<![CDATA[Fluid catalytic cracking (FCC) is one of the most important processes in the petroleum and petrochemical industries because it converts heavy hydrocarbons into valuable transportation fuels and petrochemical feedstocks. However, FCC units exhibit highly nonlinear behavior, including multiplicity, thermal instability, Hopf bifurcations, and self-sustained oscillations, all of which can adversely affect catalyst performance, product yield, and operational stability. A nonlinear dynamic and optimal control framework is developed for an FCC process exhibiting bifurcation-induced instability. Continuation and bifurcation analyses are performed using MATCONT to identify limit points, Hopf bifurcation points, and associated limit-cycle behavior. Based on these analyses, an optimal control problem is formulated to maximize the cracking reaction rate while incorporating a Hopf-bifurcation-avoidance constraint to ensure dynamically stable operation. The bifurcation analysis reveals multiple steady states and a subcritical Hopf bifurcation, confirming the onset of self-sustained oscillatory dynamics in the FCC process. The optimal control results demonstrate that enforcing the Hopf bifurcation constraint significantly improves process performance. Specifically, the optimized cracking reaction rate increases from 6.254 in the unconstrained case to 7.443 when the Hopf constraint is imposed, corresponding to an approximately 19% improvement while maintaining dynamic stability. The proposed framework demonstrates that integrating bifurcation analysis with optimal control provides an effective strategy for simultaneously enhancing process stability and operational performance in FCC systems. The results highlight the industrial significance of incorporating nonlinear dynamic constraints into process optimization to achieve safer, more efficient, and higher-performing FCC operation.]]>
