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Modelling and well-posedness of a nonlinear hybrid system in fed-batch production of 1,3-propanediol with open loop glycerol input and pH logic control

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Publication Date
Volume
12
Issue
1
Identifiers
DOI: 10.1016/j.nonrwa.2010.06.022
Keywords
  • Nonlinear Hybrid System
  • Ph Logic Control
  • State-Based Switching
  • Non-Zeno Behavior
  • Continuous Dependence

Abstract

Abstract A fed-batch fermentation of glycerol by Klebsiella pneumoniae with open loop substrate input and pH logic control is considered in this paper. We propose a nonlinear hybrid system to describe this process, which consists of discrete variables to represent the flow rate of glycerol and alkali and continuous variables for substance concentrations. The hybrid system includes both time- and state-based switchings, which are respectively determined by a pre-assigned times sequence and an output equation of the pH. It is proved that the hybrid system is non-Zeno. Some basic properties of solutions to the hybrid system are also explored, including existence, uniqueness, boundedness and continuous dependence on initial state and parameters. Additionally, a numerical simulation is carried out to show that the proposed hybrid system can describe the fed-batch culture properly.

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