RU2752305C1 - Method for situational terminal control of descent module in earth's atmosphere on ricocheting trajectory of return from moon - Google Patents

Abstract

FIELD: aircraft industry.

SUBSTANCE: invention relates to the control of the movement of the descent module (DM) in the Earth's atmosphere in the presence of disturbances of both the DM and the environment. The DM enters the atmosphere at a near-parabolic speed from the southern hemisphere along a trajectory with two (I, III) dives into the atmosphere, an extra-atmospheric (II) section, and lands (L) on the territory of the Russian Federation. The descent range (from V1 to P) is 5000...10000 km. This type of trajectory is very sensitive to control and disturbing influences. In the descent control algorithm, adaptation based on autonomous measurements of the apparent acceleration of the DM is carried out with separate identification of the actual aerodynamic quality of the DM and the density of the disturbed atmosphere, as well as the errors of the navigation altitude. This allows choosing the right control in the area of its maximum efficiency - near the rebound point.

EFFECT: guaranteed increase in the accuracy (up to 2.7 km) of bringing the DM to the landing point, limiting the duration of action and the maximum value (up to 6g) of the overload, as well as reducing the fuel consumption of the control engines.

1 cl, 4 dwg

Description

The invention relates to the field of control of the movement of a spacecraft in the atmosphere in the presence of aggregate disturbances (the spacecraft itself and the environment). The proposed method can be used to control the movement of the descent vehicle (SC), which, upon returning from the Moon, enters the Earth's atmosphere at a near-parabolic speed from the southern hemisphere, uses a ricocheting trajectory with two dives into the atmosphere, separated by an extra-atmospheric (ballistic) section, and lands in a limited area on the territory of the Russian Federation (RF). FIG. 1 schematically shows the return trajectory. Two dives (sections I and III) are necessary and sufficient for landing on the territory of the Russian Federation when approaching from the south, which ensures that the overload limit is met. An increase in the number of dives complicates the implementation of the specified landing accuracy and is not required to reach the territory of the Russian Federation when approaching from the south. The realizable range of descent (from the first entry into the atmosphere to landing) is in the range of 5000-10000 km, and such trajectories are very sensitive to control and acting disturbances (errors in aerodynamic characteristics, mass and balance, navigation measurements, control engines, variations in atmospheric density, wind and etc.). The landing requirement in the southern regions of the Russian Federation determines the required targeting accuracy (about 3-4 km). Additionally, restrictions are imposed on overload (about 6g) and fuel consumption.

There is a known method of controlling the probe "Zond-7" returned from the Moon, which, after flying around the Moon, landed on the territory of the USSR in Kazakhstan with a gap of 50 km. The method is based on tracking the reference dependence of the apparent acceleration on the apparent speed [1]. The control was one-parameter, i.e. only the longitudinal slip was eliminated. The resulting alignment accuracy corresponded to its time. The main disadvantage of this method is the low accuracy of targeting, which makes it impossible to land in the southern regions of the Russian Federation.

In the American Apollo program, one-parameter terminal control of the longitudinal descent range was used. The lateral miss was kept within the specified corridor due to roll overturns [2]. The predicted miss was calculated using approximate final formulas, and the achieved accuracy was about 10 km at splashdown distances in the range of 2200-2800 km on descent trajectories without ricochets [3]. The main disadvantage of this method is the low accuracy of targeting even at a range of about 3000 km.

For the promising American manned spacecraft Orion, the PredGuid terminal control algorithm is being developed, which is an improved version of the Apollo algorithm and should provide control on a ricocheting descent trajectory with a range of about 10,000 km when returning from the Moon with a splashdown or landing in any continental United States. It uses a numerical prediction of the remaining trajectory to eliminate the longitudinal miss. The side slip is adjusted as in the Apollo algorithm. In individual control phases, correction factors are introduced in order to clarify the actual aerodynamic quality of the vehicle and the density of the atmosphere. The predicted alignment accuracy is about 5 km [4]. In the future, it is planned to modify the PredGuid algorithm for two-parameter control with simultaneous elimination of a slip in the longitudinal and lateral directions. The main drawback of the existing algorithm is the lack of tight control of lateral miss and maximum overload.

The prototype of the proposed algorithm is the Terminal Descent Control Algorithm - Modified TAUS-M [5]. In this algorithm, adaptation to the actual descent conditions is carried out without separating aerodynamic and atmospheric errors, and the navigation altitude error is not identified. As a result, it is possible to provide the specified accuracy of bringing the spacecraft to the landing site only with a probability of 97%, and the maximum overload reaches 7.3g.

The proposed control algorithm TAUS-MS (Terminal Descent Control Algorithm - Modified Situational), by analogy with the prototype, implements two-parameter control with a numerical forecast of the remaining trajectory to correct the command dependence of the roll angle on the apparent speed. At each step of the correction, the value of the roll angle and the apparent speed of the next roll over are specified. Three numerical predictions of the remaining part of the trajectory are made for the calculation by the method of finite differences of partial derivatives of the miss components (x, z) by the control parameters (the value of the roll angle γ and the apparent rate of change of its sign V _k ). The system of two linear equations for the corrections Δγ, ΔV is solved [6]:

(x ₀ , z ₀ - coordinates of the predicted miss with the control obtained at the previous correction step).

The calculation of the refined control parameters Δγ, ΔV is performed during one correction step (duration 1 s) with the forecast of the current state vector (radius vector and velocity vector) one step ahead to set the initial forecast conditions, i.e. at the current correction step, a “predictive” control is determined for the next step, which will be used in one step. This takes into account the time for calculating the corrections Δγ, ΔV in the on-board computer.

For high-precision terminal control, it is of particular importance to identify the actual driving conditions and take them into account when correcting the command dependence of the roll angle on the apparent speed.

Based on navigational measurements of the apparent acceleration vector and angular velocity with the help of coupled accelerometers and angular velocity sensors TAUS-MS, it is possible to identify the relative aerodynamic quality of the vehicle _krel (the ratio of the actual aerodynamic quality to the calculated, i.e. onboard), to construct an approximate function of the relative atmospheric density ρ _rel (the ratio of the actual density ρ _fak to the density ρ _cm according to the onboard monthly average model at the navigation altitude) and determine the navigation altitude error Δh (the difference between the navigation altitude and the actual), which can reach ± 2 km on the first dive and ± 3 km on the section second dive. All this is realized from the very beginning of the entry into the atmosphere, to the point of rebound, when, in essence, the entire ricochet trajectory is formed. In TAUS-MS, a method for separating aerodynamic errors and atmospheric disturbances has been proposed and implemented for the first time, and the navigation altitude error is also determined, which significantly increases the control tolerance to operating disturbances, making it independent of the disturbance model.

To adapt to operating disturbances, TAUS-MS sequentially performs the following operations. Adaptation coefficient is calculated from navigation measurements

where W _Vmeas is the measured projection of the apparent acceleration vector onto the navigation vector of the airspeed CA, W _Vcalc is a similar calculated value calculated using onboard models of aerodynamic characteristics and the average monthly atmosphere, as well as the adaptation coefficient

where W _{ps meas} , W _{ps calc} are the corresponding values of the apparent acceleration vector orthogonal to the airspeed vector. The relative aerodynamic quality is calculated by the formula

and to take into account the relative density of the atmosphere, a formula is proposed based on functions (2) and (3):

This formula coincides with the relative density with an accuracy of 3-6% and makes it possible to separate aerodynamic errors (generated by errors in aerodynamics itself and errors in the actual position of the center of mass) and atmospheric errors. The separation of aerodynamic errors (which do not change on a given trajectory) and the atmosphere made it possible to increase the accuracy of the disturbed atmosphere identification and control correction.

The navigation altitude error during the first atmospheric dip begins to increase almost linearly after the bounce point (i.e. after passing the minimum altitude). Therefore, adaptation to the actual driving conditions begins before the bounce point, when basically the entire bouncing trajectory is formed. By formula (4), the relative aerodynamic quality of the aircraft is determined, which is maintained throughout the entire trajectory. In this case, in the calculation of the predicted aerodynamic coefficients of the SA in the hypersonic section, the actual balancing angle of attack is taken into account according to the navigational measurements of the angular motion of the SA, since on the descending branch the amplitude of oscillations can reach 3 ° -6 ° relative to the actual balancing position. Only in the vicinity of the ricochet point do the oscillations almost damp, but by this time the ricochet trajectory is practically formed. The relative density of the atmosphere (5) is tabulated on the descending branch of the first descent of the SA into the atmosphere and is used to predict the movement on the ascending branch. At altitudes below the achieved one, ρ _rel = 1 is taken, which corresponds to the average monthly atmosphere. During the second dive, the relative density of the atmosphere is refined to an altitude of 70 km, i.e. until the navigation altitude error appears, which in this section can reach ± 3 km. Below the point of the obtained measurements, the relative density of the atmosphere is predicted as a linear function of the altitude from the current value to one at zero altitude.

The relative aerodynamic quality (4) is recalculated into the correction to the coefficient of the pitching moment according to the formula

Here dm _z / dα is the derivative of the pitching moment coefficient with respect to the angle of attack, _kcalculated is the calculated value of the aerodynamic quality, dk / dα is the derivative of the aerodynamic quality with respect to the angle of attack. For close to real values of nominal aerodynamic coefficients, we have, according to (6)

Depending on the value to _{0Т11, the} correction factor Δm _z <0 for k _rel > 1, Δm _z = 0 for k _rel = 1 and Δm _z > 0 for k _rel <1.

Using (7), according to the complete table of nominal ("calculated") aerodynamic characteristics (including the drag coefficients C _xa , lift C _ya , and _{pitching moment m z} , depending on the angle of attack a, the number M and the height h), forecast balancing coefficients C _{xa prog} and C _{ya prog} , which correspond to the condition

where m _z is the coefficient of the pitching moment of the nominal characteristics, Δm _z is the correction coefficient (7), -0.002 is the empirical coefficient for creating an additional "margin" for the descent range. The predicted aerodynamic characteristics corresponding to these disturbing factors according to (8) do not change during the descent.

Using the measured value of the total aerodynamic acceleration W _Σmeas , the correction factor β is calculated by the formula

where W _Σcalc is the calculated value of the total aerodynamic acceleration. According to the table of standard atmosphere CA-81 (GOST 4401-81), there is a correction Δh, for which the condition

Formulas (9) and (10) determine the navigation altitude correction Δh, which makes it possible to refine the initial state vector when calculating the forecast.

The SA makes 2 roll rolls during the first immersion into the atmosphere and 3 rolls during the second, which saves fuel consumption. This number of flips is necessary and sufficient to obtain the required alignment accuracy.

The technical result of the invention is a guaranteed (100%) increase in the accuracy of bringing the SA to the landing site up to ~ 2.7 km with a descent range of about 10,000 km under the action of all disturbing factors, limiting the maximum overload to about 6g while maintaining the permissible overload time of more than 5g according to Man standards -System Integration Standards NASA-STD-3000 [7], as well as saving fuel consumption for the operation of control engines.

The technical result is achieved by the fact that according to the autonomous measurements of the apparent acceleration vector in the projections on the axis of the associated coordinate system of the SA, situational (i.e. personal) adaptation to the acting disturbances on a specific disturbed descent trajectory is carried out. In this, TAUS-MS qualitatively differs from the prototype TAUS-M, which implements general adaptation with one adaptation coefficient Δm _z = -0.004 for the entire set of acting disturbances. The reliability of the efficiency of the TAUS-MS algorithm is confirmed by statistical tests of several thousand perturbed descent trajectories using a mathematical model of the complete motion of the SA (i.e., movement of the center of mass and relative to the center of mass) and a perturbation model, which includes the following components (with normal and uniform distribution):

- errors of aerodynamic characteristics,

- errors of mass, moments of inertia and centering,

- disturbed atmosphere (density variations and wind),

- navigation errors (accelerometers, angular velocity sensors, the initial alignment of the measuring axes and the accuracy of its knowledge, satellite navigation equipment),

- errors in the operation of control motors (thrust, specific thrust, on-off delay).

The results of statistical tests of TAUS-MS on 1000 perturbed trajectories show that the accuracy of bringing the vehicle to the landing site at a distance of about 10,000 km is better than 2.7 km, the maximum overload is about 6g, and the fuel consumption is less than the available stock. FIG. 2 in the Oxyz landing coordinate system, the endpoints of the VA targeting at an altitude of ~ 4.5 km, where the parachute system is put into operation, are presented. The origin O is at the landing point, the Ox axis is directed in the initial plane along the motion, the Oy axis is along the local vertical, the Oz axis closes the right coordinate system. The numbers show the numbers of the disturbed trajectories. Only for two perturbed trajectories out of 1000, the miss is more than 2.5 km, and for the rest, it is less than 2.5 km. FIG. 3 shows the maximum overloads n _max depending on the apparent speeds V _n at which they are achieved. On one trajectory out of 1000, the overload for a short time reaches 6.3g, and on the other trajectories, the overload does not exceed 6g. The duration of the increased overload does not exceed the allowable one according to NASA-STD-3000. The fuel consumption m _t as a function of the slip r = (x ² + z ² ) ^{0.5 is} shown in Fig. 4. Only on one trajectory the flow rate reaches 232 kg, and on the other trajectories the flow rate is less than 225 kg with simultaneous switching on of two motors in each control channel. Such results were obtained for the first time in statistical mathematical tests of a two-parameter terminal control algorithm on bouncing trajectories with a descent range of about 10,000 km.

List of cited sources

[1] Glazkov A.G., Ibragimov K.Z., Klimin A.V., Trunov Yu.V., Khazan M.A., Khitrik M.S., Yaroshevsky V.A. Control of a spacecraft when entering the atmosphere. Space Research 1969, vol. 7, no. 2, p. 163-170.

[2] Morth R. Reentry Guidance for Apollo. // 2-nd IF AC Symposium on Automatic Control in Space, 1967, preprint.

[3] Pavlovsky J.E., Leger L.G.St. Apollo Experience Report-Thermal Protection Subsystem // NASA Technical Note NASA TN D-7564, 1974.

[4] Rea J.R., Putnam Z.R. A Comparison of Two Skip Entry Guidance Algorithms // AIAA-2007-6424, 2007.

[5] Evdokimov C.H., Klimanov S.I., Korchagin A.N., Mikrin E.A., Samotokhin A.S., Sikharulidze Yu.G., Tuchin A.G. Modification of the terminal descent control algorithm when returning from the Moon as applied to "enhanced" disturbances // Cosmic research, 2020, v. 58, p. 149-164.

[6] Okhotsimsky DE, Golubev Yu.F., Sikharulidze Yu.G. Algorithms for controlling a spacecraft when entering the atmosphere. - M., Science, 1975.

[7] Vernis P., Spreng F., Gellys G. Accurate Skip-Entry Guidance for low to medium L / D spacecrafts return missions requiring high range capabilities // AIAA 2011-6649, 2011.

Claims (1)

The method of terminal control of the descent vehicle in the Earth's atmosphere on the ricocheting trajectory of return from the Moon using two-parameter flight control and numerical prediction of the remaining trajectory to correct the dependence of the roll angle on the apparent velocity, the associated coordinate system of the descent vehicle is carried out taking into account the current situation and with separate identification of the actual aerodynamic quality of the vehicle, the actual density of the disturbed atmosphere and the navigation altitude error.

Images