Multivariable feedback linearizing control of Chlamydomonas reinhardtii photoautotrophic growth process in a torus photobioreactor

Abstract

The objective of this paper is to design and to validate a nonlinear multivariable controller, based on the exact feedback linearization technique, which has the capacity to stabilize the photoautotrophic microalgae growth in photobioreactor regardless of the operation point or the transient trajectory. Two measurable outputs were selected, namely the biomass concentration and the pH, whose simultaneous control can be realized by manipulating the dilution rate and the injected carbon dioxide gas flowrate. A mechanistic dynamical model describing the interactions between physicochemical and biological phenomena inside the photobioreactor was used as a starting point for the controller design. Given its complexity, the model was reduced by differentiating the states with slow dynamics from the ones with fast dynamics that were converted into algebraic expressions. In addition, a dynamic time-varying expression was derived for the concentration of hydrogen ions (negative antilogarithm of pH) thus obtaining an appropriate I/O model for control purposes. The degree of interaction between I/O channels was determined through a relative gain array analysis, in order to establish if the system allows the implementation of decentralized SISO controllers or requires a centralized MIMO controller. The feedback linearization method was associated with a model based technique to furnish the immeasurable variables required by the nonlinear control algorithm. The nonlinear controller was implemented on a laboratory torus photobioreactor piloted at constant incident light flux intensity throughout the photoautotrophic growth of a Chlamydomonas reinhardtii culture, its efficiency being proved under several operating points.