Orthonormal Filters for Identification in Active Control Systems

TL;DR

This paper investigates orthonormal filter banks for adaptive system identification in active control, demonstrating their robustness and efficiency, especially with uncertain prior knowledge, through numerical and experimental validation.

Contribution

It introduces a procedure to determine fixed parameters for orthonormal filter banks and analyzes their performance under uncertainties, comparing them with FIR filters.

Findings

Lower computational effort with filter banks under certain conditions.

Performance degrades with imprecise prior knowledge but can be mitigated by higher filter order.

Numerical and experimental results confirm advantages over FIR filters.

Abstract

Many active noise and vibration control systems require models of the control paths. When the controlled system changes slightly over time, adaptive digital filters for the identification of the models are useful. This paper aims at the investigation of a special class of adaptive digital filters: Orthonormal filter banks possess the robust and simple adaptation of the widely applied Finite Impulse Response (FIR) filters, but at a lower model order, which is important when considering implementation on embedded systems. However, the filter banks require prior knowledge about the resonance frequencies and damping of the structure. This knowledge can be supposed to be of limited precision, since in many practical systems, uncertainties in the structural parameters exist. In this work, a procedure using a number of training systems to find the fixed parameters for the filter banks is applied. The effect of uncertainties in the prior knowledge on the model error is examined both with a basic example and in an experiment. Furthermore, the possibilities to compensate for the imprecise prior knowledge by a higher filter order are investigated. Also comparisons with FIR filters are implemented in order to assess the possible advantages of the orthonormal filter banks. Numerical and experimental investigations show that significantly lower computational effort can be reached by the filter banks under certain conditions.