Closed- versus open-loop active vibration control in the presence of finite precision arithmetic

A closed-loop and an open-loop active vibration control technique are critically compared, accounting for the effects of finite precision arithmetic. The main result is that the relevance of such effects is pointed out and characterised, as rigorously as possible at the present state of the research, in a suitably idealised context, and with specifically devised indicators. Also, the differences between the compared methods, and in particular the different relevance of finite precision-related facts, are put to evidence and synthetically investigated. The ideas proposed herein can be extended to other types of vibration control methods, the final goal of such an overall research being a general framework to study and compare those methods, in suitably defined nominal conditions, and accounting for realistic implementation facts.