Adaptive algorithms for active control of periodic disturbances

An active disturbance control system cancels or attenuates disturbances by introducing signals that are opposite in sign to the disturbance signals. This dissertation describes the development, analysis, and implementation of multivariable adaptive schemes for active control of periodic disturbances of unknown frequency at multiple sensor locations. The disturbances are assumed to contain multiple harmonics associated with a single fundamental frequency, as is the case if the source of the disturbances is a rotating machine. A parameter estimator based on an amplitude/phase-locked loop approach is first presented that is designed to estimate the frequencies, amplitudes, and phases of the components of a periodic signal. Although only the fundamental component contributes to the estimation of the fundamental frequency in the basic design of the estimator, a modified estimator is also proposed that extracts the information from multiple harmonics or components of other signals with the same fundamental frequency. The basic and modified frequency estimators are used to estimate the disturbance frequency in a new adaptive control scheme for periodic disturbances. The so-called indirect approach is applied to reduce periodic acoustic noise in a small room, and experimental results show the effectiveness of the scheme. Superior performance of the modified frequency estimator is observed even when the amplitudes become large or very small, due to acoustic resonances and frequency variations. Another adaptive scheme, called the “direct approach,” is proposed, where a nonlinear control law is used to directly adjust the parameters of the control signals. Although the scheme is highly nonlinear, approximations yield an analysis that enables a linear time-invariant design of the feedback algorithm. The analysis also gives useful information about the dynamic behavior of the system and the selection of the design parameters. Experimental results on the active noise control application show that the direct scheme is also capable of reducing significantly acoustic noises with constant or time-varying characteristics at multiple locations.