Iterative Learning Based Accumulative Disturbance Observer for Repetitive Systems via a Virtual Linear Data Model

This work explores the problem of observing nonrepetitive disturbances under an almost data-driven framework. First, a linear data model among the inputs, states, and outputs is built for a repetitive system (linear or nonlinear) between two consecutive iterations where the nonrepetitive disturbances are accumulated along time axis as a total one. The accumulative disturbance contains all the influences on the system states or outputs caused by the disturbances from the initial time instant to the current time instant between two consecutive iterations. Furthermore, an iterative updating algorithm is designed to estimate the gradient matrix in the derived linear data model. Subsequently, iterative learning-based accumulative disturbance observer (ILADOB) is proposed employing the state information in the iteration domain when the system states are measurable; otherwise, when the states are immeasurable, an output-based ILADOB is presented as an alternative. The proposed two ILADOB methods are executed along the iteration direction all over the finite time interval pointwisely using the system data from preceding trials. The convergence and stability are proved mathematically. The simulation study confirms the validity of the state-based and output-based ILADOB methods.