Технические науки/ Авиация и космонавтика

Dr Nickolay Zosimovych, Dr Alex Noel Joseph Raj

Shantou University, Shantou, China

SYNTHESIS OF STABILIZATION ALGORITHMS IN THE SYSTEM CONTROLLING ROTATIONS OF THE OPERATING DEVICE

Keywords: Space probe (SP), propulsion system (PS), angular velocity sensor (AVS), operating device (OD), space vehicle (SV), feedback (FB), control actuator (CA), control system (CS), angular stabilization (AS), center of mass (CM).

I. Introduction. In some cases, when using a control system built according to the principle of program control (the "robust trajectories" method) the efficiency of task solution is much influenced by the accuracy of the spacecraft stabilization system in the powered portion of flight. This concerns, for example, the trajectory correction phases during interplanetary and transfer flights, when the rated impulse execution errors during trajectory correction resulting from various disturbing influences on the spacecraft in the active phase, greatly affect the navigational accuracy. Hence, reduction of the cross error in the control impulse on the final correction phase during the interplanetary flight, facilitates almost proportional reduction of spacecraft miss in the "perspective plane". For example, in some space probes (SP) like Deep Impact [1, 2] and Rosetta missions [3, 4] reduction of cross error by one order during the execution of correction impulse (for modern stabilization systems this value shall be results in reduction of spacecraft miss in the "perspective plane" from 200 to 20 Such reduction of the miss accordingly increases a possibility of successful implementation of the flight plan, as well as the accuracy of the research and experiments conducted [5].

The Martian Moons Exploration (MMX) mission is scheduled to launch from the Tanegashima Space Center in September 2024. The spacecraft will arrive at Mars in August 2025 and spend the next three years exploring the two moons and the environment around Mars. During this time, MMX will drop to the surface of one of the moons and collect a sample to bring back to Earth. Probe and sample should return to earth in the summer 2029 [6].

Objectives: to solve the task of significant increase in stabilization accuracy of center of mass tangential velocities during the trajectory correction phases when using the "rigid" trajectory control principle.

Subject of research: The center of mass movement stabilization system in the transverse plane, which is used during the trajectory correction phases.

In order the control actions could be created during the spacecraft trajectory correction phase, a high-thrust service propulsion system with a tilting or moving in linear direction combustion chamber shall be used.

II. Content of the Problem. We study motions of the spacecraft in the normal plane of the inertial coordinate system (Fig. 1) [5]. The center of the inertial coordinate system at the beginning of the active phase is the same as the center of mass of the spacecraft; the axis coincides with the direction of the required correction impulse axis together with axis form a normal plane. The angular position of the spacecraft in the normal plane is determined by an angle between axis of the inertial coordinate system and X- axis of the bound coordinate system. Control of the spacecraft in the active phase shall be done by deflection of combustion chamber of PS at an angle between X-axis of the spacecraft and X-axis of the nozzle symmetry of PS [7].

Fig. 1. Spacecraft diagram in the inertial coordinate system

The following assumptions and conditions were used in the process of synthesis of the stabilization algorithms [5]:

1. We assume that the spacecraft is subject to disturbances in the active phase (force and moment which are mainly caused by working PS (tilt and thrust misalignment). Because of their nature, these parameters shall slowly change in time throughout the active phase (except for the period from the start of PS till switching to the nominal operation mode For this reason, the disturbances may be considered permanent within the active phase with a reasonable degree of accuracy: We shall consider the work of the stabilization system within the entire possible range of disturbances: (experrience shows that the maximum force and moment are respectively about 0.3⁰ and 3.5⁰ in the equivalent deviation angles of PS).

2. The motion of the spacecraft is considered as movement of the absolute rigid body in vacuum relative to the reference trajectory in the normal plane of the inertial coordinate system.

3. A high-thrust chemical engine is used to control the spacecraft in the active phase. Control is provided by deflecting PS combustion chamber. The servo control, which deflects the combustion chamber includes a feedback control actuator.

To stabilize the angular position of the spacecraft we shall use the information about deviation of the spacecraft body-fixed axes from the axes of the inertial coordinate system implemented in the gyro stabilized platform (CST) on board the spacecraft and the angular velocity sensors (AVS). The information on the deviation of the tangential velocities shall be taken from the accelerometers installed on CSP.

III. Mathematical model of the spacecraft center of mass motion stabilization system. Taking in consideration the above assumptions and suppositions we can set down a system of equations (1) describing the behavior of the spacecraft center of mass motion stabilization system under study:

(1)

where is the center of mass drift coordinate in the inertial coordinate system; are dynamic coefficients of the spacecraft; where is PS thrust, is mass of the spacecraft; where is the distance from the gimball assembly of PS to the center of mass of the spacecraft, is momentum of inertia of the spacecraft relative to the axis of the bound coordinate system; is a velocity performance index of the control actuator; is a control actuator feedback index; is a response function of the angular stabilization controller; is a response function of the stabilization controller through the center of mass channel.

Fig. 2. Block diagram of the spacecraft center of mass motion stabilization system under study

Fig. 3. Block diagram of a standard center of mass motion stabilization system of a spacecraft

According to the above mathematical model, a block diagram of the stabilization system under study shall be as follows (Fig. 2) [5, 7].

In order to improve accuracy of stabilization while using synthesized algorithms, a model of a model of a standard stabilization system shall be made. It is to be used as a reference model for comparison. The standard stabilization model uses a known stabilization controller [8-10], which provides control proportionally to the angle of the spacecraft angular rotation velocity in the normal plane linear drift and the drift velocity A block diagram of the standard stabilization system is shown in Fig. 3 [5, 7].

IV. Method to solve an invariant problem. As mentioned above, usage of methods of the invariant theory [11-18] is seen as a way to improve the accuracy of the automatic regulation system. In the present case, it is not possible to synthesize the invariant stabilization system using the method of combined regulation, which is traditional for invariant systems because actual measurements of the disturbing effects are not available. However, publications [19, 20] observe that it is possible to build an invariant system without use of combined regulation methods, if we apply the principle of dual-channel impact distribution in the controlled object. The principle of dual-channel impact distribution resides in the fact that if the controlled object has two distribution channels of the same impact, we may achieve mutual compensation of the impact transferred through the above channels by selecting a respective law of control so that the regulated value becomes invariant (independent) of the said impact.

Fig. 2 shows that the controlled object under study has two channels of distribution of disturbing moment [5]. Therefore we can improve the accuracy of the stabilization system by using the invariant theory principle. So we select synthesis of high-precision stabilization systems based on the principles of the invariant theory as a method helping us to solve the problem set.

Conclusion. Based upon research results we can conclude the following:

1. It is impossible to implement a center of mass stabilization system, which is absolutely invariant regarding both the disturbing force and disturbing moment.

2. It is possible to build an absolutely invariant system regarding the disturbing moment due to presence of two distribution channels in the controlled object.

3. A stabilization system, which is partially invariant regarding the disturbing moment, is the easiest to implement in practice. In order to meet the invariance conditions, a positive feedback is required from the flight control actuator with a gain in angular deviation of the object in the angular stabilization channel.

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