A synthetic approach for robust constrained iterative learning control of piecewise affine batch processes

For industrial nonlinear batch processes that can be practically divided into a series of piecewise affine operating regions, a two-dimensional (2D) closed-loop iterative learning control (ILC) method is proposed for robust tracking of the set-point profile against cycle-to-cycle process uncertainties and load disturbances. Both state feedback and output feedback are considered for the control design, together with the process input and output constraints for implementation. Based on a 2D system description for the batch operation, a few synthetic performance and robust control objectives are proposed for developing the 2D ILC schemes, in combination with the 2D Lyapunov-Krasovskii functions that can guarantee monotonic state energy (or output error) decrease in both the time (during a cycle) and batch (from cycle to cycle) directions. Both the polyhedral and norm-bounded descriptions of process uncertainties are considered to derive the corresponding linear matrix inequality (LMI) conditions for the closed-loop ILC system robust stability. An important merit of these LMI conditions is that there are adjustable convergence indices prescribed for both the time and batch directions, and an adjustable robust control performance level for the closed-loop system. By specifying/optimizing these adjustable parameters to solve these LMI conditions, the 2D ILC controller can be explicitly derived for implementation. The application to a highly nonlinear continuous stirred tank reactor (CSTR) is shown to illustrate the effectiveness and merits of the proposed ILC method.