Optimal Structure of Learning-Type Set-Point in Various Set-Point-Related Indirect ILC Algorithms

Abstract

According to the literature statistics, only less than 10% of reported iterative learning control (ILC) methods have been devoted to the indirect approach. Motivated by the full potential of research opportunities in this field, a number of studies on indirect ILC were proposed recently, where ILC-based P-type control and learning-type model predictive control (L-MPC) are two successful stories. All indirect ILC algorithms consist of two loops: an ILC in the outer loop and a local controller in the inner loop. The local controllers are, respectively, a P-type controller in the ILC-based P-type control and a model predictive control (MPC) in the L-MPC. Logically, this leads to the question of what type of ILC should be chosen respectively for the two above-mentioned indirect ILC methods. In this study, P-type ILC and anticipatory P-type (A-P-type) ILC are studied and compared, because they are typical and widely implemented. Based on mathematical analysis and simulation test, it has been proved that the A-P-type ILC should be used in the ILC-based P-type control and while the P-type ILC should be used in the L-MPC. Furthermore, an improved L-MPC with batch-varying learning gain was proposed to handle the trade-off between convergence rate and robustness performance. The simulation results on injection molding process and a nonlinear batch process validated the feasibility and effectiveness of the proposed algorithm.

110th Anniversary: An Overview on Learning-Based Model Predictive Control for Batch Processes

“…A simple but plausible implementation of the functional is where the increment Δ r can be decided based on a broad range of criteria, such as optimizing some indices of clinical or economic interest . Among all, the simplest determination may be making Δ r be proportional to the tracking error in the past: which leads to the P-type indirect ILC . Here, we consider the most general case by putting the subscript t back to emphasize the time variation.…”

“…Indirect ILC was initially developed within a framework of adaptive control to simplify stability analysis, , and was later shaped to integrate with various types of feedback control, such as PID control and robust control for different application purposes. − The first integration with MPC was determined in ref , which presents technical details on how to design the learning increment Δ r and determine the learning gain K in eq . The corresponding stability analysis using two-dimensional system theory was given in ref , and a successful clinical application was reported in ref .…”

“…In view of the resemblance between the indirect ILMPC and ILMPC presented in Section , this incentivizes us to study the stability of the indirect ILMPC along a similar idea as ILMPC when constraints are absent. Typical examples include refs and . By contrast, the stability analysis for the system using constrained MPC (the inner controller) is not clear, motivating more-careful inspections.…”

“…− − which leads to the P-type indirect ILC. 67 Here, we consider the most general case by putting the subscript t back to emphasize the time variation. Then, the reference seamless fits into the framework of Problem…”