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Disturbance observer-based tracking control for roll-to-roll slot die coating systems under gap and pump rate disturbances

Zezhi Tang, Christopher Passmore, Andrew I Campbell, Jonathan Howse, J Anthony Rossiter, Stephen Ebbens, George Panoutsos

TL;DR

This work addresses thickness control in roll-to-roll slot-die coating by integrating a disturbance observer-based optimal tracking framework (DOBOTC) with a data-driven, camera-informed model of the deposition process. It develops an augmented LQR formulation for output tracking and introduces a generalized disturbance observer to reject both matched and mismatched disturbances, producing a composite DOBTOC controller. Validation includes a data-driven state-space model identified via N4SID from experimental data, matched/mismatched disturbance scenarios, and hardware-oriented implementation plans with a meniscus-camera setup. The results demonstrate improved thickness tracking and disturbance robustness, offering a practical pathway toward high-precision, high-throughput slot-die coating systems in industries such as lithium-ion batteries, solar cells, and optical films.

Abstract

Roll-to-roll slot die coating is a widely used industrial manufacturing technique applied in a diverse range of applications such as the production of lithium-ion batteries, solar cells and optical films. The efficiency of roll-to-roll slot die coating depends on the precise control of various input parameters such as pump rate, substrate velocity and coating gap. However, these inputs are sensitive to disturbances in process conditions, leading to inconsistencies in the various characteristics of the produced film. To address this challenge, a \gls{DO} is utilized for detecting disturbances, which may occur in the same or different channels as the control signal within the system. A generalized compensator is then implemented to mitigate the impact of these disturbances on the output, thereby enhancing uncertainty suppression. Additionally, integrating the disturbance rejection system with an output tracking controller enables the coating system to maintain the desired thickness under varying input conditions and disturbances. The effectiveness of this approach is then validated using a test rig equipped with a camera system, which facilitates the development of a data-driven model of the dynamic process, represented by state-space equations. The simulation results were demonstrated to showcase the effectiveness of the DOBOTC system, which provides a resilient solution for the output tracking issue in a data-driven model with generalized disturbances.

Disturbance observer-based tracking control for roll-to-roll slot die coating systems under gap and pump rate disturbances

TL;DR

This work addresses thickness control in roll-to-roll slot-die coating by integrating a disturbance observer-based optimal tracking framework (DOBOTC) with a data-driven, camera-informed model of the deposition process. It develops an augmented LQR formulation for output tracking and introduces a generalized disturbance observer to reject both matched and mismatched disturbances, producing a composite DOBTOC controller. Validation includes a data-driven state-space model identified via N4SID from experimental data, matched/mismatched disturbance scenarios, and hardware-oriented implementation plans with a meniscus-camera setup. The results demonstrate improved thickness tracking and disturbance robustness, offering a practical pathway toward high-precision, high-throughput slot-die coating systems in industries such as lithium-ion batteries, solar cells, and optical films.

Abstract

Roll-to-roll slot die coating is a widely used industrial manufacturing technique applied in a diverse range of applications such as the production of lithium-ion batteries, solar cells and optical films. The efficiency of roll-to-roll slot die coating depends on the precise control of various input parameters such as pump rate, substrate velocity and coating gap. However, these inputs are sensitive to disturbances in process conditions, leading to inconsistencies in the various characteristics of the produced film. To address this challenge, a \gls{DO} is utilized for detecting disturbances, which may occur in the same or different channels as the control signal within the system. A generalized compensator is then implemented to mitigate the impact of these disturbances on the output, thereby enhancing uncertainty suppression. Additionally, integrating the disturbance rejection system with an output tracking controller enables the coating system to maintain the desired thickness under varying input conditions and disturbances. The effectiveness of this approach is then validated using a test rig equipped with a camera system, which facilitates the development of a data-driven model of the dynamic process, represented by state-space equations. The simulation results were demonstrated to showcase the effectiveness of the DOBOTC system, which provides a resilient solution for the output tracking issue in a data-driven model with generalized disturbances.
Paper Structure (17 sections, 3 theorems, 32 equations, 13 figures, 3 tables)

This paper contains 17 sections, 3 theorems, 32 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Description of experimental equipment
  4. Disturbances in roll-to-roll slot die coating
  5. Active DOBOTC system
  6. Mathematical formulation of the problem
  7. Optimal output tracking system
  8. Generalized disturbance rejection scheme
  9. DO design
  10. Composite DOBTOC architecture
  11. Simulation results
  12. Experimental results
  13. Dynamic model analysis
  14. Matched disturbance rejection
  15. Mismatched disturbance compensation
  16. ...and 2 more sections

Key Result

Lemma 1

Let $\overline{A}$, $\overline{B}_u$, $Q$, and $R$ be given matrices with $Q$ and $R$ being positive definite. The solution $P$ to the Algebraic Riccati Equation (ARE): exists and is unique. The optimal gain matrix $k$ that minimizes the cost function is given by:

Figures (13)

  • Figure 1: Image of experimental roll-to-roll slot die coating platform.
  • Figure 2: Side-view of slot die coating process, showing pinned meniscus and wide-angle camera.
  • Figure 3: Composite DO-based-LQR output tracking design architecture.
  • Figure 4: Graph showing process input and process output data from the roll-to-roll slot die coater.
  • Figure 5: Graph illustrating the calibration of thickness based on mean grey values, showcasing data that conforms to a power-shaped curve.
  • ...and 8 more figures

Theorems & Definitions (11)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 5
  • ...and 1 more