Dynamics and control of a large spacecrafts

assembled in an orbit

V.Yu.Rutkovskiy, V.M.Sukhanov, S.D.Zemlyakov, V.M.Glumov

V.A.Trapeznikov Institute of Control Sciences, RAS

Russia

The task of the current mathematical model on-line computer based derivation of a discretely evolving structure (DES) current was solved. The graph-model of the object dynamics is obtained. The method of synthesis of the assembly optimal trajectory is suggested. Some problems of the DES control in the course of its assembly and possible approaches of their solution were discussed. The synthesis of the adaptive control algorithm with using the elements of intelligent diagnostics of the construction elastic modes was considered. The structure of adaptive system with two adaptation levels of the base algorithm adjusted parameter is suggested. The example of computer simulation that illustrates efficiency of suggested algorithm is adduced. The article is the survey of the investigations that were carried out in Trapeznikov Institute of Control Sciences of RAS.

 

Development of some global projects for the next stage of mastering the space has started in the mid-1980s. It was required design of a new type of large-size spacecraft that was called as the large space structure (LSS) (or discretely evolving structure). The scale of these projects may be illustrated by well-known examples. For instance, in order to replace the decreasing resources of energy carriers, it is planned to construct in the near-earth space the large solar power stations provided with solar cell panels of size running up to that of the football ground. There exists also a project of using the large orbiting reflectors to illuminate by solar light the northern regions during the polar nights in order to promote development of these under populated territories. The most important direction in development of astronomy lies in design and deployment of large radio-telescopes in the near-earth orbit.

Such objects as LSS can not be inserted into orbit because of their desirable size. So it is necessary to realize step-by-step in-orbit LSS assembly. In the course of the assembly LSS passes three qualitatively different periods of its existence.

1.        The initial period is the rigid carrying body.

2.        Once the first construction flexible element and some other flexible elements are attached to the assembled object begins to exhibit the properties of a flexible mechanical system, which is characterized by the presence of one or several comparatively high-frequency (~1¸10 Hz) vibration modes. Such type of the object usually is called as flexible spacecraft.

3.        As the number of the flexible elements increases, the assembled object turns into a hard-to-control system. Such system is distinguished by a big inertia moment and many low elastic modes frequencies (~0,1 Hz). These frequencies close with the fundamental frequency of the "rigid" motion of the object. Such space object is LSS.

Hence LSS in the course of its in-orbit assembly is discretely evolving structure (DES). As the control object it is multi-frequency oscillating system with discretely time-varying parameters and number of freedom degrees.

In this work it is adduced the survey of the papers that are due to DES control and that were performed in the Institute of Control Sciences Russian Academy of Sciences (Moscow). Mathematical models of DES, principles of step-by-step in-orbit their assembly and methods of design of the control systems for such space structures are considered.

A DES of a sufficiently simple form, which can be represented by umbrella-type structure is considered. In such DES, the passive bodies, the rods that form the required frame surface, are sequentially attached to the carrying body and to each other. Although the rods are supposed to be rigid bodies, we take into account the link elasticity at their attachment points (it is possible to consider the rods as a weightless elastic ones, which are attached to carrying body and to each other rigidly).

In early works the mathematical technique to support the on-line computer-based derivation of the current mathematical model of the three-dimensional motion of the umbrella-type DES is developed. The following problems were solved:

1.                               Mathematical technique for computer-based derivation of the three-dimensional motion equations for the DES of complete structure (LSS).

2.                               Mathematical technique for computer-based derivation of the three-dimensional motion equations for the DES of any intermediate structure and structure with extra constraints imposed.

3.                               Computer-based linearization of the mathematical model for all special cases.

4.                               Computer-based reducing the linearized mathematical model of the DES motion to the main (normal) coordinates.

5.                               Computer-based constructing modal-physical models of partial motions.

Obtained results are constructive and can be used for getting all types of the DES mathematical models in symbolic (Maple) and in numerical (Matlab) forms.

The large space structures assembling in orbit are the objects of the immediate future. At the present time the control theory of such kind objects is poorly developed. In this paper some new problems of this theory are discussed. The graph-models of feasible assembly trajectory and object's dynamics, optimal assembly trajectory were represented. New strategy of adaptive control was considered. But of course these results are only the first steps in the control theory of large space structures.