Method of control over spacecraft descent in atmosphere of planets

FIELD: aircraft engineering.

SUBSTANCE: invention relates to spacecraft control in atmosphere of planet by adjusting its aerodynamics. Spacecraft velocity in atmosphere at initial flight part increases (spacecraft flies toward conditional orbit pericentre). Atmosphere density is low yet to cause notable spacecraft deceleration. As spacecraft reaches atmosphere dense layers its velocity decreases to reach atmosphere enter velocity for angle of roll (γ) γ=π to be changed to γ=0. This manoeuvre allows changing the spacecraft to flight part with maximum aerodynamic performances. In flight with γ=0 continuous skip path is maintained whereat spacecraft velocity decreases monotonously. Maximum skip height reached, angle of attack o spacecraft increases, hence, spacecraft intensive deceleration occurs.

EFFECT: decreased final velocity at soft landing system operation, fuel savings.

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The invention relates to space exploration, in particular to control the descent of a SPACECRAFT (SC) in the atmosphere of the planet, using controlled aerodynamic braking and minimizing the final speed of the spacecraft.

A known method of controlling the descent of a spacecraft in the atmosphere of the planet, using controlled aerodynamic braking and providing the lower end of the speed of the spacecraft, described in the book - Ivanov N. M., Martynov A. I. "the Motion of spacecraft in the atmospheres of the planets. M.: Nauka, 1985, pp. 168-173 - [1]. This method is to control the aerodynamic braking by changing the roll angle γ of the spacecraft. The motion of the spacecraft is carried out with a constant value of angle of attack corresponding to maximum aerodynamic balancing. The method involves one-time switching of the roll angle γ with values equal to π glad to zero, which corresponds to the switching of the effective aerodynamic qualities from the minimum value (-K) to the maximum (+K).

The disadvantage of this method is that it does not control the angle of attack of the spacecraft α. This significantly reduces the possibility of quenching speed, because the ku increasing the angle of attack α leads to an increase in the intensity of the aerodynamic drag of the spacecraft.

The closest to the technical nature of the claimed method of controlling the descent of a spacecraft in the atmosphere of the planet, using controlled aerodynamic braking and providing the lower end of the speed of the spacecraft is described in the book - Ivanov N. M., Martynov A. I. "motion Control of spacecraft in the atmosphere of Mars. Moscow, Nauka, Main editorial Board for physical and mathematical literature, 1977, pages 192-213 - [2], which is selected by the prototype. This method is the two-parameter control roll angles and attack of the spacecraft. The entry of the spacecraft into the atmosphere of the planet is roll angle γ=π rad and angle of attack α, corresponding to the maximum value of the balancing aerodynamic quality. On the initial flight phase switches of the roll angle γ to zero. After reaching the angle of the velocity vector to the local horizon zero value of the roll angle γ is determined from the condition for the provision of space vehicle flight on izolyatsia the plot (the plot with constant height). Then you can switch the roll angle γ to zero, providing the movement of the spacecraft on ricochetnaya trajectory with increasing altitude. On this site happens HC is the increase of angle of attack α from the value corresponding to the maximum aerodynamic lift coefficient, to the value corresponding to the maximum aerodynamic coefficient of drag.

The disadvantages of this method are that it does not fully implemented the provisions of the control spacecraft on the effective damping rate. This is due to the following factors. First, there is no justification for the optimal moment of switching of the roll angle from π glad to zero pleased by the criterion of minimizing the final speed. At this time switch has a significant impact on the dynamics of the braking KA on subsequent phases of flight. Secondly, the use of isonicotinic plots shortens the total duration of the trajectories of descent and thereby reduces the efficiency of inhibition of CA in the atmosphere. Thirdly, control of the angle of attack occurs at relatively short plot: at the beginning of this section, for example, during the descent in the atmosphere of Mars flight speed is about 1 km/s and a height of less than 10 km. however, earlier management of the angle of attack also allows you to increase the intensity of the damping rate due to the increase in aerodynamic drag of the SPACECRAFT.

The technical result of the proposed method of control the descent of the SPACECRAFT in the atmosphere of the planet is reduced of course the speed when commissioning the soft landing system at the expense of rational management of roll angles and attack. This gives the possibility to reduce fuel consumption on the implementation of the soft-landing a SPACECRAFT on the surface of the planet. The application of the proposed method, depending on the design of the ballistic characteristics of the spacecraft, boundary conditions and parameters of the planet of destination allows to reduce fuel consumption ~ 10-20% compared to using the prototype method.

The invention consists in the rational management of the roll angles of attack which minimizes the final speed of the flight SPACECRAFT. This is achieved by introducing a new episode of the control compared to the prototype. First, the choice of appropriate conditions switching of the roll angle from π to zero pleased: the switching is performed when the speed of the AC becomes less than the speed of its entry into the atmosphere of the planet. As is known, the velocity of the SPACECRAFT at the initial part of flight in the atmosphere increases as the apparatus moves in the direction of the conditional pericenter oscillating orbits, and the density of the atmosphere is still relatively small and has no significant effect on the inhibition of AC. Then, when reaching the KA dense layers of the atmosphere, its speed begins to decrease and at a certain point in time is reduced up to speed entry into the atmosphere. It was at this point it is necessary to perform switching of the roll angle is π glad to zero and transfer the SPACECRAFT into a trajectory with maximum glide. In an earlier switching angle γ (when flight speed KA, greater speed entry into the atmosphere), the resulting lifting force can lead to the departure of the SPACECRAFT from the atmosphere and to the failure of the main tasks of the space mission - planting apparatus in a predetermined area of the surface of the planet. Later switching roll angle γ leads to a decrease in the duration of the descent trajectory and, consequently, to reduce the intensity of the braking KA. Second, a favorable factor for the effectiveness of reducing the final speed is earlier compared to the prototype, the beginning of the control angle of attack α. After putting the SPACECRAFT on flight mode with γ=0 rad implemented long nicoletiidae trajectory, where the velocity of the SPACECRAFT decreases monotonically. At the maximum height of the rebound, for example ~50-60 km in terms of reduction in the atmosphere of Mars and ~200-250 km with a reduction in the atmosphere of Jupiter, there is an increase in the angle of attack and, therefore, more intensive braking KA. Such a condition is the beginning of the control angle α is rational for the following reasons: the earlier the change in the angle α (to complete the set maximum height) decreases the maximum height of rebound reduce the duration of the flight and to reduce the integral effects of atmospheric drag on the SPACECRAFT. When more than the late introduction of the control angle α (at lower altitude KA) device as a rule, no time to repay the speed at the end of the descent trajectory to the lowest possible values.

The essence of the claimed method of controlling the descent of a spacecraft in the atmosphere of the planet lies in its spatial orientation and management of aerodynamic deceleration, stabilization of the spacecraft during entry into the atmosphere of the planet on the roll angle γ equal to about π rad, and angle of attack α for maximum aerodynamic performance of the spacecraft, determining the current values of velocity, density of the atmosphere and the altitude of the spacecraft, the establishment of the roll angle γ is equal to about 0 rad in the process of deceleration of the spacecraft in the atmosphere of the planet, in the implementation of the motion of the spacecraft in the atmosphere of the planet with the subsequent commissioning of the soft landing of a space vehicle, this set the roll angle γ of the spacecraft equal to about 0 rad, providing movement of the spacecraft on ricochetnaya trajectory with increasing altitude, in the process of deceleration of the spacecraft in the atmosphere of the planet when the condition is met:

V_i<V_I,

where: V_i- the current value of the speed of the spacecraft during its deceleration in the atmosphere of the planet;

V_I- speed WMO is the spacecraft into the atmosphere of the planet,

take further motion of the spacecraft on ricochetnaya trajectory

and when the condition is met:

h_i<h_max,

where: h_i- the current value of the altitude of the spacecraft in the atmosphere of the planet;

h_max- maximum flight altitude of the spacecraft during its movement on ricochetnaya trajectory

set the value of the angle of attack α of a spacecraft in accordance with the mathematical expression:

,

where:

;;

α_i- the angle of attack α of the spacecraft at time t_i;

V_i- the current value of the velocity of the spacecraft at time t_i;

ρ_i- the density of the atmosphere of the planet at time t_i;

Δt_ithe time intervals between subsequent measurements, i=1, 2, 3, ...;

C_x- aerodynamic drag coefficient of the spacecraft;

S - the area of the fuselage mid-section of the spacecraft;

m is the mass of the spacecraft;

β is the logarithmic rate of change of the density of the atmosphere from a height;

l, n - constant coefficients of the approximation of the dependency of the aerodynamic coefficients on the angle of attack of the spacecraft to the analytical mind;

upon reaching the angle of attack α of the spacecraft of α*, corresponding to the maximum value of the aerodynamic coefficient of drag, fly a mission with this value of angle of attack α* before commissioning the soft landing system.

The claimed method of controlling the descent of a spacecraft in the atmosphere of the planet is illustrated by a drawing, which shows the dependence of the velocity V, the height h of the spacecraft, its roll angles γ and attack α from the time the motion in the atmosphere of Mars t while minimizing the final speed.

In addition, the drawing and the text made the following notation: t_p- the time of switching of the roll angle with π rad 0 rad.

According to [2], page 194 aerodynamic coefficients of drag and lift forces with a high degree of accuracy can be approximated by the following analytical dependencies:

C_x=C_x0+Asin²(nα+l),

C_y=C_y0+Asin(nα+l)cos(nα+l).

In particular, when using forms spacecraft type carrying case: C_x0=0,2; C_y0=-0,1; A=2,3; n=1,125; l=5,625°.

For other types of forms can be used similar dependencies with other values of the s coefficients - [2], page 194.

The technical result of the invention is to reduce the required energy costs for the implementation of space missions to study the planets of the Solar system and, consequently, increasing the share of the payload in the overall weight balance of the spacecraft.

This technical result is achieved due to the installation aboard the landers management system glide and development of rational management programs roll angles and attack KA, namely due to the fact that in the method of controlling the descent of a spacecraft in the atmosphere of the planet, the selected prototype consists of a spatial orientation of the SPACECRAFT and the management of its aerodynamic deceleration, stabilization of the spacecraft during entry into the atmosphere of the planet on the roll angle γ equal to about π rad, and angle of attack α for maximum aerodynamic performance of the spacecraft, determining the current values of velocity, density of the atmosphere and the altitude of the spacecraft, the establishment of the roll angle γ is equal to about 0 rad in the process of deceleration of the spacecraft in the atmosphere of the planet, in the implementation of the motion of the spacecraft in the atmosphere of the planet with the subsequent commissioning of the soft landing of a spacecraft, in addition establish Hugo the roll γ spacecraft, equal to about 0 rad, providing movement of the spacecraft on ricochetnaya trajectory with increasing altitude, in the process of deceleration of the spacecraft in the atmosphere of the planet when the condition is met:

V_i<V_I,

where: V_i- the current value of the speed of the spacecraft during its deceleration in the atmosphere of the planet;

V_Ithe entrance velocity of the spacecraft in the atmosphere of the planet,

take further motion of the spacecraft on ricochetnaya trajectory

and when the condition is met:

h_i<h_max,

where: h_i- the current value of the altitude of the spacecraft in the atmosphere of the planet;

h_max- maximum flight altitude of the spacecraft during its movement on ricochetnaya trajectory

set the value of the angle of attack α of a spacecraft in accordance with the mathematical expression:

,

where:

;;

α_i- the angle of attack α of the spacecraft at time t_i;

V_i- the current value of the velocity of the spacecraft at time t_i;

ρ_i- the density of the atmosphere of the planet at time t_i;

Δt_ithe time intervals between subsequent of erenee, i=1, 2, 3, ...;

C_x- aerodynamic drag coefficient of the spacecraft;

S - the area of the fuselage mid-section of the spacecraft;

m is the mass of the spacecraft;

β is the logarithmic rate of change of the density of the atmosphere from a height;

l, n - constant coefficients of the approximation of the dependency of the aerodynamic coefficients on the angle of attack of the spacecraft to the analytical mind;

a₁, a₂, a₃- constant coefficients, obtained by integration of differential equations of the adjoint variables at angle of attack α of the spacecraft of α*, corresponding to the maximum value of the aerodynamic coefficient of drag, fly a mission with this value of angle of attack α* before commissioning the soft landing system.

We will show the possibility of carrying out the invention, i.e., the possibility of its industrial applications. A feature of the conduct of space activities in many countries is to enhance the study of the planets of the Solar system. In the framework of the Federal space program 2016-2025, provided the work to create a spacecraft to explore Mars, Venus, Jupiter, mercury, including design landers. However, one of the major problems of having aetsa develop key technologies management providing massively reduce energy costs in all areas of interplanetary flights. The successful solution of this problem is largely provided when placing aboard the landers control systems aerodynamic braking, using the principles of management of roll angles and attack described in the present invention.

As for the technical means to ensure control glide KA, i.e. the management of its roll angles and attack, they are known - see, for example, [1], page 37, [2], page 57, 270, and Navigation flight of the orbital complex "SALYUT-6" - "SOYUZ" - "PROGRESS"" responsible editors B. N. Petrov, I. K. Bazhinov, Moscow, Nauka, 1985, Chapter 1 - [3].

Notes.

1. The applicant was placed in the Annex to the application materials rationale used them (in the description and the claims) of the mathematical expression to calculate the angle of attack of the SPACECRAFT on its final part of the descent in the atmosphere of the planet that do not unnecessarily overload the description of the invention. However, if the expert deems appropriate, the applicant will not argue for its inclusion in the description.

2. According to p. 2.3.1 of the Guidelines for examination of applications for inventions from 25.07.2011, the use in the claims of the sign "about" in describing the values of the number of the s parameters are valid.

3. The applicant in the application materials have used two identical term "switch" the value of the roll angle γ KA (is used to describe analogues) and "set" the value of the roll angle γ KA (in the claims), as, in his opinion, is more preferable. While believing that the unity of terminology in this case is not broken.

App. Refers to the application for the invention "Method of controlling the descent of a spacecraft in the atmosphere of the planet" (managed using aerodynamic braking and minimizing the final velocity of the spacecraft (note the Applicant)).

Conclusion the mathematical dependences for calculation of angle of attack on the final section of the descent of a SPACECRAFT (SC) in the atmosphere of the planet.

The motion of the SPACECRAFT in the atmosphere of the planet according to the works [1, 2] is described by the system of differential equations in the velocity coordinate system with the influence of gravitational, aerodynamic, centrifugal and Coriolis forces in the assumption of the centrality of the gravitational field is:

Here V is the velocity of the SPACECRAFT, θ is the angle of the velocity vector to the local horizon, ε is the heading angle, r is the radius - vector connecting the center of the planet and the position of the KA, λ and φ is the longitude and latitude of subsatellite points KA, respectively, m is the SPACECRAFT mass, t is time, ρ is the energy density is the ability of the atmosphere, C_xand C_y- aerodynamic coefficients of drag and lift forces, respectively, R is the planetary radius, h is the altitude, g is the acceleration of gravity, µ is the product of the constant of gravity on the mass of the planet, S - the area of the fuselage mid-section.

The values of the control parameters α and γ can vary:

0≤α≤α_max, -π≤γ≤π.

Transform the original equation (1) given the introduction of the assumptions previously used in a number of domestic and foreign operations, in particular in the works [1, 2]:

h<<R, ρ=ρ₀exp(-βh), F_to+F_C<<F_g<<F_and,

where ρ₀- the density of the atmosphere on the surface of Mars, β is the logarithmic rate of change of the density of the atmosphere with height, F_toF_CF_gF_and- Coriolis, centrifugal, gravitational and aerodynamic forces, respectively.

We will consider only the final section of the descending SPACECRAFT, beginning with the time the device maximum height after the flight on ricochetnaya trajectory and ending on the date of entry into force of the soft landing system.

Using these assumptions, considering the motion of the SPACECRAFT in the plane of entry into the atmosphere and taking into account that the target area is descent with zero roll angle, convert the system of equations to the form:

,,,

where M is a piecewise constant function, according to the works [1, 2].

The solution of the problem of finding the optimal SPACECRAFT control with the minimum final speed was performed using the Pontryagin maximum principle. Let us write the Hamiltonian H and the conjugate variables Ψ_i:

,

,

,.

Comparing the equations for the functions H, Ψ₁, Ψ₃convert formulas for the adjoint variables as follows:

,.

From the transversality conditions at the end point the SPACECRAFT trajectory, it follows that

Given that the Hamiltonian does not depend explicitly on time of flight, it is lawful to record the equation:

H≡0.

It allows to represent the dependencies for the calculation of the adjoint variables in the form:

,.

Integrating these equations, taking into account formulas (2), we obtain:

,

, Ψ₃(t)=a₃=const.

Provided continuous measurement of the current values of flight velocity V_iand the density of the atmosphere ρ_ipair the by variables with a high degree of accuracy at the time of measurement t _ican be calculated by the formula:

where Δt_ithe time intervals between subsequent measurements.

The dependency analysis for the calculation of conjugate variables taking into account the equality to zero of the Hamiltonian has shown that Ψ₁(t) is negative monotonically increasing function, reaching the end point of the trajectory values of -1; Ψ₂(t) is a positive monotone decreasing function, reaching the end point of the trajectory values of zero; Ψ₃(t) is a constant function with a negative value.

Define the optimal control law the angle of attack of the conditions for the achievement of the extremum of the Hamiltonian:

.

Solving this equation, we obtain:

Given the described character changes adjoint variables Ψ₁and Ψ₂we come to the conclusion that the expression ∂C_x/∂C_yhas a negative value on all final flight. This corresponds to a monotonic increase of angle of attack: in this case, ∂C_x>0, and ∂C_y<0. Moreover, the intensity change of the angle of attack is increased monotone decreasing the speed of flight of the SPACECRAFT.

According to the works [1, 2] aerodynamic coefficients windshield resisting film to prevent the means and the lifting force with a high degree of accuracy can be approximated by the following analytical dependencies:

C_x=C_x0+Asin²(nα+l),

C_y=C_y0+Asin(nα+l)cos(nα+l).

For landers-type bearing housing C_x0=0,2; C_y0=-0,1; A=2,3; n=1,125; l=5,625°.

Taking into account these dependencies formula (5) is converted to the following:

.

Then the equation for determining the current values of angles of attack in moments of measurement parameters KA can be written as follows:

,

where the variables Ψ_1iand Ψ_2iare calculated by the formulas (3), (4). The analysis of this equation showed that the angle of attack α in the area of flight KA monotonically increases from α≈45÷50° to α≈70÷85°, which corresponds to the maximum value of the aerodynamic coefficient of drag.

Sources of information

1. Ivanov N. M., Martynov A. I. "the Motion of spacecraft in the atmospheres of the planets. M.: Nauka, 1985, pp. 168-173.

2. N. M. Ivanov, A. I. Martynov, "motion Control of spacecraft in the atmosphere of Mars. Moscow, Nauka, Main editorial Board for physical and mathematical literature, 1977, pp. 159-169.

The method of controlling the descent of a spacecraft in the atmosphere of the planet, lies in its spatial orientation and management of aerodynamic deceleration, stabilization of the spacecraft during entry into the atmosphere of the planet at the Lou roll γ, equal to about π rad, and angle of attack α for maximum aerodynamic performance of the spacecraft, determining the current values of velocity, density of the atmosphere and the altitude of the spacecraft, the establishment of the roll angle γ is equal to about 0 rad in the process of deceleration of the spacecraft in the atmosphere of the planet, in the implementation of the motion of the spacecraft in the atmosphere of the planet with the subsequent commissioning of the soft landing of a spacecraft, wherein installing the roll angle γ of the spacecraft is equal to about 0 rad, providing movement of the spacecraft on ricochetnaya trajectory with increasing altitude, in the process of deceleration of the spacecraft in the atmosphere of the planet when the condition is met:
V_i<V_I,
where: V_i- the current value of the speed of the spacecraft during its deceleration in the atmosphere of the planet,
V_Ithe entrance velocity of the spacecraft in the atmosphere of the planet,
take further motion of the spacecraft on ricochetnaya trajectory
and when the condition is met:
h_i<h_max
where: h_i- the current value of the altitude of the spacecraft in the atmosphere of the planet,
h_max- maximum flight altitude of the spacecraft during its movement on R is cochairwoman path,
set the value of the angle of attack α of a spacecraft in accordance with the mathematical expression:
,
where:
;,
α_i- the angle of attack α of the spacecraft at time t_i,
V_i- the current value of the velocity of the spacecraft at time t_i,
ρ_i- the density of the atmosphere of the planet at time t_i,
Δt_ithe time intervals between subsequent measurements, i=1, 2, 3, ...,
C_x- aerodynamic drag coefficient of the spacecraft,
S - the area of the fuselage mid-section of the spacecraft,
m is the mass of the spacecraft;
β is the logarithmic rate of change of the density of the atmosphere with height,
l, n - constant coefficients of the approximation of the dependency of the aerodynamic coefficients on the angle of attack of the spacecraft in analytical form,
a₁, a₂, a₃- constant coefficients, obtained by integration of differential equations of the adjoint variables,
and upon reaching the angle of attack α of the spacecraft of α*, corresponding to the maximum value of the aerodynamic coefficient of drag, fly a mission with this value of angle of attack α* before commissioning the system to me is some planting.