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This article focuses on the active control of a combination of incommensurate sinusoids and its subsets. Two sliding mode control (SMC) algorithms are proposed to enhance the conventional least mean squares (LMS) algorithm maintaining its inherent advantages. The SMC is utilized to update the filter coefficients, and a feedback loop with the SMC is introduced in the adaptive filtering system. The proposed methods are evaluated for several cases by comparing the results with the LMS algorithm. An experiment with an active strut is also constructed and longitudinal vibrations excited by an amplitude modulated type signal are measured before and after the control for each adaptive filtering algorithm. Overall, the proposed algorithms demonstrate faster convergence and reduce amplitudes at multiple peaks even when only one frequency is targeted. [ABSTRACT FROM PUBLISHER]

Abstract: Conventional adaptive filtering algorithms, typically limited to the control of single or multiple sinusoids, are not appropriate to control modulated vibrations, especially in the presence of rich side band structures. To overcome this deficiency, a new control algorithm is proposed that introduces a feedback loop with the model predictive sliding mode control (MPSMC) in the adaptive filtering system. Several amplitude and frequency modulation cases are first computationally studied, and conventional and proposed methods are comparatively evaluated in terms of estimation error, performance in time and frequency domains, stability, and uncertainty in the reference signal. To experimentally validate the proposed algorithm, an active strut (with longitudinal vibrations) is constructed. Overall, the proposed adaptive algorithm yields superior reductions at the main frequencies and at side bands; also, good attenuation is found on a broadband basis. [Copyright &y& Elsevier]