Active Attenuation With Overall System Modeling

Abstract

Adaptive filters are an attractive approach for control of an active attenuation system due to their ability t o adapt t o changes in the acoustical system or noise source. One approach, based on the filtered-X algorithm, uses a finite impulse response (FIR) filter structure with coefficients that are adapted using the least mean squares (LMS) algorithm [ll. The filtered-U algorithm features an infinite impulse response (IIR) filter structure and uses the recursive least mean squares (RLMS) adaptive algorithm [21. Both algorithms require knowledge of auxiliary path transfer functions following the adaptive filter to ensure proper convergence of the algorithm. One approach to obtaining these transfer functions has been previously described by the authors and uses an independent random noise source, as shown in Fig. 1, for the filtered-U algorithm [31. This presentation will explore the use of an alternative approach to auxiliary path modeling that does not require an additional noise source. This approach utilizes an overall system model, Q, and auxiliary path model, T, and is known as the Q-T modeling algorithm [2,4]. As shown in Fig. 2, two error signals are combined in this approach to form an overall error signal, ET(z), that is used t o adapt Q(z) and T(z): where the residual acoustic noise, and the difference of the outputs of models Q and T, EJz) = E(i<)-E(z) (1) The model, M(z), adapts to minimize E(z) while Q(z) and T(z) adapt to minimize E,Cz). The model, M(z), may use either a finite impulse response (FIR) filter structure or an infinite impulse response (IIR) filter structure. The supplementary models, Q(z) and T(z), could also use either an FIR or IIR model structure. Adaptation can be done using the LMS o r RLMS algorithms for the FIR or IIR structures, respectively. The error signal, E(z), goes t o zero for an IIW model formed from A(z) and B(z) when: M(z) = P(z)/[H(z)(l-P(~)F(z))l = A(z)/[l-B(z)] (4) where P(z> is the direct plant, F(z) is the feedback plant, and H(z) is the auxiliary path transfer function. In general, there are many possible solutions for A(z) and B(z) for various physical parameters. The overall error signal, ET(z), goes to zero and the residual noise is minimized when: E(z) = E'(z) = 0 (5) which requires $!(z)~(z) = M(z) = P(z)/[H(z)(l-P(~)F(z))l (6) and there are again many solutions for Q(z) and T(z) for various physical parameters. However, T(z) is also used …