© 2019 by German Aerospace Center (DLR). Published by the American Institute of Aeronautics and Astronautics, Inc.A model reference adaptive controller effective for systems under periodic disturbances is proposed. The disturbance on the system is assumed to be purely periodic. The parametrization of the adaptive controller uses single hidden layer neural network architecture. The basis functions of this parametrization are formed by elements of Fourier series. The adaptation is done by using a Lyapunov based weight update law which also uses the results of the FFT calculations of the estimated periodic disturbance on the system, as roots of the sigma modification. Proposed adaptation method vary from the adaptation mechanisms discussed in the literature in the following way. First, it takes the disturbance estimation from state-space to time domain, then it carries it to frequency domain. The effectiveness of the method against periodic disturbances is demonstrated through simulations.