Chemical Engineering Science, Vol.74, 79-92, 2012
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, Poincare 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. (C) 2012 Elsevier Ltd. All rights reserved.