  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.
