Robust adaptive attenuation of unknown periodic disturbances in uncertain multi-input multi-output systems

In high-performance high-accuracy systems, the attenuation of vibrational disturbances is essential. In this paper, we design and analyze a robust output-feedback adaptive control scheme to attenuate noise-corrupted vibrational disturbances with unknown characteristics for multi-input multi-output linear time-invariant systems in the presence of plant unstructured modeling uncertainties. The conditions and the design parameters that contribute to the performance of the closed-loop system are investigated. The main ingredients of the proposed scheme include the use of a compensator to properly shape the singular values of the plant model, a robust adaptive law to handle unmodeled dynamics and output random noise, as well as an over-parametrization in the estimated parameters in order to provide flexibility for performance improvement. Analysis and simulations together with practical design considerations are presented to demonstrate the efficacy of the proposed scheme.