# Method of correction of parameters of longitudinal motion change program at terminal control of cryogenic stage guidance on preset orbit

FIELD: space engineering; on-board terminal control facilities of cryogenic stages with non-controllable cruise engines.

SUBSTANCE: parameters of motion of cryogenic stage at moment of cruise engine cutoff are predicted and radius of deviation of radius and radial velocity of cryogenic stage from their preset magnitudes are determined. Signals for correction of pitch angle and rate of pitch are shaped for compensation of said deviation. Pitch angle correction signal is limited at preset level and its excess above this level is determined. When signal is shaped for limitation, addition to correction pitch rate signal is formed. This correction is equal to product of said excess by ratio of functions of sensitivity of radial velocity of cryogenic stage to pitch angle and rate of pitch. Resultant pitch rate correction signal is formed as sum of this signal determined without taking into account pitch angle correction signal limitation and addition. Thus, priority follow-up of velocity error is ensured at limited pitch angle correction.

EFFECT: enhanced accuracy of forming preset orbit due to reduction of disturbance level on angular stabilization loop.

9 dwg, 1 tbl

The present invention relates to the field associated with the pointing of spacecraft and spacecraft into orbit. Using terminal control provides adjusted the parameters of their movement at the end of the active maneuver. Such methods of control are used in control systems spreader blocks, providing a transition from one orbit to another, and spacecraft performing landing on the moon or other planets.

The closest technical solution is the way to adjust the parameters of the program changes longitudinal movement in terminal management guidance upper stage into orbit, namely, that in the process of implementing active maneuver periodically predict the motion parameters of the booster unit at the time of main engine cutoff, determined according to him, the predicted deviation of the radius and radial velocity from their values on a given orbit, calculate the sensitivity function of the deviation of the radius and radial velocity to change program settings control angle and angular velocity of the pitch, form correction signals by the angle and angular velocity of the pitch, providing compensation for deviations in the radius and radial velocity, and limit the correction signal according to the pitch angle at a given level [1].

Weeks the STATCOM known way to adjust the parameters of the program changes the terminal management is an abrupt change these settings whenever you update a control program. With significant jumps in program management in the contours of angular stabilization of the upper stage, there are additional perturbations due to fluctuations of the liquid fuel in the tanks.

The technical result of the invention is to reduce the level of perturbations acting on the contour angular stabilization of the upper stage, by limiting the quantities of corrections and providing with these limitations, the priority testing deviation of radial velocity from its value on a given orbit.

This technical result is achieved by the fact that in the known method of correction parameters of the program changes longitudinal movement in terminal management guidance upper stage into orbit, namely, that predict the motion parameters of the booster unit at the time of cutoff of the main engine, determine the deviation of the radius and radial velocity from their values on a given orbit, calculate the sensitivity function of the deviation of the radius and radial velocity to change program settings control angle and angular velocity of the pitch, form correction signals by the angle and angular velocity of the pitch, providing compensation for deviations in the radius and radial velocity limit signal correction the pitch angle at a given level, additionally determine elaut excess of the correction signal by the angle of pitch with respect to its limited as the difference between the correction signal for the pitch angle and its limited value, form a Supplement to the signal correction angular velocity of the pitch, equal to the product obtained exceeding the ratio of the sensitivity function of the radial velocity on the corner of the pitch to the function of its sensitivity to the angular velocity of the pitch, form the correction signal from the angular velocity of the pitch as the sum of a correction signal according to the angular velocity of the pitch, determined without regard to the restrictions on the correction signal on the corner of the pitch, with addition defined by the output signal of the correction of the pitch angle on the constraint.

Figure 1 shows the block diagram of the correction device orientation parameters of the terminal control by a known method prototype; figure 2 shows the change in the angular velocityand anglepitch in tact terminal control T_{y}; figure 3 shows the variation of radius ΔR and radial velocity ΔV the predicted values of R_{CR}V_{r CR}from their values on a given orbit; figure 4 shows the phase plane parameters ΔR and ΔV at the beginning of the maneuver with the boundary lines I, II, III; figure 5 presents the boundary lines I, II, III, and changes the initial deviations ΔR and ΔV in one clock terminal control; figure 6 on the phase plane parameters ΔR, ΔV shows their treason is their method-prototype (so
A, a',...) and for the proposed method (so a, C', C"...), figure 7 shows the block diagram of the device parameters correction program changes longitudinal movement by the proposed method; Fig shows the process of working out the initial deviations in limiting the corrective amendments in the corner of the pitchthe method of the prototype; figure 9 shows the process of refining the initial deviations in limiting the corrective amendments in the proposed method.

The structural scheme of the device parameters correction program changes the terminal control according to the method prototype is presented in figure 1, where: 1 - unit forecast variance (BPO) from a given orbit and calculation of sensitivity functions, 2 - block of corrections (BKP) software control, 3 - block correction (BC) parameters control programs.

In block 1 on each step of the terminal control are determined by variations in the radius-vector ΔR and radial velocity ΔV from the parameters given in orbit predicted the end of the maneuver t_{f}. Settings ΔR, ΔV from the first and second outputs of the block 1 are received at first and second inputs of unit 2, with outputs 3-6 - to corresponding inputs of a block of 2 - calculated values of the sensitivity functions L, J, S, Q deviations ΔV ΔR to the changing the settings, program control angle and angular velocity of the pitch,
and with outputs 7, 8 to the inputs 3, 4 unit 3 receives the program settings control pitch ϑ_{oi-1}and the angular velocity of pitchat which predicts the movement of the upper stage.

In unit 2 based on the calculated sensitivity functions of the conditions of zero deviations ΔV ΔR is calculated corrective amendments in the corner of the pitch Δϑ_{oi}and the angular velocity of pitchand their values come from the outputs 1, 2 to corresponding inputs of unit 3, which is the correction of the parameters of the management programmes and are determined by their values at time intervals until the next beat of terminal control. The adjusted control parameters ϑ_{oi},c outputs 1, 2 block 3 act 1 and 2 unit 1 for forming control program on the next cycle of terminal control.

For the upper stage, as control parameters terminal control parameters are used with linear-time programs change the orientation of the spacecraft, determining the direction of action of the thrust of its main engine.

Terminal control is executed periodically with a given interval T_{y}between the bars.

For longitudinal movement program Orient the AI on the corner of the pitch at the beginning of the i-th terminal quantum control has the form ϑ
_{i}=ϑ_{oi-1}+t, where time t is measured from the start of the beat terminal control, the initial value of the pitch angle ϑ_{oi-1}and its rate of change_{}taken equal to the values of these parameters at the end of the previous (i-1)-th stage and the first stage is equal to the values specified in the flight task.

During terminal movement control of the booster unit at each clock cycle to perform the following operations:

- prediction of motion parameters on the predicted end of the management process, as defined by the time T remaining to disconnect the main engine running when the preset value functions;

- identification of deviations from the estimated parameters of the orbit at the radius-vector ΔR and radial velocity ΔV predicted the end of the maneuver;

- determination of the sensitivity functions settings ΔR, ΔV when changing control parameters:

- define corrective amendments Δϑ_{oi},according to the control parameters, ensuring cheating deviations ΔR, ΔV;

- currencyformatter control (figure 2):

As a model forecast of the trajectory of movement of the accelerating unit a system of differential equations:

t_{s}=t-t_{o},

where- the radius vector of the center of mass of the upper stage;

the vector of absolute speed booster;

is the unit thrust vector in generlaly coordinate system;

- the apparent acceleration;

S - specific impulse propulsion engine;

t - current time;

t_{o}- the start time of the forecast;

T - conditional time of combustion of the mass of the accelerating unit available at the time t_{o}.

Prediction of motion parameters of the accelerating unit (at the time of main engine cutoff (t_{f}) is carried out by numerical integration of the equations of motion using the Runge-Kutta method.

Initial values for parameters,determined according to the information received from the navigation system.

In the orbit plane (figure 3) variances radius ΔR radial velocity Δ V are determined by the formula

ΔR=R_{CR}-R

ΔV=V_{r CR}-V_{r},

where R_{CR}R - values of the predicted and calculated radii at the time of main engine cutoff, respectively;

V_{r CR}V_{r}- values of the predicted and the estimated radial velocity, respectively.

When the change management program for small values Δϑ_{0},change acceleration motionin the direction normal to the nominal trajectory can be described by the equation

where- the apparent acceleration, defined as

R - engine thrust;

m_{0}is the mass of the spacecraft at time t=0;

second mass flow.

The apparent accelerationdefined by these parameters, can be written in the form

where- the specific impulse;

- conventional combustion time of initial mass m_{0}the spacecraft.

With this in mind, we write equation (1) in the form

Integrating equation (3) from 0 to T,

where T is ostavsheesa the time to turn off the main engine, network

and re-integration should

In the last equations of the sensitivity function are [2]:

S=TL-J,

Assuming thatand y_{n}=ΔR from the system of equations

determined corrective amendments on control parameters for compensating deviations ΔR, ΔV:

where

Calculations show that the corrective amendments angular velocitysignificantly smaller amendments corner Δϑ_{0}. So, for a long maneuver in the time remaining until shutdown main engine, T=576 s, T=1405,3 and with the values of the sensitivity functions L=2384 m/s, J=745000 m, S=629015 m, Q=133155000 MS to compensate for deviations ΔR=10 km corrective amendments Δϑ_{0}=2,8°,=0,009 °/c, and ΔV=100 m/s - Δϑ_{0}=5,4°,
=0,024 °/c.

In this regard, in control systems imposed a hard limit only on the magnitude of the corrective amendments in the corner of the pitch:

However, this measure in the cases leading to the exit amendments Δϑ_{o}at the limit, can result in significant overshoot in the transition process to simulate deviations ΔV ΔR. short exercises with short duration of operation of the main engine, this leads to the incompleteness of the transition process and errors derive upper stage into orbit.

For the analysis of processes of change of the variance in the correction control program on the phase plane parameters ΔV ΔR (figure 4), select the following lines:

Line I - boundary, corresponding to the condition=0 and is determined from equation (5):

Line II - boundary corresponding to the condition=0 and is determined from equation (6):

where

Line III - parallel lines I and define the range of conditions corresponding to the change in the corrective amendmentsthe value of. The equation of these lines can be found from equation 5) when =±:

where

For the above conditions when=2°, R_{Zϑ}=7,08 km (for reference: lines similar to the lines III and parallel lines II, when=2 °/c would be=2212 km).

Lines I, II divide the phase plane parameters ΔV ΔR for region 1, 2, 3, 4.

Let the results of the forecast values are defined initial deviations corresponding to figure 4, the point a located outside the area bounded by a line III. If there is no restriction on the amount of corrective amendmentsor if it has not exceeded the limit, i.e. when the point a within the zone bounded by the lines III-III testing of these deviations with the new values of the control software causes the point a to the origin along the vector A0.

When there are restrictionsthe initial deflection ΔV_{0}that ΔR_{0}to the predicted end of the maneuver will be changed to the values ΔV_{C}that ΔR_{C}:

and new values of deviations ΔV_{H}that ΔR_{H}for the next cycle, the term is a high control would be

From equations (10) taking into account equations (6) and (9) we find:

Suppose that the functions of sensitivity for one cycle of the terminal management has not changed, which is true for the conditions of the beginning of prolonged exercise. Values of corrections for deviations ΔV_{H}that ΔR_{H}will have the value

If ||>then, the calculated correctionlimited at the accepted level. Substituting into the second equation (12) the values of equations (11), we obtain

Thus, the point a moves to point b on the line II.

Provided that

from equations (11) we get

that is, when condition (14) the offset of the starting point And on the phase plane to a point on the line II is parallel to the line I.

If the sensitivity function is not changed, then for each subsequent cycle translation adjustments when= and=0 the point In moving to the point 0 in accordance with equations (9)

occupying a position In',","'... on the line S up until it will not enter the area bounded by the lines III-III, of which will get to the point of 0.

Figure 5 vectors shown move the initial deviations ΔR_{0}that ΔV_{0}values ΔV_{H}that ΔR_{H}when using corrections,.

Because of the presence of restrictions on amendmentwhen the initial deviations in regions 2, 4 (4, 5), new values ΔV_{H}that ΔR_{H}in some cases, can significantly exceed the initial value.

If for some initial conditions the maneuver formation of a given orbit is completed in time, corresponding to a point In^{to}on the phase plane (figure 4) with residual deviations ΔV_{To}that ΔR_{To}this will lead to errors on the parameters generated by the orbit.

Two errors ΔV ΔR on the accuracy of formation of a given orbit largely influenced by the error in radial velocity. The sensitivity of the parameters of the orbit error ΔV ΔR, expressed in h is the local derivative of the radius of apogee R_{
a}radius of perigee R_{p}and eccentricity e on ΔV ΔR, defined at the end of the maneuver generated orbits presented in the table.

Orbita | ||||||

sec | sec | s/m | - | - | 1/m | |

Geostationary | ||||||

14000 | 32000 | 0,000325 | 3 | 14 | 2·10^{-8} | |

Haaparanta | ||||||

333 | -500 | 1,1·10^{-4} | 1,8 | 0,8 | -2·10^{-7} |

To reduce errors formation orbits in the proposed method, the formation of corrections with limited angular amendment on the corner of the pitch the task of bringing residuals speed ΔV to zero through the formation of a mixture of angular velocity pitch.

With limited amendment on the corner of the pitchthe initial deflection ΔV ΔR to the predicted end of the maneuver for the 1st time terminal control will change to

When ΔV_{With}=ΔV amendment on the angular velocity of pitchproviding zero deflection ΔV, is determined from (16)

and with this in mind, from (17)

Thus, on the first beat of the terminal control when=the amendment on the angular velocity of pitchis determined from the condition of zero residuals ΔV, the discrepancy ΔR varies with size ΔR_{with}and on subsequent cycles (when ΔV=0 and=by the amount of

On the phase plane parameters ΔR, ΔV (6) with the proposed method, the formation of corrections dots',","'... the convoy is aceno change settings Δ R ΔV on each step of the terminal management from initial conditions corresponding to the point A.

Corrective amendment on the angular velocityrepresents the sum of:

wherecorrective amendment on the angular velocity of the pitch, determined without regard to the restrictions on the amendment by the angle of pitch (17);

- Supplement to the value ofwhen the output of the amendments on the corner of the pitch to the constraint.

The value ofdefined as

and by using the relations (18), (17) is reduced to the form

where

Figure 7 shows the block diagram of the device parameters correction program changes longitudinal movement on the proposed method, where the following notation: 1 - unit forecast variance (BPO) from a given orbit and calculation of sensitivity functions, 2 - block of corrections (BKP) software control, 3 - block correction (BC) parameters control programs, 4 - stop angular corrections (PMO), 5 - shaping unit exceeded (FFT) angular correction level restrictions, 6 - multiplier (M), 7 - adder (C).

When adjusting the AI settings program change terminal control according to the invention, in block 1 of scheme 7 are determined by the deviation from the target orbit at the radius-vector Δ
R and radial velocity ΔV in predictable time off the main engine and the sensitivity function L, J, S, Q by the control settings. These settings outputs 1-6 unit 1 is received on the corresponding input unit 2, and outputs 7, 8 to the inputs 3, 4 unit 3 are program settings control pitch ϑ_{0i-1}and the angular velocity of pitchwhen executed, the prediction of the motion of the upper stage.

In unit 2 are determined corrective amendments and a signal For determining the ratio of the sensitivity function of the radial velocity on the pitch angle J to the function of its sensitivity to the angular velocity of the pitch L:Amendment Δϑ_{0i}c first output unit 2 is supplied through a limiter angular amendment 4 to the first input unit 3 and to the second input of the processing unit exceeding the angular correction of level 5, at the first input of which receives the amendment.

From the output of the shaping unit exceeding the angular correction of level 5 on the first input of the multiplier 6 signal arrives excess representing the difference between the corrective amendment pitch and its limited unit 4 is:

and to the second input signal To the second output unit 2. The signal is of ihoda multiplier 6 is supplied to the 2nd input of the adder 7.

The third output unit 2 to the first input of the adder 7 is supplied corrective amendment on the angular velocityand with the release of this adder for 2-d input block parameters correction control programs 3 total comes corrective amendmentthe angular velocity of the pitch in the form

If calculated in block 2 corrective amendment on the corner of the pitch Δϑ_{0i}limitsthe output unit 5 to the multiplier 6 receives the zero signal and the 2-d input unit 3 receives the calculated corrective amendment on the angular velocity unchanged.

In block 3 executes the correction of the parameters of the program control dependencies

and the orientation program as a booster for the i-th interval of the terminal control is made in the form

The effectiveness of the proposed method of formation of corrections when developing the initial deviations ΔR=5000 km and ΔV=-5 m/s in terminal management with tact T_{y}=20 visible from the presented transients on Fig (method prototype) and Fig.9 (the proposed method).

On Fig, 9 shows the changes of the following parameters: 1 - deviation RA is odr-vector Δ R (km), 2 - deviation of the radial velocity ΔV (m/s), 3 - amendment on the corner of the pitch Δϑ (deg), restricted to the level=2 deg., 4 - adjustment for the angular velocity of pitch(deg/s). On Fig parameter ΔR is increased 10 times, and settings Δϑ and100 times; in Fig.9increased 10 times.

Thus, the proposed method of correction parameters of the program changes longitudinal movement in terminal management guidance upper stage into orbit improves the accuracy of formation of a given orbit when performing maneuvers of short duration.

Sources of information

1. Cheese A.S., Sokolov V.N., Yezhov CENTURIES, Kislik LI Algorithm targeting upper stage with unregulated main engines and small thavarungkul. Aerospace engineering and technology, 1998, No. 1, pp.31-33.

2. Apertures the basics of flight control spacecraft and ships. M.: Mashinostroenie, 1977, s.

The correction method, the parameters of change of longitudinal movement in terminal management guidance upper stage into orbit, namely, that predict the motion parameters of the booster unit at the time of main engine cutoff, determined by the t of the deviation of the radius and radial velocity of the accelerating unit from their values on a given orbit, compute function of the sensitivity of these deviations to change program settings control angle and angular velocity of the pitch, form correction signals by the angle and angular velocity of the pitch, providing compensation for these variations of the radius and radial velocity spreader block, restrict the correction signal according to the pitch angle at a given level, wherein determine the excess of the correction signal for a pitch angle relative to a set when the constraint level, form a Supplement to the signal correction angular velocity of the pitch, equal to the product of this excess on the ratio of the sensitivity functions of the radial velocity as a booster to the pitch angle and angular velocity of the pitch, form the correction signal in the angular velocity of the pitch as the sum of a correction signal according to the angular velocity of the pitch, determined without regard to the limitations of the correction signal by the angle of pitch, and the admixture determined when the output signal of the correction of the pitch angle at its specified limit.

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