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On the global stability of conventional PID control for a class of chemical reactors

The stabilization properties of derivative control for chemical reactor stabilization have been rarely studied in the literature. In a pioneering work, Aris and coworkers (textitChem. Eng. Sci. 1959; 11:199–206.) used linear analysis to show that derivative control offers greater stabilization flexibility than proportional control. The aim of this work is to show that mixed derivative and proportional control can yield global stabilization for a large class of continuously stirred tank reactors (CSTR) characterized by having stable isothermical dynamics. The stability proof exploits the structure of CSTR models where the nonlinearity is concentrated in the chemical reaction kinetics. It is shown that the proportional mode is a type of energy shaping to induce a unique equilibrium point, while the derivative mode can be interpreted as a global damping injection to reduce undesired transient effects, such as temperature overshooting and oscillations. A numerical example is used to illustrate the different features of mixed proportional and derivative control in chemical reactor dynamics. Copyright © 2011 John Wiley & Sons, Ltd.