Data-driven identification of a continuous type bioreactor

ABSTRACT

The aim of this paper is to provide a data-driven approach for modeling of a continuous type bioreactor. The data sets used for identification are gathered in the presence of various types of noises such as white and colored ones which reflects the practicality of the problem. Our purpose is generally to identify the bioreactor, in the presence of such noises, in which several model structures are employed, and then the best structure for each case is determined based on a performance index. The main originality of the paper is presenting the best model structure with optimum convergence rate and optimum orders (as low as possible) in the estimation algorithm of parameters. In this regard, for every proposed model structure, the maximum fitness indices have been selected so that for BJ, OE, ARMAX, ARX the maximum fitness are 98.14%, 64.85%, 97.29%, 96.26%, respectively. In particular, since the bioreactor is a multi-model system due to the different operating phases, by use of a forgetting factor, the identification is successfully carried out in the change of phases (e.g., from growth to the stationary) which depicts the effectiveness of the proposed techniques. All these results are supported by illustrative numerical simulations.

KEYWORDS:

• System identification
• Bioreactor
• Recursive identification
• Multi-model
• Forgetting factor

Nomenclature

$b$	=	Biomass concentration [g/L]
$s$	=	Substrate concentration [g/L]
$\mu$	=	Specific growth rate
$k_1$	=	Kinetic parameter [L/g]
$k_m$	=	Kinetic parameter [L/g]
$r_c$	=	Rate of substrate consumption
$y$	=	Cell mass yield [-]
$V$	=	The volume of the reactor [L]
$q$	=	Volumetric flow
$D$	=	Dilution rate [1/hr]
${\mu }_{max}$	=	Maximum specific growth rate [1/hr]
$r_g$	=	Rate of cell generation
CTB	=	Continuous type bioreactor
FOH	=	First-order hold
RLSFF	=	Recursive least square with forgetting factor
FIT	=	Fitness index
LS	=	Least square
RLS	=	Recursive least square
IV	=	Instrumental variable
RIV	=	Recursive instrumental variable
ARMAX	=	Autoregressive moving average exogenous
BJ	=	Box-Jenkins
OE	=	Output error
ARX	=	Autoregressive with exogenous input
SI	=	System identification
PRBS	=	Pseudorandom binary sequence
MBE	=	Mass balance equations
ZOH	=	Zero-order hold
PEM	=	Prediction error method

Additional information

Notes on contributors

Abolfazl Simorgh

Abolfazl Simorgh was born in Bushehr, Iran in 1995. He received his B.Sc. degree in Control Systems from Persian Gulf University, Bushehr, Iran, and now he is a M.Sc student in Control Systems at Persian Gulf University, Bushehr, Iran. His research interests include optimal control systems, system identification and adaptive control.

Abolhassan Razminia

Abolhassan Razminia was born in Bushehr, Iran in 1982. He received his B.Sc. degree in Control Systems from Shiraz University, Shiraz, Iran, in 2004, the M.Sc. degree in Control Systems from Shahrood University of Technology, Shahrood, Iran, in 2007, and the Ph.D. degree in Control Systems from Tarbiat Modares University, Tehran, Iran, in 2012. He is currently an Associate Professor with the Department of Electrical Engineering, School of Engineering, Persian Gulf University, Bushehr, Iran. His research interests include optimal control systems, nonlinear dynamical systems, and system identification.

Vladimir I. Shiryaev

Vladimir I. Shiryaev was born in the Soviet Union in 1946. He graduated from Chelyabinsk Polytechnic Institute in 1969 and worked at Applied Mathematics Department as an engineer, senior lecturer, associate professor. Now he is a professor, chief of Control Systems Department, SUSU. His scientific interests lie in the field of control in the presence of uncertain, inaccurate or incomplete measurements, multiextremal optimization, chaotic dynamics, and econometrics.