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

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 capable of handling temperature constraints and heating-power saturation while delivering enhanced precision and overshoot control compared to state-of-the-art methods. We employ a Non-linear Auto-Regressive with Exogenous inputs model, which is linearized 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 $0.9^{\circ } \mathrm {C}$ ( $7^{\circ } \mathrm {C}$ 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 of $5.3^{\circ } \mathrm {C}$ and $1^{\circ } \mathrm {C}$ , respectively. Note to Practitioners—This work addresses a key challenge in the thermoforming process: precisely controlling sheet temperature during the heating phase to improve product quality and reduce waste. We present a data-driven control approach that can be implemented on existing thermoforming systems to enhance temperature accuracy and consistency. The proposed method uses historical process data to build a simplified model of heating dynamics. This model is then used in a predictive control framework to optimize real-time heater settings. The key advantages of the proposed method are improved temperature precision, faster settling times than conventional methods, the ability to handle practical constraints like maximum temperatures and heating power limits, and robustness to process variations and disturbances. Complex physics-based models or extensive system modifications are not needed. To implement this approach, practitioners would need to collect temperature and heater power data from their existing process, use it to train the data-driven model and integrate the control algorithm with their PLC or control system.