Continuous ‐ discrete interval observers for monitoring microalgae cultures

Abstract

Algorithms estimating unmeasured component concentrations play a key role in bioprocess applications where only a few on-line measurements are usually available. In this article, interval observers are designed to provide guaranteed intervals for the key components involved in cultures of microalgae. In contrast with most of the published studies focusing on continuous-time measurements, this study considers discrete-time measurements with possibly long and irregular sampling and defines predictors based on model equations and state transformations to ensure the enclosure of the state variables between two measurement times. The methods are validated with experimental data where the remaining inorganic nitrogen and the microalgal internal quota are estimated.

Continuous cultivation of photosynthetic microorganisms: Approaches, applications and future trends

“…In real situations, continuous, on-line and direct monitoring of certain compounds (e.g., intracellular product) or biomass properties is not practical or, sometimes, even possible. To overcome this problem, discrete measurements coupled with mathematical models (or estimators) that describe the bioprocess can be used (Goffaux et al, 2009). Alternatively, the mathematical models can be associated with an indirect parameter (e.g., pH, dissolved O 2 or irradiance) that is directly related to different aspects of the bioprocess.…”

Hurdles and challenges for modelling and control of microalgae for CO2 mitigation and biofuel production

“…In Bernard et al (1998), a high gain observer is developed in order to estimate both internal quota and remaining nutrients. In Goffaux et al (2009), an interval observer provides these estimates with a confidence interval, taking into account the discrete nature of the measurements. Other authors use inorganic carbon (Becerra-Celis et al, 2008) or oxygen production (Su et al, 2003) to estimate microalgal production.…”

Monitoring of Microalgal Processes

“…Biomass concentration is estimated together with specific growth rate, PE, and average light intensity using a growth model and DO measurement [66]. Biomass concentration and nitrogen concentration in biomass and in the medium were estimated continuously in cultivations of Dunaliella tertiolecta and Isochrysis galbana by a continuous-discrete Droop model based an interval observer using intermittent offline biomass measurements [255]. Biomass concentration and specific growth rate estimation in a hydrogen production process with the photosynthetic bacterium Rhodobacter capsulatus was carried out with a sliding-mode observer based on Monod and Luedeking-Piret model and measurement of produced hydrogen volume [256,257].…”