Deep Koopman-based Control of Quality Variation in Multistage Manufacturing Systems

TL;DR

The paper addresses quality variation in nonlinear multistage manufacturing systems by introducing a feedforward control framework that uses a stochastic deep Koopman (SDK) model to linearize and propagate per-stage quality dynamics. The SDK encodes stage measurements into a latent quality indicator $H_k$, propagates via Koopman transition $\mathbf{K}_{k-1}$ to obtain $H_k$, and predicts stage outputs $\tilde{Y}_k$ with an MLP, all trained end-to-end with a loss $\mathcal{L}_{\text{total}}$ combining prediction, reconstruction, and KLD terms. A downstream feedforward optimization minimizes $\mathbb{E}(\Delta_Y^T Q \Delta_Y) + \Delta_X^T R \Delta_X$ subject to the Koopman-based propagation and $\Delta X_l \in \mathcal{X}_l$, solved by IPOPT in CasADi in a receding-horizon fashion. Validation on two roll-to-roll case studies demonstrates accurate quality prediction and real-time compensation, reducing downstream variations with limited physics knowledge. The approach offers practical benefits for real-time quality management in nonlinear MMSs, while acknowledging data requirements and the need to relax the downstream compensability assumption in future work.

Abstract

This paper presents a modeling-control synthesis to address the quality control challenges in multistage manufacturing systems (MMSs). A new feedforward control scheme is developed to minimize the quality variations caused by process disturbances in MMSs. Notably, the control framework leverages a stochastic deep Koopman (SDK) model to capture the quality propagation mechanism in the MMSs, highlighted by its ability to transform the nonlinear propagation dynamics into a linear one. Two roll-to-roll case studies are presented to validate the proposed method and demonstrate its effectiveness. The overall method is suitable for nonlinear MMSs and does not require extensive expert knowledge.

Figures (8)

• Figure 1: Modeling of quality propagation using an SDK framework. This approach yields a latent space with higher dimension compared to the original input space, due to the use of Koopman operators.
• Figure 2: Feedforward quality control schemes anticipate the quality variation caused by disturbances in $X_1$ (red arrow) and plan for adjustments in $X_2$ through $X_N$ (blue arrows).
• Figure 3: Layout of the R2R testbed shui2018twofold.
• Figure 4: SDK predictions versus the ground truth, top: tension, and bottom: pitch length. A drift in pitch length is noticed in the enlarged section.
• Figure 5: Schematic of the simulated R2R system.