* Corresponding author. Tel.: #52-5-8044649; fax: #52-5-8044900. E-mail address: cdp@xanum.uam.mx (J. Alvarez-Ramirez). Chemical Engineering Science 55 (2000) 5497}5507 PI control of continuously stirred tank reactors: stability and performance Jose Alvarez-Ramirez*, America Morales Departamento de Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico DF, 09340 Mexico Received 9 November 1999; accepted 2 May 2000 Abstract The proportional-integral (PI) control of continuously stirred tank reactors (CSTR) is addressed in this paper. The main ingredient in the formulation is the use of a novel PI control con"guration derived from modeling error compensation ideas. The main theoretical contribution is a novel stability analysis of a wide class of CSTR. It is shown that the performance of an inverse dynamics feedback control can be recovered by classical PI control. This performance recovery includes the region of attraction and transient response.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Process control; Chemical reactors; PI control; Stability; Performance; Antireset windup 1. Introduction The control of the operation of chemical reactors has attracted the attention of researchers for a long time. The underlying motivation relies on the fact that industrial chemical reactors are frequently operated at unstable operating conditions, which often corresponds to opti- mal process performance. Polymerization processes (Alvarez, Suarez & Sanchez, 1990; Viel, Buesvelle & Gauthier, 1995) and #uidized catalyst cracking units (Grosdidier, Mason, Aitolahti, Heinonen & Vanhumaki, 1993) are important examples of large-scale chemical reactors operated at unstable conditions. In the recent literature, input/output (I/O) feedback linearization methodologies have been widely explored for the stabilization of chemical reactors (e.g., Kravaris & Palanki, 1988; Alvarez et al., 1990; Daoutidis, Soroush & Kravaris, 1990; Viel, Jadot & Bastin, 1997). Adaptive versions of feedback linearizations have been also pro- posed (Kravaris & Palanki, 1988; Fradkov, Ortega & Bastin, 1997). However, in virtually all present day industrial applications, the basic reactor control problem is e$ciently solved using proportional plus integral (PI) controllers. Surprisingly, there is a lack of rigorous re- sults and systematic approaches to studying the problem of control of continuously stirred tank reactors (CSTR) under PI control algorithms. Whereas traditional analy- sis of CSTR controlled with PI control algorithms resort to linearization and treatment of linear methods (e.g., Lee, Coronella, Bhadkamkar & Seader, 1993; Urretabiz- kaia, Leisa & Asua, 1994; Khandelakar & Riggs, 1995; Brown, Gonyie, Schwber & James, 1998; Ratto, 1998; Chang & Liao, 1999) only few works deal directly with the nonlinear equations of motion. Recently, the stabiliz- ation of chemical reactors by output feedback with PI- type controllers has been reviewed and treated in detail in a Ph.D. thesis (Jadot, 1996) where nonlinear PI control con"gurations have been proposed to achieve global stabilization. Calorimetric balances have been used in Alvarez-Ramirez, Suarez and Femat (1996) and Alvarez- Ramirez (1999) to propose a robust control scheme in the face of uncertain chemical kinetics for a class of CSTR. It has been showed that the proposed controller has the structure of PI control where the integral action is either of discrete- or continuous-time nature. The work deals solely with the stability problem, rather than providing results related to performance of the system in a transient situation. The PI control of CSTR about a desired operating point is addressed in this paper. The main ingredient in 0009-2509/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 1 7 3 - 1