Explicit laws for tuning power gyroscopic complexes of multiple circuits in problems of controlling the orientation of a spacecraft

1Yefymenko, MV
1«Hartron-UKOM» scientific manufacturing company, Limited Liability Company, Zaporizhia, Ukraine
Space Sci. & Technol. 2019, 25 ;(1):27-37
https://doi.org/10.15407/knit2019.01.027
Publication Language: Russian
Abstract: 
Currently, the most effective way to obtain data on the Earth's surface is satellite imagery. To obtain high-quality images of the earth's surface, the satellite must be oriented in space with very high accuracy. The required orientation accuracy is 2–5 angular minutes, and the error of stabilization in angular velocity, depending on the spatial resolution, should be no worse than 10–3 … 10–4 degrees per second. In addition, such devices are subject to high demands on the dynamic characteristics of spatial turns during shooting. The turn must be carried out from any current to any given position. The angular velocity during the rotation can reach a value of 2¾3 degrees per second. Power gyroscopic complexes (PGC) are usually used as the actuators to ensure such high dynamic characteristics of satellites in their orientation systems. PGC is a redundant system (more than 3) of two-degree power gyroscopes (gyrodynes).
      The article deals with the problem of spatial reorientation of a spacecraft using a PGC.  A control algorithm for the PGC is proposed, which ensures a given orientation of the spacecraft and the optimal configuration of gyrodynes. The proposed algorithm is based on explicit laws for tuning gyroscopic complexes, which are nonlinear algebraic equations relative to tuning options. In contrast to the well-known works, it is proved that the nonlinear algebraic equations underlying the explicit laws of the setting are compressive mappings. Thereby, the simple iteration method can be applied to find the settings from these equations. Computationally, the method is very simple and can be used in onboard algorithms. The results of numerical modeling of the proposed algorithm are given.
Keywords: attitude control, gyrodyne, spacecraft
References: 
1. Bakhvalov N. S. Numerical methods / Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M. – 6th ed. M.: BINOM. Laboratory of Knowledge, 2008. 636 p. [in Russian].
2. Vasiliev V. N. Control of a system of two-stage power gyroscopes with parallel precession axes. Izv. Academy of Sciences of the USSR. Solid mechanics. N 3. 14—20 (1982) [in Russian].
3. Vasiliev V. N. Optimization of setting the minimum redundant system of girodins. Izv. RAS. Solid mechanics. N 4. 3—10 (1999) [in Russian].
4. Vasiliev V. N. Controlling the angular position of a longterm orbital station with the help of two-degree power gyroscopes. In: V. N. Vasiliev, D. M. Weinberg, N. N. Sheremetyevsky. Izv. Academy of Sciences of the USSR. Solid mechanics. N 5. 3—9 (1978) [in Russian].
5. Efimenko N. V. Synthesis of control algorithms for spatial reorientation of a spacecraft using dynamic equations of the rotational motion of a rigid body in the Rodrig - Hamilton parameters. Control problems and informatics. N 3. 145—155 (2015) [in Russian].
6. Karpachev Yu. A. Equal-modular program-frequency control of the minimally redundant structure of two-degree power gyroscopes. Izv. Acadamy of Science USSR. Solid mechanics. N 2. 3—10 (1986) [in Russian].
7. Legostaev V. P. The scope of power gyrosystems / V. P. Legostaev, E. N. Turner. Space Research. Vol. 28, N 3. 352—359 (1990) [in Russian].
8. Somov E. I. Dynamics of control spacecraft for earth view the power gyrosystems. Gyroscopy and navigation. N 4 (39). 54—55 (2002) [in Russian].
9. Somov E. I. Optimization of the rotational maneuver and synthesis of the laws of governance of power gyrosystems guidance of spacecraft and free-flying robots. Proceedings of the Samara Scientific Center of the Russian Academy of Sciences. Vol. 9, N 3. 824—834 (2007) [in Russian].
10. Somov E. I. Topological analysis of singular states and the synthesis of explicit laws for tuning power gyroscopic complexes of multiple schemes. Proceedings of the Samara Scientific Center of the Russian Academy of Sciences. Vol. 11, N 3. 132—140 (2009) [in Russian].
11. Somov E. I. Synthesis of a gyrosil system of spatial stabilization based on Lyapunov vector functions and parametric optimization / E. I. Somov, E. A. Bondarenko, N. B. Kapitonova. Problems of Analytical Mechanics, Stability and Motion Control. 257—264 (Novosibirsk: Nauka, 1991) [in Russian].
12. Somov E. I. et al. Explicit logical-dynamic law of control the minimum redundant system of gyrodynes for a maneuvering spacecraft / E. I. Somov, S. A. Butyrin. Traffic control and aircraft navigation. 179—184 (Samara: SSAU, 2002) [in Russian]. 13. Somov E. I. Control the power gyrocomplexes spacecrafts.Proceedings of the X St. Petersburg International Conference on Integrated Navigation Systems. 278—294 (SPb., 2003) [in Russian].
14. Somov E. I. et al. Assessment of the feasibility of a spacecraft turning maneuver with uncertainty of the accumulated kinetic moment of a force gyro complex. Proceedings of the Samara Scientific Center of the Russian Academy of Sciences. Vol. 10, N 3. 799— 807 (2008) [in Russian].
15. Sorokin A. V. et al. Comparative analysis power gyroscopic complexes of high-dynamic spacecraft. Proceedings of the X St. Petersburg International Conference on Integrated Navigation Systems. 272—277 (SPb., 2003) [in Russian].
16. Tokar E. N. Criterion for setting up power gyro systems. Space research. Vol. 18, N 3. 77—82 (1980) [in Russian].
17. Avanzini G., Radice G., Ali I. Potential approach for constrained autonomous maneuvers of a spacecraft equipped with a cluster of control moment gyroscopes. Journal of Aerospace Engineering. Vol. 223, N 3. 285—296 (2009).
18. Crenshaw J. W. 2-Speed, a single gimbal control moment gyro attitude control system. AIAA Paper. N 73-895. 1—10. (1973).
19. Leeghim H., Bang H., Jong-Oh Park. Singularity avoidance of control moment gyros by one-step ahead singularity index. Acta Astronautica. Vol. 64, N 9/10. 935—945 (2009).