Saddle-focus bifurcation and chaotic behavior of a continuous stirred tank reactor using PI control

The saddle-focus bifurcation and chaotic behavior of a continuous stirred tank reactor (CSTR) with two PI controllers (PI1 and PI2) to produce propylene glycol is analyzed in this paper. First, a simplified reactor model is used to show that disturbances in the inlet flow rate and variation of the parameters in the PI2 controller may give rise to a homoclinic orbit. Then, a complete reactor model is considered, for which the analysis of the saddle-focus bifurcation around the homoclinic orbit demonstrates the presence of chaotic dynamics. The chaotic behavior is corroborated from the sensitive dependence, Lyapunov exponents, power spectral density, Poincaré sections and bifurcation diagrams. Once the chaotic dynamics has been reached, it is possible to modify the strange attractor by changing the proportional PI2 constant, which in turn allows improving the reactor performance in chaotic regime. The results of the analytical calculations are verified throughout full numerical simulations.

► Mathematical model of a CSTR to research chaos and saddle-focus bifurcations.
► Analysis of the appearance of homoclinic and double-pulse homoclinic orbits.
► New chaotic dynamic of a CSTR generated by two PI controllers.
► New route to chaotic dynamic varying the parameters of a PI controller.
► Increment of the reactor performance by interchanging the chaotic dynamic.