RU2089468C1 - Method of control of space vehicle turn manoeuvre - Google Patents

Abstract

FIELD: space engineering; control of attitude of space vehicles and orbital stations. SUBSTANCE: space vehicle is turned over free motion trajectory and parameters over falling trajectory - vector and turn are automatically determined; to this end, control system uses iteration method, thus solving the boundary-value problem algorithmically: initial angular velocities are determined do that space vehicle should take final attitude from initial attitude due to uncontrolled rotation at preset time interval. After imparting calculated angular velocities to space vehicle, moment of transition to section of rotation of space vehicle about Euler's axis is determined such that fuel consumption for corrective turn is minimum and then respective efficiency function is continuously calculated in control system; corrective turn of space vehicle is effected at minimum magnitude of this efficiency function. EFFECT: low consumption of fuel, enhanced accuracy of turn at any unknown disturbances. 2 cl, 2 dwg

Description

 The invention relates to the field of space technology and can be used to control the angular position of spacecraft (SC) and orbital stations.

заданный вектор. Кинематические уравнения желаемого движения космического аппарата записываются через компоненты кватерниона

причем Λ_н = Λ(o) кватернион начального положения КА;
Λ_к = Λ(T_к) кватернион конечного положения КА;
T_к время разворота КА.Known methods for controlling the rotary maneuver of the spacecraft [1]
In the specified method of controlling the spacecraft rotation to the required final angular position, the spacecraft rotation is carried out along the designated path, according to the angular acceleration control principle:

given vector. The kinematic equations of the desired motion of the spacecraft are written through the components of the quaternion

moreover, Λ _n = Λ (o) quaternion of the initial position of the spacecraft;
Λ _k = Λ (T _k ) quaternion of the final position of the spacecraft;
T _{by the} time of turning the spacecraft.

Ближайшим по технической сущности аналогом является способ управления поворотным маневром (переориентацией динамически симметричного) КА, включающий определение параметров разворота, определение кинетического момента

требуемого для приведения космического аппарата при свободном его вращении в заданное угловое положение Λ_к, в заданный момент времени разгон космического аппарата и по окончании участка свободного движения торможение космического аппарата [2] При этом способе управления предполагается, что КА движется по коническим траекториям, совершая при этом регулярную прецессию. Движение состоит из участков, где действуют максимальный момент m₀ (участки разгона и торможения КА), и участка свободного движения, на котором управляющий момент равен нулю.With many advantages of the system, built on the principle of acceleration control, as applied to the control of the spacecraft’s spatial turn, the noted system has a significant drawback, the assigned paths must be set analytically, and therefore, movement along them does not minimize fuel consumption for the turn. In addition, not any assigned trajectory of the spacecraft rotation can be physically realized due to the limited control moments:

The closest in technical essence analogue is a method of controlling a rotary maneuver (reorientation of dynamically symmetric) of a spacecraft, including determining the parameters of a turn, determining the kinetic moment

required to bring the spacecraft with its free rotation to a given angular position Λ _k , at a given point in time, the spacecraft accelerates and at the end of the free motion section the spacecraft brakes [2] With this control method, it is assumed that the spacecraft moves along conical trajectories, performing at this is a regular precession. The movement consists of sections where the maximum moment m ₀ acts (acceleration and deceleration sections of the spacecraft), and a section of free movement, in which the control moment is zero.

(вектор разворота) и угла разворота ψ, с учетом инерционных характеристик КА.Bringing the spacecraft from the initial angular position to the desired final position is performed by calculating the direction of the calculated kinetic moment

(rotation vector) and the rotation angle ψ, taking into account the inertial characteristics of the spacecraft.

 The disadvantage of the prototype method is the low accuracy of the turn in the case of an asymmetric spacecraft and when turning at large angles, since the kinematic parameters are not controlled in the free-motion section.

 The technical result of this invention is a significant increase in the accuracy of the rotation of an arbitrary spacecraft with relatively low fuel consumption.

, требуемого для приведения космического аппарата при свободном его вращении в заданное угловое положение Λ_к, в заданный момент времени разгон космического аппарата и по окончании участка свободного движения торможение космического аппарата, на участке свободного движения определяют параметры доворота от текущего углового положения космического аппарата до заданного:

Определяют значение целевой функции

где λ_дi компоненты кватерниона доворота Λ_д;
ω_i компоненты вектора угловой скорости космического аппарата;

вектор кинетического момента космического аппарата;
I_i моменты инерции космического аппарата;
C_i коэффициенты расхода топлива ( C_i= const > 0 ),
фиксируют параметры доворота Λ_д в момент, когда G_y минимальна, затем определяют и фиксируют кинетический момент доворота

и прикладывают к космическому аппарату управляющий момент для осуществления указанного доворота.The specified technical result is achieved by the fact that in the proposed method of controlling the rotary maneuver of the spacecraft, including determining the parameters of the rotation, determining the kinetic moment

required to bring the spacecraft with its free rotation to a given angular position Λ _k , at a given point in time, the acceleration of the spacecraft and at the end of the free motion section the braking of the spacecraft, in the free motion section determine the rotation parameters from the current angular position of the spacecraft to the specified:

Determine the value of the objective function

where λ _di components of the quaternion dovor Λ _d ;
ω _i components of the angular velocity vector of the spacecraft;

the vector of the kinetic moment of the spacecraft;
I _i moments of inertia of the spacecraft;
C _i fuel consumption coefficients (C _i = const> 0),
fix the parameters of the turnaround Λ _d at the moment when G _{y is} minimal, then determine and fix the kinetic moment of the turnaround

and apply to the spacecraft a control moment for the implementation of the specified turn.

где Λ_н кватернион, определяющий угловое положение космического аппарата.Moreover, in a preferred embodiment of the method, the determination of the objective function G _{y is} performed from the time at which the condition
θ _ost = 0.1 θ _o , (4)
where the angles of the equivalent rotation of the spacecraft, respectively, from the initial and current to a given position are determined by the relations:

where Λ _n quaternion defining the angular position of the spacecraft.

не может быть найден аналитически. Однако, имея математическую модель фактического КА и применяя метод последовательных приближений, удалось определить для любых начального и конечного положений КА и времени разворота направление вектора кинетического момента, соответствующего траектории свободного движения КА, проходящей через начальное и конечное положения КА. Для обеспечения высокой точности управления при подходе КА к требуемому конечному положению формирование управляющих моментов происходит из условия вращения КА вокруг эйлеровой оси. Весь процесс разворота делится на четыре участка: разгон КА до требуемого кинетического момента, неуправляемое вращение КА по траектории свободного движения, коррекция и доворот КА вокруг оси Эйлера, торможение КА. На участках разгона и торможения управляющие моменты максимальны, а на участке доворота имеют незначительную величину.The essence of the proposed method is to control the spacecraft in such a way that it rotates along the trajectory of free motion almost to the final angular position. In this case, the motion of the spacecraft significantly differs from the regular precession (since the spacecraft does not have dynamic symmetry and disturbing moments act) and the rotation vector

cannot be found analytically. However, having a mathematical model of the actual spacecraft and applying the method of successive approximations, it was possible to determine for any initial and final positions of the spacecraft and the turn time the direction of the kinetic moment vector corresponding to the trajectory of free motion of the spacecraft passing through the initial and final positions of the spacecraft. To ensure high accuracy of control when approaching the spacecraft to the required final position, the formation of control moments occurs from the condition of rotation of the spacecraft around the Euler axis. The entire rotation process is divided into four sections: acceleration of the spacecraft to the required kinetic moment, uncontrolled rotation of the spacecraft along the trajectory of free motion, correction and rotation of the spacecraft around the Euler axis, braking of the spacecraft. In the areas of acceleration and braking, the control moments are maximum, and in the area of the turnaround they are insignificant.

 In FIG. 1 presents a functional logic diagram of a spacecraft control system for implementing the proposed method; in FIG. 2 shows the laws of control applied to the spacecraft moment when practicing the prototype method and the proposed method.

 The spacecraft rotary maneuver control system includes a spacecraft input and storage input and storage device 1 (UVHHKP) 1, a spacecraft inertia moment setter (BZMI) 2, a rotation time input device 3 (UVR), a strapdown inertial navigation system (BINS) 4, block 5 angular velocity sensors (BDS), a computing device (WU) 6, a control law coefficient storage unit (BHKZU) 7, a fuel consumption coefficient adjuster 8 (ZKRT), a matching-converting device (SPU) 9, executive bodies (IO) 10, this is the first out One device for input and storage of the initial and final position of the spacecraft is connected with the first input of the strapdown inertial navigation system 4 and with the first input of the computing device 6, the second output of the input device 1 is connected with the second input of the computing device 6, the output of the unit 2 of the moment of inertia of the spacecraft is connected with the third input of the computing device 6, the output of the device 3 input time reversal associated with the fourth input of the computing device 6, the output of strapdown inertial navigation system 4 communication with the fifth input of the computing device 6, the output of the block 5 of the angular velocity sensors is connected to the second input of the strapdown inertial navigation system 4 and the sixth input of the computing device 6, the output of this computing device is connected to the input of the matching-converting device 9; the first output of the control law coefficient storage unit 7 is connected to the seventh input of the computing device 6; the second output of the control law coefficient storage unit 7 is connected to the eighth input of the computing device 6, the output of the adjuster 8 of the fuel consumption coefficients is connected to the 9 input of the computing device 6; the first output of the matching-converting device 9 is connected to the executive bodies 10 of the first channel (10.1), the second output of the matching-converting device 9 is connected to the executive bodies 10 of the second channel (10.2), the third output of the matching-converting device 9 is connected to the executive bodies 10 of the third channel (10.3).

 Computing device 6 performs all the mathematical operations necessary to implement the method, and contains a mathematical model of the angular motion of the spacecraft. A digital computer can be used as a computing device, and then it is necessary to introduce an information exchange interface with measuring instruments and executive bodies into the system.

 A system is operating that implements the proposed method for controlling the spacecraft rotary maneuver as follows.

Далее по начальному и конечному положениям КА, времени разворота и инерционным характеристикам КА в ВУ6 осуществляется расчет требуемого кинетического момента

по методу итераций.From the values of the moments of inertia of the spacecraft I ₁ , I ₂ , I ₃ VU6 calculates the value of the equatorial moment of inertia I according to the expression

Then, according to the initial and final positions of the spacecraft, the turn time and the inertial characteristics of the spacecraft in VU6, the required kinetic moment is calculated

by the iteration method.

The deviation of the predicted position of the spacecraft Λ (T _k ) from the required Λ _k is determined by mathematical modeling in VU6.

повторяется, пока

Рассчитанному таким образом вектору кинетического момента

соответствует угол разворота ψ и вектор разворота

По углу разворота и времени разворота ВУ определяет время разгона (торможения) τ по выражению:

В исходном состоянии

выход вычислительного устройства замаскирован, и

. В момент поступления команды на разворот ВУ6 формирует управляющий момент

который прикладывают к КА посредством ИО10. Расчет текущего кинетического момента

ВУ6 производит непрерывно по показаниям ДУС 5, дающим вектор

, и моментам инерции

Как только КА будет сообщен расчетный кинетический момент, выход ВУ6 маскируется, управляющие моменты отсутствуют и КА производит свободное вращение. При этом ВУ6 непрерывно определяет метры доворота по формуле (1) и вычисляет значение целевой функции G_y.Intergration process

repeated until

The kinetic moment vector calculated in this way

corresponds to a pivot angle ψ and a pivot vector

The angle of the turn and the time of the turn of the control unit determines the time of acceleration (braking) τ by the expression:

In the initial state

the output of the computing device is masked, and

. At the time of receipt of the command to turn the VU6 generates a control moment

which is applied to the spacecraft through IO10. Calculation of the current kinetic moment

VU6 produces continuously according to the indications of DUS 5, giving a vector

, and moments of inertia

As soon as the calculated kinetic moment is reported to the spacecraft, the VU6 output is masked, there are no control moments and the spacecraft rotates freely. At the same time, VU6 continuously determines the metering by the formula (1) and calculates the value of the objective function G _y .

путем приложения управляющих моментов по осям КА

где k_i, r_i постоянные коэффициенты.At the time when this function assumes the minimum value, the parameters of the retraction Λ _d are fixed, according to which VU6 calculates and fixes the kinetic moment of the retraction (3). Spacecraft report corrective pulse

by applying control moments along the SC axes

where k _i , r _{i are} constant coefficients.

и кинетический момент

поддерживаются постоянными. Одновременно ВУ6 вычисляет угол доворота (6), определяет и фиксирует угол θ_пор на который развернется КА при торможении.Further angular velocity

and kinetic moment

maintained constant. At the same time, VU6 calculates the angle of rotation (6), determines and fixes the angle θ of the _pores through which the spacecraft will turn during braking.

Когда

выход ВУ6 маскируется, исполнительные органы отключены, поворотный маневр окончен. Система готова к следующему поворотному маневру КА.At the moment of equality θ _ost = θ _{then the} spacecraft is braked, and control moments along the spacecraft axes are formed based on the expression

When

VU6 output is masked, executive bodies are turned off, the turning maneuver is over. The system is ready for the next rotary maneuver of the spacecraft.

The objective function (2) with the free rotation of the spacecraft will decrease and its minimum will be near the final position Λ _k . Therefore, in the proposed method, the value of this function (2) begins to be determined from a certain point in time at which the angles from the final position to the initial and current positions correspond to condition (5), (6), that is, it is in a certain proportion (4). Based on the results of mathematical modeling of a series of spacecraft rotary maneuvers, it was found that the proportionality coefficient should be taken equal to K 0.1.

 Timing diagrams of the spacecraft control process are shown in FIG. 2.

 The effectiveness of the proposed method is determined primarily by the fact that for most of the trajectory of motion the control moment is zero, which significantly saves fuel. At the same time, the method offers a terminal control principle in the vicinity of a given angular position of the spacecraft, which ensures high accuracy of the turn under conditions of significant external disturbing moments.

Claims (2)

1. A method for controlling a rotary maneuver of a spacecraft, including determining the parameters of a turn, determining the kinetic moment

required to bring the spacecraft with its free rotation to a predetermined angular position, determined by the quaternion Λ _k at a given point in time, the acceleration of the spacecraft and at the end of the free motion section the braking of the spacecraft, characterized in that in the free movement section determine the parameters of the turn from the current angular position spacecraft defined by the quaternion Λ, up to a given

Where

Λ quaternion conjugate,
determine the value of the objective function

Where

components of the quaternion dovor Λ _d
ω _i are the components of the angular velocity vector of the spacecraft;
K is the vector of the actual kinetic moment of the spacecraft;
J _i moments of inertia of the spacecraft;
C _i fuel consumption coefficients (C _i const> 0),
fix the parameters of the turnaround Λ _d at the moment when G _{у is} minimal, then determine and fix the kinetic moment of the turnaround

and apply to the spacecraft a control moment for the implementation of the specified turn. 2. The method according to claim 1, characterized in that the determination of the objective function G _{y is} produced from the point in time at which the condition
θ _ost = 0.1θ _o
where the angles of the equivalent rotation of the spacecraft, respectively, from the initial and current to a given position are determined by the relations

where Λ _n is the quaternion, which determines the initial angular position of the spacecraft.

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