Periodic disturbance cancellation with uncertain frequency

This paper presents a new algorithm to cancel periodic disturbances with uncertain frequency. The disturbances are cancelled using an internal model structure with adaptive frequency, in parallel with a stabilizing controller. The time-varying internal model controller's states, in steady state, can be mapped to two time-invariant variables: the magnitude or energy of the internal model and frequency of the disturbance. An additional integral controller then can be used to reduce the difference between the internal model controller (IMC) and disturbance frequency to zero. The stability of the feedback control system with this algorithm and convergence of the algorithm to the correct frequency with exact disturbance cancellation are justified by singular perturbation and averaging theories. The algorithm is locally exponentially stable, rather than asymptotically stable. Simulations demonstrate the performance of the algorithm, the ability of this algorithm to identify the frequency of periodic disturbances and to reject periodic disturbances with uncertain frequency.