Nonlinear bounded control for a class of continuous agitated tank reactors

Abstract

Chemical reactors planned under efficiency and tight product quality considerations usually lead to a process where sensitivity and nonlinearity are essentials. This poses a nonlinear control problem where the control input exhibits propensity to meet its bounds. Control saturation induces an additional nonlinearity whose effect on stability must be understood when designing a control scheme. In practice, the bounded control problem design is circumvented by first designing a stable control for the no saturation case, and then by tuning its gains so that control bounds are no met, and successful implementation demands extensive tuning and testing. In fact, such designs may have unnecessary conservative dynamic performance. In this work, we address the bounded nonlinear control problem for a class of two-state chemical reactors where heat removal rate is the manipulated variable. Based on physical restrictions, reactor open-loop dynamics and nonlinear control via complete and partial linearization, we devise a global nonlinear geometric framework to establish solvability of the problem and to characterize its closed-loop dynamics. A specific reactor example and numerical simulations are used to illustrate and corroborate results.