Modelling and optimization for a switched system in microbial fed-batch culture

• Published in: Applied mathematical modelling Vol. 35; no. 7; pp. 3276 - 3284
• Main Authors: Gong, Zhaohua, Liu, Chongyang, Feng, Enmin, Wang, Lei, Yu, Yongsheng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.07.2011; Elsevier
• Subjects: Applied sciences; Biological and medical sciences; Bioreactors; Biotechnology; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Fed-batch culture; Fermentation; Fermented food industries; Food industries; Fundamental and applied biological sciences. Psychology; Mathematical analysis; Mathematical models; Methods. Procedures. Technologies; Microorganisms; Modelling; Optimization; Process control. Computer integrated manufacturing; Switched system; Switching; Time-scaling transform; Various methods and equipments; Time-scaling transform; Fed-batch culture; Switched system; Optimization; Biotechnology; Multimodel control; Switching function; Fermentation; Modeling; Hybrid system; Smoothing; Inequality constraint; Batch process; State constraint
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2011.01.023

This paper considers modelling and optimization of a microbial fed-batch fermentation process. A switched system with variable switching instants is proposed to describe the fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). Taking the concentration of 1,3-PD at the terminal time as the cost function and the switching instants as optimization variables, an optimization model involving switched system and subject to continuous state inequality constraints is then presented. By introducing a time-scaling transform, the optimization model is transcribed into an equivalent one with parameters and fixed switching instants. A computational approach to seek the optimal solution is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD can be increased considerably compared with previous results.