Dynamics and Control of Infinite-Dimensional Models of Jet Engine Compression Systems

摘要

The objective of this project was to study dynamics and control of jet engine compression systems within the new framework that we have developed for the infinite dimensional Moore Greitzer model. In this framework, the Moore Greitzer model of compressor dynamics was reformulated as a set of nonlinear evolution equations (one partial differential equation, and two ordinary differential equations). We designed control laws for the infinite dimensional Moore Greitzer model that can be truncated to finite dimensional laws for the purpose of implementation. Finite dimensionality is thus not a control architecture issue but an implementation issue. Stability and dynamics of stall cells was investigated numerically and analytically within the new framework. We have investigated the Moore Greitzer model in cases when the number of stages is not very large. We have shown that the solution in this case is still a travelling wave that travels around the annulus with the speed that is equal to $1/2$ of the rotor speed. We have also shown that there are no other travelling wave solutions, i.e. the stall cell can not travel at any other speed. We have developed a large scale, averaged model that reduces to the Moore Greitzer model in a certain limit and investigated its properties. The model is based on measurable quantities and thus avoids the problem of having the phenomenological compressor characteristic as one of the assumptions. Based on symmetry considerations, we have shown that the assumption of Moore and Greitzer that the disturbance travels through the compressor is indeed valid rigorously in the asymptotic limit where the rotational effects due to rotors dominate the compressor dynamics.