Robust iterative learning control for batch processes with input delay subject to time‐varying uncertainties

A robust iterative learning control (ILC) method is proposed for industrial batch processes with input delay subject to time‐varying uncertainties, based on a two‐dimensional (2D) system description of batch process operation. To compensate the input delay, a 2D state predictor is established to predict the augmented system states, such that a 2D ILC design is developed for the ‘delay‐free’ 2D system based on using only the measured output errors of current and previous cycles. Delay‐dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free‐weighting matrices. By solving these matrix inequalities using a cone complementarity linearisation method, the ILC controller is explicitly derived together with an adjustable H infinity performance index. An important merit is that perfect tracking can be realised for a batch process with arbitrarily long input delay if the delay‐free part of the 2D system can be stabilised, in no presence of time‐varying uncertainties. Moreover, the time integral of tracking error can be added as an extended 2D system state for ILC design to eliminate steady‐state output error for all batches. An illustrative example of injection moulding process is given to demonstrate the effectiveness of the proposed method.