Towards Indirect Data-Driven Predictive Control for Heating Phase of Thermoforming Process

TL;DR

This paper introduces an indirect data-driven predictive control method for the heating phase in thermoforming, improving temperature regulation and robustness using NARX models and MPC, validated through simulations and lab experiments.

Contribution

It develops a novel control approach combining NARX models with MPC for precise temperature control in thermoforming, handling constraints and uncertainties.

Findings

Achieved overshoot and steady-state error below 2°C in simulations.

Demonstrated effective temperature regulation with less than 5.3°C overshoot in experiments.

Enhanced control performance over existing methods.

Abstract

Shaping thermoplastic sheets into three-dimensional products is challenging since overheating results in failed manufactured parts and wasted material. To this end, we propose an indirect data-driven predictive control approach using Model Predictive Control (MPC) capable of handling temperature constraints and heating-power saturation while delivering enhanced precision, overshoot control, and settling times compared to state-of-the-art methods. We employ a Non-linear Auto-Regressive with Exogenous inputs (NARX) model to define a linear control-oriented model at each operating point. Using a high-fidelity simulator, several simulation studies have been conducted to evaluate the proposed method's robustness and performance under parametric uncertainty, indicating overshoot and average steady-state error less than $2^\circ \mathrm{C}$ and $0.7^\circ \mathrm{C}$ ($7^\circ \mathrm{C}$ and $2^\circ \mathrm{C}$) for the nominal (worst-case) scenario. Finally, we applied the proposed method to a lab-scale thermoforming platform, resulting in a close response to the simulation analysis with overshoot and average steady-state error metrics less than $5.3^\circ \mathrm{C}$ and $1^\circ \mathrm{C}$, respectively.