title: Ð£Ð¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð°Ñ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð°Ñ Ð¿Ð¾ÑÐ°Ð´ÐºÐ° Ð¿ÐµÑÐ²Ð¾Ð¹ ÑÑÑÐ¿ÐµÐ½Ð¸ ÑÐ°ÐºÐµÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Controlled vertical landing of the first stage of the rocket
Creators: name: ÐÐ°ÑÑÐ»Ð¸Ð½, ÐÐµÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¿ÐµÑÐ²Ð°Ñ ÑÑÑÐ¿ÐµÐ½Ñ ÑÐ°ÐºÐµÑÑ
Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð°Ñ Ð¿Ð¾ÑÐ°Ð´ÐºÐ°
Ð¾Ð±ÑÐ°ÑÐ½ÑÐµ ÑÐ²ÑÐ·Ð¸
ÑÐ¸ÑÑÐµÐ¼Ð° ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
Ð´Ð²Ð¸Ð¶ÑÑÐ¸Ðµ ÑÐ¸Ð»Ñ
first stage of the rocket
vertical landing
feedback
control system
propulsive forces

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description: This work is devoted to the study of controlled landing of the first stage of the rocket. Object of study â the returnable first stage of a rocket. The objective to develop a mathematical model for the vertical landing of the first stage of the rocket. In this research, a control system for the engines has been devised, employing multiple channels of feedback based on preliminary calculations of the primary thrust vector and the main moment generated by the propulsive forces. PD controllers were employed to determine the primary thrust vector and main moment applied to the rocket body. The design of the control system incorporates negative feedback mechanisms, ensuring a smooth and controlled landing for the first stage of the rocket. Control of the propulsive forces has been achieved by considering them as functions of the primary thrust vector and main moment, encompassing a set of processed signals indicating discrepancies across three independent coordinates. An algorithm has been developed to calculate the feedback coefficients, guaranteeing a lack of overshooting during transitional processes. The dynamic processes of the vertical landing for the first stage of the rocket have been analyzed under different initial conditions using the established methodology for generating propulsive forces within specified acceptable engine thrusts. Open educational resources and information retrieval and analysis programs have been utilized. Automation tools, such as computers, have been employed in the development process. The software MATHCAD has been applied and tested.