Vol. 337 No. 2 (2026)
DOI https://doi.org/10.18799/24131830/2026/2/5482
Adaptive search for the desired particle size distribution of oil-in-water emulsion using a modulating search signal
Relevance. Separation of oil-in-water emulsions remains one of the key tasks in oil treatment systems. The efficiency of physical treatment methods, including acoustic ones, strongly depends on the dispersed composition: the sizes of emulsion globules determine the required range of operating frequencies and treatment regimes. In practice, emulsions are polydisperse, and the globule size distribution varies over time, which makes manual selection of treatment parameters and achievement of the required distribution labor-intensive and poorly reproducible. Aim. To develop and analytically substantiate an adaptive algorithm for searching a tuning parameter that ensures convergence of a dispersed system toward a prescribed globule size distribution based on a feedback signal. Object. Oil-in-water emulsion. Methods. Extremum seeking with a modulating harmonic signal, demodulation and frequency filtering, Taylor series expansion of the objective function in the vicinity of an extremum, and analysis of the closed-loop system in the form of a differential equation. Results. The paper introduces the objective function linking the current dispersed-state parameter to a reference value, and proposed the reciprocal of the globule radius as the tuning parameter. The authors have developed a structural scheme of adaptive tuning with a modulating signal. It is shown that the position of the current operating point relative to the extremum is determined by the phase relationship between the input and output harmonic signals. The authors performed signal demodulation with extraction of the error component, and obtained a differential equation of the closed loop, which solution is aperiodic and ensures convergence of the tuning parameter to the extremal value provided that the integrator gain is properly selected. The paper introduces the characteristic signal waveforms at the stages of modulation, filtering, and after closing the feedback loop.
Keywords:
oil-in-water emulsion, adaptive system, objective function, entropy, extremum seeking, particle radius distribution
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