Active control of the onset of stall instabilities in axial flow compression systems is pursued using bifurcation analysis of a dynamical model proposed by Moore and Greitzer. The state variables of this model are the mass flow rate, pressure rise, and the amplitude of the first-harmonic mode of the asymmetric component of the flow. A subcritical pitchfork bifurcation is found to occur at the inception of stall, resulting 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 stall is linearly uncontrollable. This, along with uncertainty of the post-stall linearized model, motivates a consideration of nonlinear feedback control laws for mitigation of the jump and hysteresis behavior occurring at stall onset. Following the bifurcation control calculations introduced by Abed and Fu [Abed, E. H. and J. H. Fu (1986). Local feedback stabilization and bifurcation control, I. Hopf bifurcation. Syst. Control Lett., 7, 11-17. and Abed, E. H. and J. H. Fu (1987). Local feedback stabilization and bifurcation control, II. Stationary bifurcation. Syst. Control Lett., 8, 467-473], it is found that feedback incorporating a term quadratic in the first-harmonic flow asymmetry variable renders the pitchfork bifurcation supercritical. This introduces a new stable equilibrium near the nominal equilibrium after the nominal equilibrium itself has lost stability, thus eliminating the undesirable jump and hysteresis behavior of the uncontrolled system.
- Control applications
- Nonlinear control systems