Advanced PI control with simple learning set-point design: Application on batch processes and robust stability analysis

Abstract

According to the literature statistics, less than 10% of reported iterative learning control (ILC) methods are of the indirect form. Under an indirect ILC, the closed-loop system consists of two loops. Despite of the advantages in controller design and practical implementation, analysis on the corresponding system's stability and robustness becomes troublesome compared with the direct ILC methods. To address this open issue, a combination of PI control and ILC, referred to ILC-based PI control, is therefore developed in this study. Under the proposed ILC-based PI controller, the closed-loop system can be transformed into a 2-dimensional (2D) Roesser's system. Based on the 2D system formulation, a sufficient condition for robust asymptotical stability is first derived for multi-input multi-output linear batch processes. Correspondingly, an advanced PI control with ILC-based set-point is developed which requires smaller memory for operation together with less degree of freedom to design. Moreover, the proposed control algorithm can lead to superior steady-state tracking performance and good robustness against load disturbance and measurement noise, without requiring the internal state information of the process. Finally, the effectiveness and merits of the proposed method are illustrated by application to an injection molding process and a batch reactor, in comparison with a typical PI-type direct ILC method recently developed.