##### Department of Mathematics,

University of California San Diego

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### MATH 196/296 - Student Colloquium

## Bob Bitmead

#### UCSD \\ MAE Department

## Jet Engine Controller Certification - A Day At The (Math) Zoo

##### Abstract:

\indent A hard practical problem will be described associated with the experimental certification of a jet engine together with its feedback controller. This has recently become much more difficult as engine controllers have become fully MIMO (multiple-input/multiple-output), which requires evaluation of vector input and output signals and their relative gains to establish a quantitative acceptance criterion. Linear algebra and matrix operator norms need to introduced to provide a rigorous foundation to the approach. The requirement to scale the data strongly affects the numerical answers, so scaling arises as a central issue. Finding the correct scaling then becomes a constrained optimization problem associated with minimizing the operator norms. Thus, interior point methods for linear matrix inequalities are introduced into the mix. Finally, to accommodate the sampled nature of the data, these scaling matrices must be extended to a smooth matrix function of a single complex variable, which requires the inclusion of interpolation theory and complex analysis. This brings us back to linear algebra and the so-called Nevanlinna-Pcik problem.\\ This brief excursion through the math zoological garden is intended to demonstrate the importance of rigorous theory providing underpinnings to hard practical approaches to engineering problems. The presence of this foundation permits advancing with a significantly greater degree of surety and confidence than would the case relying solely on experience and guesswork, particularly for problems of a complexity exceeding simple human capabilities. The end result is an experimental protocol for the acceptance of engine-controller pairs.

### November 9, 2010

### 11:00 AM

### AP&M B412

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