Switching-based Rejection of Multi-sinusoidal Disturbance in Uncertain Stable Linear Systems under Measurement Noise

This paper addresses the problem of designing an Adaptive Feedforward Control (AFC) system for uncertain linear systems affected by a multi-sinusoidal disturbance with known frequencies. A novel State-Norm Estimator-based (SNE-based) switching mechanism is proposed to remove the long-standing assumption that either the sign of the real part or the imaginary part of the transfer function of the plant at the frequencies of excitation are needed to be known. The distinctive feature of the proposed mechanism in comparison to previous solutions from the authors is a lower order of the controller. This feature is achieved with the use of suitable notch filters, allowing a decoupled design of the switching mechanism. Furthermore, the presence of the bounded noise is considered in the analysis. The effectiveness and robustness of the proposed method are illustrated by means of numerical examples.