Stabilization of stable manifold of upright position of the spherical pendulum

Authors
Ludvigsen, H Shiriaev, A Egeland, O
Citation
H. Ludvigsen et al., Stabilization of stable manifold of upright position of the spherical pendulum, MODEL IDENT, 22(1), 2001, pp. 3-14
Citations number
9
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
MODELING IDENTIFICATION AND CONTROL
ISSN journal
03327353 → ACNP
Volume
22
Issue
1
Year of publication
2001
Pages
3 - 14
Database
ISI
SICI code
0332-7353(200101)22:1<3:SOSMOU>2.0.ZU;2-A
Abstract
The stabilization problem of the upright position of the sherical pendulum is treated in detail. This problem is reduced to the stabilization of the s table manifold Omega (st) of the upright position of the unforced spherical pendulum. It is shown that for any smooth feedback control derived by the speed-gradient algorithm with the objective to stabilize Omega (st) the clo sed loop system has a limit cycle T, which does not belong to the desired a ttractor Omega (st). It is shown that Gamma is hyperbolic.