Estimating Industrial Process Stability by Whitney's Singularity Theory When Choosing a Sufficient Time-Sampling Frequency of the Control Signal

Abstract. In this paper, we estimate the stability of continuous-type automated industrial processes and choose a sufficient time-sampling frequency of the control signal using Whitney’s singularity theory. The proposed stability analysis approach is based on constructing typical bifurcations for the historical data of a technological object under different time-sampling frequencies of its control signal. The singularity equation serves for obtaining the equation of the equilibrium state curves of the system and a sufficient time-sampling frequency of the control signal corresponding to the vertex of the resulting curve. As an illustrative example, the developed method is applied to the control system of the mass balance stripping section in the purification process of a styrene distillation column of the ethylbenzene, styrene, and polystyrene plants. Based on the quantitative analysis results, we construct a bifurcation and determine a sufficient time-sampling frequency of the control signal to ensure system stability.

Keywords: catastrophe theory, bifurcation, dynamical systems, stability criteria.

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Rabotnikov, M.A., Stafeichuk, B.G., Shumikhin, A.G., Estimating Industrial Process Stability by Whitney’s Singularity Theory When Choosing a Sufficient Time-Sampling Frequency of the Control Signal. Control Sciences 6, 29–34 (2022). http://doi.org/10.25728/cs.2022.6.4