Scholarly Communications Project

Application of the Filtered-X LMS Algorithm for Disturbance Rejection in Time-Periodic Systems


Leslie Paige Fowler

Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of



Harry H. Robertshaw, Chair
William R. Saunders
Harley H. Cudney

May 3, 1996
Blacksburg, Virginia


Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting time-periodic disturbances for time-periodic systems.

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