Active Control of Instabilities in Jet Engines

摘要

Advances in several areas of robust control theory and its applications were madeduring the extension of this program. Our emphasis has been in the development of computable measures of performance robustness for both linear and nonlinear systems, and in the development of computationally sound identification algorithms. In the following paragraphs we briefly discuss the main areas of our program. A detailed description of the results obtained and the future directions to be explored follows. In the detailed description, we will point to the different publications that resulted from this research. Robust stability and performance analysis with real parametric uncertainty can be naturally formulated as a Structured Singular Value, or u problem, where the block structured uncertainty description is allowed to contain both real and complex blocks. It is now well known that computation for the general mixed u problem is NP complete. Thus, to obtain acceptable computation, we do not attempt to solve the mixed u problem exactly but rather to obtain good bounds. The key to obtaining a lower bound lies in the fact that the u problem may be reformulated as a real eigenvalue maximization since for any Q Q, pr(QMJ) < u(Mi). The computational complexity of this problem manifests itself in the fact that this function is non-convex and so it is difficult to find the global maximum. Any local maximum, however, is a lower bound to the global maximum. We are currently working on an efficient way to compute a local maximum of the this function using a simple power iteration. We describe this algorithm in more detail in Section 3.