Control of Fluctuations of Pendulum on the Mobile Platform
Author(s):
Alexander V. Bratishchev
Don State Technical University,
Professor of Applied Mathematics Department
Professor, doctor fiz.-mat. Nauk
avbratishchev@spark-mail.ru
Abstract:
In this article, we derive the equation of motion of a system of two stationary
connected material points, one of which can move in a horizontal plane. It follows
from the normal form of the corresponding autonomous system of equations that
it is impossible to find its equilibrium states analytically. The resulting system
is partially integrated. We consider a force field that allows us to dampen
system vibrations at any initial state that is not a state of physical equilibrium.
The method of analytical design of aggregated controllers (ACAR) is used to
control the speed of rotation of the pendulum around the vertical axis.
An executable S-model of free and managed systems in the Simulink package is designed.
The conclusions based on the results of numerical experiments are made about
the behavior of the system when changing its parameters and the field parameters.
Keywords
- force field
- Lagrange equation
- pendulum
- platform
- synergetic control
References:
- Efimov, V. V. [Mathematical description of the cargo movement on the external suspension of the helicopter]. Nauchniy Vestnik MGTU GA. Seriya: Aeromikhanika i prochnost’, 2007; (111):121-128. (In Russ. )
- Efimov, V. V. [ Investigation of vibrations of a physical pendulum with a movable suspension point as a simplified model of a cargo on the external suspension of a helicopter]. Nauchniy Vestnik MGTU GA. Seriya: Aeromikhanika i prochnost’, 2009; (138):126-133. (In Russ. )
- Butenin, N. V., Fufaev, N. A. Vvedenie v analiticheskuyu mekhaniku [Introduction to analytical mechanic]. Moscow, Nauka Publ., 1991, 256 p
- Dabney, J., Harman, T. Mastering Simulink 4, New Jersey, Prentice Hall Publ., 2001, 230 p
- Bratishchev, A. V. [Factorization of the characteristic polynomial of the equilibrium state of an Autonomous system with an invariant set]. Differencial'nie uravnenya i processy upravlenya, 2019, no. 3 (In Russ. ) Available at: http://www.math.spbu.ru/diffjournal/pdf/bratichshev.pdf //
- Kolesnikov, A. A. Sinergeticheskye metodi upravleniya slozhnimi sistemami. Teoriya sistemnogo analiza [Synergetic methods of managing complex systems. Theory of system analysis]. Moscow, Komkniga Publ., 2006, 240 p
