Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties

Based on a two-dimensional (2D) system description of a batch process in industry, a robust closed-loop iterative learning control (ILC) scheme is proposed for batch processes with state delay and time-varying uncertainties. An important merit is that the proposed ILC method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of setpoint trajectory in both the time (during a cycle) and batchwise (from cycle to cycle) directions. Only measured output errors of current and previous cycles are used to design a synthetic ILC controller consisting of dynamic output feedback plus feedforward control, for the convenience of implementation. By introducing a comprehensive 2D difference Lyapunov function that can lead to monotonical state energy decrease in both the time and batchwise directions, sufficient conditions are established in terms of linear matrix inequality (LMI) constraints for holding robust stability of the closed-loop ILC system. By solving these LMI constraints, the ILC controller is explicitly formulated, together with an adjustable robust H infinity performance level. An illustrative example of injection molding is given to demonstrate effectiveness and merits of the proposed ILC method.