Lefschetz Center for Dynamical Systems Seminar
Abstract: For systems described by ordinary differential equations, we consider the problem of how to design a feedback law to alter a subcritical steady-state/Hopf bifurcation to a supercritical one, when the bifurcating mode is linearly unstabilizable. Under certain nondegeneracy conditions, algebraic necessary and sufficient conditions of stabilizability are given. The effect of magnitude saturation of feedback controllers are analyzed. Geometric interpretations of stabilizability are given for some of the conditions. And sufficient conditions are obtained for systems governed by functional differential equations.
In models describing rotating stall in gas turbine engines, subcritical Hopf bifurcations are asssociated with abrupt inception of instabilities and hysteresis. We give a qualitative analysis on the effects of magnitude saturation, dandwidth, and rate limits on active control of rotating stall. The theoretical analysis is compared with experiments n a low speed, single stage compressor.
Brown Analysis Seminar
PDE Seminar
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