RU2093433C1 - Method of control of space vehicle turn - Google Patents

Abstract

FIELD: space engineering; space vehicle, orbital station and special- purpose module attitude control systems. SUBSTANCE: method is realized through automatic determination of axis of turn of space vehicle in space ensuring turn of space vehicle at minimum moment of momentum, calculation of angles of turn about found axis and longitudinal axis of space vehicle for shifting it to final position; programmed angular-velocity vector is formed according to selected nominal trajectory of rotation. Control of turn of space vehicle is effected continuously with the aid of computer and programmed angular-velocity vector forming unit with angular-rate sensors and strap-down inertial navigation system connected to them. Terminal brake control of space vehicle enhances accuracy of orientation. EFFECT: enhanced accuracy of orientation; enhanced economical efficiency due to rotation at minimum moment of momentum. 3 cl, 8 dwg

Description

 The invention relates to the field of space technology and can be used to effectively control the angular position of spacecraft, orbital stations and specialized modules.

где

кватернионы начального и конечного угловых положений КА.There are many ways to control the turn of a spacecraft (SC). The simplest and most common is to change the angular position of the spacecraft by performing sequential turns at certain angles around the axes rigidly connected to the apparatus [1]. For example, this order of turns can be rotated around the transverse axis of the spacecraft until its longitudinal axis X is aligned with its desired final position X _to and then the rotation of the spacecraft around the longitudinal axis X to combine the axes YZ associated with the spacecraft with the required position in the space Y _to Z _k . The values of the rotation angles around the transverse axis β and the longitudinal axis a are determined through the components of the quaternion:

Where

quaternions of the initial and final angular positions of the spacecraft.

 The angular velocity of the turn can be selected from the condition of minimizing the magnitude of the kinetic moment in the process of performing a turning maneuver.

 Control systems that implement turns around connected SC axes are widely known and well studied. With many advantages of such systems, including their simplicity and reliability, they have one significant drawback - the long duration of the maneuver with equal cost of the kinetic moment.

. Определяющими характеристиками процесса разворота являются расчетная величина скорости разворота ω и время разгона КА t.The closest in technical essence analogue is the spacecraft rotation control method [2], which includes determining the angular velocity of the rotation, acceleration of the spacecraft at a given time and at the end of the section of motion with a constant angular velocity, the braking of the spacecraft. In this control method, it is assumed that the spacecraft rotates around the Euler axis, and the direction of the angular velocity vector of the spacecraft is constant. The orientation of the Euler axis relative to the axes associated with the spacecraft is determined by the turn quaternion

. The determining characteristics of the U-turn process are the calculated value of the U-turn speed ω and the spacecraft acceleration time t.

где

расчетное угловое ускорение;
J тензор инерции КА;

текущая угловая скорость КА;

ортвектора ориентации оси Эйлера.Control moments are formed in the areas of acceleration and deceleration, based on the expression:

Where

calculated angular acceleration;
J spacecraft inertia tensor;

current angular velocity of the spacecraft;

orthvector orientation of the Euler axis.

 The “+” sign corresponds to the acceleration section, and the “-” sign corresponds to the braking section. In the spacecraft’s motion with a constant angular velocity, the control moments are also constant and compensate for the gyroscopic moments that arise when the solid rotates around an axis that does not coincide with the main central axis of inertia.

в требуемое конечное положение

производится следующим образом. По имеющимся параметрам разворота (

) определяют расчетную угловую скорость

. По расчетной величине угловой скорости и эффективности исполнительных органов определяют время разгона t.Bringing the spacecraft from the initial angular position

to the desired end position

produced as follows. According to available reversal parameters (

) determine the estimated angular velocity

. The calculated value of the angular velocity and efficiency of the executive bodies determine the acceleration time t.

не станет равной расчетному значению

. В момент равенства этих скоростей начинается участок движения КА с постоянной угловой скоростью, а управляющие моменты формируются следящей системой таким образом, чтобы это условие как можно точнее выполнялось. Через заданное время разворота КА (T) производят торможение КА.From the moment a command for a turn is received, a control moment (1) is applied to the spacecraft until the actual angular velocity

will not be equal to the calculated value

. At the moment of equality of these speeds, the spacecraft motion section begins with a constant angular velocity, and the control moments are formed by the tracking system in such a way that this condition is met as accurately as possible. After a predetermined spacecraft turn time (T), spacecraft is braked.

 The disadvantage of the prototype method is the relatively large value of the kinetic moment of the spacecraft during a U-turn.

 The technical result of this invention is a significant reduction in the kinetic moment of the spacecraft in the process of a U-turn.

.The specified technical result is achieved by the fact that in the proposed method of controlling the turn of the spacecraft, including determining the angular velocity of the turn, at a given point in time, the acceleration of the spacecraft, the rotation of the device with a constant angular velocity, the braking of the spacecraft, in contrast to the prototype, determine the angle of the axis deviation precession from the longitudinal axis of the apparatus n, determine the angle of rotation around the axis of precession b and the angle of rotation around the longitudinal axis a, form and apply to the space th unit control torque, providing a simultaneous rotation of the machine around the precession axis and around the longitudinal axis with a constant angular velocity

.

где ω_x - угловая скорость относительно продольной оси КА;
ω_y,ω_z - угловые скорости относительно поперечных осей КА;
t время с начала разворота;
τ - расчетное время торможения КА;
ψ - обобщенный угол разворота, равный α+β(|cosν|+|sinν|).The specified technical result is also achieved by the fact that the start time of the braking section is determined by the condition:

where ω _x is the angular velocity relative to the longitudinal axis of the spacecraft;
ω _y , ω _z are the angular velocities relative to the transverse axes of the spacecraft;
t time from the beginning of the U-turn;
τ is the estimated spacecraft braking time;
ψ is the generalized turning angle equal to α + β (| cosν | + | sinν |).

На фиг. 1 изображена зависимость ν(Φ) при различных κ для соотношения моментов инерции КА: J_y > J_x; на фиг. 2 зависимость n(χ) при различных Φ для того же случая J_y > J_x; на фиг. 3 - зависимость n(Φ) при различных κ для случая: J_y <J_x; на фиг. 4 зависимость n(χ) при различных Φ для случая J_y <J_x; на фиг. 5 поясняется физический смысл углов k и n на фиг. 6 приведена функциональная схема системы, реализующей способ; на фиг. 7 величина экономии кинетического момента для случая J_y > J_x; на фиг. 8 - величина экономии кинетического момента для случая J_y <J_x.The specified technical result is also achieved by determining the angle of rotation from the initial to the desired final angular position Φ, continuously measuring the angle of rotation from the current to the required final angular position v _ost , and the braking of the spacecraft begins from the moment the condition is met:

In FIG. Figure 1 shows the dependence ν (Φ) for various κ for the ratio of the moments of inertia of the spacecraft: J _y > J _x ; in FIG. 2 the dependence n (χ) for different Φ for the same case J _y > J _x ; in FIG. 3 - dependence n (Φ) for various κ for the case: J _y <J _x ; in FIG. 4 the dependence n (χ) for various Φ for the case J _y <J _x ; in FIG. 5, the physical meaning of the angles k and n in FIG. 6 shows a functional diagram of a system that implements the method; in FIG. 7 value of kinetic moment saving for the case J _y > J _x ; in FIG. 8 is the value of the kinetic moment saving for the case J _y <J _x .

 An example implementation of the proposed method is presented in FIG. 6, where it is indicated: 1 device for input and storage of rotation parameters (UFHPR), 2-block of units of moment of inertia of the spacecraft (BZMI), 3 device for input and storage of time of rotation (UVHVR), 4 block of angular velocity sensors (BDS), 5 - strapdown inertial navigation system (SINS), 6 unit for determining the angle of deviation of the axis of precession from the longitudinal axis of the spacecraft (BOWA), 7 - computing device (WU), 8 unit for generating the program vector of angular velocity (BFPS), 9 matching-converting device (SPU), 10 - system of executive bodies (SIO), 11 -pr grammno-time device (SSP). The first output of UVHPR 1 is connected to the first input of VU 7, the second output of UVHPR 1 is connected to the first input of BOUO 6 and to the second input of VU 7. The output of BZMI 2 is connected to the second input of BOUO 6 and to the third input of VU 7. The output of UVHVR 3 is connected to the fourth VU 7 input, BDUS 4 output is connected to VINS 5 input and VU 7 fifth input. VINS 5 output is connected to VU 7 sixth input, BOUO 6 output is connected to VU 7 seventh input and BFPS 8 first input. VU 7 first output is connected to the second input of BFPUS 8, the second output of VU 7 is connected to the third input of BFPUS 8, the third output of VU 7 is connected to the fourth input of BFPUS 8, the fourth you the progress of WU 7 is connected to the input of the control unit 9. The output of the BFPS 8 is connected to the eighth input of the WU 7, the output of the control unit 9 is connected to the input of the SIO 10, the output of the FIA 11 is connected to the fifth input of the BFPS 8.

The unit for determining the angle of deviation of the precession axis from the longitudinal axis of the spacecraft consists of a set of matrices of approximating coefficients of the function n (λ _o , λ ₁ ), corresponding to several characteristic combinations of moments of inertia (J _x , J _y ), and the actual calculator of the nonlinear function of the arguments λ _o , λ ₁ .

и угла v_o, расчет времени разгона τ и пороговых значений j_расч,Φ,Φ_ост, а также содержит в себе алгоритм формирования требуемых величин проекций управляющего момента на связанные с КА оси, обеспечивающий выбранную кинематику движения КА.The computing device performs all the mathematical operations necessary for the implementation of the method: calculation of the required angular velocities by the angle ν

and angle v _o , the calculation of the acceleration time τ and threshold values j _calc , Φ, Φ _ost , and also contains an algorithm for generating the required projection values of the control moment on the axis associated with the spacecraft, providing the selected kinematics of the spacecraft motion.

 The unit for generating the angular velocity vector program generates the calculated value of the angular velocity vector as a function of time corresponding to the programmed trajectory of the spacecraft rotation.

 Temporary synchronization of the BFPUS 8 operation is carried out by the PVU 11 (sets the U-turn command and generates harmonic functions).

 If the spacecraft motion control system includes a computer, then the latter can not only be used as a VU 7, but also perform the functions of the BOUO 6 and BFPUS 8. The above matrices of approximating coefficients can be performed on the ROM.

 A system is operating that implements the proposed method for controlling the spacecraft rotation, as follows.

и углу ν. По времени разворота T (информации с УВХВР) ВУ 7 вычисляет угловые скорости вращения

, по которым совместно с v_o БФПУС 8 формирует программное значение вектора угловой скорости

. Одновременно ВУ 7 определяет и время разгона t. В момент поступления с ПВУ 11 команды на разворот ВУ 7 формирует управляющий момент (1), исходя из программных значений проекций вектора угловой скорости на связанные оси:

где

При этом ВУ 7 выдает соответствующие сигналы в СПУ 9, которое и переводит их в соответствующие команды на исполнительные органы СИО 10. Во все время разворота контроль осуществляют ВУ 7 по информации от БДУС 4 И БИНС 5.Based on the available inertial characteristics of the spacecraft, the corresponding matrix of approximating coefficients is selected in BOUO 6. Based on the given installation parameters of the turn using the selected matrix of coefficients, the angle ν of the deviation of the precession axis from the longitudinal axis is calculated. In WU 7, the task of guiding the determination of the angles a, β, and Φ _o is solved by the rotation parameters

and angle ν. According to the turnaround time T (information from UVHVR) WU 7 calculates the angular velocity of rotation

according to which together with v _o БФПУС 8 forms the program value of the angular velocity vector

. At the same time WU 7 determines the acceleration time t. At the moment of receipt of a command for turning UW 7 from PVA 11, VU 7 generates a control moment (1), based on program values of the projections of the angular velocity vector on the connected axes:

Where

At the same time, VU 7 gives the corresponding signals to SPU 9, which transfers them to the corresponding teams to the executive bodies of the SIO 10. At all times, the control is carried out by VU 7 according to information from BDUS 4 AND BINS 5.

, система переходит в режим поддержания с высокой точностью заданной угловой скорости при условии:

откуда получаются соответствующие программные значения управляющего момента (1).As soon as the actual angular velocity of the spacecraft becomes equal

, the system enters the maintenance mode with high accuracy of the specified angular velocity under the condition:

where do the corresponding program values of the control torque (1) come from.

 When implementing the proposed method, the calculation and integration of the generalized angular velocity is continuously carried out, and at the moment when the accumulated generalized angle becomes equal to the threshold value, the spacecraft is decelerated by applying moment (1) of the necessary sign.

за обобщенную скорость, пропорциональную величине кинетического момента, находим условие (2), определяющее момент начала участка торможения, причем:

где m максимальная эффективность исполнительных органов.The moment of the start of braking is determined from the assumption that when braking (as during acceleration), the change in the magnitude of the kinetic moment occurs uniformly. Taking value

for the generalized speed proportional to the magnitude of the kinetic moment, we find condition (2), which determines the moment of the start of the braking section, and:

where m is the maximum efficiency of the executive bodies.

,
где N кватернион фактического углового положения КА.For greater accuracy in determining the moment of the start of braking, it is necessary to control the spacecraft motion not only by the angular velocity, but also by the actually remaining angle to the final position:

,
where N is the quaternion of the actual angular position of the spacecraft.

 Considering that the integral of the generalized speed in the braking section is related to a given angle of rotation in the same way as the generalized angle with the angle of rotation, we obtain the above criterion (3) for the formation of a brake signal.

 A distinctive feature in the implementation of the method is the presence of a procedure for determining the optimal direction of the axis of the precession of the spacecraft in inertial space, determining the angle of deviation from this direction of the longitudinal axis of the spacecraft and angles of rotation of the spacecraft around the precession axis and the longitudinal axis, as well as the presence of an orientation system that provides the required programmed motion of the spacecraft with high accuracy during which (4) takes place.

 At the time of execution (3) WU 7 issues a command to decelerate the spacecraft. When the angular speed of rotation is reset, the output of the VU 7 is masked, the executive bodies turn off the turn is over. The system is ready for the next maneuver.

 The effectiveness of the proposed method is determined, first of all, by a significant reduction in the required kinetic momentum for a turn, which is especially important when controlling the spacecraft by inertial actuators (power hydroscopes by the gyrodynamic system). The greatest effect is achieved when turning at large angles, when the Euler axis does not lie in the transverse plane of the spacecraft. The results of mathematical modeling depending on the reversal conditions are shown in FIG. 7 and 8. The proposed method is most appropriate for controlling the orientation of large massive spacecraft such as the Mir orbital complex and will significantly expand the capabilities for controlling and conducting scientific experiments, since it provides a significant reserve of the kinetic moment of the gyrosystem during dynamic operations.

Claims (1)

1. A method of controlling the turn of a spacecraft, including determining the angular velocity of a turn, at a given point in time, acceleration of the spacecraft, rotation of the spacecraft with a constant angular velocity, braking of the spacecraft, characterized in that the angle of deviation of the precession axis from the longitudinal axis of the spacecraft ν is determined, determine the angle of rotation around the axis of precession β and the angle of rotation around the longitudinal axis a, form and apply to the spacecraft a control moment that provides simultaneous apparatus rotation around the precession axis and around the longitudinal axis with constant angular velocities

2. The method according to claim 1, characterized in that the braking of the spacecraft begins from the moment the condition is met

where ω _x is the angular velocity relative to the longitudinal axis of the apparatus;
ω _z , ω _y are the angular velocities relative to the transverse axes of the apparatus;
t time from the beginning of the U-turn;
τ is the estimated braking time of the apparatus;
ψ is the generalized rotation angle defined by the expression
Ψ = α + β (| cosν | + | sinν |).
3. The method according to claims 1 and 2, characterized in that they determine the angle of rotation from the initial to the desired end angular position Φ, continuously measure the angle of the turn from the current to the desired end angular position Φ _ost , and the braking of the spacecraft begins from the moment the condition

I am

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