Adaptive regulation via weighted robust estimation and automatic controller tuning

This paper proposes a methodology to adaptively reduce time-varying additive disturbances in a feedback system, comprised a plant with uncertainty and an adaptable linear feedback controller. Adaptive regulation is done via the direct estimation of a perturbation on the feedback controller in a Youla–Kucera parametrization. Uncertainty on the plant dynamics bounds the size of the allowable controller perturbation for adaptation to maintain stability robustness. By simultaneously minimizing the variance of the plant output signal and a control output signal, the direct estimation of the controller perturbation is formulated as a weighted robust estimation problem that is implemented recursively for a real-time implementation. The methodology is applied to a vibration control benchmark to demonstrate how the proposed adaptive feedback regulation can effectively reduce unknown harmonic disturbances with a time-varying frequency for a mechanical system with unmodelled dynamics.