Control of deep-hysteresis aeroengine compressors

Frequencies of higher-order modes of fluid dynamic phenomena participating in aeroengine compressor instabilities far exceed the bandwidth of availabl e (affordable) actuators. For this reason, most of the heretofore experimen tally validated control designs for aeroengine compressors have been via lo w-order models-specifically, via the famous Moore-Greitzer cubic model (MG3 ). While MG3 provides a good qualitative description of open-loop dynamic b ehavior, it does not capture the main difficulties for control design. In p articular, it fails to exhibit the so-called "right-skew" property which di stinguishes the deep hysteresis observed on high-performance axial compress ors from a small hysteresis present in the MG3 model. In this paper we stud y fundamental feedback control problems associated with deep-hysteresis com pressors. We first derive a parametrization of the MG3 model which exhibits the right skew property. Our approach is based on representing the compres sor characteristic as a convex combination of a usual cubic polynomial and a nonpolynomial term carefully chosen so that an entire family of right-ske w compressors can be spanned using a single parameter epsilon. Then we deve lop a family of controllers which are applicable not only to the particular parametrization, but to general Moore-Greitzer type models with arbitrary compressor characteristics. For each of our controllers we show that it ach ieves a supercritical (soft) bifurcation, that is, instead of an abrupt dro p into rotating stall, it guarantees a gentle descent with a small stall am plitude. Two of the controllers have novel, simple, sensing requirements: o ne employs only the measurement of pressure rise and rotating stall amplitu de, while the other uses only pressure rise and the mass flow rate (1D sens ing). Some of the controllers which show excellent results for the MG3 mode l fail on the deep-hysteresis compressor model, thus justifying our focus o n deep-hysteresis compressors. Our results also confirm experimentally obse rved difficulties for control of compressors that have a high value of Grei tzer's B parameter. We address another key issue for control of rotating st all and surge-the limited actuator bandwidth-which is critical because even the fastest control valves are often too slow compared to the rates of com pressor instabilities. Our conditions show an interesting trade-off: as the actuator bandwidth decreases, the sensing requirements become more demandi ng. Finally, we go on to disprove a general conjecture in the compressor co ntrol community that the feedback of mass flow rate, known to be beneficial for shallow-hysteresis compressors, is also beneficial for deep-hysteresis compressors. [S0022-0434(00)03101-4].