An Original Extremum Seeking Strategy applied to Photobioreactors

“An efficient optimizing feedback control which does require a priori process knowledge”

Unlike model reference adaptive controllers and self-tuning regulators that are commonly used to drive complex systems to desired set-points, model-free extremum-seeking controllers are capable of optimizing a performance index by operating the system close to a priori unknown operating point. Being adaptive controllers, they require little information about the considered process. However, their slow convergence due to three-time scale separation remains the main challenge. Therefore, development of various approaches for speeding up the convergence is highly desirable.

A possible solution makes use of block-oriented models for approximating a wide range of nonlinear systems. These models include Hammerstein, Wiener, and Wiener- Hammerstein representations includingnonlinear static and linear dynamic blocks. Even though this approach can be used to effectively achieve process identification, its performance in closed-loop systems is yet to be explored.

In a recent paper published in the research journal, Industrial & Engineering Chemistry Research, University of Mons (Belgium) and Université du Québec à Rimouski (Québec) researchers: Eng. Christian Feudjio, Dr. Laurent Dewasme, Prof. Jean-Sébastien Deschênes and Prof. Alain Vande Wouwer designed an adaptive slope seeking strategy as a general framework comprising of extremum-seeking and suboptimal control objectives. Their main goal was to achieve any reachable operating point on the input/output map of a dynamic single-input single-output system with enhanced convergence.

They showed that the considered process could be approximated either by Hammerstein (H), Wiener (W) or Wiener-Hammerstein (W-H) models. The adaptive strategy includes a recursive estimator for online identification of the block-oriented models, a slope reference generator for converting the setpoints specified by the user into gradient set points in line with the parameters provided by the recursive estimator and finally a controller for driving the estimated gradient towards the gradient set point. A pole placement controller design successfully replaces the heuristic integrator gain tuning which is prevalent in classical extremum-seeking schemes.

The auxiliary model-recursive prediction error method algorithm was effectively used for online identification of the block-oriented modelss. The three models (H, W, W-H) were found to be equivalent in the identification perspective as they lead to similar input and output regressions.. To avoid any potential parameter identification problems in closed-loop configurations, superimposing a sufficiently rich signal to the input such as a pseudo-random binary signal is highly recommended.

As proof of the concept, the authors successfully applied the proposed control strategy to biomass productivity optimization of a microalgae photo-bioreactor. Microalgae have particularly attracted significant research attention owing to their potential application in numerous areas such as biofuel and food production and treatment of wastewaters

In summary, the presented adaptive slope seeking strategy requires little prior information about the process. Additionally, due to its efficiency and portability, the computation procedure can be used in different processes without any modifications. Therefore, the study presents essential information that will maximize biomass productivity in microalgae cultures as well as other related applications.