Periodic Signal Tracking for Lightly Damped Systems

The focus of this paper is on the development of time-delay filters to accomplish tracking of periodic signals with zero phase errors. The class of problems addressed include systems whose dynamics are characterized by lightly damped modes. A general approach for the zero-phase tracking of periodic inputs is presented followed by an illustration of single harmonic tracking of underdamped second-order systems with relative degree two. A general formulation of the approach is then posed for higher-order systems and systems including zeros. The paper concludes with the illustration of enforcing constraints to desensitize the time-delay filter to uncertainties in the location of the poles of the system and forcing frequencies. A numerical practical design case based on a medical X-ray system is used to illustrate the potential of the proposed technique.