Brief Paper: Feedback Control of Limit Cycle Amplitudes from A Frequency Domain Approach

Authors:
DANIEL W. BERNS;JORGE L. MOIOLA;GUANRONG CHEN
Affiliations:
Departamento de Electrónica, Universidad Nacional de la Patagonia San Juan Bosco, (9000) Comodoro Rivadavia, Argentina;Departamento de Ingeniera Eléctrica, Universidad Nacional del Sur, (8000) Baha Blanca, Argentina;Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4793, USA
Venue:
Automatica (Journal of IFAC)
Year:
1998

Citing 4
Cited 4

Local feedback stabilization and bifurcation control, I. Hopf bifurcation

Systems & Control Letters
Local feedback stabilization and bifurcation control, II. Stationary bifurcation

Systems & Control Letters
Stabilization of period doubling bifurcations and implications for control of chaos

Physica D
Bifurcation control of a chaotic system

Automatica (Journal of IFAC)

Multivariable harmonic balance for central pattern generators

Automatica (Journal of IFAC)
Bifurcation control in small-world networks

Neurocomputing
Hybrid Control of Hopf Bifurcation for an Internet Congestion Model

ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Hybrid control of Hopf bifurcation in complex networks with delays

Neurocomputing

Quantified Score

Hi-index	22.15

Visualization

Abstract

In this paper, a problem in feedback control of limit cycle amplitudes is studied. A graphical approach for this bifurcation control problem is developed by means of higher-order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs. The approach starts with the familiar Hopf bifurcation mechanism, and employs the second, fourth, and sixth-order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs. This sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs. Degenerate Hopf bifurcation theory is used to formulate an appropriate control objective of capturing small-amplitude limit cycles, which can avoid reaching unstable equilibria or other undesirable limit sets. A rich cubic planar model is presented for illustration of the proposed control method.