Control of Exponentially Damped Sinusoidal Signals

An internal model based adaptive algorithm for canceling disturbances composed of sums of exponentially damped sinusoidal (EDS) signals is presented. The time varying state variables of an internal model principle controller in a feedback loop can provide estimates of the EDS signal parameters, the frequency and the damping factor. By using additional integral controllers, the estimation errors can be eliminated to achieve perfect cancellation. The convergence of the proposed adaptive algorithm and the stability of the feedback control system including the algorithm are justified using singular perturbation theory and averaging theory. Simulation results demonstrate the validity of the convergence and stability analysis.