Two ‐dimensional iterative learning control under infinite horizon optimization for batch processes with partial actuator failures

Abstract For the control problem of industrial batch processes under partial actuator failure, this paper proposes a new two‐dimensional iterative learning control with PID‐type (2D‐IHLQILC‐NPIDILC) strategy based on infinite horizon optimization. First, a new PID iterative learning control (NPIDILC) strategy is formulated by integrating the incremental form of PID control strategy and the PID ILC strategy, which simultaneously takes into account the convergence performance along the batch direction and the performance along the time direction. Second, a set value learning (SVL) strategy is constructed using historical batch tracking error information, which significantly improves the learning ability of the controller. Furthermore, by integrating actuator inputs, process outputs, and tracking error information, a two‐dimensional extended non‐minimal state space (2D‐ENMSS) model is constructed, which avoids the need for additional observers and provides greater controller design flexibility. Concurrently, by incorporating the SVL strategy and NPIDILC strategy into the 2D‐ENMSS model, a novel 2D‐ENMSS (2D‐NENMSS) model is developed. Finally, a control law for the 2D‐IHLQILC‐NPIDILC strategy is designed by combining the 2D‐NENMSS model and infinite horizon linear quadratic control theory, which can optimize the relevant parameters of the NPIDILC in real time. In two types of injection speed control systems under model/plant mismatch uncertainty and partial actuator failures, the presented 2D‐IHLQILC‐NPIDILC demonstrated significantly superior performance and iterative learning capability compared with the corresponding traditional control.