Deployment the Spoke of a Large-Sized Transformable Refl ector Using a Sequential Optimization Algorithm

The use of large-sized opening reflectors close-packed in spacecraft is associated with spreading the spokes at a given angle, extending the fragments of the spokes and adjusting the shape of the radio-reflecting mesh. The problem of optimizing these processes with automatic output of the reflector to the deployed working state is urgent. The optimal control problem of spreading spokes of a large-sized space-based reflector with respect to bending vibrations is investigated in the article. The optimization process is complicated by ensuring convergence of iterative procedure for control finding. The bending vibrations of the spokes complicate the task of spreading. That makes it difficult to fix spokes when reaching the stops. In this paper the mathematical model of spoke dynamics is improved with respect to spoke’s bend change in length and in time, the model takes into account the presence of stop and retainer devices and an actuator. It is proposed to consider a hierarchy of two target composed functions and develop an algorithm for sequential optimization for a smooth exit to the stops. It is suggested to include the terminal condition for the angular spreading rate in the first criterion. A study was carried out using mathematical simulation for the process of turning the spoke by a given angle at small values of the angular velocity at the final moment of time taking into account bending vibrations. The exact values of the weight coefficients included in the target composed functions are found. Weight coefficients influence on transient processes is investigated. The performance of the algorithm was checked when the value of the optimization interval was changed. The comparison of the results of simulation modeling with control options using the PID controller, application of an algorithm with a predictive model and an algorithm with optimal correction of the control structure, revealed by means of the maximum principle, was carried out. The results of simulation modeling foe spokes spreading process using the sequential optimization algorithm demonstrate the achievement of the required accuracy with permissible tolerance residual vibrations. The developed algorithm of sequential optimization forms control in a real time and it is recommended to use it in more complex solutions under random disturbances using measurement process and optimization of observation intervals.

1. Siriguleng B., Zhang W., Liu T., Liu Y. Z. Vibration modal experiments and modal interactions of a large space deployable antenna with carbon fiber material and ring-truss structure, Engineering Structures, 2020, vol. 207, pp. 148—153.

2. Polyanskii I. S., Arkhipov N. S., Misyurin S. Y. On solving the optimal control problem, Automation and Remote Control, 2019, vol. 80, no. 1, pp. 66—80.

3. Yangmin X., Hang S., Alleyne A. G., Yang B. Feedback Shape Control for Deployable Mesh Reflectors Using Gain Scheduling Method, Acta Astronautica, 2016, vol. 121, pp. 241—255.

4. Rahmat-Samii Y., Manohar V., Kovitz J. M. et al. Development of Highly Constrained 1 m Ka-Band Mesh Deployable Offset Reflector Antenna for Next Generation CubeSat Radars, IEEE Aerospace and Electronic Systems Magazine, 2019, vol. 67, no. 10, pp. 6254—266.

5. Kabanov S. A., Zimin B. A., Mitin F. V. Development and Research of Mathematical Models of Deployment of Mobole Parts of Transformable Space Construction. Part I, Mekhatronika, Avtomatizatsiya, Upravlenie, 2020, vol. 21, no. 1, pp. 51—64 (in Russian).

6. Kabanov S. A., Zimin B. A., Mitin F. V. Development and Research of Mathematical Models of Deployment of Mobole Parts of Transformable Space Construction. Part II, Mekhatronika, Avtomatizatsiya, Upravlenie, 2020, vol. 21, no. 2, pp. 117—128 (in Russian).

7. Bellman R. Adaptive control processes, Moscow, Nauka, 360 p. (in Russian).

8. Kabanov S. A. Controling systems based on predictive models, St. Petersburg, St. Petersburg State University Publishing House, 1997, 200 p. (in Russian).

9. Krasovskij A. A. ed. Handbook on the theory of automatic control, Moscow, Nauka, 1987, 712 p. (in Russian).

10. Malushev V. V., Kabanov D. S. Algorithm for correcting the control structure of an automatic underwater vehicle for constructing the reachable region, Journal of Instrument Engineering, 2012, vol. 55, no. 7, pp. 21—27 (in Russian).

11. Kabanov S. A. Optimization of system dynamics with correction of control structure parameters, Vestn. S. — Peterburg. un. Ser. 1, 2014, iss. 2, pp. 254—260.

12. Kabanov S. A. Mitin F. V. Optimization of the processes of deployment and creating the shape of a transformable spacebased reflector, Journal of Computer and Systems Sciences International, 2021, no. 2, pp. 106—125.

13. Kabanov S. A., Mitin F. V. Optimization of the stages of unfolding a large-sized space-based reflector, Acta Astronautica, 2020, no. 176, pp. 717—724.

14. Panovko Y. G. Internal friction during vibrations, Moscow, FIZMATLIT, 1960, 193 p. (in Russian).

15. Kabanov S. A. Optimization of the dynamics of systems under the influence o f perturbations, Moscow, FIZMATLIT, 2008, 200 p. (in Russian).

16. Malushev V. V., Krasilshikov M. N., Karlov V. I. Optimization of surveillance and control of aircraft, Moscow, Mashinostroenie, 1989, 312 p. (in Russian).