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