One of the basic requirements in control systems is that they had the ability to regulate the controlled variables to reference commands without a steady-state error against unknown and unmeasurable disturbance inputs . Control systems with this property are called servo systems . In servo systems design , the internal model principle plays an important role . Based on the internal model principle for perfect tracking or rejecting an input signal , a model of signal should be inserted in stable closed loop system . In practice , we often encounter the situations where the reference commands to be tracked and/or disturbance input to be rejected are periodic signals . Examples are industrial robots , disc drives , numerical control machines , servo scanners and every system that rotates or repeats the same task on a periodic basis . Repetitive control is a potential solution to this kind of precision systems . When the periodic disturbance is not purely sinusoidal and contains infinite harmonics in its Fourier series expansion , according to the internal model principle , a finite dimensional compensator can not achieve disturbance rejection perfectly even though the frequency is known . In this thesis we address this control problem in the case of unknown frequency . For this purpose , the thesis proceeds with introducing a chain of n filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids , and of decomposing it into its constituent components . It shown that by tending n to infinity , we reach to a linear time delay system which when furnished with a frequency estimator block is capable of estimating the fundamental frequency of any periodic signal . Another ability of proposed estimator is reproducing the periodic signal . In contrary it could not decomposed the periodic signal to its components . In compersion with the previous methods , the proposed fundamental frequency estimator has a simple structure , high convergence rate and accurate estimated value . The proposed estimator is employed in the structure of a repetitive control system to track or reject periodic signals with unknown frequency . The proposed structure has robust properties with respect to uncertainties in plant and frequency of periodic input and also is adaptive with respect to frequency of periodic input . Stability analysis of proposed stractures is carried out based on the concepts of integral manifold of slow adaptation and averaging theory . Various simulations confirm the desirable performance of proposed structures . Keywords: Repetitive Control , Disturbance Rejection , Periodic Signals , Fundamental Frequency Estimation.