Identification of periodic signals with uncertain frequency

This paper presents a new algorithm to identify periodic signals with uncertain frequency. The approach is based on the behavior of an internal model in an error feedback system. As such, the signal is fed to a fictitious plant with a feedback controller. The feedback controller is based on a traditional controller in parallel with an internal model which identifies and cancels the periodic disturbances. Under ideal circumstances, the phase plot of the states of the internal model form an ellipse. The speed of rotation about this ellipse can be used to calculate the difference between the nominal frequency of the model and the true frequency of the periodic signal. An integral controller or a least-squares estimator can be used to drive this error to zero. Simulations demonstrate the validity of this approach with time-varying frequency, and the algorithm is then applied to some data collected from a spot welder that has been corrupted by a sinusoidal signal whose frequency is between 1 Hz and 5 KHz.