A novel PID type iterative learning controller optimized by two-dimensional infinite horizon linear quadratic iterative learning control for batch processes

Although a proportional integral derivative type iterative learning control (PIDILC) scheme can achieve good performance, its application is limited by open-loop structure, parameter tuning, and initial state. In this paper, a novel PIDILC optimized by two-dimensional infinite horizon linear quadratic regulator (PIDILC-2D-IHLQR) is proposed. First, by synthesizing the advantage of the conventional PIDILC method and proportional integral derivative (PID) strategy, a novel closed-loop PIDILC scheme is obtained. Then, a novel two-dimensional infinite horizon linear quadratic regulator (2D-IHLQR) is developed to optimize the parameters of the PIDILC strategy. The limitations of parameter tuning and initial state are solved by this PIDILC-2D-IHLQR method. Therefore, the proposed method not only solves the aforementioned limitations but also inherits the advantages of PIDILC algorithm, PID method, and the novel 2D-IHLQR scheme. Moreover, a stability condition is given based on Lyapunov theory and it can help judge whether the selection of control parameters meets the stability condition. The effectiveness of the proposed method is demonstrated by the case study on an injection modelling process.