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 behaviour of a notch filter 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 PI controller in parallel with an internal model which identifies and cancels the periodic disturbances. This controller was introduced in previous papers. Under ideal circumstances the time-varying states of the internal model can be mapped to two time invariant variables, the magnitude or energy of the internal model and the difference between the nominal frequency and the true frequency of the periodic signal. An additional integral controller then can be used to reduce this error to zero. The output of the notch filter will be the periodic component of the signal, while the input to the fictitious plant will be the non-periodic random component. An improvement to the basic feedback controller is also given to reduce this error by using continuous-time least-squares estimation. A second algorithm based on the Fourier Transform (FT) technique is presented and used to confirm the performance of the feedback based algorithm. The frequency of the periodic signal can be found by an optimal algorithm which considers the windowing effect of FT's. Simulations demonstrate the validity of this approach and the algorithm is then applied to some data collected from a spot welder that has been corrupted by a sinusoidal signal whose frequency varies between 30Hz and 1KHz.