Stabilization of Re-Entrant Manufacturing Systems With Actuator Saturation: A Low-Gain Approach

Abstract

This paper addresses the feedback control design problem for a category of re-entrant manufacturing systems (RMSs) with actuator saturation. Based on the mass conservation law, a continuum model is first developed to represent the multiple-line RMSs with actuator saturation in terms of a nonlinear hyperbolic partial differential equation (PDE). Then a key technical lemma is established to bridge the boundedness of the spatial derivative and the pointwise boundedness of the state, which is essential for the stability analysis of systems under saturation. The main control synthesis results include both state feedback and output feedback controller designs. First, for the state feedback case, a fundamental result is established linking the overall unsaturated system stability to its subsystems. Based on this, a low-gain control strategy is developed within the framework of semi-global stabilization to handle the saturation nonlinearity, achieving exponential convergence to the desired equilibrium for any given bounded set. Second, for the observer-based output feedback case, a counterpart separation principle is established for the considered hyperbolic PDE systems, which facilitates the subsequent low-gain controller design. Similarly, this output feedback strategy ensures exponential convergence for any given bounded set of initial states within the semi-global stabilization framework. Finally, the effectiveness of the proposed approaches is demonstrated through the numerical simulations. Note to Practitioners—The motivation of this work originates from the need to develop effective control strategies for complex re-entrant manufacturing plants, such as semiconductor wafer fabrication facilities and printed circuit board (PCB) production lines. In practical industrial scenarios, these systems are strictly constrained by physical limitations, such as the maximum capacity of input rates or processing speeds, that is, actuator saturation. Discrete-event approaches have been extensively employed in manufacturing processes. However, when dealing with large-scale coupled multi-line re-entrant manufacturing plants, those methods often suffer from the curse of dimensionality. To address these challenges, this paper develops a PDE-based control framework for RMSs with actuator saturation. The proposed approach provides semi-global stabilization guarantees for the considered PDE model under both state-feedback and observer-based output-feedback settings. It offers a theoretical basis for the capacity regulation of RMSs with re-entrant material flows and actuator constraints.