Stabilization by vertical vibrations

Daniel Núñez; Pedro J. Torres

doi:10.1002/mma.1082

Stabilization by vertical vibrations

Daniel Núñez
, Pedro J. Torres

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We consider a general version of the classical problem of the stabilization of the inverted pendulum by a vertical periodic vibration of the point of suspension. Instead of the usual harmonic motion, we propose an oscillatory control with a piecewise-constant acceleration, obtaining explicit conditions over the frequency or the amplitude leading to the desired stabilization.

Original language	English
Pages (from-to)	1118-1128
Number of pages	11
Journal	Mathematical Methods in the Applied Sciences
Volume	32
Issue number	9
DOIs	https://doi.org/10.1002/mma.1082
State	Published - Jun 2009
Externally published	Yes

Keywords

Inverted pendulum
Stability
Twist
Vibrational control

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10.1002/mma.1082

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title = "Stabilization by vertical vibrations",

abstract = "We consider a general version of the classical problem of the stabilization of the inverted pendulum by a vertical periodic vibration of the point of suspension. Instead of the usual harmonic motion, we propose an oscillatory control with a piecewise-constant acceleration, obtaining explicit conditions over the frequency or the amplitude leading to the desired stabilization.",

keywords = "Inverted pendulum, Stability, Twist, Vibrational control",

author = "Daniel N{\'u}{\~n}ez and Torres, \{Pedro J.\}",

year = "2009",

month = jun,

doi = "10.1002/mma.1082",

language = "English",

volume = "32",

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T1 - Stabilization by vertical vibrations

AU - Núñez, Daniel

AU - Torres, Pedro J.

PY - 2009/6

Y1 - 2009/6

N2 - We consider a general version of the classical problem of the stabilization of the inverted pendulum by a vertical periodic vibration of the point of suspension. Instead of the usual harmonic motion, we propose an oscillatory control with a piecewise-constant acceleration, obtaining explicit conditions over the frequency or the amplitude leading to the desired stabilization.

AB - We consider a general version of the classical problem of the stabilization of the inverted pendulum by a vertical periodic vibration of the point of suspension. Instead of the usual harmonic motion, we propose an oscillatory control with a piecewise-constant acceleration, obtaining explicit conditions over the frequency or the amplitude leading to the desired stabilization.

KW - Inverted pendulum

KW - Stability

KW - Twist

KW - Vibrational control

UR - https://www.scopus.com/pages/publications/67649784370

U2 - 10.1002/mma.1082

DO - 10.1002/mma.1082

M3 - Article

AN - SCOPUS:67649784370

SN - 0170-4214

VL - 32

SP - 1118

EP - 1128

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 9

ER -

Stabilization by vertical vibrations

Abstract

Keywords

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