VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University302410.18287/2412-7329-2016-15-1-97-106UnknownMathematical model of angular motion of nanosatellites with inertial actuatorsMoldabekovM. M.<p><span lang="EN-US">Doctor of Science (Engineering), Professor<br />Academician of the National Academy of Sciences of the Republic of Kazakhstan</span></p>moldabekov.m@istt.kzAhmedovD. S.<p><span lang="EN-US">Doctor of Science (Engineering)<br />Director</span></p>lacp@mail.ruElubaevS. A.<p><span lang="EN-US">Head of the Laboratory of Space System Simulation Modeling and Development</span></p>elubaev.s@istt.kzSukhenkoA. S.<p><span lang="EN-US">Head of Sector, Laboratory of Space System Simulation Modeling and Development</span></p>suhenko.a@istt.kzBopeevT. M.<p><span lang="EN-US">Head of Sector, Laboratory of Space System Simulation Modeling and Development</span></p>bopeyev.t@istt.kzAlipbayevK. A.<p><span lang="EN-US">Doctor of Science (Engineering)<br />Deputy Head of the Laboratory of Space System Simulation Modeling and Development</span></p>alipbayev.k@istt.kzMikhailenkoD. L.<p><span lang="EN-US">Research associate of the Laboratory of Space System Simulation Modeling and Development</span></p>mikhaylenko.d@istt.kzInstitute of Space Systems and Technologies, Almaty27042016151971062804201628042016Copyright © 2016, VESTNIK of the Samara State Aerospace University2016<p>The problem of developing a nanosatellite attitude control system using three reaction wheels mounted along the main central axes of inertia is discussed in the paper. The law of controlling a nanosatellites attitude is based on a PD - controller. The stability of the process of controlling the nanosatellite attitude using the Lyapunov function method has been analyzed. It allows us to prove that the obtained control law provides the asymptotic stability of nanosatellite angular motion. Hereafter, the function of control voltage for electric motors of reaction wheels taking into account their specifications is obtained based on the developed mathematical model of reaction wheel dynamics. Numerical calculations of controlled angular motion have been carried out for the nanosatellite CubeSat3U with actuators on the basis of a commercial DC motor. Several cases of controlling the satellites rotation by different angles are considered in the course of the numerical experiments. The results of numerical experiments showed the adequacy of the developed mathematical model.</p>Nanosatellitethree-axis orientationreaction wheelangular motion control lawstability investigationНаноспутниктрёхосная ориентациямаховикзакон управления угловым движениемисследование устойчивости[1. Sevastianov N.N., Branets V.N., Panchenko V.A., Kazinski N.V., Kondranin T.V. Negodyaev S.S. Advanced approaches to Earth observation small satellite development. Trudy Moskovskogo fiziko-tekhnicheskogo instituta. 2009. V. 1, no. 3. P. 14-22. (In Russ.)][2. Wertz J.R., Larson W.J. Space mission analysis and design. Torrance, California: Microcosm Inc., 1992. 827 p.][3. Sidi M.J. Spacecraft dynamics and control. Cambridge: Cambridge University Press, 1997. 41 p.][4. Amel’kin N.I. Kinematika i dinamika tverdogo tela (kvaternionnoe izlozhenie) [Kinematics and dynamics of a rigid body (quarternionic presentation)]. Moscow: Moscow Institute of Physics and Technology Publ., 2000. 61 p.][5. Hoevenaars T., Engelen S. and Bouwmeester J. Model-Based Discrete PID Controller for CubeSsat Reaction Wheels Based on COTS Brushless DC Motors. Materials of First IAA Conference on dynamics and control of space systems. 2012. V. 145. P. 379-395.][6. Dando A.J. Robust adaptive control of rigid spacecraft attitude maneuvers: PhD’s thesis – Queensland, 2008. 282 p.][7. Topland M.T., Gravdahl J.T. Nonlinear attitude control of the Micro-Satellite ESEO. International Astronautical Federation 55th International Astronautical Congress. 2004. V. 2. P. 757-767.][8. Sevast′yanov N.N. The concept of building the system of orientation and motion control of the Yamal communication satellite. The nominal operation scheme. Tomsk State University Journal of Mathematics and Mechanics. 2013. No. 2 (22). P. 85-96. (In Russ.)][9. Yadeta Z. Lyapunov’s Second Method for Estimating Region of Asymptotic Stability. Open Science Repository Mathematics. 2013. DOI: <a href='http://doi.org/10.7392/Mathematics.70081944'>10.7392/Mathematics.70081944</a>][10. Kvaternaak H., Sivan R. Lineynye optimal'nye sistemy upravleniya [Linear optimal control systems]. Moscow: Mir Publ., 1977. 653 p.]