Implementation of PLL and FLL trackers for signals with high harmonic content and low sampling frequency

The accurate tracking of phase, frequency, and amplitude of different frequency components from a measured signal is an essential requirement for many digitally controlled equipment. The accurate and robust tracking of a frequency component from a complex signal was successfully applied for example in: grid connected inverters, sensorless motor control for rotor position estimation, grid voltage monitoring for ac-dc converters etc. Usually, the design of such trackers is done in continuous time domain. The discretization introduces errors which change the performance, especially when the input signal is rich in harmonics and the sampling frequency is close to the tracked frequency component. In this paper different discretization methods and implementation issues, such as Tustin, Backward-Forward Euler, are discussed and compared. A special case is analyzed, when the input signal is reach in harmonics and the sampling frequency is only 10 times larger than the tracked frequency component.