Stabilization of stochastic operating modes in the flow reactor

I Bashkirtseva

doi:10.1088/1757-899x/192/1/012005

Abstract

A conceptual multistable model of the flow reactor proposed by Volter and Salnikov is studied in the presence of random disturbances. A stochastic excitability of this system, even in a zone of stable equilibria, is explained by the high stochastic sensitivity. Such high stochastic sensitivity of the equilibrium can be a basic reason of the noise-induced destruction of the operating mode. For the stabilization of the stochastic flow reactor, a theory of the synthesis of the assigned low stochastic sensitivity is suggested. It is shown how to use this control approach and construct an appropriate regulator which suppresses unwanted large-amplitude stochastic oscillations and provide a proper operation of the flow reactor.

Highlights

Many manufacturing processes are described by nonlinear dynamic systems with equilibrium operating modes
A deterministic stability of the equilibrium is considered as a condition of the proper operation
The system (1) exhibits three dynamic regimes: for a < a1 = 1.580079, the system is monostable with an equilibrium as a single attractor; for a1 < a < a2 = 1.582843, the system is bistable with coexisting equlibrium and limit cycle; for a > a2, the system is monostable with a limit cycle as a single attractor

Summary

Introduction

Many manufacturing processes are described by nonlinear dynamic systems with equilibrium operating modes. A deterministic stability of the equilibrium is considered as a condition of the proper operation. Such stability can be insufficient, especially in nonlinear systems. Mathematical models of flow chemical reactors demonstrate a wide variety of the nonlinear dynamic regimes with complex oscillations [12,13,14].

Deterministic model of the flow chemical reactor

Model of the flow reactor with stochastic disturbances

Conclusion