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Title Constrained least mean square algorithm and its applications to active noise and vibration control
Author H.S.Na
Type KAIST Ph.D. Dissertation
Year of Pub. 1996
In this paper, the concept of "constrained least mean square (CLMS) algorithm" is proposed and it's usefulness to active noise and vibration control is validated through computational simulations and experiments. The conventional LMS algorithm is developed without considering the constrained structure of the problems. Hence, conventional methods need a large number of weights and require considerable training time. A novel method is proposed to overcome the drawback of the conventional approchs for constrained problems. The proposed CLMS algorithm is fast and does not destroy the constrained structures of the weights during update. It is based on steepest descent algorithm commonly used in adaptive signal processing for a wide variety of purposes. Many of the active noise and vibration control systems utilize a form of the least mean square (LMS) algorithm. In the active control of noise, it is common practice to locate an error microphone far from the control source to avoid the near-field effects by evanescent waves. Such a distance between the control source and the error microphone makes a certain level of time-delay inevitable and, hence, may yield undesirable effects on the convergence properties of control algorithms such as filtered-x and filtered-u LMS. This paper discusses the dependence of the convergence rate on the acoustic error path in these popular algorithms and introduces new algorithms "constrained filtered-x and constrained filtered-u LMS" based on CLMS algorithm. This methods increase the convergence region regardless of the time-delay in the acoustic error path. In the algorithms, coefficients of the controller are adapted using the residuals of constrained structure which are defined in such a way that the control process become stationary. Advantages of constrained filtered-x/u LMS algorithm is illustrated by convergence analysis in the mean and mean square sense. The issue of rejecting periodic disturbance / noise rises in various applications dealing with rotating machinery. We propose a novel adaptive controller for periodic disturbance / noise cancellation, with a frequency tracking capability. It can be added to an existing feedback control system without altering the original closed-loop characteristics such as stability margin and transfer functions. Adaptive algorithm derived for the proposed controller based on the LMS and CLMS algorithm turns out to be identical to the popular delayed-x and constrained delayed-x LMS algorithms respectively. The proposed controller not only estimate the magnitude and phase of the tonal disturbance but also track the frequency of the tone, if it changes in quasi-static manner. The algorithm uses the instantaneous frequency approach for the frequency tracking. A number of computer simulations are carried out in order to demonstrate the effectiveness of proposed ANC algorithm under various conditions. An experimental ANC system has been built and tested. Some experiments have been successfully conducted in showing the superiority of the proposed methods. The results provide some insights for efficient implementation of the active noise and vibration control.