Two-dimensional delay compensation based iterative learning control scheme for batch processes with both input and state delays

Abstract

This paper investigates two-dimensional (2-D) delay compensation based iterative learning control (ILC) schemes for batch processes with both input and state delays with the help of an equivalent 2-D Fornasini–Marchsini system description for the batch process operation. A single 2-D observer-predictor is firstly introduced to predict the future state of the transformed 2-D system, and subsequently extended to sequential 2-D observer-predictors such that each of sequential 2-D observer-predictors only predicts the future system state in terms of a fraction of delay length. Based on the predicted 2-D system state, delay compensation based ILC schemes are developed such that input delay that can be arbitrarily large but bounded is compensated completely. Necessary and sufficient conditions for the asymptotic stability of the resulting 2-D closed-loop systems are established with respect to the asymptotic stability of some independent 2-D state-delay systems. Also, sufficient conditions in terms of matrix inequalities are provided to separately compute ILC laws and observer gains, while ensuring the asymptotic stability of the 2-D closed-loop system. When the state delay is unknown, another design of 2-D delay compensation based ILC scheme is further proposed. Finally, the effectiveness of the proposed methods are validated by an illustrative example.