Stabilization of a Double Inverted Pendulum Installed on a Seesaw

Formalskii, A.M.; Kruchinin, P.A.; Voitsitskaya, K.L.

Авторы: Formalskii A.M., Kruchinin P.A., Voitsitskaya K.L.
Журнал: Mechanics of Solids
Том: 56
Номер: 8
Год издания: 2021
Издательство: Allerton Press Inc.
Местоположение издательства: United States
Первая страница: 1599
Последняя страница: 1610
DOI: 10.3103/s0025654421080070
Аннотация: https://rdcu.be/cJnihThe problem of the control synthesis to stabilize the double inverted pendulum installed on the seesaw is considering. The movement in the vertical plane of such kind of the pendulums is studying. The seesaw is a segment of the cylinder whose axis is horizontal. This cylindrical segment oscillates while rolling on the horizontal surface without any slipping. The lower (first) link of the pendulum is fastened to the seesaw by the cylindrical joint. The axis of this joint is parallel to the axis of the cylinder and to the axis of the inter-link joint also. The limited in the absolute value torque is applied to the pendulum in the inter-link joint. Thus, the described above system has three degrees of freedom and the single control action only. The open-loop system has an unstable equilibrium position with the both links of the pendulum directed vertically upwards. The seesaw in this equilibrium position is not tilted. The control stabilizing the desired unstable equilibrium is constructed in the feedback form on two "unstable" Jordan variables of an open-loop linearized system. By this way we design the feedback control with maximal as possible the attraction domain of the equilibrium position. Some properties of the controllability and attraction domains are studied. The results of the numerical studies are presented
Добавил в систему: Кручинин Павел Анатольевич

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Stabilization of a Double Inverted Pendulum Installed on a Seesawстатья