The effects of plant and disturbance uncertainties in active control systems on the placement of transducers

Previous studies of active control systems have shown that the overall perf ormance could be greatly improved by optimizing the transducer positions. T he robustness of such an optimized control system is investigated here for both unstructured, i.e., random, changes in the control environment, and fo r structured changes, such as those due to the presence of acoustical diffr acting objects in an enclosure, for example. The study concentrates on how to simply describe the changes which occur in the plant response and distur bance in practice, and investigates how the cost function used in transduce r positioning optimization techniques can be modified so that the performan ce is least affected by these changes. Mathematical and numerical analyses are used to help understand the overall robustness of an active control sys tem to uncertainties in the plant response and disturbance. It is found tha t the degradation in performance due to small random changes in the disturb ance is not affected by transducer location, whereas the degradation due to small random changes in the plant response does depend on transducer locat ion. The effects of diffracting objects in an enclosure are analyzed in ter ms of the changes in the singular-value matrix of the nominal plant respons e, in which the objects are not present. Theoretical analysis showed that t ransducer positions:with low control effort are generally good:choices for robust performance. Several fitness functions were tested for use in the se arch for the optimum transducer locations and the results showed that use o f the proper fitness function Can effectively filter out the actuator posit ions with high control effort and can select transducer positions which can perform robustly. (C) 2000 Academic Press.