Control of oscillatory damped disturbances-an indirect approach

This paper is concerned with the identification and rejection of exponentially damped sinusoidal (EDS) signals. For identification, a new algorithm, based on adaptive identifier concept is presented for online estimation of damping factor and frequency of an EDS signal. Stability analysis of the proposed algorithm is carried out using averaging theory. For rejection, the estimated parameters are employed in an adaptive feedforward cancelation scheme to cancel the EDS type disturbances affecting a linear system. The approach is an indirect algorithm in the sense that the frequency and damping factor of the disturbance are estimated, and the estimates are used in another adaptive algorithm which continuously adjust the control parameters and cancel the effect of the disturbance. The proposed algorithm is simple in structure and can be easily designed, as long as the plant is known and stable. Simulation results are also presented to confirm the analytical derivations and the desirable performance of the proposed algorithm.