Finite-precision implementation issues in narrowband active control

The domain of active control of narrowband disturbances, of either vibrational or acoustic noise source, poses several methodological and implementational issues. Besides all the problems that normally arise in digital control, some specific issues are related to the attenuation of harmonic or quasi-harmonic signals, which require the usage of control blocks approaching, or even touching, the stability limit, such as notch filters or dynamic oscillators. The finite-precision implementation of these blocks can evidence several problems related to nonlinear effects such as signal quantization, numerical representation, and approximate computation. This paper focuses on the effects related to finite-precision computations and floating point numerical representation, and, after a brief literature review, shows the necessity of extending conventional methodologies for the analysis of finite-precision controller implementation. Some illustrative examples are also provided to illustrate the implementation problems discussed.