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 performance could be greatly improved by optimizing the transducer positions. The robustness of such an optimized control system is investigated here for both unstructured, i.e., random, changes in the control environment, and for structured changes, such as those due to the presence of acoustical diffracting objects in an enclosure, for example. The study concentrates on how to simply describe the changes which occur in the plant response and disturbance in practice, and investigates how the cost function used in transducer positioning optimization techniques can be modified so that the performance is least affected by these changes. Mathematical and numerical analyses are used to help understand the overall robustness of an active control system to uncertainties in the plant response and disturbance. It is found that the degradation in performance due to small random changes in the disturbance is not affected by transducer location, whereas the degradation due to small random changes in the plant response does depend on transducer location. The effects of diffracting objects in an enclosure are analyzed in terms of the changes in the singular-value matrix of the nominal plant response, in which the objects are not present. Theoretical analysis showed that transducer positions with low control effort are generally good choices for robust performance. Several fitness functions were tested for use in the search for the optimum transducer locations and the results showed that use of the proper fitness function can effectively filter out the actuator positions with high control effort and can select transducer positions which can perform robustly.