Towards Indirect Data-Driven Predictive Control for Heating Phase of Thermoforming Process
Hadi Hosseinionari, Mohammad Bajelani, Klaske van Heusden, Abbas S. Milani, Rudolf Seethaler
TL;DR
This paper tackles overheating during the heating phase of thermoforming by proposing an indirect data-driven predictive control framework that embeds a linearized NARX control-oriented model within Model Predictive Control to handle temperature constraints and actuator saturation. The approach leverages a high-fidelity simulator for robust, parametric-uncertainty evaluation and uses PRBS-based data collection to train a low-order model that supports real-time MPC. Key contributions include a structured NARX-MPC methodology, rigorous model validation (fitness and whiteness tests) and a comprehensive comparison against AMPC and MPC-guided DRL, showing substantially reduced overshoot and tighter terminal error bounds; laboratory experiments further validate the simulation results with close agreement and practical feasibility. The work demonstrates that the proposed indirect data-driven strategy is scalable to larger heater banks, offers low online computational burden, and provides robust performance across parameter variations, indicating strong potential for industrial thermoforming applications. Future directions include developing direct data-driven control without explicit SysID and extending the framework to even larger, more complex heating systems.
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.