Separation and Estimation of Periodic/Aperiodic State

Periodicity and aperiodicity can exist in a state simultaneously and typically become quasi-periodicity and quasi-aperiodicity in a dynamically changing state. The quasi-periodic and quasi-aperiodic states existing in the periodic/aperiodic state mostly correspond to different phenomena and require different controls. For separation control of these states, this paper defines the periodic/aperiodic, quasi-periodic, and quasi-aperiodic states to construct a periodic/aperiodic separation filter that separates the periodic/aperiodic state into the quasi-periodic and quasi-aperiodic states. Based on these definitions, the linearity of periodic-pass and aperiodic-pass functions and the orthogonality of quasi-periodic and quasi-aperiodic state functions are proved. Subsequently, the periodic/aperiodic separation filter composed of periodic-pass and aperiodic-pass filters that realize the periodic-pass and aperiodic-pass functions is designed and integrated with a Kalman filter for estimation of the quasi-periodic and quasi-aperiodic states.