Two‐dimensional iterative learning linear quadratic regulator control for batch processes based on reference trajectory learning scheme

Abstract

This work proposes a novel two‐dimensional infinite horizon iterative learning linear quadratic regulator (2D‐RTL‐IHILLQR) for batch processes, which incorporates a reference trajectory learning (RTL) scheme into the optimal control framework. First, an RTL scheme is constructed as an outer loop to actively cope with time delay and disturbances. By leveraging the tracking error from the previous cycle, the RTL scheme generates a compensated reference trajectory to compensate for time delay and disturbances in advance, which then serves as the updated reference trajectory for the inner‐loop 2D‐IHILLQR scheme. Second, a modified extended non‐minimal state space (ENMSS) model is established by incorporating both the compensated reference trajectory and the actual controlled variable. Since this modified ENMSS model embeds the compensated reference trajectory directly into the system state, it is endowed with the capability of advance compensation for time delay and disturbances. Finally, on the basis of this ENMSS model, the 2D‐RTL‐IHILLQR method is derived. Through a dual‐loop structure with outer‐loop feedforward compensation and inner‐loop feedback suppression, the 2D‐RTL‐IHILLQR method effectively mitigates adverse effects caused by time delay and disturbances and enhances overall control effect. The effectiveness of the 2D‐RTL‐IHILLQR method is validated in both linear and nonlinear systems via two case studies, namely packing pressure control in an injection moulding process and the temperature control in the reactor.