 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.M. Formalskii, P.A. Kruchinin, and K.L. Voitsitskaya, "Stabilization of a Double Inverted Pendulum Installed on a Seesaw," Mech. Solids. 56 (8), 1599-1610 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1599-1610 |
| DOI |
10.3103/S0025654421080070 |
| Title |
Stabilization of a Double Inverted Pendulum Installed on a Seesaw |
| Author(s) |
A.M. Formalskii (Moscow State University, Moscow, 119991 Russia, formal@imec.msu.ru)
P.A. Kruchinin (Moscow State University, Moscow, 119991 Russia, pkruch@mech.math.msu.su)
K.L. Voitsitskaya (Moscow State University, Moscow, 119991 Russia) |
| Abstract |
The problem of synthesizing a control law to stabilize a double inverted pendulum installed
on a seesaw is considered. The movement of such kind of pendulums in the vertical plane is studied.
The seesaw is a segment of a cylinder whose axis is horizontal. This cylindrical segment may perform
oscillations while rolling on the horizontal surface without slipping. The lower (first) link of the pendulum is fastened to the seesaw by a cylindrical joint. The axis of this joint is parallel to the cylinder
axis as well as to that of the interlink joint. A control torque, whose absolute value is bounded, is
applied to the pendulum at the interlink joint. Thus, the system described above has three degrees of
freedom and a single control action. Without control, the open-loop system has an unstable equilibrium position, in which both links of the pendulum are directed vertically upwards, and the seesaw is
not tilted. Control stabilizing the desired unstable equilibrium is performed in the feedback form with
respect to two “unstable” Jordan variables of the open-loop linearized system so as to make, if possible, the attraction domain of the system maximal. Some properties of the controllability and attraction
domains are studied. The results of numerical studies are presented. |
| Keywords |
double inverted pendulum, seesaw, controllability domain, attraction domain, stabilization |
| Received |
07 April 2021 | Revised |
24 August 2021 | Accepted |
10 September 2021 |
| Link to Fulltext |
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