Dynamic and Control in a Three-Variable Chemical Reaction Model


== Abstract ==

<p>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.</p>

== Document ==
<pdf>Media:Draft_Sanchez Pinedo_334734394-1068-document.pdf</pdf>