CONTROL OF COMPRESSOR STALL INCEPTION - A BIFURCATION-THEORETIC APPROACH

Active control of the onset of stall instabilities in axial how compre ssion systems is pursued using bifurcation analysis of a dynamical mod el proposed by Moore and Greitzer. The state variables of this model a re the mass Row rate, pressure rise, and the amplitude of the first-ha rmonic mode of the asymmetric component of the how. A subcritical pitc hfork bifurcation is found to occur at the inception of stall, resulti ng in a large-amplitude instability and associated hysteresis behavior . Using the throttle opening of the compression system for actuation, it is found that the eigenvalue that becomes zero at the onset of stal l is linearly uncontrollable. This, along with uncertainty of the post -stall linearized model, motivates a consideration of nonlinear feedba ck control laws for mitigation of the jump and hysteresis behavior occ urring at stall onset. Following the bifurcation control calculations introduced by Abed and Fu [Abed, E. H. and J. H. Fu (1986). Local feed back stabilization and bifurcation control, I. Hopf bifurcation. Syst. Control Lett, 7, 11-17. and Abed, E. Ii. and J. Fl. Fu (1987). Local feedback stabilization and bifurcation control, II. Stationary bifurca tion. Syst. Control Lett, 8, 467-473], it is found that feedback incor porating a term quadratic in the first-harmonic flow asymmetry variabl e renders the pitchfork bifurcation supercritical. This introduces a n ew stable equilibrium near the nominal equilibrium after the nominal e quilibrium itself has lost stability, thus eliminating the undesirable jump and hysteresis behavior of the uncontrolled system.