Amplitude control of limit cycle in a van der Pol--Duffing system
Ouyang Ke-Jian(欧阳克俭)a)†, Tang Jia-Shi(唐驾时)b), and Liang Cui-Xiang(梁翠香)b)
a College of Civil Engineering, Hunan University, Changsha 410082, China; b College of Mechanics and Aerospace, Hunan University, Changsha 410082, China
Abstract This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol--Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh--Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol--Duffing system but also of the strongly nonlinear van der Pol--Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.
Received: 14 February 2009
Revised: 04 April 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10672053).
Cite this article:
Ouyang Ke-Jian(欧阳克俭), Tang Jia-Shi(唐驾时), and Liang Cui-Xiang(梁翠香) Amplitude control of limit cycle in a van der Pol--Duffing system 2009 Chin. Phys. B 18 4748
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