Dynamic Analysis and Control for a Bioreactor in Fractional Order

Abstract

In this paper, a mathematical model was developed to describe the dynamic behavior of a bioreactor in which a fermentation process takes place. The analysis took into account the bioreactor temperature controlled by the refrigerant fluid flow through the reactor jacket. An optimal LQR control acting in the water flow through a jacket was used in order to maintain the reactor temperature during the process. For the control design, a reduced-order model of the system was considered. Given the heat transfer asymmetry observed in reactors, a model considering the fractional order heat exchange between the reactor and the jacket using the Riemann–Liouville differential operators was proposed. The numerical simulation demonstrated that the proposed control was efficient in maintaining the temperature at the desired levels and was robust for disturbances in the inlet temperature reactor. Additionally, the proposed control proved to be easy to apply in real life, bypassing the singularity problem and the difficulty of initial conditions for real applications that can be observed when considering Riemann–Liouville differential operators.

Modified fractional order PID structure for non‐integer model bioreactor control

“…[25][26][27] Many works have been reported on fractional order controllers for bioreactor processes. [28,29] A survey of fractional order controllers for temperature control for different processes is given in the work of Jamil et al [30] Dynamic analysis and control of a bioreactor in fractional order considering Riemann-Liouville differential operators is given in the work of Tusset et al [29] Detailed discussions on fractional order PID controllers investigating the progress since their initial implementation in the control system, its application in various upcoming fields, and multiple problems that arise with conventional PID are provided in the cited literature. [31][32][33][34][35] A comprehensive evaluation of the milestones, challenges, and opportunities for fractional order PID controllers in industrialization and their advantages is given in the work of Tepljakov et al [36] Irrespective of the slow adaptation, fractional order PID controllers' superiority in flexibility and robustness is well recognized and has shown more promising results than classical PID.…”

Coordinated Symmetrical Altitude Position and Attitude Control for Stratospheric Airship Subject to Strong Aerodynamic Uncertainties

“…To mitigate the impact of these uncertainties, the use of a disturbance observer has emerged as a practical and unique technique. Implementing a disturbance observer allows for the estimation and compensation of multiple uncertainties, enhancing the robustness of the control system [14,15]. It is worth noting that while there have been numerous investigations focused on horizontal trajectory tracking for airships [16][17][18][19][20][21][22][23], research specifically targeting the altitude position control for stratospheric airships has been relatively scarce.…”

Regional boundary controllability of semilinear subdiffusion Caputo fractional systems

“…A fractional system of Riemann-Liouville type can effectively capture the complex behavior of the biological reactor, where the fractional derivative represents the asymmetric heat transfer and the hysteresis effect of temperature variation. Tusset et al studied the controllability of a cooling fluid flow that passes through the fermented jacket, in order to maintain the ideal temperature in the biological reactor in two cases: integer-order system and Riemann-Liouville type fractional system, in addition to some successful numerical results in both cases [28]. To do the regional boundary controllability, our approach consists to study the regional controllability in an internal subregion that contains a part of the boundary, based on a generalization of the Gronwall-Bellman inequality, and then to bring the state to the boundary by projection.…”