title: Ð£Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð³ÑÑÐ¿Ð¿Ð¾Ð¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð±ÑÐµÐºÑÐ¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Control of a group of dynamic objects
Creators: name: ÐÐ¾ÑÐ°ÑÐ¾Ð²Ð°, ÐÐ½Ð½Ð°
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: 2021
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÑ
ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
ÐÐ¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ
ÐÐ²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð³ÑÑÐ¿Ð¿Ñ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ¾Ð² Ñ Ð¿Ð¾Ð´Ð²ÐµÑÐµÐ½Ð½ÑÐ¼ Ðº Ð½Ð¸Ð¼ Ð³ÑÑÐ·Ð¾Ð¼. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÑÑ Ð¸ Ð¾ÑÐ¾Ð±ÑÐ°ÑÑ Ð°ÐºÑÑÐ°Ð»ÑÐ½ÑÐµ Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð² Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½ÑÐµ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ñ, Ð²ÐºÐ»ÑÑÐ°Ñ ÑÑÐ°ÑÑÐ¸, ÑÐµÑÐµÑÐ°ÑÑ, Ð´Ð¸ÑÑÐµÑÑÐ°ÑÐ¸Ð¸, ÑÑÐµÐ±Ð½ÑÐµ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ñ Ð¸ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ñ. 2. ÐÑÐ¾Ð²ÐµÑÑÐ¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð´Ð»Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ ÑÑÑÑÐºÑÑÑÐ½Ð¾-Ð¸Ð½Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð³ÑÑÐ¿Ð¿Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð±ÑÐµÐºÑÐ¾Ð². 3. Ð Ð°ÑÐ¿Ð¸ÑÐ°ÑÑ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸, ÑÑÐ¸ÑÑÐ²Ð°Ñ Ð¿ÑÐ¸ÐºÑÐµÐ¿Ð»ÐµÐ½Ð½ÑÐ¹ Ð½Ð° Ð¶ÐµÑÑÐºÐ¾Ð¹ ÑÑÐµÐ¿ÐºÐµ Ð³ÑÑÐ· Ð¸ Ð½Ð° Ð½ÐµÐ²ÐµÑÐ¾Ð¼ÑÑ Ð½Ð¸ÑÑÑ. 4. ÐÑÐ¾Ð²ÐµÑÐ¸ÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ñ Ð½Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð´Ð»Ñ ÑÑÐµÑ ÑÐ°Ð·Ð½ÑÑ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ: Ð´Ð»Ñ Ð¿Ð¾Ð»ÐµÑÐ° Ð²Ð²ÐµÑÑ, Ð¿Ð¾Ð»ÐµÑÐ° Ð¿ÑÐ¸ ÑÐ°Ð½Ð³Ð°Ð¶Ðµ Ð¸ Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ ÑÑÑÐºÐ°Ð½ÑÑ. 5. ÐÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð¾ÐºÐ°Ð¶ÐµÑÑÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾Ð¹, Ð¿Ð¾ÑÑÑÐ¾Ð¸ÑÑ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð¾ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ ÑÑÐ°ÐµÐºÑÐ¾ÑÐ¸Ð¸ Ð´Ð»Ñ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼Ð¾Ð¹ Ð³ÑÑÐ¿Ð¿Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð±ÑÐµÐºÑÐ¾Ð². ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐ°ÑÑÐµÑÑ, Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÐ¸Ðµ Ð½Ð°Ð³Ð»ÑÐ´Ð½Ð¾, ÐºÐ°Ðº ÑÐºÐ°Ð·ÑÐ²Ð°ÐµÑÑÑ Ð½Ð° Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ð¸ Ð³ÑÑÐ¿Ð¿Ñ ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ¾Ð² Ð½Ð°Ð»Ð¸ÑÐ¸Ðµ Ð³ÑÑÐ·Ð°. ÐÐ½Ð°Ð»Ð¸Ð· Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ SimInTech Ð¸ Simulink Matlab, Ð¾ÑÐ½Ð°ÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð±Ð»Ð¾ÐºÐ°Ð¼Ð¸ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐ¼Ð¸ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð³ÑÑÐ¿Ð¿Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² (ÐºÐ²Ð°Ð´ÑÐ¾ÐºÐ¾Ð¿ÑÐµÑÐ¾Ð²) Ñ Ð¿Ð¾Ð´Ð²ÐµÑÐµÐ½Ð½ÑÐ¼ Ð³ÑÑÐ·Ð¾Ð¼, ÑÐ¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ ÑÐ°ÐºÐ¾Ð¹ Ð³ÑÑÐ¿Ð¿Ñ Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ñ Ð³ÑÑÐ·Ð¾Ð¼ Ð¸ Ð±ÐµÐ·.
description: This work is devoted to the construction of the control of a dynamic model on the example of a group of quadrocopters with a load suspended from them. Tasks that were solved in the course of the study: 1. Review and select relevant literature materials for research in the chosen field, including articles, abstracts, dissertations, educational materials and manuals. 2. To analyze the system of Lagrange equations for constructing a structure-invariant model for a group of dynamic objects. 3. Describe the changes for the model, taking into account the weight attached to the rigid hitch and on the weightless threads. 4. Check the resulting system for stability for three different states of the system: for flight up, flight at pitch and in yaw conditions. 5. If the resulting system is stable, construct controls along a complex trajectory for the group of dynamic objects under consideration. Calculations were carried out, showing clearly how the presence of cargo affects the movement of a group of quadrocopters. The analysis was carried out by mathematical modeling using SimInTech and Simulink Matlab software, equipped with the technical blocks necessary for modeling. As a result, a model of a group of dynamic objects (quadrocopters) with a suspended load was analyzed, control for such a group was modeled, and the model with and without a load was analyzed.