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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 3685941, 13 pages
Research Article

Dynamics Analysis and Biomass Productivity Optimisation of a Microbial Cultivation Process through Substrate Regulation

1School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China
2Faculty of Biological Sciences, Department of Biotechnology, University of Zielona Góra, Ulica Szafrana 1, 65-516 Zielona Góra, Poland
3School of Information Engineering, Dalian University, Dalian 116622, China

Received 24 February 2016; Revised 1 April 2016; Accepted 13 April 2016

Academic Editor: Carmen Coll

Copyright © 2016 Kaibiao Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A microbial cultivation process model with variable biomass yield, control of substrate concentration, and biomass recycle is formulated, where the biochemical kinetics follows an extension of the Monod and Contois models. Control of substrate concentration allows for indirect monitoring of biomass and dissolved oxygen concentrations and consequently obtaining high yield and productivity of biomass. Dynamics analysis of the proposed model is carried out and the existence of order-1 periodic solution is deduced with a formulation of the period, which provides a theoretical possibility to convert the state-dependent control to a periodic one while keeping the dynamics unchanged. Moreover, the stability of the order-1 periodic solution is verified by a geometric method. The stability ensures a certain robustness of the adopted control; that is, even with an inaccurately detected substrate concentration or a deviation, the system will be always stable at the order-1 periodic solution under the control. The simulations are carried out to complement the theoretical results and optimisation of the biomass productivity is presented.