Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

Abstract

This gaper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator,which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.

Hopf bifurcation control for stochastic dynamical system with nonlinear random feedback method

“…Typical objectives of bifurcation control include stabilizing the unstable bifurcation solution or branch [1][2][3][4][5]; delaying the onset of an inherent bifurcation [6,7]; changing the parameter value of an existing bifurcation point [8,9]; producing a new bifurcation by designing the system parameters [10][11][12][13][14][15][16]; changing the equilibrium; modifying the shape or type of a bifurcation [17]; monitoring the multiplicity, amplitude or frequency of the limit cycles [18,19], and so on. The methods of bifurcation control employ linear and nonlinear state feedback controls [20,21], time-delayed feedback [19], apply a washoutfilter-aided dynamical feedback controller [16,22,23], use harmonic balance approximations [24][25][26] and utilize quadratic invariants in normal forms [1,[27][28][29][30].…”