Gas turbine engine performance is limited by aerodynamic instabilities called rotating stall and Currently there are several control strategies for enhancing the operability boundary of laboratory compressors by actively controlling rotating stall and surge. Models which capture the qualitative behavior of the aerodynamic instabilities have been found to exhibit abundant dynamic behavior and to be useful for designing control laws. Operability boundary is defined as the operating point where steady axisymmetric flow is unstable and untolerable amount of rotating stall and surge is present in the system. Operability enhancement is defined as the gap between the operability boundary for the controlled system and that for the uncontrolled system. Operability enhancement is one of the main goals for active control of rotating stall and surge. Actuator limits and system noise are found to limit the operability enhancement. We are interested in two problems: Analysis problem: given a controller with actuator limits and certain noise level, find the operability enhancement; Synthesis problem: given a set of controllers with actuator limits and certain noise level, find one that maximize the operability enhancement. It turns out that the synthesis problem is a minimax problem. We try to answer the analysis problem and the synthesis problem by nonlinear reduction using bifurcation theory and invariant manifold theory. For stall control with bleed valve actuators, we have derived analytic formulas that agree qualitatively with the experimental results on a low speed rig. We have solved the synthesis problem for the case when surge inception is close to stall inception by normal form reduction for a low order compressor model. We are also interested in extending the above control problems to general dynamical systems. We think center manifold reduction and normal form reduction are potential tools.Gas turbine engine performance is lim...
