Robust Identification of Smart Foam Using Set Mem-bership Estimation in A Model Error Modeling Frame-work

Abstract

The aim of this paper is robust identification of smart foam, as an electroacoustic transducer, considering unmodeled dynamics due to nonlinearities in behaviour at low frequencies and measurement noise at high frequencies as existent uncertainties. Set membership estimation combined with model error modelling technique is used where the approach is based on worst case scenario with unknown but bounded uncertainties. The outcome is a robust identified model which consists of a nominal model with its uncertainty bounds that fits exactly the H_∞ robust control scheme which has been utilized in active noise control in recent years. While the nominal model has the desired physical characteristics as cut-off frequency and the anticipated slope and flatness before and after this frequency, respectively, it is maintained in the acceptably tight uncertainty upper and lower limits, thus validating the identification procedure. Looseness and tightness of uncertainty strip has also been discussed regarding nonlinearities and measurement noise in low and high frequency regions. Meanwhile the identified nominal model can also be utilized in non-robust noise control methods due to its lower order, reflecting the advantage of the applied identification approach.