Controllability of start-ups in CSTRs under PI control

An analysis of start-ups of PI-controlled CSTRs, based on the study of the time evolution of the divergence of the vector field defined by the reactor model differential equations, is presented. The divergence is linked to th e dynamics of the an n-volume of initial conditions in the phase space. Whe n the divergence is positive, nearby trajectories tend to diverge, implying that the reactor dynamics is sensitive to perturbations. So the divergence is effective for the study of the controllability characteristics of the r eactor dynamics. The method, which is based on the complete non-linear mode l, is quite simple and synthetic portraits in the space of initial conditio ns can be obtained, for the controllability of start-ups. The effectiveness of the approach in the study of PI-controlled CSTRs is also discussed. (C) 2001 Published by Elsevier Science Ltd.