Chemical Engineering Science 55 (2000) 4435}4450 Robust H  control of nonlinear plants based on multi-linear models: an application to a bench-scale pH neutralization reactor Omar Gala H n*, Jose H A. Romagnoli, Ahmet Palazoglu Laboratory of Process Systems Engineering, Department of Chemical Engineering, University of Sydney, NSW 2006, Australia Department of Chemical Engineering and Materials Science, University of California Davis, CA 95616, USA Received 26 April 1999; accepted 18 January 2000 Abstract This work is aimed at developing a methodology to design controllers for nonlinear plants where desirable robustness and performance properties must be maintained across a large range of operating conditions. The approach is based on the multi-linear model representation and the H  control design that allows inclusion of plant nonlinearities by representing the original system as a set of local uncertain linear plants. To assess the merits of the proposed technique, experiments are performed on a bench-scale pH neutralization reactor. The results demonstrate robust performance and robust stability in the presence of disturbances and set-point variations.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Robust control; Multi-linear models; H-in"nity; pH control; Robust stability; Robust performance 1. Introduction The nonlinear and uncertain nature of processes often exacerbate the control problem. It is well-known and also intuitive that a controller designed around a speci"c operating point may not be able to accommodate large variations in process dynamics and o!er satisfactory tracking control without some performance degradation or even instability. This is explained primarily by the presence of system nonlinearities, causing the dynamic behavior to be qualitatively di!erent from one operating regime to another. However, one can obtain linear pro- cess models valid within a `smalla region about the linearization point, and the traditional solution for this control problem has been to perform local designs for a large set of operating conditions and then construct a gain-scheduling scheme that interpolates controller gains as the process traverses the operating region (Shinskey, 1996; Shama & Athans, 1991; Rugh, 1991). This procedure is time consuming and expensive, but is well accepted and yielded satisfactory results in many * Corresponding author. Tel.: #61-2-9351-2455; fax: #61-9351- 2854. E-mail addresses: omarg@chem.eng.usyd.edu.au (O. Gala H n), an- palazoglu@ucdavis.edu (A. Palazoglu). applications. A similar concept is followed where the interpolation is facilitated through the use of validity or imembership functions, and local controllers are selected as a function of the current state of the process (Howitt & Luss, 1993; Foss, Johasen & Sorensen, 1995). Practic- ally, such a multi-linear modeling technique seems to be the natural precursor to extend the well-known linear controller design tools to complex nonlinear systems (Murray-Smith & Johansen, 1997). An interesting ap- proach based on this methodology uses switching, learn- ing and tuning or adaptation (Narendra, Balakrishnan & Ciliz, 1995). This strategy is particularly suitable for time-varying systems with fast dynamics. For linear systems, H  control theory o!ers the possi- bility of including robustness considerations explicitly in the design and the opportunity to formulate physically meaningful performance objectives that can be expressed as H  design speci"cations (Skogestad, Morari & Doyle, 1988; Doyle, Glover, Khargonekar & Francis, 1989). Therefore, one can exploit the H  theory and the multi-model approach, so that the system nonlinearities can be taken into account and stability and performance objectives can be achieved over a larger region of operation. The goals of this paper are to represent nonlinear process dynamics within an uncertain, multi-linear model framework and to design a controller that would 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 0 2 8 - 2