Title :
Stabilization of stable manifold of upright position of the spherical pendulum
Author :
Ludvigsen, H. ; Shiriaev, A. ; Egeland, O.
Author_Institution :
Dept. of Eng. Cybern., Norwegian Univ. of Sci. & Technol., Trondheim, Norway
Abstract :
The stabilization problem of the upright position of the controlled spherical pendulum is treated in detail. This problem is reduced to the stabilization of the stable manifold Ωst 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 Ωst the closed loop system has a limit cycle Γ, which does not belong to the desired attractor Ωst. It is shown that Γ is hyperbolic
Keywords :
closed loop systems; feedback; limit cycles; nonlinear control systems; pendulums; stability; attractor; closed loop system; hyperbolic limit cycle; passive nonlinear system; smooth feedback control; speed-gradient algorithm; stabilization; stable manifold; unforced spherical pendulum; upright position; Acceleration; Closed loop systems; Control systems; Feedback control; Gravity; Limit-cycles; Linear approximation; Nonlinear control systems; Nonlinear systems; Vectors;
Conference_Titel :
American Control Conference, 1999. Proceedings of the 1999
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4990-3
DOI :
10.1109/ACC.1999.786294
