《A New Approach to Active Noise and Vibration Control-Part II The Unknown Frequency Case 》.pdf

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 2009 3387 A New Approach to Active Noise and Vibration Control—Part II: The Unknown Frequency Case ´ Maciej Niedzwiecki, Member, IEEE, and Michał Meller, Student Member, IEEE Abstract— This paper presents a new approach to rejection of LMS (FXLMS) compensation, internal model principle, or complex-valued sinusoidal disturbances acting at the output of a phase-locked loop—for references see [4]. Methodological discrete-time stable linear plant with unknown and possibly time- aspects aside, the proposed solutions differ in the assumptions varying dynamics. It is assumed that both the instantaneous fre- quency of the sinusoidal disturbance and its amplitude may be made about the controlled plant and sinusoidal disturbance. slowly varying with time and that the output signal is contami- The most important design premises are those concerning the nated with wideband measurement noise. It is not assumed that a following: reference signal, correlated with the disturbance, is available. The • known/unknown/time-varying plant dynamics; proposed disturbance rejection algorithm is an extension of the al- • known/unknown/time-varying amplitude of the distur- gorithm derived for the constant-known-frequency case, described bance; in Part I of this paper. • known/unknown/time-varying frequency of the distur- Index Terms—Adaptive filtering, disturbance rejection, sys