Online frequency estimation of periodic signals

Abstract

The problem of estimating online the unknown period of a periodic signal is considered, with no a priori information on the period: this is a crucial problem in the design of learning and synchronizing controls, in fault detection, and for the attenuation of periodic disturbances. Given a measurable continuous, bounded periodic signal, with nonzero first harmonic in its Fourier series expansion, a dynamic algorithm is proposed which provides an online globally exponentially convergent estimate of the unknown period. The period estimate converges from any initial condition to a neighborhood of the true period whose size is explicitly characterized in terms of the higher order harmonics contained in the signal. The accuracy of the frequency estimation can be arbitrarily improved by increasing the order of a prefilter which is incorporated in the estimation algorithm, at the expense of reducing the rate of the exponential convergence. This online frequency estimation algorithm can be used to design hybrid disturbance attenuation controllers for periodic disturbances with unknown period.