Robust Control of Multi-Line Re-Entrant Manufacturing Plants via Stochastic Continuum Models

This paper investigates the robust intelligent control problem of multi-line re-entrant manufacturing plants. The control system is designed with a hierarchical architecture, where a nonlinear stochastic hyperbolic partial differential equation (PDE) is used to describe the system dynamics and a robust controller is designed to exponentially drive the manufacturing plants to a desired operation mode with steady feeding and production rates. The developed robust control scheme is shown to be practically implementable through convex optimization techniques. Numerical experiments are presented to demonstrate the feasibility and advantages of the proposed approach. Note to Practitioners - The motivation of this work originates from the need to develop an intelligent robust control strategy for a class of practical complex re-entrant manufacturing plants, for instance, the semiconductor wafer factory and the chemical production lines with numerous process procedures. Discrete-model-based algorithms have been extensively employed in this field due to their excellent convenience and great accuracy. However, when dealing with coupled multi-line re-entrant manufacturing plants with nonlinearities, traditional discrete-model-based methods lack rigorous theoretical analysis and, more importantly, suffer from the curse of dimensionality in many cases. To equip the re-entrant manufacturing plant with a desired operation mode that enjoys significant robustness against stochastic noises, we propose a continuum-model-based intelligent robust control strategy. The proposed method is practically useful in the sense that it can be conveniently applied to various industrial scenarios with re-entrant characteristics and the control design problem can be well solved via available convex optimization algorithms.