title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ ÑÐ¸Ð½ÑÐµÐ· ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ¾Ð¼ Ð¤ÑÑÑÑÑ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¸Ð½ÑÐµÐ³ÑÐ°ÑÐ¾ÑÐ°
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: Modeling and control synthesis of the Furuta pendulum using a variational integrator
Creators: name: ÐÐ¾ÑÐ²Ð¸Ð½ÑÐµÐ², ÐÐ°Ð½Ð¸Ð¸Ð»
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: Ð¼Ð°ÑÑÐ½Ð¸Ðº Ð¤ÑÑÑÑÑ
Ð»Ð°Ð³ÑÐ°Ð½Ð¶Ð¸Ð°Ð½
Ð¼Ð¾Ð´ÐµÐ»Ñ
Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¸Ð½ÑÐµÐ³ÑÐ°ÑÐ¾Ñ
Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ
Furuta pendulum
lagrangian
model
variational integrator
simulation
control

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description: The research set the following goals: 1) Modeling of the Furuta pendulum using a variational integrator without control. 2) Synthesis of control for the Furuta pendulum. 3) Visualization of the model. 4) Analysis of the model results. In this work, an analysis of the pendulum and the variational integrator is performed, theoretical calculations are carried out and a plan for synthesizing the modeling and control of the pendulum is prepared. Numerical experiments are also performed, the results are analyzed, and conclusions are drawn about the characteristics of the Furutaâs pendulum. Chapter one analyzes the problem domain, gives general historical information about the pendulum, formulates the problem, and gives an overview of the variational calculus. Chapter two analyzes the methods used in the study and gives an overview of the necessary concepts, the variational calculus, and its mathematical foundations. Also in this chapter has information about used methods of control synthesis. In the third chapter, two experiments were conducted; within the first experiment, a model of the Furutaâs pendulum without control using the variational integrator was created, and the results of the models operation were analyzed. Within the second experiment, control was synthesized for the Furutaâs pendulum model, the pendulum was simulated considering the synthesized control, and the results of this models operation were analyzed. As part of the control synthesis, a cost function, that takes into account the necessary parameters of system behavior, was composed, and the problem of minimizing the cost functional concerning several variables was solved.