Abstract
This research introduces dynamic modeling and real-time control of fractal structure in particulate materials fabricated by the ball milling process, specifically addressing challenges of unavailable real-time non-destructive and non-invasive imaging measurements in the enclosed rotating vials. A description of the internal temperature dynamics in the container is established along with a thermal regulator based on external temperature feedback. The fractal dimension is introduced as a structural measure, and its dynamics is established via an analytical formulation through a lumped model, along with a full thermostructural computational model of the ball milling particulate microstructure. These models are used as real-time observers of inaccessible internal states during the process. In addition, they are used as model references in an adaptive control system, regulating the fractal structure with adaptation via external temperature measurements, available experimentally via an infrared thermocouple. The controller is designed on the basis of the dynamic models and is tested experimentally. The controller is demonstrated to command the duration of the process at steady conditions to obtain the necessary thermal exposure yielding the desired microstructure for the ball-milled particulates.