Linear versus quadratic amplitude feedback in active control of compressorrotating stall

Several issues that have been overlooked or only partially addressed in pre vious literature related to the active control of compressor rotating stall are clarified. This is accomplished via a detailed local stability analysi s of the rotating stall inception point and the locally branched unstalled and stalled equilibria. The analysis is based on the first-term Galerkin ap proximation of the Moore-Greitzer model (Moore, F. K., and Greitzer, E. M., "A Theory of Post-Stall Transients in Axial Compressor Systems, Part 1, De velopment of Equations," Journal of Turbomachinery, 1986), and it is valid for an arbitrary compressor map and a parabolic throttle characteristic. It is generically performed for a rather large class of throttle feedback con trol laws. Each such law is proportional to the rotating stall amplitude, r aised to a strictly positive exponent. The proportionality constant is a no nnegative feedback gain. It is shown that linear feedback renders the rotat ing stall inception point and the neighboring stalled branch locally asympt otically stable for any value of the feedback gain. Quadratic feedback on t he other hand represents a limiting case of control effectiveness and can a t best lead to conditional local stability; that is, it can render the stal l inception point and the neighboring stalled branch locally asymptotically stable only for sufficiently high values of the feedback gain. Finally, su blinear feedback, namely, feedback with an exponent less than unity, not on ly unconditionally stabilizes the stall inception point and the neighboring stalled branch, but also completely smooths out any transition to rotating stall. These results extend and in some places contrast previous work on t he subject that has dismissed such linear or sublinear feedback and concent rated mainly on quadratic feedback as a viable means of controlling compres sor rotating stall.