Adaptive algorithms for the rejection of sinusoidal disturbances acting on unknown plants

The dissertation is concerned with the development and analysis of adaptive algorithms for the rejection of unknown periodic disturbances acting on an unknown system. The rejection of periodic disturbances is a problem frequently encountered in control engineering, and in active noise and vibration control in particular. A new adaptive algorithm is presented for situations where the plant is unknown and may be time-varying. Known as the adaptive harmonic steady-state or ADHSS algorithm, the approach consists in obtaining on-line estimates of the plant frequency response and of the disturbance parameters. The estimates are used to continuously update control parameters and cancel or minimize the effect of the disturbance. The dynamic behavior of the algorithm is analyzed using averaging theory. Averaging theory allows the nonlinear time-varying closed-loop system to be approximated by a nonlinear time-invariant system. Extensions of the algorithm to systems with multiple inputs/outputs and disturbances consisting of multiple frequency components are provided.;After considering the rejection of sinusoidal disturbances of known frequency, the rejection of disturbances of unknown frequency acting on an unknown and time-varying plant is considered. This involves the addition of frequency estimation to the ADHSS algorithm. It is shown that when magnitude phase-locked loop (MPLL) frequency estimation is integrated with the ADHSS algorithm, the two components work together in such a way that the control input does not prevent frequency tracking by the frequency estimator and so that the order of the ADHSS can be reduced. While MPLL frequency estimation can be combined favorably with ADHSS disturbance rejection, stability is limited due to the local convergence properties of the MPLL. Thus, a new frequency estimation algorithm with semiglobal stability properties is introduced. Based on the theory of asynchronous electric machines, the induction motor frequency estimator, or IMFE, is shown to be appropriate for disturbance cancellation and, with modification, is shown to increase stability of the combined ADHSS/MPLL algorithm. Extensive active noise control experiments demonstrate the performance of the algorithms presented in the dissertation when disturbance and plant parameters are changing.