Dynamic and Control in a Three-Variable Chemical Reaction Model

Abstract

Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications.This study investigates the suppression of chaos in a three-variable reaction system through an optimal linear feedback strategy, formulated via the solution of an algebraic Riccati equation.The proposed control approach effectively eliminates chaotic oscillations, guiding the system to equilibrium even under parameter uncertainties of up to 20%. Numerical simulations confirm that the control action maintains high robustness, ensuring convergence with minimal effort. The stabilization time for x1 remains close to 29 s across different tolerances, while x2 and x3 converge nearly instantly, demonstrating the rapid effectiveness of the method. Furthermore, the control signal stabilizes at a small positive value after a short transient, reinforcing the computational efficiency and practical feasibility of this approach. These findings demonstrate that optimal linear control techniques provide a reliable and theoretically sound framework for managing nonlinear chemical systems, offering an accessible solution for real-world applications in engineering and process optimization.

Document