Nonlinear dynamic analysis and control of an isothermal autocatalytic bioreactor using integer and fractional-order models

Â. Tusset, Luan J. F. Ferreira, José M. Balthazar, V. Piccirillo, O. D. dos Santos, G. Lenzi

Abstract

This study investigates the nonlinear dynamics and control of an isothermal autocatalytic bioreactor exhibiting chaotic behavior through both integer-order and fractional-order mathematical formulations. The fractional-order model is developed using the Riemann–Liouville operator to account for memory effects inherent to biochemical processes. The system dynamics are characterized using time histories, phase portraits, bifurcation diagrams, and Lyapunov exponents, thereby enabling the identification of periodic and chaotic operating regimes. The results reveal that the bioreactor is highly sensitive to variations in the nonlinear reaction parameters. Moreover, the fractional-order formulation exhibits remarkable sensitivity, with a variation of only 0.001 in the fractional derivative order being sufficient to induce a transition from chaotic to periodic behavior. To suppress chaotic oscillations and stabilize the desired operating point, a control framework combining feedforward and feedback actions is proposed. The feedforward controller compensates process disturbances and parameter variations, whereas the feedback controller is implemented independently using the Optimal Linear Feedback Control (OLFC) and the nonlinear State-Dependent Riccati Equation (SDRE) approaches. Both controllers successfully drive the system to the desired equilibrium, achieving steady-state errors below 10−6 and 10−8 for the OLFC and SDRE controllers, respectively. Robustness analyses under parametric uncertainties demonstrate that both controllers maintain satisfactory performance, while the SDRE approach exhibits superior robustness to parameter variations and changes in the fractional derivative order owing to its nonlinear state-dependent formulation. However, this improved robustness comes at the expense of substantially higher computational cost, whereas the OLFC controller reduces the computational effort by approximately 98%. These findings provide new insights into the influence of fractional-order dynamics on chaotic biochemical systems and establish quantitative trade-offs between robustness and computational efficiency, offering practical guidance for designing control strategies for nonlinear bioreactors.

Source: semanticscholar · PDF

Read the AI summary and key takeaways for traders on WOBR Quant Research.