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The University of Southampton

Research project: Robust transducer selection - Dormant

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There are often many more potential locations for transducers than can be practically used in a real-time control system. There may be 80 possible locations for loudspeakers inside a small aircraft for example (see figures below) but only 10 of these locations can be used by a practical active control system with a limited weight and processing power. The number of ways of choosing 10 from 80 is very large, however, about 1.6 x 1012, due to the combinatorial nature of the problem and it would take about 500,000 years to exhaustively calculate the performance of all possible combinations, even if each calculation took only 10 seconds.

Instead of exhaustive searches, practical transducer selection methods thus use methods such as guided random search algorithms to reduce the number of cases whose performance has to be evaluated. Examples of these algorithms are Genetic Algorithms and Simulated Annealing. Either of these techniques can find combinations of transducers whose performance is close enough to the optimal for engineering applications by searching only a small fraction of all the possible transducer combinations.

Unfortunately, even such a sophisticated search will not reveal whether the chosen set of transducers will continue to perform well if the system under control changes slightly. Clearly such robustness is an important requirement in practical systems.

Various methods have been suggested for selecting transducer locations which are robust to such changes. They all use either an implicit or explicit model of the practical uncertainties in the system under control. The simplest method is to incorporate a degree of control effort weighting in the criterion used to evaluate the different transducer locations. The search will then discriminate against badly conditioned arrangements, whose performance is very sensitive to the assumed conditions.

Other robust design methods for transducer selection has been discussed by Baek and Elliott (1999), which includes the use of the average performance of several perturbed arrangements in the criterion used to evaluate a transducer selection.

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