Adaptive sinusoidal disturbance rejection in linear systems with application to noise cancellation.

A solution to the problem of rejecting sinusoidal disturbance inputs with unknown amplitudes, frequencies, and phases is presented. The solution is based on using the Youla parametrization of stabilizing controllers to construct a set of stabilizing controllers for the given plant, and searching, online, within this set for a controller that achieves regulation. Three discrete time controller adaptation algorithms are presented and their convergence properties analyzed. The robustness properties of the proposed approach, in the continuous time case, to uncertainties in the plant coprime factor representation is also investigated. Using averaging techniques, it is shown that with slow adaptation, with the initial conditions of the adaptive system close to their desired values, and with appropriately bounded perturbation terms, the adaptive system maintains its performance. Motivated by problems in noise cancellation, the problem of disturbance rejection, described above, using an FIR controller and a gradient type adaptation algorithm is analyzed. Conditions for the adaptive system to achieve regulation are also presented. The adaptive regulation algorithms presented above for discrete time systems were experimentally evaluated on a noise cancellation experiment. The algorithms yielded good results for some disturbance frequency ranges with reduction in the disturbance response of up to 50 dB. At other disturbance frequency ranges, the adaptive control system did not perform well. The possible link between the deterioration of the adaptive system performance and the nonlinearities in the plant is suggested.PhDAerospace engineeringApplied SciencesElectrical engineeringMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129940/2/9711922.pd