A digital twin of evaporative thermo-fluidic process in the fixation unit of DoD inkjet printers

In inkjet printing, optimal paper moisture is essential for high print quality. Commercial printers achieve this through hot-air impingement in a fixation unit, whose drying performance is crucial to overall print quality. This paper presents a modular digital twin of the fixation unit that models the thermo-fluidic drying process and adaptively monitors its spatio-temporal performance. The core novelty lies in formulating the digital twin as an infinite-dimensional state estimator that infers spatio-temporal fixation states from limited sensor data while remaining optimally robust to external disturbances. Specifically, modularity is achieved by deriving a graph-theoretic model in which each node is governed by PDEs representing the thermo-fluidic processes within individual sections of the fixation unit. Evaporation is modeled as a nonlinear boundary effect coupled with each node’s dynamics via Linear Fractional Representation. Using the Partial Integral Equation (PIE) framework, we develop a unified approach for stability, input–output analysis, numerical simulation, and rapid prototyping of the fixation process, validated with operational data from a commercial inkjet printer. Based on the validated model, an H ∞ -optimal Luenberger state estimator is synthesized to estimate the fixation unit’s thermal states from available sensor data. Together, the graph-theoretic model and optimal estimator constitute the digital twin of a commercial printer’s fixation unit, enabling real-time monitoring of spatio-temporal thermal effects on paper sheets—capabilities otherwise unattainable in traditional printing processes.