A tube feedback iterative learning control for batch processes

Optimization-based iterative learning control (OILC) has been widely applied to batch processes due to its fast convergence, good control performance and ability to handle constraints. However, how to guarantee constraint satisfaction and convergence of tracking error in the presence of unknown system nonlinearity remains open in the framework of OILC. It is important to address this issue since unknown nonlinearity is common in practice and detrimental to good control performance. In this paper, we propose a tube feedback OILC to investigate the applicability of linear-model based control strategy on batch processes with an unknown nonlinear term. First, a state feedback control law is designed to stabilize the system. The stabilized system is then decomposed into two subsystems: repeatable and unrepeatable subsystems; Second, an invariant set of states corresponding to the unrepeatable subsystem is computed, based on which an OILC is further developed for the repeatable subsystem to improve the control performance. Meanwhile, the feedback controller steers the states within a tube around the trajectory of OILC. In this way, convergence and constraint satisfaction are ensured simultaneously. Compared with the currently existing methods, the proposed method has the following advantages: (1) generality covering both stable and unstable systems; (2) low computation complexity; and (3) rigorous stability. The simulation results on injection molding velocity control demonstrate that the proposed method has superior performance.