Tunable interactions under the influence of external electric and magnetic fields open the way to controlled transport and self-organization in model and living systems. In this paper, we establish new experimental system parameters  for tuning interparticle interactions in colloidal systems using a three-dimensional precessing conical magnetic field. The paper presents a digital twin of the experimental setup, simulation of electromagnetic fields in order to find the  optimal self-assembly parameters. The results of pilot experiments with magnetic particles of silicon dioxide 2.47 µm in size in deionized water are demonstrated, the phenomenon of controlled self-assembly is shown.