Stochastic identification of bioreactor process exhibiting input multiplicity

Bioreactor systems involve complex biochemical reactions, which make the systems highly non-linear in nature. Developing model based controllers for such processes require mathematical representations, which are simple, yet capable of capturing the non-linear process characteristics. Continuous bioreactor falls under the class of non-linear systems that exhibit input multiplicity in the optimal operating region, i.e., the operating region where identical outputs are obtained for multiple inputs. Linear modeling techniques are not useful for the referred class of systems for obvious reasons. Even for non-linear modeling techniques, the real bottleneck is to capture the bell-shaped parabolic structure of steady state characteristics exhibited by these systems. The stochastic approach of modeling, which is based on process input/output time-series data, is very useful for this purpose. The aim of this paper is to address the stochastic modeling issues related to bioreactor processes. In this work, three efficient modeling techniques have been studied, viz. block oriented NARMAX structure (Pearson and Pottmann in J Process Control 10:301-315, 2000), Bootstrap structure detection for NARMAX model (Kukreja et al. in Int J Control 77(2):132-143, 2004) and Wavelet-NARMAX model (Billings and Wei in Int J Syst Sci 36(3):137-152, 2005).