Moving Horizon Estimation for Al‐Doped ZnO Nanoparticle Synthesis: An Online UV‐vis Spectroscopy Approach

ABSTRACT Nanoparticles play a pivotal role in various applications, including electronics and photovoltaics. Among the diverse synthesis techniques, the sol‐gel process is widely utilized for producing transparent conductive nanostructures, such as aluminum‐doped zinc oxides (AZO), which serve as cost‐effective alternatives to indium tin oxide (ITO) for transparent electrodes. However, achieving precise control over critical particle properties, e.g., particle size distribution (PSD) remains a major challenge due to the inherent complexity of online monitoring during synthesis. This study develops a moving horizon estimator (MHE) to dynamically predict AZO nanoparticle properties during sol‐gel synthesis. The proposed approach combines online UV–vis spectroscopy with a population balance equation (PBE) model to estimate the PSD and related parameters. To reduce computational complexity, the high‐dimensional PBE model is simplified using dynamic mode decomposition with control (DMDc), retaining essential dynamics while enabling real‐time state estimation. The MHE‐based observer optimizes the consistency between measured and estimated AZO concentrations, demonstrating accurate real‐time prediction of PSD. Experimental validation shows strong agreement between the predicted PSD and offline measurements, confirming the observer's effectiveness. This approach paves the way for model predictive control, enhancing reproducibility and product quality in the synthesis of functional semiconductor nanoparticles.