Feedback Stabilization of the Self-oscillatory System Based on Washout Filter Algorithm
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.
Andronov-Hopf bifurcationtransient dynamicsnumber of filtersaugmented system
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