Observer-based error correction in finite memory approaches for pseudo state estimation of fractional dynamic models

Fractional system models have gained in importance during recent years to account for non-standard dynamics that are characterized by long-term memory effects. An important field of application is the modeling, simulation, and control design for electrochemical energy converters such as batteries and fuel cells. Although such models are generally capable to capture (infinite horizon) memory properties, the numerical evaluation may be complicated by the same effect leading to a continuous increase in memory and computing time if no appropriate countermeasures are taken. This is especially true in (pseudo) state estimation procedures in which a periodic integrator reset takes place. Such integrator resets become necessary as a countermeasure against the increase of memory requirements and computing times. Bounding both is necessary to meet the strict requirements of real-time applicability. Additionally, such resets occur when predictor–corrector state estimators are employed for systems with bounded uncertainty. This article provides a thorough review of observer-based methods for the quantification and enhancement of the aforementioned truncation errors. Exemplary results are shown for the pseudo state estimation of a simplified fractional model of charging and discharging of lithium-ion batteries.