Chinese Journal of Engineering Mathematics ›› 2024, Vol. 41 ›› Issue (3): 577-586.doi: 10.3969/j.issn.1005-3085.2024.03.015
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CHAI Xinming, YI Yunfan, ZHAI Chi
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Abstract: Considering the self-oscillating system evolved from Andronov-Hopf bifurcation and the corresponding linearized system no longer share the same differential manifold, but would exhibit multi-dimensional nonlinear coupling characteristics. Previous study adopts Washout filter to stabilize the oscillatory system, while, the number of filters needed for a particular system is still unsolved. Based on normal form analysis of the Andronov-Hopf bifurcation system, this work explores to connect two filters on the dual-unstable eigenspace, however, feedback design based on state-space method may cause the results being high ordered, which cannot be realized by a Washout filter compartment physically. Through transient dynamics analysis on the Laplace transfer function, we propose to decouple the feedback loop and reduce the Washout algorithm to 1-ordered, which is able to be realized by stable Washout filters physically. A simulation example of the self-oscillation reaction process further verifies the fea-sibility and effectiveness of the obtained control scheme.
Key words: Andronov-Hopf bifurcation, transient dynamics, number of filters, augmented system
CLC Number:
TP3
CHAI Xinming, YI Yunfan, ZHAI Chi. Feedback Stabilization of the Self-oscillatory System Based on Washout Filter Algorithm[J]. Chinese Journal of Engineering Mathematics, 2024, 41(3): 577-586.
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URL: http://jgsx-csiam.org.cn/EN/10.3969/j.issn.1005-3085.2024.03.015
http://jgsx-csiam.org.cn/EN/Y2024/V41/I3/577