A modified filtered-error algorithm with fast convergence in systems with delay

In this paper a multi-channel feedforward adaptive control algorithm is described which has good convergence properties while having relatively small computational complexity. This complexity is similar to that of the filtered-error algorithm. In order to obtain these properties, the algorithm is based on a preprocessing step for the actuator signals using a stable and causal inverse of the transfer path between actuators and error sensors, the secondary path. The latter algorithm is known from the literature as postconditioned filtered-error algorithm, which improves convergence speed for the case that the minimum-phase part of the secondary path increases the eigenvalue spread. However, the convergence speed of this algorithm suffers from delays in the adaptation path, because, in order to maintain stability, adaptation rates have to be lower for larger delays. By making a modification to the postconditioned filtered-error scheme, the adaptation rate can be set to a higher value. Consequently, the new scheme also provides good convergence if the system contains significant delays. Furthermore, an extension of the new scheme is given in which the inverse of the secondary path is regularized in such a way that the derivation of the modified filtered-error scheme remains valid.