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On the global stability of conventional PID control for a class of chemical reactors
Author(s) -
AlvarezRamirez Jose,
Alvarez Jesus,
Schaum Alexander
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1716
Subject(s) - continuous stirred tank reactor , control theory (sociology) , chemical reactor , pid controller , derivative (finance) , nonlinear system , work (physics) , flexibility (engineering) , equilibrium point , time derivative , stability (learning theory) , chemical process , chemistry , mathematics , computer science , temperature control , thermodynamics , control (management) , physics , mathematical analysis , statistics , quantum mechanics , artificial intelligence , machine learning , financial economics , economics , organic chemistry
SUMMARY 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.