Hopf Bifurcation in PD Controlled Pendulum or Manipulator

[+] Author and Article Information
Tom Bucklaew

Raytheon Missile Systems, Guidance, Navigation, and Control Center, Building 805, M/S M4, 1151 E. Hermans Road, Tucson, AZ 85706-1151e-mail: Tom_P_Bucklaew@raytheon.com

Ching-Shi Liu

Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, 316 Jarvis Hall, Buffalo, NY 14260e-mail: chingliu@eng.buffalo.edu

J. Dyn. Sys., Meas., Control 124(2), 327-332 (May 10, 2002) (6 pages) doi:10.1115/1.1455025 History: Received April 13, 2000; Online May 10, 2002
Copyright © 2002 by ASME
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Grahic Jump Location
Increase in α from 0.450 (a) to 0.500 (b) produces Hopf bifurcation to steady-state limit cycle
Grahic Jump Location
Control performance in disturbance parameter plane for β=0.500 (a) and β=1.00 (b)
Grahic Jump Location
Control performance in (α,β) parameter plane for Ω=1.00 (a) and Ω=2.50 (b)
Grahic Jump Location
Influence ofγ on control stability
Grahic Jump Location
Competing attractors for the given parameter set and initial conditions of 30 (top) and 45 degrees




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