analytic solution of the trajectory of the boosting section is deduced by adopting a regular perturbation method, the analytic solution consists of a zero attack angle trajectory analytic solution and an analytic solution of trajectory increment caused by a non-zero attack angle, the analytic solution is expressed as a function of an attack angle value at an interpolation node, and the terminal speed, the trajectory inclination angle and the height of the boosting section can be predicted with high precision. Then, an optimal guidance method meeting strong terminal constraints is designed based on the analytic solution. The guidance method disperses the optimal control problem into an optimization problem by utilizing an analytic solution, converts the solved variable into an attack angle value at an interpolation node from an attack angle curve, then obtains an optimized variable by utilizing linear approximation iteration, and finally fits the attack angle curve by utilizing a Chebyshev interpolation polynomial.
The method comprises the following steps:
step 1: establishing a boosting section dynamic model:
neglecting the earth rotation, the longitudinal motion equation of the booster in the track coordinate system is shown in the following formula (1):
wherein V, gamma, h and m are respectively the speed, trajectory inclination angle, height and mass of the booster;
is the derivative of the booster's speed with respect to time;
is the derivative of the trajectory inclination of the booster with respect to time;
is the derivative of the height of the booster over time;
to assist in the propulsionThe derivative of the mass of the device with respect to time; alpha is the attack angle of the booster; r is the distance between the center of mass of the booster and the geocentric; q. q.smMass second flow rate of the engine being the booster; p is the thrust of the booster and the mass second flow of the engine and the local atmospheric pressure are related; l and D are the lift and drag of the booster, respectively, and are related to the angle of attack, mach number, and dynamic pressure of the aircraft.
Wherein P is represented by the following formula:
P＝Ispqmg0-PaSe
in the formula IspThe specific impulse of the booster engine is obtained; seIs the area of the engine exhaust nozzle; g0Is the ground gravitational acceleration; paIs the local atmospheric pressure and is related to the flying height.
L, D are the lift and drag of the booster, respectively, and the expression is as follows:
(2)
in the above formula, ρ is the local atmospheric density, which is related to the flying height; s is the pneumatic reference area of the booster; clAnd CdLift coefficient and drag coefficient, respectively, which can be fitted to a first and second order function of the angle of attack, respectively, i.e.:
wherein the content of the first and second substances,
is the coefficient of the lifting line, Cd0The resistance coefficient of the material is zero liter,
to induce drag coefficients, these coefficients can each be fitted as a function of Mach number Ma.
Step 2: and (3) solving zero attack angle trajectory analysis in a boosting stage, which comprises the steps of establishing a regular perturbation model and solving analysis of a zero order term and a first order term:
2.1 building regular perturbation model
When the boosting section flies at zero attack angle, obviously there are
Utilize
In this relationship, ρ is the local atmospheric density, which is related to the altitude of the flight, S is the aerodynamic reference area of the booster, ClIs the lift coefficient. The kinematic equation for a zero angle of attack trajectory (also called a kinematic model) can thus be found as:
wherein m is0And t is the initial mass and time of flight of the booster, respectively; subscript 'b' characterizes zero angle of attack trajectory, Vb、hb、gbAnd ρbVelocity, altitude, gravitational acceleration and atmospheric density for a zero angle of attack trajectory; thetabTrajectory inclination gamma of zero angle of attack trajectorybAngle of inclination-dependent variable, thetab＝ln[(1+sinγb)/(1-sinγb)]；Cd0A zero lift drag coefficient; r isbIs the distance between the centroid and the centroid of the zero angle of attack trajectory, γbAnd marking and controlling the trajectory inclination angle of the trajectory.
From the formula (3), V can be seenb、θbAnd hbThere is a complex coupling relationship between them, so it is not possible to directly resolve the solution. The problem is solved here by a regular perturbation method, introducing a small parameter epsilon and setting it equal to a constant k. According to the regular perturbation method, the state equation needs to be rewritten as
Wherein x isb＝[Vb θb hb]T。
In equation (3), the velocity differential equation equal sign of the zero angle of attack trajectory can be divided into two parts to the right, as follows:
in the above formula, FaveFrom an average axial force, FεFor perturbing the axial force, their expressions are respectively as follows:
in the above formula, mave、γave、Vave、ρaveAnd gaveRespectively, average mass, average ballistic angle of attack, average velocity, average density, and average gravitational acceleration, which values may be considered as averages of the initial and terminal values. In the boost section, the thrust force is typically much greater than the change in aerodynamic drag and the axial component of gravity. Thus, the perturbation axial force is sufficiently small to be considered as a correction term. Furthermore, the variation of the ballistic inclination at zero angle of attack is small. Thus, sin γ can be reducedbApproximately as shown below with respect to Δ θb(Δθb＝θb-θ0) Linear function of (c):
sinγb≈sinγ0+c1Δθb (8)
in the formula (I), the compound is shown in the specification,
c1＝(sinγbf-sinγ0)/(θbf-θ0) (9)
wherein, γbfAnd thetabfAre respectively gammabAnd thetabThe terminal value of (1).
Then, the kinetic equation for the zero angle of attack trajectory is rewritten as
According to the theory of regular perturbation, Vb、θbAnd hbCan be expressed as a polynomial on ε as follows:
in the above equation, superscript (i) characterizes the ith order term of the canonical perturbation. Each order of dynamic equation can be obtained by substituting the formula (11) into the formula (10) and performing taylor series expansion, wherein the zero order dynamic equation of the zero attack angle trajectory is shown as the formula (12):
it should be noted that in the formula (12), in order to express θbAnd hbIs decoupled because the variation of the geocentric distance r is greater than the initial value r0Much smaller, with the term related to the geocentric distance r at the initial value r0Taylor expansion is performed.
The first order kinetic equation for a zero angle of attack trajectory is shown in equation (13):
wherein superscripts '(0)' and '(1)' respectively represent the zeroth and first order terms of the canonical perturbation;
and
respectively for zero-order terms of the boosting section for marking and controlling the ballistic velocity, ballistic inclination angle related variables and height,
and
their first derivatives with respect to time, respectively;
and
respectively is a first-order term for marking and controlling the trajectory speed, trajectory inclination angle related variable and height in the boosting stage,
and
their first derivatives with respect to time, respectively. FaveAre constants related to average thrust, drag and ballistic dip; r is0、γ0And giInitial earth center distance, trajectory inclination angle and gravitational acceleration of the trajectory are respectively marked and controlled by the boosting section c1Are constants associated with them.
Is the zeroth order term of the ballistic inclination angle, which can be determined from
Calculated according to the following formula:
it should be noted that this is because
Neglecting the sum of
The item concerned.
Further, the initial values of the zeroth order term and the first order term are respectively
Wherein, V0、θ0And h0The initial values of velocity, ballistic dip angle related terms, and altitude, respectively.
2.2 zeroth order analytic solution
And respectively carrying out analytical integration by using the obtained differential equation (12) of the zero-order term of the regular perturbation of the boosting section, so as to obtain the zero-order term analytical solution of the velocity, the ballistic inclination angle related variable and the height. First, the first equation of (13) is integrated,
(16)
in the formula, T and VeAre constants associated with the booster engine, and the expression is as follows:
(17)
obviously, the differential equations of the other variables are all equal to
On, therefore, the analytical solutions for these variables will be expressed as
As a function of (c). For simplicity, a dimensionless variable is introduced,
and will be considered as independent variables in the derivation process later. It can be obtained from the formula (16),
is expressed as
Wherein，
Is a variable quantity
The initial value of (c). The formula is substituted into the formula to obtain the final product,
the derivative with respect to time t can be expressed as
The second and third differential equations of equation (12) for the zeroth order kinetic equation are divided by equation (19) respectively
In the formula (I), the compound is shown in the specification,
by integrating equation (20)
Is resolved into
In the formula
Is expressed as
although the integral term is simple, it does not have an analytical solution. The integrand can be approximated here by a chebyshev interpolation polynomial. Order to
Wherein the content of the first and second substances,
is defined as
In the formula, interpolation node xi(i-0, …, N) E (-1,1) is the root of Chebyshev polynomial, expressed as
xi＝cos[(2i+1)π/(2N+2)],i＝0,...,N (27)
It is clear that,
is a polynomial of order N which can be rewritten as
Polynomial coefficient in formula
Expression ofThe formula is as follows:
wherein the content of the first and second substances,
the following recurrence relation is satisfied:
thus, the coefficient
Is expressed as
By substituting the formula (25) into the formula (24), the compound can be obtained
Is resolved into
Wherein the content of the first and second substances,
is expressed as
Then, formula (31) is substituted for formula (30),
can be rewritten as
Wherein the content of the first and second substances,
is expressed as
(35)
In fig. 2, comparing the primitive function with the result obtained by using the 6 th-order chebyshev interpolation polynomial shown in equation (34), it can be seen that the result obtained by using the chebyshev interpolation polynomial has higher accuracy. By substituting formula (25) for formula (22)
Is resolved into
To derive for
Introduces an integral term as shown below:
by using the step-by-step integral formula, it can be obtained
Is resolved into
Wherein the content of the first and second substances,
is expressed as
Then, the integral of equation (21) can be obtained
Is resolved into
In the formula (I), the compound is shown in the specification,
2.3 first order term analytic solution
The equation (13) of the first order differential equation is divided by the equation (19),
and
to pair
The derivative of (c) is:
in the formula (I), the compound is shown in the specification,
and
are all dimensionless variables;
and
is a constant coefficient.
By integrating the first term of equation (59), the product can be obtained
Is resolved into
Wherein the content of the first and second substances,
due to the fact that
Is not related to
Of the linear function, hence the integral term
Analytical solution cannot be performed. However, its integrand is only
In this regard, we can approximate it using the Chebyshev interpolation polynomial. Order to
In the formula (I), the compound is shown in the specification,
as shown in fig. 3, the approximate polynomial has sufficient accuracy compared to the primitive function. Then it is determined that,
can be expressed as
By integrating the second equation of equation (42), it is possible to obtain
Is resolved into
Wherein the content of the first and second substances,
and
are all about
Respectively, the expressions of
In the formula (I), the compound is shown in the specification,
formula (47) also has two integral terms, and the specific expression cannot be directly solved by analysis. To obtain its expression, we also approximate the integrand using the Chebyshev interpolation polynomial. Order to
In the formula, coefficient
Is expressed as
Then, the solution of the integral term in equation (47) can be expressed as
In the formula
And
is an integral term as follows:
by using the step-by-step integral formula, it can be obtained
And
is resolved into
In the formula (I), the compound is shown in the specification,
and
is expressed as
Substituting the formulae (55) and (58) into the formula (47),
can be expressed as
For the
The analytic solution of (2), its integrand
All variables in (1) such as
And
all of which have been obtained and are expressed as about
So we can use the chebyshev interpolation polynomial pair
An approximation is made. Order to
Then it is determined that,
can be expressed as
And step 3: the non-zero attack angle ballistic increment analysis solving comprises the steps of derivation of a dynamic equation of ballistic increment, establishment of a regular perturbation model, zero-order item analysis solving and first-order item analysis solving:
3.1 kinetic equation for ballistic increment
When the booster flies at a non-zero attack angle, the increment of the solution of the speed, the trajectory inclination angle and the height relative to the zero attack angle is respectively delta V, delta gamma and delta h, and the kinetic equation can be obtained by the difference between the actual kinetic equation of the booster and the kinetic equation of the zero attack angle. To simplify the derivation, the following taylor expansion approximation is used in the solution.
The kinetic equation for ballistic increment is found as shown in equation (67):
wherein, CdIs the coefficient of resistance. Since r > Δ h in this equation, the effect of the increment in height on 1/r is ignored in the above equation. Dividing equation (67) by equation (19) yields Δ V, Δ γ, and Δ h pairs
Respectively is
Wherein f isV1～fV6、fγ1～fγ5And fh1～fh4Are all made of
Respectively, the expressions of
An analytical solution for ballistic increment can be obtained by integrating equation (66), but the angle of attack curve is generally expressed as a function of time of flight t, which needs to be converted to a function of time of flight t
The functional relationship of (a). From formula (18)T and
the relationship between can be expressed as:
then, using equation (70) one can obtain the angle of attack with respect to
The functional relationship of (a).
3.2 building regular perturbation model
As is clear from the formula (8), Δ V, Δ γ, and Δ h are coupled to each other, and therefore, the analytical solution cannot be directly obtained. Here, the regular perturbation method is also used to solve the coupling problem. According to the theory of regular perturbation, the kinetic equation for ballistic increment needs to be written in the form:
wherein Δ x ═ Δ V Δ γ Δ h]T. By analyzing the orders of magnitude of the three differential equations in equation (68), the kinetic equation shown in equation (68) can be rewritten as:
according to the canonical perturbation theory, Δ V, Δ θ, and Δ h are expressed as polynomials with respect to the parameter ∈:
in the above equation, superscript (i) characterizes the ith order term of the canonical perturbation. The equation (73) is substituted into the equation (72) and subjected to Taylor series expansion to obtain each order of kinetic equation, wherein the zeroth order term differential equation is as follows:
similarly, the differential equation for a first order correction term can be expressed as:
the initial values of the zero-order term and the first-order correction term are both zero.
3.3 zeroth order term resolution
It is apparent that the zeroth order differential equations shown in equation (74) are uncoupled. Therefore, integrating these differential equations in order can obtain Δ γ(0)、ΔV(0) And Δ h(0) Respectively is
Although the integral term in the above formulas is relatively complex, the integrand is only related to the independent variable
It is related. Therefore, we can also approximate the integrand using the Chebyshev interpolation polynomial to find the analytical solution of the integral term. Then, Δ γ(0)、ΔV(0)And Δ h(0)The analytic solution can be expressed as:
for the convenience of subsequent applications, the above three formulas are represented in the form of a matrix. Wherein, Delta gamma(0)Can be expressed as
In the formula, the vector α is:
in the formula, vector
Expression (2)
Fγ1Is a diagonal matrix with the value of the ith diagonal being a function fγ1At interpolation node
A value of (i) i
Substitution of formula (78) for a second expression of formula (77), Δ V(0)Can be expressed as
In the formula, the vector αsquIs composed of
In the formula, matrix AcbIs composed of
FV1And FV3Are diagonal matrices, the value of the ith diagonal is the function fV1And fV3At interpolation node
A value of (i) i
Substituting formulae (78) and (83) for the third expression of formula (77), Δ h(0)The analytic solution of (d) can be expressed as:
in the formula, coefficient matrix
And
are respectively expressed as
F in formulae (89) and (90)h1And Fh2Are diagonal matrices, the value of the ith diagonal is the function fh1And fh2At interpolation node
The value of (a) is:
3.4 analytic solution of first order correction term
For the first order term, its analytical solution can be obtained by integrating the three differential equations shown in equation (75).Similar to the zeroth order term solution process, here again the integrand is approximated using a Chebyshev interpolation polynomial. Then, Δ γ(1)The analytic solution of (d) can be expressed as:
similar to equation (88), the first term in equation (92) may be expressed as
In the formula (I), the compound is shown in the specification,
for the second term in equation (92), substituting equations (80) and (88) therein, the expression thereof can be obtained as
In the formula (I), the compound is shown in the specification,
and
the coefficient matrices are respectively as follows:
where I (i) is the ith row of the N + 1-dimensional identity matrix. Then, in combination of formulae (93) and (95), the results are obtained
Approximation of the integrand by Chebyshev interpolation polynomial to obtain Δ V: (1)Can be expressed as
Similar to equation (88), the first term in equation (98) may be expressed as
In the formula (I), the compound is shown in the specification,
for the second term in equation (98), substituting equations (80) and (88) therein, the expression can be obtained as:
in the formula (I), the compound is shown in the specification,
then, by combining the formulae (99) and (101), Δ V can be obtained(1)Is resolved into
Δ h, similarly to equations (92) and (98)(1)The analytic solution of (d) can be expressed as:
substituting equation (103) for the first term of equation (104), the analytical expression can be written as:
in the formula (I), the compound is shown in the specification,
similar to equation (105), the second term of equation (104) may be expressed as
In the formula (I), the compound is shown in the specification,
for the third term of equation (104), equations (80) and (83) are substituted therein, which can be expressed as
In the formula (I), the compound is shown in the specification,
then, combine formula (105), (107) and (109), Δ h(1)The analytic solution of (d) can be expressed as:
in the formula (I), the compound is shown in the specification,
by combining the analytical solutions of the zeroth and first order terms, the approximate analytical solution of the ballistic increment can be expressed as
In the formula, A and AsquIs a block diagonal matrix as shown below:
A＝diag{α,α,α},Asqu＝diag{αsqu,αsqu,αsqu} (114)
coefficient matrix
Is composed of
Wherein each term coefficient value can be determined by the sum of the zeroth order term and the first order term.
And 4, step 4: solving the optimal guidance instruction of the boosting section based on the analytic solution:
the purpose of the boost segment guidance is to create good initial conditions for subsequent flights. Therefore, the terminal state of the boost segment should satisfy some constraints. Based on a model prediction control idea, the current state of the booster is used as an initial state, and a guidance problem can be converted into a series of optimal control problems with terminal constraints.
The performance indicators of the defined optimal control problem include the performance indicators of the boosters in the boost section and the terminal constraints, as shown in formula (116):
wherein, t0And tfRespectively the initial time and the terminal time of the guidance section; the coefficient n is an optional variable, and the attack angle curve can be shaped by changing the value of n.
The dynamic constraints shown in equation (1) and the dead-end constraints shown in equation (117) need to be satisfied during the flight of the thrusters:
ψ(x(tf))＝0 (117)
the dynamical constraints shown in equation (1) can be converted into algebraic constraints as shown in equation (118) using the analytical solutions derived in step 2 and step 3:
similarly, by approximating the integrand using the Chebyshev interpolation polynomial, the integral-type performance functional represented by equation (116) can be expressed as:
wherein Q ∈ R(N+1)×(N+1)Is a positive definite diagonal matrix with diagonal elements of
Therefore, the nonlinear optimal control problem is converted into a nonlinear constraint optimization problem, the optimization variable is the vector α, the objective function is formula (119), and the constraint conditions are formulas (117) and (118). Based on the idea of linear approximation, the nonlinear constraint optimization problem can be further converted into a series of quadratic programming problems, and the optimal value of the optimization variable can be obtained by solving the series of quadratic programming problems through iteration.
By performing Taylor expansion of equations (117) and (118) at the reference trajectory and ignoring the higher-order terms, the actual angle of attack α and the reference angle of attack α can be obtained as shown in equation (121)pIs a linear terminal constraint function of the variables.
In the formula, alphapIs a reference angle of attack vector, each element of which is a reference angle of attack alphapAt an interpolation node
A value of (i), i.e
δα＝α-αpActual angle of attack alpha and reference angle of attack alphapAt an interpolation node
A difference of (d);
is the terminal constraint function psi (-) versus the terminal state quantity x (t)f) The partial derivative of (a), whose expression is related to the specific expression of ψ (·);
is the partial derivative of the terminal state quantity to the attack angle value at the interpolation node, and the expression is
In the formula (I), the compound is shown in the specification,
xpfthe terminal state quantity value under the action of the reference attack angle is represented by the following expression:
for the objective function shown in equation (119), δ α is taken as an optimization variable, which is also rewritten as an expression of quadratic form:
the solution of the quadratic programming problem can be obtained by using a Lagrange multiplier method, and the solution meets the following linear equation system:
Sz＝K (126)
wherein the matrices S and K are respectively
K＝-[Qαp；ψ(xpf)] (127)
z＝[δαT,υT]TAnd the v is a variable to be solved, wherein the v is a Lagrange multiplier vector. Solving the linear equation set can obtain delta alpha, then the attack angle is in the interpolation sectionThe value at a point is
α＝αp+δα (128)
Then, alpha is adjustedpUpdating to alpha and continuously iteratively calculating delta alpha until | psi (x (t)f))||<δ (where δ is the desired error range). It should be noted that the terminal state x (t)f) Can be expressed as a function of the attack angle value on the interpolation node and some coefficients irrelevant to the attack angle, so that only one analytic integral is needed in a plurality of iterations of a guidance period.
Finally, the attack angle value at the time t can be obtained by approximation through a Chebyshev interpolation polynomial, and the expression is
In the formula (I), the compound is shown in the specification,
is a variable at time t
The value of (c) can be calculated by the formula (18).
In order to verify the guidance method of the boosting section based on the analytic solution, a certain secondary carrier rocket is used as a booster model, wherein the first stage adopts program pitch angle guidance, and the second stage adopts the guidance method of the boosting section based on the analytic solution, so that only the result of the second stage is given during simulation, and the parameters of the second stage are shown in table 1. Initial value set to V in simulation0＝875m/s、γ020deg and h0The terminal constraints are shown in table 2 at 32 km. In the simulation process, the value of the parameter n is 0.5.
TABLE 1 parameters of Booster model
TABLE 2 boost segment guided simulation terminal constraints
| | Case | 1 | |
|
|
| Ballistic inclination (deg) | 0 | 0 | 5 | 5 | |
| Height (Km) | 40 | 45 | 45 | 40 |
Table 3 shows the terminal deviation values for four cases, and figures 4 and 5 show the altitude-trajectory inclination curves and the angle of attack curves. From table 3 and fig. 5, it can be seen that the guidance laws presented herein can guide the thrusters to achieve the desired terminal ballistic inclination and terminal elevation. FIG. 5 compares the angle of attack curves for the guidance law herein with those for open-loop optimal control using Gaussian pseudo-spectra. It can be seen that although there is some deviation in the model, the two almost coincide, verifying the optimality of the proposed law.
TABLE 3 guidance terminal bias for boost phase
Fig. 6 further shows the calculated time for each guidance cycle. It can be seen that the calculation time is within 0.01s, and most of the calculation time is distributed between 0.001s and 0.003s and is far smaller than the guidance period. Therefore, the method can be well applied to online guidance.
The boosting section guidance method based on the analytic solution has the following advantages:
(1) a method for characterizing a relationship between an angle of attack curve and a terminal state using an interpolation polynomial is presented based on which the terminal state can be represented as a function of the angle of attack value at an interpolation node.
(2) And a regular perturbation method is adopted to analyze and solve the longitudinal non-zero attack angle trajectory of the boosting section, and high-precision analysis solutions of speed, trajectory inclination angle and height are obtained.
(3) The optimal guidance method for the boosting section based on the trajectory analytic solution can simultaneously meet the requirements of the terminal height of the boosting section and trajectory inclination angle constraints, and meanwhile, an attack angle curve is almost the optimal value.
Corresponding to the above method embodiment, an embodiment of the present invention further provides a guidance device for a boost phase based on a ballistic analytic solution, as shown in fig. 7, where the guidance device includes:
the model building module 700 is used for building a boosting section trajectory step-by-step solving model of the carrier rocket;
the first solving module 702 is used for solving a ballistic analytic solution of the boosting section by utilizing a regular perturbation theory under the condition that the attack angle of the carrier rocket is zero based on a boosting section ballistic step-by-step solving model;
a second solving module 704, configured to solve the model step by step based on the trajectory of the boosting section and an analytic solution of the trajectory of the boosting section when the angle of attack of the carrier rocket is zero, and solve the analytic solution of the trajectory of the boosting section when the angle of attack of the carrier rocket is not zero by using a regular perturbation method;
and the optimal guidance module 706 is used for solving an optimal guidance instruction of the carrier rocket in the boosting section according to the trajectory analytic solution and the predetermined guidance strategy.
Further, the model building module is further configured to: based on a predetermined dynamic model of a boosting section of the carrier rocket, establishing a dynamic model of a trajectory of the boosting section under the condition that an attack angle of the carrier rocket is zero; based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is not zero; and determining the kinetic model and the incremental kinetic model of the boosting section trajectory as a boosting section trajectory step-by-step solving model.
The guidance device for the boosting section based on the ballistic analytic solution provided by the embodiment of the invention has the same technical characteristics as the guidance method for the boosting section of the carrier rocket based on the ballistic analytic solution provided by the embodiment, so that the same technical problems can be solved, and the same technical effects can be achieved.
An embodiment of the present invention further provides an electronic device, which is shown in fig. 8 and includes a processor 130 and a memory 131, where the memory 131 stores machine executable instructions capable of being executed by the processor 130, and the processor 130 executes the machine executable instructions to implement the above-mentioned method for guided vehicle rocket assisted propulsion segment based on ballistic analysis solution.
Further, the electronic device shown in fig. 8 further includes a bus 132 and a communication interface 133, and the processor 130, the communication interface 133, and the memory 131 are connected through the bus 132.
The Memory 131 may include a high-speed Random Access Memory (RAM) and may also include a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. The communication connection between the network element of the system and at least one other network element is realized through at least one communication interface 133 (which may be wired or wireless), and the internet, a wide area network, a local network, a metropolitan area network, and the like can be used. The bus 132 may be an ISA bus, PCI bus, EISA bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 8, but that does not indicate only one bus or one type of bus.
The processor 130 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware or instructions in the form of software in the processor 130. The Processor 130 may be a general-purpose Processor, and includes a Central Processing Unit (CPU), a Network Processor (NP), and the like; the device can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. The various methods, steps and logic blocks disclosed in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in the memory 131, and the processor 130 reads the information in the memory 131 and completes the steps of the method of the foregoing embodiment in combination with the hardware thereof.
The embodiment of the invention also provides a machine-readable storage medium, wherein the machine-readable storage medium stores machine-executable instructions, and when the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the carrier rocket boosting section guidance method based on the trajectory analysis solution.
The carrier rocket assisted propulsion section guidance method, device and electronic device based on ballistic analysis solution provided by the embodiments of the present invention include a computer readable storage medium storing program codes, instructions included in the program codes may be used to execute the method in the foregoing method embodiments, and specific implementation may refer to the method embodiments, and will not be described herein again.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a gateway electronic device, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A carrier rocket boosting section guidance method based on trajectory analytic solution is characterized by comprising the following steps:
establishing a boosting section trajectory step-by-step solving model of the carrier rocket;
based on the boosting section trajectory step-by-step solution model, solving a trajectory analytic solution of the boosting section by using a regular perturbation theory under the condition that the attack angle of the carrier rocket is zero;
based on the boosting section trajectory step-by-step solving model and the analytic solution of the boosting section trajectory under the condition that the attack angle of the carrier rocket is zero, solving the trajectory analytic solution of the boosting section by using a regular perturbation method under the condition that the attack angle of the carrier rocket is not zero;
and solving an optimal guidance instruction of the carrier rocket in a boosting section according to the trajectory analysis solution and a predetermined guidance strategy.
2. The method of claim 1, wherein the step of establishing a stepwise solution model of the launch vehicle's booster trajectory comprises:
establishing a dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is zero based on a predetermined dynamic model of the boosting section of the carrier rocket;
based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that an attack angle of the carrier rocket is not zero;
and determining the kinetic model of the boosting section trajectory and the incremental kinetic model as a stepped solution model of the boosting section trajectory.
3. The method of claim 2, wherein the step of solving a ballistic solution of the booster section based on the booster section ballistic step-by-step solution model using a regular perturbation theory under the condition that the angle of attack of the launch vehicle is zero comprises:
on the basis of the condition that the attack angle of the carrier rocket is zero, a first regular perturbation model is established by utilizing a regular perturbation theory on the basis of the dynamical model of the boosting section trajectory;
generating a zero-order differential equation of a zero-attack-angle trajectory and a first-order differential equation of the zero-attack-angle trajectory based on the first regular perturbation model;
obtaining a zero-order term analytic solution of the zero-attack-angle trajectory based on a zero-order term differential equation of the zero-attack-angle trajectory;
obtaining a first-order analytic solution of the zero-attack-angle trajectory based on a first-order differential equation of the zero-attack-angle trajectory;
generating an approximate trajectory analysis solution of the boosting section under the condition that the attack angle of the carrier rocket is zero based on a zero-order analysis solution of the zero-attack-angle trajectory and a first-order analysis solution of the zero-attack-angle trajectory;
and determining the approximate trajectory analytic solution as the trajectory analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is zero.
4. The method according to claim 3, wherein the step of solving the ballistic analytical solution of the booster section by using a regular perturbation method when the angle of attack of the carrier rocket is not zero based on the booster section ballistic step-by-step solution model and the analytical solution of the booster section ballistic when the angle of attack of the carrier rocket is zero comprises:
on the basis of the increment dynamic model of the boosting section trajectory under the condition that the attack angle of the carrier rocket is not zero, establishing a second regular perturbation model by using a regular perturbation theory;
generating a zero-order differential equation of the ballistic increment and a first-order differential equation of the ballistic increment based on the second regular perturbation model;
obtaining a zero-order analytic solution of the ballistic increment based on a zero-order item differential equation of the ballistic increment;
obtaining a first-order analytical solution of the ballistic increment based on a first-order differential equation of the ballistic increment;
generating an approximate analytic solution of the ballistic increment based on a zeroth order analytic solution of the ballistic increment and a first order analytic solution of the ballistic increment;
and determining the sum of the ballistic analytic solutions of the boosting section to be the ballistic analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is not zero and the approximate analytic solution of the ballistic increment and the attack angle of the carrier rocket are zero.
5. The method of claim 1, wherein the step of finding optimal guidance instructions for the launch vehicle in a boost phase based on the ballistic resolution and a predetermined guidance strategy comprises:
obtaining a relational expression between the terminal state and an attack angle curve based on the trajectory analytic solution;
establishing a correction model of the terminal state deviation based on the relational expression;
approximating the performance index of the carrier rocket in the boosting section through Chebyshev interpolation polynomial to obtain a discrete performance index;
establishing an analytical solving model of optimal guidance correction based on the correction model of the terminal state deviation and the discrete performance index;
and solving an optimal guidance instruction based on the analysis solving model of the optimal guidance correction and a predetermined guidance strategy.
6. A guidance device for a boost phase based on ballistic analytic solution, comprising:
the model establishing module is used for establishing a boosting section trajectory step-by-step solving model of the carrier rocket;
the first solving module is used for solving a ballistic analysis solution of the boosting section under the condition that the attack angle of the carrier rocket is zero by utilizing a regular perturbation theory based on the boosting section ballistic step-by-step solving model;
the second solving module is used for solving an analytic solution of the trajectory of the boosting section under the condition that the attack angle of the carrier rocket is zero by utilizing a regular perturbation method based on the stepwise solving model of the trajectory of the boosting section and the analytic solution of the trajectory of the boosting section under the condition that the attack angle of the carrier rocket is not zero;
and the optimal guidance module is used for solving an optimal guidance instruction of the carrier rocket in a boosting section according to the trajectory analytic solution and a predetermined guidance strategy.
7. The apparatus of claim 6, wherein the model building module is further configured to:
establishing a dynamic model of a boosting section trajectory under the condition that the attack angle of the carrier rocket is zero based on a predetermined dynamic model of the boosting section of the carrier rocket;
based on a boosting section dynamic model of the carrier rocket, establishing an incremental dynamic model of a boosting section trajectory under the condition that an attack angle of the carrier rocket is not zero;
and determining the kinetic model of the boosting section trajectory and the incremental kinetic model as a stepped solution model of the boosting section trajectory.
8. The apparatus of claim 7, wherein the first solving module is further configured to:
on the basis of the condition that the attack angle of the carrier rocket is zero, a first regular perturbation model is established by utilizing a regular perturbation theory on the basis of the dynamical model of the boosting section trajectory;
generating a zero-order differential equation of a zero-attack-angle trajectory and a first-order differential equation of the zero-attack-angle trajectory based on the first regular perturbation model;
obtaining a zero-order term analytic solution of the zero-attack-angle trajectory based on a zero-order term differential equation of the zero-attack-angle trajectory;
obtaining a first-order analytic solution of the zero-attack-angle trajectory based on a first-order differential equation of the zero-attack-angle trajectory;
generating an approximate trajectory analysis solution of the boosting section under the condition that the attack angle of the carrier rocket is zero based on a zero-order analysis solution of the zero-attack-angle trajectory and a first-order analysis solution of the zero-attack-angle trajectory;
and determining the approximate trajectory analytic solution as the trajectory analytic solution of the boosting section under the condition that the attack angle of the carrier rocket is zero.
9. An electronic device comprising a processor and a memory, the memory storing machine executable instructions executable by the processor, the processor executing the machine executable instructions to implement the method of any one of claims 1-5.
10. A machine-readable storage medium having stored thereon machine-executable instructions which, when invoked and executed by a processor, cause the processor to implement the method of any of claims 1-5.
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| CN105549387A (en) * | 2015-12-07 | 2016-05-04 | 北京航空航天大学 | Boost phase generalized standard miss distance analysis guidance method |
| CN106091817A (en) * | 2016-06-08 | 2016-11-09 | 北京航空航天大学 | The mark control miss distance of terminal guidance section resolves method of guidance |
| CN106382853A (en) * | 2016-10-11 | 2017-02-08 | 北京航空航天大学 | Singular perturbation suboptimal guidance law with terminal ballistic inclined angle and attack angle constraints |
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